pyscf.scf package¶

Submodules¶

pyscf.scf.addons module¶

pyscf.scf.addons.canonical_orth_(S, thr=1e-07)¶: Löwdin’s canonical orthogonalization

pyscf.scf.addons.convert_to_ghf(mf, out=None, remove_df=False)¶

Convert the given mean-field object to the generalized HF/KS object

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mf object. If mf is an second order SCF (SOSCF) object, the SOSCF layer will be discarded. Its underlying SCF object mf._scf will be converted.

Args:

mf : SCF object

Kwargs

remove_dfbool: Whether to convert the DF-SCF object to the normal SCF object. This conversion is not applied by default.

Returns:

An generalized SCF object

pyscf.scf.addons.convert_to_rhf(mf, out=None, remove_df=False)¶

Convert the given mean-field object to the restricted HF/KS object

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mf object. If mf is an second order SCF (SOSCF) object, the SOSCF layer will be discarded. Its underlying SCF object mf._scf will be converted.

Args:

mf : SCF object

Kwargs

remove_dfbool: Whether to convert the DF-SCF object to the normal SCF object. This conversion is not applied by default.

Returns:

An unrestricted SCF object

pyscf.scf.addons.convert_to_uhf(mf, out=None, remove_df=False)¶

Convert the given mean-field object to the unrestricted HF/KS object

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mf object. If mf is an second order SCF (SOSCF) object, the SOSCF layer will be discarded. Its underlying SCF object mf._scf will be converted.

Args:

mf : SCF object

Kwargs

remove_dfbool: Whether to convert the DF-SCF object to the normal SCF object. This conversion is not applied by default.

Returns:

An unrestricted SCF object

pyscf.scf.addons.dynamic_level_shift(mf, factor=1.0)¶: Dynamically change the level shift in each SCF cycle. The level shift value is set to (HF energy change * factor)

pyscf.scf.addons.dynamic_level_shift_(mf, factor=1.0)¶: Dynamically change the level shift in each SCF cycle. The level shift value is set to (HF energy change * factor)

pyscf.scf.addons.dynamic_occ(mf, tol=0.001)¶

pyscf.scf.addons.dynamic_occ_(mf, tol=0.001)¶

pyscf.scf.addons.dynamic_sz_(mf)¶: For UHF, allowing the Sz value being changed during SCF iteration. Determine occupation of alpha and beta electrons based on energy spectrum

pyscf.scf.addons.fast_newton(mf, mo_coeff=None, mo_occ=None, dm0=None, auxbasis=None, dual_basis=None, **newton_kwargs)¶: This is a wrap function which combines several operations. This function first setup the initial guess from density fitting calculation then use for Newton solver and call Newton solver. Newton solver attributes [max_cycle_inner, max_stepsize, ah_start_tol, ah_conv_tol, ah_grad_trust_region, …] can be passed through **newton_kwargs.

pyscf.scf.addons.float_occ(mf)¶: For UHF, allowing the Sz value being changed during SCF iteration. Determine occupation of alpha and beta electrons based on energy spectrum

pyscf.scf.addons.float_occ_(mf)¶: For UHF, allowing the Sz value being changed during SCF iteration. Determine occupation of alpha and beta electrons based on energy spectrum

pyscf.scf.addons.follow_state(mf, occorb=None)¶

pyscf.scf.addons.follow_state_(mf, occorb=None)¶

pyscf.scf.addons.frac_occ(mf, tol=0.001)¶

pyscf.scf.addons.frac_occ_(mf, tol=0.001)¶

pyscf.scf.addons.get_ghf_orbspin(mo_energy, mo_occ, is_rhf=None)¶

Spin of each GHF orbital when the GHF orbitals are converted from RHF/UHF orbitals

For RHF orbitals, the orbspin corresponds to first occupied orbitals then unoccupied orbitals. In the occupied orbital space, if degenerated, first alpha then beta, last the (open-shell) singly occupied (alpha) orbitals. In the unoccupied orbital space, first the (open-shell) unoccupied (beta) orbitals if applicable, then alpha and beta orbitals

For UHF orbitals, the orbspin corresponds to first occupied orbitals then unoccupied orbitals.

pyscf.scf.addons.mom_occ(mf, occorb, setocc)¶: Use maximum overlap method to determine occupation number for each orbital in every iteration. It can be applied to unrestricted HF/KS and restricted open-shell HF/KS.

pyscf.scf.addons.mom_occ_(mf, occorb, setocc)¶: Use maximum overlap method to determine occupation number for each orbital in every iteration. It can be applied to unrestricted HF/KS and restricted open-shell HF/KS.

pyscf.scf.addons.partial_cholesky_orth_(S, cholthr=1e-09, canthr=1e-07)¶

Partial Cholesky orthogonalization for curing overcompleteness.

References:

Susi Lehtola, Curing basis set overcompleteness with pivoted Cholesky decompositions, J. Chem. Phys. 151, 241102 (2019), doi:10.1063/1.5139948.

Susi Lehtola, Accurate reproduction of strongly repulsive interatomic potentials, Phys. Rev. A 101, 032504 (2020), doi:10.1103/PhysRevA.101.032504.

pyscf.scf.addons.project_dm_nr2nr(mol1, dm1, mol2)¶

Project density matrix representation from basis set 1 (mol1) to basis set 2 (mol2).

\[ \begin{align}\begin{aligned}|AO2\rangle DM_AO2 \langle AO2|\\= |AO2\rangle P DM_AO1 P \langle AO2|\\DM_AO2 = P DM_AO1 P\\P = S_{AO2}^{-1}\langle AO2|AO1\rangle\end{aligned}\end{align} \]

There are three relevant functions: project_dm_nr2nr() is the projection for non-relativistic (scalar) basis. project_dm_nr2r() projects from non-relativistic to relativistic basis. project_dm_r2r() is the projection between relativistic (spinor) basis.

pyscf.scf.addons.project_dm_nr2r(mol1, dm1, mol2)¶

Project density matrix representation from basis set 1 (mol1) to basis set 2 (mol2).

\[ \begin{align}\begin{aligned}|AO2\rangle DM_AO2 \langle AO2|\\= |AO2\rangle P DM_AO1 P \langle AO2|\\DM_AO2 = P DM_AO1 P\\P = S_{AO2}^{-1}\langle AO2|AO1\rangle\end{aligned}\end{align} \]

There are three relevant functions: project_dm_nr2nr() is the projection for non-relativistic (scalar) basis. project_dm_nr2r() projects from non-relativistic to relativistic basis. project_dm_r2r() is the projection between relativistic (spinor) basis.

pyscf.scf.addons.project_dm_r2r(mol1, dm1, mol2)¶

Project density matrix representation from basis set 1 (mol1) to basis set 2 (mol2).

\[ \begin{align}\begin{aligned}|AO2\rangle DM_AO2 \langle AO2|\\= |AO2\rangle P DM_AO1 P \langle AO2|\\DM_AO2 = P DM_AO1 P\\P = S_{AO2}^{-1}\langle AO2|AO1\rangle\end{aligned}\end{align} \]

There are three relevant functions: project_dm_nr2nr() is the projection for non-relativistic (scalar) basis. project_dm_nr2r() projects from non-relativistic to relativistic basis. project_dm_r2r() is the projection between relativistic (spinor) basis.

pyscf.scf.addons.project_mo_nr2nr(mol1, mo1, mol2)¶

Project orbital coefficients from basis set 1 (C1 for mol1) to basis set 2 (C2 for mol2).

\[ \begin{align}\begin{aligned}|\psi1\rangle = |AO1\rangle C1\\|\psi2\rangle = P |\psi1\rangle = |AO2\rangle S^{-1}\langle AO2| AO1\rangle> C1 = |AO2\rangle> C2\\C2 = S^{-1}\langle AO2|AO1\rangle C1\end{aligned}\end{align} \]

There are three relevant functions: project_mo_nr2nr() is the projection for non-relativistic (scalar) basis. project_mo_nr2r() projects from non-relativistic to relativistic basis. project_mo_r2r() is the projection between relativistic (spinor) basis.

pyscf.scf.addons.project_mo_nr2r(mol1, mo1, mol2)¶

Project orbital coefficients from basis set 1 (C1 for mol1) to basis set 2 (C2 for mol2).

\[ \begin{align}\begin{aligned}|\psi1\rangle = |AO1\rangle C1\\|\psi2\rangle = P |\psi1\rangle = |AO2\rangle S^{-1}\langle AO2| AO1\rangle> C1 = |AO2\rangle> C2\\C2 = S^{-1}\langle AO2|AO1\rangle C1\end{aligned}\end{align} \]

There are three relevant functions: project_mo_nr2nr() is the projection for non-relativistic (scalar) basis. project_mo_nr2r() projects from non-relativistic to relativistic basis. project_mo_r2r() is the projection between relativistic (spinor) basis.

pyscf.scf.addons.project_mo_r2r(mol1, mo1, mol2)¶

Project orbital coefficients from basis set 1 (C1 for mol1) to basis set 2 (C2 for mol2).

\[ \begin{align}\begin{aligned}|\psi1\rangle = |AO1\rangle C1\\|\psi2\rangle = P |\psi1\rangle = |AO2\rangle S^{-1}\langle AO2| AO1\rangle> C1 = |AO2\rangle> C2\\C2 = S^{-1}\langle AO2|AO1\rangle C1\end{aligned}\end{align} \]

There are three relevant functions: project_mo_nr2nr() is the projection for non-relativistic (scalar) basis. project_mo_nr2r() projects from non-relativistic to relativistic basis. project_mo_r2r() is the projection between relativistic (spinor) basis.

pyscf.scf.addons.remove_linear_dep(mf, threshold=1e-08, lindep=1e-10, cholesky_threshold=1e-10)¶

Args:

thresholdfloat: The threshold under which the eigenvalues of the overlap matrix are discarded to avoid numerical instability.
lindepfloat: The threshold that triggers the special treatment of the linear dependence issue.

pyscf.scf.addons.remove_linear_dep_(mf, threshold=1e-08, lindep=1e-10, cholesky_threshold=1e-10)¶

Args:

thresholdfloat: The threshold under which the eigenvalues of the overlap matrix are discarded to avoid numerical instability.
lindepfloat: The threshold that triggers the special treatment of the linear dependence issue.

pyscf.scf.atom_hf module¶

class pyscf.scf.atom_hf.AtomHF1e(mol)¶

Bases: pyscf.scf.rohf.HF1e, pyscf.scf.atom_hf.AtomSphericAverageRHF

eig(f, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

class pyscf.scf.atom_hf.AtomSphericAverageRHF(mol)¶

Bases: pyscf.scf.hf.RHF

dump_flags(verbose=None)¶

eig(f, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_occ(mo_energy=None, mo_coeff=None)¶: spherically averaged fractional occupancy

scf(*args, **kwargs)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

pyscf.scf.atom_hf.frac_occ(symb, l, atomic_configuration=[[0, 0, 0, 0], [1, 0, 0, 0], [2, 0, 0, 0], [3, 0, 0, 0], [4, 0, 0, 0], [4, 1, 0, 0], [4, 2, 0, 0], [4, 3, 0, 0], [4, 4, 0, 0], [4, 5, 0, 0], [4, 6, 0, 0], [5, 6, 0, 0], [6, 6, 0, 0], [6, 7, 0, 0], [6, 8, 0, 0], [6, 9, 0, 0], [6, 10, 0, 0], [6, 11, 0, 0], [6, 12, 0, 0], [7, 12, 0, 0], [8, 12, 0, 0], [8, 13, 0, 0], [8, 12, 2, 0], [8, 12, 3, 0], [8, 12, 4, 0], [6, 12, 7, 0], [6, 12, 8, 0], [6, 12, 9, 0], [6, 12, 10, 0], [7, 12, 10, 0], [8, 12, 10, 0], [8, 13, 10, 0], [8, 14, 10, 0], [8, 15, 10, 0], [8, 16, 10, 0], [8, 17, 10, 0], [8, 18, 10, 0], [9, 18, 10, 0], [10, 18, 10, 0], [10, 19, 10, 0], [10, 18, 12, 0], [10, 18, 13, 0], [8, 18, 16, 0], [8, 18, 17, 0], [8, 18, 18, 0], [8, 18, 19, 0], [8, 18, 20, 0], [9, 18, 20, 0], [10, 18, 20, 0], [10, 19, 20, 0], [10, 20, 20, 0], [10, 21, 20, 0], [10, 22, 20, 0], [10, 23, 20, 0], [10, 24, 20, 0], [11, 24, 20, 0], [12, 24, 20, 0], [12, 24, 21, 0], [12, 24, 22, 0], [12, 24, 21, 2], [12, 24, 20, 4], [12, 24, 20, 5], [12, 24, 20, 6], [12, 24, 20, 7], [11, 24, 20, 9], [10, 24, 20, 11], [10, 24, 20, 12], [10, 24, 20, 13], [10, 24, 20, 14], [11, 24, 20, 14], [12, 24, 20, 14], [12, 25, 20, 14], [12, 24, 22, 14], [12, 24, 23, 14], [10, 24, 26, 14], [10, 24, 27, 14], [10, 24, 28, 14], [10, 24, 29, 14], [10, 24, 30, 14], [11, 24, 30, 14], [12, 24, 30, 14], [12, 25, 30, 14], [12, 26, 30, 14], [12, 27, 30, 14], [12, 28, 30, 14], [12, 29, 30, 14], [12, 30, 30, 14], [13, 30, 30, 14], [14, 30, 30, 14], [14, 30, 31, 14], [14, 30, 32, 14], [14, 30, 30, 17], [14, 30, 30, 18], [14, 30, 30, 19], [13, 30, 30, 21], [12, 30, 30, 23], [12, 30, 30, 24], [12, 30, 30, 25], [12, 30, 30, 26], [12, 30, 30, 27], [12, 30, 30, 28], [13, 30, 30, 28], [14, 30, 30, 28], [14, 30, 31, 28], [14, 30, 32, 28], [14, 30, 33, 28], [12, 30, 36, 28], [12, 30, 37, 28], [12, 30, 38, 28], [12, 30, 39, 28], [12, 30, 40, 28], [13, 30, 40, 28], [14, 30, 40, 28], [14, 31, 40, 28], [14, 32, 40, 28], [14, 33, 40, 28], [14, 34, 40, 28], [14, 35, 40, 28], [14, 36, 40, 28]])¶

pyscf.scf.atom_hf.get_atm_nrhf(mol, atomic_configuration=[[0, 0, 0, 0], [1, 0, 0, 0], [2, 0, 0, 0], [3, 0, 0, 0], [4, 0, 0, 0], [4, 1, 0, 0], [4, 2, 0, 0], [4, 3, 0, 0], [4, 4, 0, 0], [4, 5, 0, 0], [4, 6, 0, 0], [5, 6, 0, 0], [6, 6, 0, 0], [6, 7, 0, 0], [6, 8, 0, 0], [6, 9, 0, 0], [6, 10, 0, 0], [6, 11, 0, 0], [6, 12, 0, 0], [7, 12, 0, 0], [8, 12, 0, 0], [8, 13, 0, 0], [8, 12, 2, 0], [8, 12, 3, 0], [8, 12, 4, 0], [6, 12, 7, 0], [6, 12, 8, 0], [6, 12, 9, 0], [6, 12, 10, 0], [7, 12, 10, 0], [8, 12, 10, 0], [8, 13, 10, 0], [8, 14, 10, 0], [8, 15, 10, 0], [8, 16, 10, 0], [8, 17, 10, 0], [8, 18, 10, 0], [9, 18, 10, 0], [10, 18, 10, 0], [10, 19, 10, 0], [10, 18, 12, 0], [10, 18, 13, 0], [8, 18, 16, 0], [8, 18, 17, 0], [8, 18, 18, 0], [8, 18, 19, 0], [8, 18, 20, 0], [9, 18, 20, 0], [10, 18, 20, 0], [10, 19, 20, 0], [10, 20, 20, 0], [10, 21, 20, 0], [10, 22, 20, 0], [10, 23, 20, 0], [10, 24, 20, 0], [11, 24, 20, 0], [12, 24, 20, 0], [12, 24, 21, 0], [12, 24, 22, 0], [12, 24, 21, 2], [12, 24, 20, 4], [12, 24, 20, 5], [12, 24, 20, 6], [12, 24, 20, 7], [11, 24, 20, 9], [10, 24, 20, 11], [10, 24, 20, 12], [10, 24, 20, 13], [10, 24, 20, 14], [11, 24, 20, 14], [12, 24, 20, 14], [12, 25, 20, 14], [12, 24, 22, 14], [12, 24, 23, 14], [10, 24, 26, 14], [10, 24, 27, 14], [10, 24, 28, 14], [10, 24, 29, 14], [10, 24, 30, 14], [11, 24, 30, 14], [12, 24, 30, 14], [12, 25, 30, 14], [12, 26, 30, 14], [12, 27, 30, 14], [12, 28, 30, 14], [12, 29, 30, 14], [12, 30, 30, 14], [13, 30, 30, 14], [14, 30, 30, 14], [14, 30, 31, 14], [14, 30, 32, 14], [14, 30, 30, 17], [14, 30, 30, 18], [14, 30, 30, 19], [13, 30, 30, 21], [12, 30, 30, 23], [12, 30, 30, 24], [12, 30, 30, 25], [12, 30, 30, 26], [12, 30, 30, 27], [12, 30, 30, 28], [13, 30, 30, 28], [14, 30, 30, 28], [14, 30, 31, 28], [14, 30, 32, 28], [14, 30, 33, 28], [12, 30, 36, 28], [12, 30, 37, 28], [12, 30, 38, 28], [12, 30, 39, 28], [12, 30, 40, 28], [13, 30, 40, 28], [14, 30, 40, 28], [14, 31, 40, 28], [14, 32, 40, 28], [14, 33, 40, 28], [14, 34, 40, 28], [14, 35, 40, 28], [14, 36, 40, 28]])¶

pyscf.scf.chkfile module¶

pyscf.scf.chkfile.dump_scf(mol, chkfile, e_tot, mo_energy, mo_coeff, mo_occ, overwrite_mol=True)¶: save temporary results

pyscf.scf.chkfile.load_scf(chkfile)¶

pyscf.scf.cphf module¶

Restricted coupled pertubed Hartree-Fock solver

pyscf.scf.cphf.kernel(fvind, mo_energy, mo_occ, h1, s1=None, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶

Args:

fvindfunction: Given density matrix, compute (ij|kl)D_{lk}*2 - (ij|kl)D_{jk}

Kwargs:

hermiboolean: Whether the matrix defined by fvind is Hermitian or not.

pyscf.scf.cphf.solve(fvind, mo_energy, mo_occ, h1, s1=None, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶

Args:

fvindfunction: Given density matrix, compute (ij|kl)D_{lk}*2 - (ij|kl)D_{jk}

Kwargs:

hermiboolean: Whether the matrix defined by fvind is Hermitian or not.

pyscf.scf.cphf.solve_nos1(fvind, mo_energy, mo_occ, h1, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶: For field independent basis. First order overlap matrix is zero

pyscf.scf.cphf.solve_withs1(fvind, mo_energy, mo_occ, h1, s1, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶

For field dependent basis. First order overlap matrix is non-zero. The first order orbitals are set to C^1_{ij} = -1/2 S1 e1 = h1 - s1*e0 + (e0_j-e0_i)*c1 + vhf[c1]

Kwargs:

hermiboolean: Whether the matrix defined by fvind is Hermitian or not.

Returns:

First order orbital coefficients (in MO basis) and first order orbital energy matrix

pyscf.scf.dhf module¶

Dirac Hartree-Fock

class pyscf.scf.dhf.DHF(mol)¶

Bases: pyscf.scf.hf.SCF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for Dirac-Hartree-Fock

with_ssssbool, for Dirac-Hartree-Fock only: If False, ignore small component integrals (SS|SS). Default is True.
with_gauntbool, for Dirac-Hartree-Fock only: Default is False.
with_breitbool, for Dirac-Hartree-Fock only: Gaunt + gauge term. Default is False.

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> e0 = mf.scf()
>>> mf = scf.DHF(mol)
>>> e1 = mf.scf()
>>> print('Relativistic effects = %.12f' % (e1-e0))
Relativistic effects = -0.000008854205

EFG(*args, **kwargs)¶

Gradients(*args, **kwargs)¶: Unrestricted Dirac-Hartree-Fock gradients

NMR(*args, **kwargs)¶: magnetic shielding constants

SSC(*args, **kwargs)¶

SpinSpinCoupling(*args, **kwargs)¶

analyze(verbose=None)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

build(mol=None)¶

conv_tol = 1e-08¶

dip_moment(mol=None, dm=None, unit='Debye', verbose=3, **kwargs)¶

Dipole moment calculation

\[\begin{split}\mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A\end{split}\]

where \(\mu_x, \mu_y, \mu_z\) are the x, y and z components of dipole moment

Args:: mol: an instance of Mole dm : a 2D ndarrays density matrices
Return:: A list: the dipole moment on x, y and z component

dump_flags(verbose=None)¶

gen_response(mo_coeff=None, mo_occ=None, with_j=True, hermi=0, max_memory=None)¶: Generate a function to compute the product of DHF response function and DHF density matrices.

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_hcore(mol=None)¶

get_jk(mol=None, dm=None, hermi=1, with_j=True, with_k=True, omega=None)¶

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices
with_jboolean: Whether to compute J matrices
with_kboolean: Whether to compute K matrices
omegafloat: Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

get_occ(mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray: Obital energies
mo_coeff2D ndarray: Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

get_ovlp(mol=None)¶

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)¶: Dirac-Coulomb

init_direct_scf(mol=None)¶

init_guess_by_atom(mol=None)¶

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:: Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)¶

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:: Density matrix, 2D ndarray

init_guess_by_huckel(mol=None)¶

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:: Density matrix, 2D ndarray

init_guess_by_minao(mol=None)¶: Initial guess in terms of the overlap to minimal basis.

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)¶

One-particle density matrix in AO representation

Args:

mo_coeff2D ndarray: Orbital coefficients. Each column is one orbital.
mo_occ1D ndarray: Occupancy

mulliken_pop(mol=None, dm=None, s=None, verbose=5)¶

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

nuc_grad_method()¶: Hook to create object for analytical nuclear gradients.

reset(mol=None)¶: Reset mol and clean up relevant attributes for scanner mode

scf(dm0=None)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

sfx2c1e()¶

with_breit = False¶

with_gaunt = False¶

with_ssss = True¶

x2c()¶

x2c1e()¶

class pyscf.scf.dhf.HF1e(mol)¶

Bases: pyscf.scf.dhf.DHF

scf(*args)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

class pyscf.scf.dhf.RDHF(mol)¶

Bases: pyscf.scf.dhf.DHF

Kramers restricted Dirac-Hartree-Fock

x2c()¶

x2c1e()¶

pyscf.scf.dhf.RHF¶: alias of pyscf.scf.dhf.RDHF

pyscf.scf.dhf.UDHF¶: alias of pyscf.scf.dhf.DHF

pyscf.scf.dhf.UHF¶: alias of pyscf.scf.dhf.DHF

pyscf.scf.dhf.analyze(mf, verbose=5, **kwargs)¶

pyscf.scf.dhf.dip_moment(mol, dm, unit='Debye', verbose=3, **kwargs)¶

Dipole moment calculation

\[\begin{split}\mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A\end{split}\]

where \(\mu_x, \mu_y, \mu_z\) are the x, y and z components of dipole moment

Args:: mol: an instance of Mole dm : a 2D ndarrays density matrices
Return:: A list: the dipole moment on x, y and z component

pyscf.scf.dhf.get_grad(mo_coeff, mo_occ, fock_ao)¶: DHF Gradients

pyscf.scf.dhf.get_hcore(mol)¶

pyscf.scf.dhf.get_init_guess(mol, key='minao')¶

Generate density matrix for initial guess

Kwargs:

keystr: One of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’.

pyscf.scf.dhf.get_jk(mol, dm, hermi=1, coulomb_allow='SSSS', opt_llll=None, opt_ssll=None, opt_ssss=None, omega=None, verbose=None)¶

pyscf.scf.dhf.get_jk_coulomb(mol, dm, hermi=1, coulomb_allow='SSSS', opt_llll=None, opt_ssll=None, opt_ssss=None, omega=None, verbose=None)¶

pyscf.scf.dhf.get_ovlp(mol)¶

pyscf.scf.dhf.init_guess_by_1e(mol)¶: Initial guess from one electron system.

pyscf.scf.dhf.init_guess_by_atom(mol)¶: Initial guess from atom calculation.

pyscf.scf.dhf.init_guess_by_chkfile(mol, chkfile_name, project=None)¶

Read SCF chkfile and make the density matrix for 4C-DHF initial guess.

Kwargs:

projectNone or bool

Whether to project chkfile’s orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to swith off project.

If project is set to None, the projection is only applied when the basis sets of the chkfile’s molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms.

pyscf.scf.dhf.init_guess_by_huckel(mol)¶: Initial guess from on-the-fly Huckel, doi:10.1021/acs.jctc.8b01089.

pyscf.scf.dhf.init_guess_by_minao(mol)¶: Initial guess in terms of the overlap to minimal basis.

pyscf.scf.dhf.kernel(mf, conv_tol=1e-09, conv_tol_grad=None, dump_chk=True, dm0=None, callback=None, conv_check=True)¶: the modified SCF kernel for Dirac-Hartree-Fock. In this kernel, the SCF is carried out in three steps. First the 2-electron part is approximated by large component integrals (LL|LL); Next, (SS|LL) the interaction between large and small components are added; Finally, converge the SCF with the small component contributions (SS|SS)

pyscf.scf.dhf.mulliken_pop(mol, dm, s=None, verbose=5)¶

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

pyscf.scf.dhf.time_reversal_matrix(mol, mat)¶: T(A_ij) = A[T(i),T(j)]^*

pyscf.scf.diis module¶

DIIS

class pyscf.scf.diis.ADIIS(dev=None, filename=None, incore=False)¶

Bases: pyscf.lib.diis.DIIS

Ref: JCP 132, 054109 (2010); DOI:10.1063/1.3304922

update(s, d, f, mf, h1e, vhf)¶

Extrapolate vector

If xerr the error vector is given, this function will push the target

vector and error vector in the DIIS subspace, and use the error vector to extrapolate the vector and return the extrapolated vector. * If xerr is None, this function will take the difference between the current given vector and the last given vector as the error vector to extrapolate the vector.

class pyscf.scf.diis.CDIIS(mf=None, filename=None)¶

Bases: pyscf.lib.diis.DIIS

get_num_vec()¶

update(s, d, f, *args, **kwargs)¶

Extrapolate vector

If xerr the error vector is given, this function will push the target

vector and error vector in the DIIS subspace, and use the error vector to extrapolate the vector and return the extrapolated vector. * If xerr is None, this function will take the difference between the current given vector and the last given vector as the error vector to extrapolate the vector.

pyscf.scf.diis.DIIS¶: alias of pyscf.scf.diis.CDIIS

class pyscf.scf.diis.EDIIS(dev=None, filename=None, incore=False)¶

Bases: pyscf.lib.diis.DIIS

SCF-EDIIS Ref: JCP 116, 8255 (2002); DOI:10.1063/1.1470195

update(s, d, f, mf, h1e, vhf)¶

Extrapolate vector

If xerr the error vector is given, this function will push the target

vector and error vector in the DIIS subspace, and use the error vector to extrapolate the vector and return the extrapolated vector. * If xerr is None, this function will take the difference between the current given vector and the last given vector as the error vector to extrapolate the vector.

pyscf.scf.diis.SCFDIIS¶: alias of pyscf.scf.diis.CDIIS

pyscf.scf.diis.SCF_DIIS¶: alias of pyscf.scf.diis.CDIIS

pyscf.scf.diis.adiis_minimize(ds, fs, idnewest)¶

pyscf.scf.diis.ediis_minimize(es, ds, fs)¶

pyscf.scf.diis.get_err_vec(s, d, f)¶: error vector = SDF - FDS

pyscf.scf.ghf module¶

Non-relativistic generalized Hartree-Fock

class pyscf.scf.ghf.GHF(mol)¶

Bases: pyscf.scf.hf.SCF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for GHF method: GHF orbital coefficients are 2D array. Let nao be the number of spatial AOs, mo_coeff[:nao] are the coefficients of AO with alpha spin; mo_coeff[nao:nao*2] are the coefficients of AO with beta spin.

CISD(*args, **kwargs)¶

MP2(*args, **kwargs)¶

analyze(verbose=None, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

convert_from_(mf)¶: Create GHF object based on the RHF/UHF object

det_ovlp(mo1, mo2, occ1, occ2, ovlp=None)¶

Calculate the overlap between two different determinants. It is the product of single values of molecular orbital overlap matrix.

Return:

A list:: the product of single values: float x_a: \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\) They are used to calculate asymmetric density matrix

dip_moment(mol=None, dm=None, unit_symbol='Debye', verbose=3)¶

Dipole moment calculation

\[\begin{split}\mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A\end{split}\]

where \(\mu_x, \mu_y, \mu_z\) are the x, y and z components of dipole moment

Args:: mol: an instance of Mole dm : a 2D ndarrays density matrices
Return:: A list: the dipole moment on x, y and z component

gen_response(mo_coeff=None, mo_occ=None, with_j=True, hermi=0, max_memory=None)¶: Generate a function to compute the product of GHF response function and GHF density matrices.

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_hcore(mol=None)¶

get_jk(mol=None, dm=None, hermi=0, with_j=True, with_k=True, omega=None)¶

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices
with_jboolean: Whether to compute J matrices
with_kboolean: Whether to compute K matrices
omegafloat: Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

get_occ(mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray: Obital energies
mo_coeff2D ndarray: Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

get_ovlp(mol=None)¶

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)¶

Hartree-Fock potential matrix for the given density matrix

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

dm_lastndarray or a list of ndarrays or 0: The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_lastndarray or a list of ndarrays or 0: The reference HF potential matrix.
hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

matrix Vhf = 2*J - K. Vhf can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dm0 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf0 = scf.hf.get_veff(mol, dm0, hermi=0)
>>> dm1 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf1 = scf.hf.get_veff(mol, dm1, hermi=0)
>>> vhf2 = scf.hf.get_veff(mol, dm1, dm_last=dm0, vhf_last=vhf0, hermi=0)
>>> numpy.allclose(vhf1, vhf2)
True

init_guess_by_atom(mol=None)¶

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:: Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)¶

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:: Density matrix, 2D ndarray

init_guess_by_huckel(mol=None)¶

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:: Density matrix, 2D ndarray

init_guess_by_minao(mol=None)¶

Generate initial guess density matrix based on ANO basis, then project the density matrix to the basis set defined by mol

Returns:: Density matrix, 2D ndarray

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> scf.hf.init_guess_by_minao(mol)
array([[ 0.94758917,  0.09227308],
       [ 0.09227308,  0.94758917]])

mulliken_meta(mol=None, dm=None, verbose=5, pre_orth_method='ANO', s=None)¶

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carreid out within each subsets.

Args:

mol : an instance of Mole

dmndarray or 2-item list of ndarray: Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr: Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

mulliken_pop(mol=None, dm=None, s=None, verbose=5)¶

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

nuc_grad_method()¶: Hook to create object for analytical nuclear gradients.

spin_square(mo_coeff=None, s=None)¶

Spin of the GHF wavefunction

\[S^2 = \frac{1}{2}(S_+ S_- + S_- S_+) + S_z^2\]

where \(S_+ = \sum_i S_{i+}\) is effective for all beta occupied orbitals; \(S_- = \sum_i S_{i-}\) is effective for all alpha occupied orbitals.

There are two possibilities for \(S_+ S_-\)
1. same electron \(S_+ S_- = \sum_i s_{i+} s_{i-}\),
\[\sum_i \langle UHF|s_{i+} s_{i-}|UHF\rangle = \sum_{pq}\langle p|s_+s_-|q\rangle \gamma_{qp} = n_\alpha\]

2) different electrons \(S_+ S_- = \sum s_{i+} s_{j-}, (i\neq j)\). There are in total \(n(n-1)\) terms. As a two-particle operator,

\[\langle S_+ S_- \rangle =\sum_{ij}(\langle i^\alpha|i^\beta\rangle \langle j^\beta|j^\alpha\rangle - \langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle)\]
Similarly, for \(S_- S_+\)
1. same electron
\[\sum_i \langle s_{i-} s_{i+}\rangle = n_\beta\]
1. different electrons
\[\langle S_- S_+ \rangle =\sum_{ij}(\langle i^\beta|i^\alpha\rangle \langle j^\alpha|j^\beta\rangle - \langle i^\beta|j^\alpha\rangle \langle j^\alpha|i^\beta\rangle)\]
For \(S_z^2\)
1. same electron
\[\langle s_z^2\rangle = \frac{1}{4}(n_\alpha + n_\beta)\]
1. different electrons
\[\begin{split}&\sum_{ij}(\langle ij|s_{z1}s_{z2}|ij\rangle -\langle ij|s_{z1}s_{z2}|ji\rangle) \\ &=\frac{1}{4}\sum_{ij}(\langle i^\alpha|i^\alpha\rangle \langle j^\alpha|j^\alpha\rangle - \langle i^\alpha|i^\alpha\rangle \langle j^\beta|j^\beta\rangle - \langle i^\beta|i^\beta\rangle \langle j^\alpha|j^\alpha\rangle + \langle i^\beta|i^\beta\rangle \langle j^\beta|j^\beta\rangle) \\ &-\frac{1}{4}\sum_{ij}(\langle i^\alpha|j^\alpha\rangle \langle j^\alpha|i^\alpha\rangle - \langle i^\alpha|j^\alpha\rangle \langle j^\beta|i^\beta\rangle - \langle i^\beta|j^\beta\rangle \langle j^\alpha|i^\alpha\rangle + \langle i^\beta|j^\beta\rangle\langle j^\beta|i^\beta\rangle) \\ &=\frac{1}{4}\sum_{ij}|\langle i^\alpha|i^\alpha\rangle - \langle i^\beta|i^\beta\rangle|^2 -\frac{1}{4}\sum_{ij}|\langle i^\alpha|j^\alpha\rangle - \langle i^\beta|j^\beta\rangle|^2 \\ &=\frac{1}{4}(n_\alpha - n_\beta)^2 -\frac{1}{4}\sum_{ij}|\langle i^\alpha|j^\alpha\rangle - \langle i^\beta|j^\beta\rangle|^2\end{split}\]

Args:

moa list of 2 ndarrays: Occupied alpha and occupied beta orbitals

Kwargs:

sndarray: AO overlap

Returns:

A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> mo = (mf.mo_coeff[0][:,mf.mo_occ[0]>0], mf.mo_coeff[1][:,mf.mo_occ[1]>0])
>>> print('S^2 = %.7f, 2S+1 = %.7f' % spin_square(mo, mol.intor('int1e_ovlp_sph')))
S^2 = 0.7570150, 2S+1 = 2.0070027

stability(internal=None, external=None, verbose=None)¶

pyscf.scf.ghf.analyze(mf, verbose=5, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Dipole moment

pyscf.scf.ghf.det_ovlp(mo1, mo2, occ1, occ2, ovlp)¶

Calculate the overlap between two different determinants. It is the product of single values of molecular orbital overlap matrix.

Return:

A list:: the product of single values: float x_a: \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\) They are used to calculate asymmetric density matrix

pyscf.scf.ghf.dip_moment(mol, dm, unit_symbol='Debye', verbose=3)¶

pyscf.scf.ghf.get_jk(mol, dm, hermi=0, with_j=True, with_k=True, jkbuild=<function get_jk>, omega=None)¶

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices
with_jboolean: Whether to compute J matrices
with_kboolean: Whether to compute K matrices
omegafloat: Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

pyscf.scf.ghf.get_occ(mf, mo_energy=None, mo_coeff=None)¶

pyscf.scf.ghf.guess_orbspin(mo_coeff)¶: Guess the orbital spin (alpha 0, beta 1, unknown -1) based on the orbital coefficients

pyscf.scf.ghf.init_guess_by_chkfile(mol, chkfile_name, project=None)¶

Read SCF chkfile and make the density matrix for GHF initial guess.

Kwargs:

projectNone or bool

Whether to project chkfile’s orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to swith off project.

If project is set to None, the projection is only applied when the basis sets of the chkfile’s molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms.

pyscf.scf.ghf.mulliken_meta(mol, dm_ao, verbose=5, pre_orth_method='ANO', s=None)¶: Mulliken population analysis, based on meta-Lowdin AOs.

pyscf.scf.ghf.mulliken_pop(mol, dm, s=None, verbose=5)¶: Mulliken population analysis

pyscf.scf.ghf.spin_square(mo, s=1)¶

Spin of the GHF wavefunction

\[S^2 = \frac{1}{2}(S_+ S_- + S_- S_+) + S_z^2\]

where \(S_+ = \sum_i S_{i+}\) is effective for all beta occupied orbitals; \(S_- = \sum_i S_{i-}\) is effective for all alpha occupied orbitals.

There are two possibilities for \(S_+ S_-\)
1. same electron \(S_+ S_- = \sum_i s_{i+} s_{i-}\),
\[\sum_i \langle UHF|s_{i+} s_{i-}|UHF\rangle = \sum_{pq}\langle p|s_+s_-|q\rangle \gamma_{qp} = n_\alpha\]

2) different electrons \(S_+ S_- = \sum s_{i+} s_{j-}, (i\neq j)\). There are in total \(n(n-1)\) terms. As a two-particle operator,

\[\langle S_+ S_- \rangle =\sum_{ij}(\langle i^\alpha|i^\beta\rangle \langle j^\beta|j^\alpha\rangle - \langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle)\]
Similarly, for \(S_- S_+\)
1. same electron
\[\sum_i \langle s_{i-} s_{i+}\rangle = n_\beta\]
1. different electrons
\[\langle S_- S_+ \rangle =\sum_{ij}(\langle i^\beta|i^\alpha\rangle \langle j^\alpha|j^\beta\rangle - \langle i^\beta|j^\alpha\rangle \langle j^\alpha|i^\beta\rangle)\]
For \(S_z^2\)
1. same electron
\[\langle s_z^2\rangle = \frac{1}{4}(n_\alpha + n_\beta)\]
1. different electrons
\[\begin{split}&\sum_{ij}(\langle ij|s_{z1}s_{z2}|ij\rangle -\langle ij|s_{z1}s_{z2}|ji\rangle) \\ &=\frac{1}{4}\sum_{ij}(\langle i^\alpha|i^\alpha\rangle \langle j^\alpha|j^\alpha\rangle - \langle i^\alpha|i^\alpha\rangle \langle j^\beta|j^\beta\rangle - \langle i^\beta|i^\beta\rangle \langle j^\alpha|j^\alpha\rangle + \langle i^\beta|i^\beta\rangle \langle j^\beta|j^\beta\rangle) \\ &-\frac{1}{4}\sum_{ij}(\langle i^\alpha|j^\alpha\rangle \langle j^\alpha|i^\alpha\rangle - \langle i^\alpha|j^\alpha\rangle \langle j^\beta|i^\beta\rangle - \langle i^\beta|j^\beta\rangle \langle j^\alpha|i^\alpha\rangle + \langle i^\beta|j^\beta\rangle\langle j^\beta|i^\beta\rangle) \\ &=\frac{1}{4}\sum_{ij}|\langle i^\alpha|i^\alpha\rangle - \langle i^\beta|i^\beta\rangle|^2 -\frac{1}{4}\sum_{ij}|\langle i^\alpha|j^\alpha\rangle - \langle i^\beta|j^\beta\rangle|^2 \\ &=\frac{1}{4}(n_\alpha - n_\beta)^2 -\frac{1}{4}\sum_{ij}|\langle i^\alpha|j^\alpha\rangle - \langle i^\beta|j^\beta\rangle|^2\end{split}\]

Args:

moa list of 2 ndarrays: Occupied alpha and occupied beta orbitals

Kwargs:

sndarray: AO overlap

Returns:

A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> mo = (mf.mo_coeff[0][:,mf.mo_occ[0]>0], mf.mo_coeff[1][:,mf.mo_occ[1]>0])
>>> print('S^2 = %.7f, 2S+1 = %.7f' % spin_square(mo, mol.intor('int1e_ovlp_sph')))
S^2 = 0.7570150, 2S+1 = 2.0070027

pyscf.scf.ghf_symm module¶

Non-relativistic generalized Hartree-Fock with point group symmetry.

class pyscf.scf.ghf_symm.GHF(mol)¶

Bases: pyscf.scf.ghf.GHF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for GHF method

GHF orbital coefficients are 2D array. Let nao be the number of spatial AOs, mo_coeff[:nao] are the coefficients of AO with alpha spin; mo_coeff[nao:nao*2] are the coefficients of AO with beta spin.

Attributes for symmetry allowed GHF:

irrep_nelecdict: Specify the number of electrons for particular irrep {‘ir_name’:int, …}. For the irreps not listed in these dicts, the program will choose the occupancy based on the orbital energies.

analyze(verbose=None, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

build(mol=None)¶

canonicalize(mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the UHF Fock matrix in occupied, virtual subspaces separatedly (without change occupancy).

dump_flags(verbose=None)¶

eig(h, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_irrep_nelec(mol=None, mo_coeff=None, mo_occ=None, s=None)¶

Electron numbers for each irreducible representation.

Args:

molan instance of Mole: To provide irrep_id, and spin-adapted basis
mo_coeff2D ndarray: Regular orbital coefficients, without grouping for irreps
mo_occ1D ndarray: Regular occupancy, without grouping for irreps

Returns:

irrep_nelecdict: The number of electrons for each irrep {‘ir_name’:int,…}.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
-76.016789472074251
>>> scf.hf_symm.get_irrep_nelec(mol, mf.mo_coeff, mf.mo_occ)
{'A1': 6, 'A2': 0, 'B1': 2, 'B2': 2}

get_occ(mo_energy=None, mo_coeff=None)¶: We assumed mo_energy are grouped by symmetry irreps, (see function self.eig). The orbitals are sorted after SCF.

get_orbsym(mo_coeff=None, s=None)¶

property orbsym¶

pyscf.scf.ghf_symm.analyze(mf, verbose=5, with_meta_lowdin=True, **kwargs)¶

pyscf.scf.ghf_symm.canonicalize(mf, mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the UHF Fock matrix in occupied, virtual subspaces separatedly (without change occupancy).

pyscf.scf.ghf_symm.get_orbsym(mol, mo_coeff, s=None, check=False)¶

pyscf.scf.hf module¶

Hartree-Fock

class pyscf.scf.hf.RHF(mol)¶

Bases: pyscf.scf.hf.SCF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

CASCI(*args, **kwargs)¶

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354

CASSCF(*args, **kwargs)¶

CASCI

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
CASSCF

Extra attributes for CASSCF:

conv_tolfloat
Converge threshold. Default is 1e-7

conv_tol_gradfloat
Converge threshold for CI gradients and orbital rotation gradients. Default is 1e-4

max_stepsizefloat
The step size for orbital rotation. Small step (0.005 - 0.05) is prefered. Default is 0.03.

max_cycle_macroint
Max number of macro iterations. Default is 50.

max_cycle_microint
Max number of micro iterations in each macro iteration. Depending on systems, increasing this value might reduce the total macro iterations. Generally, 2 - 5 steps should be enough. Default is 3.

ah_level_shiftfloat, for AH solver.
Level shift for the Davidson diagonalization in AH solver. Default is 1e-8.

ah_conv_tolfloat, for AH solver.
converge threshold for AH solver. Default is 1e-12.

ah_max_cyclefloat, for AH solver.
Max number of iterations allowd in AH solver. Default is 30.

ah_lindepfloat, for AH solver.
Linear dependence threshold for AH solver. Default is 1e-14.

ah_start_tolflat, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 0.2.

ah_start_cycleint, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 2.

ah_conv_tol, ah_max_cycle, ah_lindep, ah_start_tol and ah_start_cycle can affect the accuracy and performance of CASSCF solver. Lower ah_conv_tol and ah_lindep might improve the accuracy of CASSCF optimization, but decrease the performance.
>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()[0]
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()[0]
-109.044401887945668
chkfilestr
Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.

ci_response_spaceint
subspace size to solve the CI vector response. Default is 3.

callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

scale_restorationfloat
When a step of orbital rotation moves out of trust region, the orbital optimization will be restored to previous state and the step size of the orbital rotation needs to be reduced. scale_restoration controls how much to scale down the step size.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is enabled, the active segment of mo_coeff is transformed to natural orbitals.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134

CISD(*args, **kwargs)¶

DFMP2(*args, **kwargs)¶

EFG(*args, **kwargs)¶

Gradients(*args, **kwargs)¶: Non-relativistic restricted Hartree-Fock gradients

Hessian(*args, **kwargs)¶: Non-relativistic restricted Hartree-Fock hessian

MP2(*args, **kwargs)¶

restricted MP2 with canonical HF and non-canonical HF reference

Attributes:

verboseint

Print level. Default value equals to Mole.verbose

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory

conv_tolfloat

For non-canonical MP2, converge threshold for MP2 correlation energy. Default value is 1e-7.

conv_tol_normtfloat

For non-canonical MP2, converge threshold for norm(t2). Default value is 1e-5.

max_cycleint

For non-canonical MP2, max number of MP2 iterations. Default value is 50.

diis_spaceint

For non-canonical MP2, DIIS space size in MP2 iterations. Default is 6.

level_shiftfloat

A shift on virtual orbital energies to stablize the MP2 iterations.

frozenint or list

If integer is given, the inner-most orbitals are excluded from MP2 amplitudes. Given the orbital indices (0-based) in a list, both occupied and virtual orbitals can be frozen in MP2 calculation.

>>> mol = gto.M(atom = 'H 0 0 0; F 0 0 1.1', basis = 'ccpvdz')
>>> mf = scf.RHF(mol).run()
>>> # freeze 2 core orbitals
>>> pt = mp.MP2(mf).set(frozen = 2).run()
>>> # freeze 2 core orbitals and 3 high lying unoccupied orbitals
>>> pt.set(frozen = [0,1,16,17,18]).run()

Saved results

e_corrfloat
MP2 correlation correction

e_totfloat
Total MP2 energy (HF + correlation)

t2 :
T amplitudes t2[i,j,a,b] (i,j in occ, a,b in virt)

NMR(*args, **kwargs)¶

NSR(*args, **kwargs)¶: Nuclear-spin rotation tensors

Polarizability(*args, **kwargs)¶

RotationalGTensor(*args, **kwargs)¶: HF rotational g-tensors

SSC(*args, **kwargs)¶

SpinSpinCoupling(*args, **kwargs)¶

TDA(*args, **kwargs)¶

Tamm-Dancoff approximation

Attributes:

conv_tolfloat: Diagonalization convergence tolerance. Default is 1e-9.
nstatesint: Number of TD states to be computed. Default is 3.

Saved results:

convergedbool
Diagonalization converged or not

e1D array
excitation energy for each excited state.

xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.

TDHF(*args, **kwargs)¶

Time-dependent Hartree-Fock

Attributes:

conv_tolfloat: Diagonalization convergence tolerance. Default is 1e-9.
nstatesint: Number of TD states to be computed. Default is 3.

Saved results:

convergedbool
Diagonalization converged or not

e1D array
excitation energy for each excited state.

xyA list of two 2D arrays
The two 2D arrays are Excitation coefficients X (shape [nocc,nvir]) and de-excitation coefficients Y (shape [nocc,nvir]) for each excited state. (X,Y) are normalized to 1/2 in RHF/RKS methods and normalized to 1 for UHF/UKS methods. In the TDA calculation, Y = 0.

check_sanity()¶: Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

convert_from_(mf)¶: Convert the input mean-field object to RHF/ROHF

gen_response(mo_coeff=None, mo_occ=None, singlet=None, hermi=0, max_memory=None)¶

Generate a function to compute the product of RHF response function and RHF density matrices.

Kwargs:

singlet (None or boolean)If singlet is None, response function for: orbital hessian or CPHF will be generated. If singlet is boolean, it is used in TDDFT response kernel.

get_jk(mol=None, dm=None, hermi=1, with_j=True, with_k=True, omega=None)¶

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices
with_jboolean: Whether to compute J matrices
with_kboolean: Whether to compute K matrices
omegafloat: Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)¶

Hartree-Fock potential matrix for the given density matrix

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

dm_lastndarray or a list of ndarrays or 0: The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_lastndarray or a list of ndarrays or 0: The reference HF potential matrix.
hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

matrix Vhf = 2*J - K. Vhf can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dm0 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf0 = scf.hf.get_veff(mol, dm0, hermi=0)
>>> dm1 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf1 = scf.hf.get_veff(mol, dm1, hermi=0)
>>> vhf2 = scf.hf.get_veff(mol, dm1, dm_last=dm0, vhf_last=vhf0, hermi=0)
>>> numpy.allclose(vhf1, vhf2)
True

nuc_grad_method()¶: Hook to create object for analytical nuclear gradients.

spin_square(mo_coeff=None, s=None)¶: Spin square and multiplicity of RHF determinant

stability(internal=True, external=False, verbose=None)¶

RHF/RKS stability analysis.

See also pyscf.scf.stability.rhf_stability function.

Kwargs:

internalbool: Internal stability, within the RHF optimization space.
externalbool: External stability. Including the RHF -> UHF and real -> complex stability analysis.

Returns:

New orbitals that are more close to the stable condition. The return value includes two set of orbitals. The first corresponds to the internal stability and the second corresponds to the external stability.

class pyscf.scf.hf.SCF(mol)¶

Bases: pyscf.lib.misc.StreamObject

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

CCSD(frozen=None, mo_coeff=None, mo_occ=None)¶

restricted CCSD

Attributes:

verboseint

Print level. Default value equals to Mole.verbose

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory

conv_tolfloat

converge threshold. Default is 1e-7.

conv_tol_normtfloat

converge threshold for norm(t1,t2). Default is 1e-5.

max_cycleint

max number of iterations. Default is 50.

diis_spaceint

DIIS space size. Default is 6.

diis_start_cycleint

The step to start DIIS. Default is 0.

iterative_dampingfloat

The self consistent damping parameter.

directbool

AO-direct CCSD. Default is False.

async_iobool

Allow for asynchronous function execution. Default is True.

incore_completebool

Avoid all I/O (also for DIIS). Default is False.

level_shiftfloat

A shift on virtual orbital energies to stablize the CCSD iteration

frozenint or list

If integer is given, the inner-most orbitals are frozen from CC amplitudes. Given the orbital indices (0-based) in a list, both occupied and virtual orbitals can be frozen in CC calculation.

>>> mol = gto.M(atom = 'H 0 0 0; F 0 0 1.1', basis = 'ccpvdz')
>>> mf = scf.RHF(mol).run()
>>> # freeze 2 core orbitals
>>> mycc = cc.CCSD(mf).set(frozen = 2).run()
>>> # freeze 2 core orbitals and 3 high lying unoccupied orbitals
>>> mycc.set(frozen = [0,1,16,17,18]).run()

Saved results

convergedbool
CCSD converged or not

e_corrfloat
CCSD correlation correction

e_totfloat
Total CCSD energy (HF + correlation)

t1, t2 :
T amplitudes t1[i,a], t2[i,j,a,b] (i,j in occ, a,b in virt)

l1, l2 :
Lambda amplitudes l1[i,a], l2[i,j,a,b] (i,j in occ, a,b in virt)

DIIS¶: alias of pyscf.scf.diis.CDIIS

QMMM(atoms_or_coords, charges, unit=None)¶

Embedding the one-electron (non-relativistic) potential generated by MM point charges into QM Hamiltonian.

The total energy includes the regular QM energy, the interaction between the nuclei in QM region and the MM charges, and the static Coulomb interaction between the electron density and the MM charges. It does not include the static Coulomb interactions of the MM point charges, the MM energy, the vdw interaction or other bonding/non-bonding effects between QM region and MM particles.

Args:

scf_method : a HF or DFT object

atoms_or_coords2D array, shape (N,3): MM particle coordinates
charges1D array: MM particle charges

Kwargs:

unitstr: Bohr, AU, Ang (case insensitive). Default is the same to mol.unit

Returns:

Same method object as the input scf_method with modified 1e Hamiltonian

Note:

1. if MM charge and X2C correction are used together, function mm_charge needs to be applied after X2C decoration (.x2c method), eg mf = mm_charge(scf.RHF(mol).x2c()), [(0.5,0.6,0.8)], [-0.5]). 2. Once mm_charge function is applied on the SCF object, it affects all the post-HF calculations eg MP2, CCSD, MCSCF etc

Examples:

>>> mol = gto.M(atom='H 0 0 0; F 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = mm_charge(dft.RKS(mol), [(0.5,0.6,0.8)], [-0.3])
>>> mf.kernel()
-101.940495711284

analyze(verbose=None, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

apply(fn, *args, **kwargs)¶: Apply the fn to rest arguments: return fn(*args, **kwargs). The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

as_scanner()¶

Generating a scanner/solver for HF PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total HF energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters assigned in the SCF object (DIIS, conv_tol, max_memory etc) are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf
>>> hf_scanner = scf.RHF(gto.Mole().set(verbose=0)).as_scanner()
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.1'))
-98.552190448277955
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.5'))
-98.414750424294368

build(mol=None)¶

canonicalize(mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the Fock matrix within occupied, open, virtual subspaces separatedly (without change occupancy).

check_convergence = None¶

conv_check = True¶

conv_tol = 1e-09¶

conv_tol_grad = None¶

damp = 0¶

property damp_factor¶

density_fit(auxbasis=None, with_df=None, only_dfj=False)¶

diis = True¶

diis_file = None¶

diis_space = 8¶

diis_space_rollback = False¶

diis_start_cycle = 1¶

dip_moment(mol=None, dm=None, unit='Debye', verbose=3, **kwargs)¶

Dipole moment calculation

\[\begin{split}\mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A\end{split}\]

where \(\mu_x, \mu_y, \mu_z\) are the x, y and z components of dipole moment

Args:: mol: an instance of Mole dm : a 2D ndarrays density matrices
Return:: A list: the dipole moment on x, y and z component

direct_scf = True¶

direct_scf_tol = 1e-13¶

dump_chk(envs)¶

dump_flags(verbose=None)¶

dump_scf_summary(verbose=5)¶

eig(h, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

energy_elec(dm=None, h1e=None, vhf=None)¶

Electronic part of Hartree-Fock energy, for given core hamiltonian and HF potential

… math:

E = \sum_{ij}h_{ij} \gamma_{ji}
  + \frac{1}{2}\sum_{ijkl} \gamma_{ji}\gamma_{lk} \langle ik||jl\rangle

Note this function has side effects which cause mf.scf_summary updated.

Args:

mf : an instance of SCF class

Kwargs:

dm2D ndarray: one-partical density matrix
h1e2D ndarray: Core hamiltonian
vhf2D ndarray: HF potential

Returns:

Hartree-Fock electronic energy and the Coulomb energy

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> dm = mf.make_rdm1()
>>> scf.hf.energy_elec(mf, dm)
(-1.5176090667746334, 0.60917167853723675)
>>> mf.energy_elec(dm)
(-1.5176090667746334, 0.60917167853723675)

energy_nuc()¶

energy_tot(dm=None, h1e=None, vhf=None)¶

Total Hartree-Fock energy, electronic part plus nuclear repulstion See scf.hf.energy_elec() for the electron part

Note this function has side effects which cause mf.scf_summary updated.

from_chk(chkfile=None, project=None)¶

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:: Density matrix, 2D ndarray

from_fcidump(filename, molpro_orbsym=False)¶: Update the SCF object with the quantities defined in FCIDUMP file

get_fock(h1e=None, s1e=None, vhf=None, dm=None, cycle=- 1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None)¶

F = h^{core} + V^{HF}

Special treatment (damping, DIIS, or level shift) will be applied to the Fock matrix if diis and cycle is specified (The two parameters are passed to get_fock function during the SCF iteration)

Kwargs:

h1e2D ndarray: Core hamiltonian
s1e2D ndarray: Overlap matrix, for DIIS
vhf2D ndarray: HF potential matrix
dm2D ndarray: Density matrix, for DIIS
cycleint: Then present SCF iteration step, for DIIS
diisan object of SCF.DIIS class: DIIS object to hold intermediate Fock and error vectors
diis_start_cycleint: The step to start DIIS. Default is 0.
level_shift_factorfloat or int: Level shift (in AU) for virtual space. Default is 0.

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_hcore(mol=None)¶

get_init_guess(mol=None, key='minao')¶

get_j(mol=None, dm=None, hermi=1, omega=None)¶: Compute J matrices for all input density matrices

get_jk(mol=None, dm=None, hermi=1, with_j=True, with_k=True, omega=None)¶

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices
with_jboolean: Whether to compute J matrices
with_kboolean: Whether to compute K matrices
omegafloat: Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

get_k(mol=None, dm=None, hermi=1, omega=None)¶: Compute K matrices for all input density matrices

get_occ(mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray: Obital energies
mo_coeff2D ndarray: Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

get_ovlp(mol=None)¶

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)¶

Hartree-Fock potential matrix for the given density matrix

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

dm_lastndarray or a list of ndarrays or 0: The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_lastndarray or a list of ndarrays or 0: The reference HF potential matrix.
hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

matrix Vhf = 2*J - K. Vhf can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dm0 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf0 = scf.hf.get_veff(mol, dm0, hermi=0)
>>> dm1 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf1 = scf.hf.get_veff(mol, dm1, hermi=0)
>>> vhf2 = scf.hf.get_veff(mol, dm1, dm_last=dm0, vhf_last=vhf0, hermi=0)
>>> numpy.allclose(vhf1, vhf2)
True

property hf_energy¶

init_direct_scf(mol=None)¶

init_guess = 'minao'¶

init_guess_by_1e(mol=None)¶

Generate initial guess density matrix from core hamiltonian

Returns:: Density matrix, 2D ndarray

init_guess_by_atom(mol=None)¶

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:: Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)¶

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:: Density matrix, 2D ndarray

init_guess_by_huckel(mol=None)¶

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:: Density matrix, 2D ndarray

init_guess_by_minao(mol=None)¶

Generate initial guess density matrix based on ANO basis, then project the density matrix to the basis set defined by mol

Returns:: Density matrix, 2D ndarray

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> scf.hf.init_guess_by_minao(mol)
array([[ 0.94758917,  0.09227308],
       [ 0.09227308,  0.94758917]])

kernel(*args, **kwargs)¶

An alias to method scf Function Signature: kernel(self, dm0=None, **kwargs) —————————————-

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

level_shift = 0¶

property level_shift_factor¶

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)¶

One-particle density matrix in AO representation

Args:

mo_coeff2D ndarray: Orbital coefficients. Each column is one orbital.
mo_occ1D ndarray: Occupancy

max_cycle = 50¶

mulliken_meta(mol=None, dm=None, verbose=5, pre_orth_method='ANO', s=None)¶

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carreid out within each subsets.

Args:

mol : an instance of Mole

dmndarray or 2-item list of ndarray: Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr: Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

mulliken_pop(mol=None, dm=None, s=None, verbose=5)¶

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

mulliken_pop_meta_lowdin_ao(*args, **kwargs)¶

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carreid out within each subsets.

Args:

mol : an instance of Mole

dmndarray or 2-item list of ndarray: Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr: Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

newton()¶

nuc_grad_method()¶: Hook to create object for analytical nuclear gradients.

pop(*args, **kwargs)¶

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carreid out within each subsets.

Args:

mol : an instance of Mole

dmndarray or 2-item list of ndarray: Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr: Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

reset(mol=None)¶: Reset mol and relevant attributes associated to the old mol object

scf(dm0=None, **kwargs)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

sfx2c1e()¶

to_ghf()¶

Convert the input mean-field object to a GHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_gks(xc='HF')¶

Convert the input mean-field object to a GKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_rhf()¶

Convert the input mean-field object to a RHF/ROHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_rks(xc='HF')¶

Convert the input mean-field object to a RKS/ROKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_uhf()¶

Convert the input mean-field object to a UHF object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

to_uks(xc='HF')¶

Convert the input mean-field object to a UKS object.

Note this conversion only changes the class of the mean-field object. The total energy and wave-function are the same as them in the input mean-field object.

update(chkfile=None)¶: Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_(chkfile=None)¶: Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_from_chk(chkfile=None)¶: Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

update_from_chk_(chkfile=None)¶: Read attributes from the chkfile then replace the attributes of current object. It’s an alias of function update_from_chk_.

x2c()¶

x2c1e()¶

pyscf.scf.hf.analyze(mf, verbose=5, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

pyscf.scf.hf.as_scanner(mf)¶

Generating a scanner/solver for HF PES.

The returned solver is a function. This function requires one argument “mol” as input and returns total HF energy.

The solver will automatically use the results of last calculation as the initial guess of the new calculation. All parameters assigned in the SCF object (DIIS, conv_tol, max_memory etc) are automatically applied in the solver.

Note scanner has side effects. It may change many underlying objects (_scf, with_df, with_x2c, …) during calculation.

Examples:

>>> from pyscf import gto, scf
>>> hf_scanner = scf.RHF(gto.Mole().set(verbose=0)).as_scanner()
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.1'))
-98.552190448277955
>>> hf_scanner(gto.M(atom='H 0 0 0; F 0 0 1.5'))
-98.414750424294368

pyscf.scf.hf.canonicalize(mf, mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the Fock matrix within occupied, open, virtual subspaces separatedly (without change occupancy).

pyscf.scf.hf.damping(s, d, f, factor)¶

pyscf.scf.hf.dip_moment(mol, dm, unit='Debye', verbose=3, **kwargs)¶

Dipole moment calculation

\[\begin{split}\mu_x = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|x|\mu) + \sum_A Q_A X_A\\ \mu_y = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|y|\mu) + \sum_A Q_A Y_A\\ \mu_z = -\sum_{\mu}\sum_{\nu} P_{\mu\nu}(\nu|z|\mu) + \sum_A Q_A Z_A\end{split}\]

where \(\mu_x, \mu_y, \mu_z\) are the x, y and z components of dipole moment

Args:: mol: an instance of Mole dm : a 2D ndarrays density matrices
Return:: A list: the dipole moment on x, y and z component

pyscf.scf.hf.dot_eri_dm(eri, dm, hermi=0, with_j=True, with_k=True)¶

Compute J, K matrices in terms of the given 2-electron integrals and density matrix:

J ~ numpy.einsum(‘pqrs,qp->rs’, eri, dm) K ~ numpy.einsum(‘pqrs,qr->ps’, eri, dm)

Args:

erindarray: 8-fold or 4-fold ERIs or complex integral array with N^4 elements (N is the number of orbitals)
dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> eri = _vhf.int2e_sph(mol._atm, mol._bas, mol._env)
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.dot_eri_dm(eri, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

pyscf.scf.hf.dump_scf_summary(mf, verbose=5)¶

pyscf.scf.hf.eig(h, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

pyscf.scf.hf.energy_elec(mf, dm=None, h1e=None, vhf=None)¶

Electronic part of Hartree-Fock energy, for given core hamiltonian and HF potential

… math:

E = \sum_{ij}h_{ij} \gamma_{ji}
  + \frac{1}{2}\sum_{ijkl} \gamma_{ji}\gamma_{lk} \langle ik||jl\rangle

Note this function has side effects which cause mf.scf_summary updated.

Args:

mf : an instance of SCF class

Kwargs:

dm2D ndarray: one-partical density matrix
h1e2D ndarray: Core hamiltonian
vhf2D ndarray: HF potential

Returns:

Hartree-Fock electronic energy and the Coulomb energy

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> dm = mf.make_rdm1()
>>> scf.hf.energy_elec(mf, dm)
(-1.5176090667746334, 0.60917167853723675)
>>> mf.energy_elec(dm)
(-1.5176090667746334, 0.60917167853723675)

pyscf.scf.hf.energy_tot(mf, dm=None, h1e=None, vhf=None)¶

Total Hartree-Fock energy, electronic part plus nuclear repulstion See scf.hf.energy_elec() for the electron part

Note this function has side effects which cause mf.scf_summary updated.

pyscf.scf.hf.get_fock(mf, h1e=None, s1e=None, vhf=None, dm=None, cycle=- 1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None)¶

F = h^{core} + V^{HF}

Special treatment (damping, DIIS, or level shift) will be applied to the Fock matrix if diis and cycle is specified (The two parameters are passed to get_fock function during the SCF iteration)

Kwargs:

h1e2D ndarray: Core hamiltonian
s1e2D ndarray: Overlap matrix, for DIIS
vhf2D ndarray: HF potential matrix
dm2D ndarray: Density matrix, for DIIS
cycleint: Then present SCF iteration step, for DIIS
diisan object of SCF.DIIS class: DIIS object to hold intermediate Fock and error vectors
diis_start_cycleint: The step to start DIIS. Default is 0.
level_shift_factorfloat or int: Level shift (in AU) for virtual space. Default is 0.

pyscf.scf.hf.get_grad(mo_coeff, mo_occ, fock_ao)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

pyscf.scf.hf.get_hcore(mol)¶

Core Hamiltonian

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> scf.hf.get_hcore(mol)
array([[-0.93767904, -0.59316327],
       [-0.59316327, -0.93767904]])

pyscf.scf.hf.get_init_guess(mol, key='minao')¶

Generate density matrix for initial guess

Kwargs:

keystr: One of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’.

pyscf.scf.hf.get_jk(mol, dm, hermi=1, vhfopt=None, with_j=True, with_k=True, omega=None)¶

Compute J, K matrices for all input density matrices

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether J, K matrix is hermitian

0 : not hermitian and not symmetric

1 : hermitian or symmetric

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices
with_jboolean: Whether to compute J matrices
with_kboolean: Whether to compute K matrices
omegafloat: Parameter of range-seperated Coulomb operator: erf( omega * r12 ) / r12. If specified, integration are evaluated based on the long-range part of the range-seperated Coulomb operator.

Returns:

Depending on the given dm, the function returns one J and one K matrix, or a list of J matrices and a list of K matrices, corresponding to the input density matrices.

Examples:

>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dms = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> j, k = scf.hf.get_jk(mol, dms, hermi=0)
>>> print(j.shape)
(3, 2, 2)

pyscf.scf.hf.get_occ(mf, mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray: Obital energies
mo_coeff2D ndarray: Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

pyscf.scf.hf.get_ovlp(mol)¶: Overlap matrix

pyscf.scf.hf.get_veff(mol, dm, dm_last=None, vhf_last=None, hermi=1, vhfopt=None)¶

Hartree-Fock potential matrix for the given density matrix

Args:

mol : an instance of Mole

dmndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

dm_lastndarray or a list of ndarrays or 0: The density matrix baseline. If not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_lastndarray or a list of ndarrays or 0: The reference HF potential matrix.
hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

matrix Vhf = 2*J - K. Vhf can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> from pyscf.scf import _vhf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dm0 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf0 = scf.hf.get_veff(mol, dm0, hermi=0)
>>> dm1 = numpy.random.random((mol.nao_nr(),mol.nao_nr()))
>>> vhf1 = scf.hf.get_veff(mol, dm1, hermi=0)
>>> vhf2 = scf.hf.get_veff(mol, dm1, dm_last=dm0, vhf_last=vhf0, hermi=0)
>>> numpy.allclose(vhf1, vhf2)
True

pyscf.scf.hf.init_guess_by_1e(mol)¶

Generate initial guess density matrix from core hamiltonian

Returns:: Density matrix, 2D ndarray

pyscf.scf.hf.init_guess_by_atom(mol)¶

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:: Density matrix, 2D ndarray

pyscf.scf.hf.init_guess_by_chkfile(mol, chkfile_name, project=None)¶

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:: Density matrix, 2D ndarray

pyscf.scf.hf.init_guess_by_huckel(mol)¶

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:: Density matrix, 2D ndarray

pyscf.scf.hf.init_guess_by_minao(mol)¶

Generate initial guess density matrix based on ANO basis, then project the density matrix to the basis set defined by mol

Returns:: Density matrix, 2D ndarray

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> scf.hf.init_guess_by_minao(mol)
array([[ 0.94758917,  0.09227308],
       [ 0.09227308,  0.94758917]])

pyscf.scf.hf.kernel(mf, conv_tol=1e-10, conv_tol_grad=None, dump_chk=True, dm0=None, callback=None, conv_check=True, **kwargs)¶

kernel: the SCF driver.

Args:

mfan instance of SCF class: mf object holds all parameters to control SCF. One can modify its member functions to change the behavior of SCF. The member functions which are called in kernel are

mf.get_init_guess

mf.get_hcore

mf.get_ovlp

mf.get_veff

mf.get_fock

mf.get_grad

mf.eig

mf.get_occ

mf.make_rdm1

mf.energy_tot

mf.dump_chk

Kwargs:

conv_tolfloat: converge threshold.
conv_tol_gradfloat: gradients converge threshold.
dump_chkbool: Whether to save SCF intermediate results in the checkpoint file
dm0ndarray: Initial guess density matrix. If not given (the default), the kernel takes the density matrix generated by mf.get_init_guess.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

Returns:

A list : scf_conv, e_tot, mo_energy, mo_coeff, mo_occ

scf_convbool: True means SCF converged
e_totfloat: Hartree-Fock energy of last iteration
mo_energy1D float array: Orbital energies. Depending the eig function provided by mf object, the orbital energies may NOT be sorted.
mo_coeff2D array: Orbital coefficients.
mo_occ1D array: Orbital occupancies. The occupancies may NOT be sorted from large to small.

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> conv, e, mo_e, mo, mo_occ = scf.hf.kernel(scf.hf.SCF(mol), dm0=numpy.eye(mol.nao_nr()))
>>> print('conv = %s, E(HF) = %.12f' % (conv, e))
conv = True, E(HF) = -1.081170784378

pyscf.scf.hf.level_shift(s, d, f, factor)¶

Apply level shift \(\Delta\) to virtual orbitals

\begin{align} FC &= SCE \\ F &= F + SC \Lambda C^\dagger S \\ \Lambda_{ij} &= \begin{cases} \delta_{ij}\Delta & i \in \text{virtual} \\ 0 & \text{otherwise} \end{cases} \end{align}

Returns:: New Fock matrix, 2D ndarray

pyscf.scf.hf.make_rdm1(mo_coeff, mo_occ, **kwargs)¶

One-particle density matrix in AO representation

Args:

mo_coeff2D ndarray: Orbital coefficients. Each column is one orbital.
mo_occ1D ndarray: Occupancy

pyscf.scf.hf.mulliken_meta(mol, dm, verbose=5, pre_orth_method='ANO', s=None)¶

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carreid out within each subsets.

Args:

mol : an instance of Mole

dmndarray or 2-item list of ndarray: Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr: Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

pyscf.scf.hf.mulliken_pop(mol, dm, s=None, verbose=5)¶

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

pyscf.scf.hf.mulliken_pop_meta_lowdin_ao(mol, dm, verbose=5, pre_orth_method='ANO', s=None)¶

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carreid out within each subsets.

Args:

mol : an instance of Mole

dmndarray or 2-item list of ndarray: Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr: Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

pyscf.scf.hf.pack_uniq_var(x, mo_occ)¶: Extract the unique variables from the full orbital-gradients (or orbital-rotation) matrix

pyscf.scf.hf.uniq_var_indices(mo_occ)¶: Indicies of the unique variables for the orbital-gradients (or orbital-rotation) matrix.

pyscf.scf.hf.unpack_uniq_var(dx, mo_occ)¶: Fill the full orbital-gradients (or orbital-rotation) matrix with the unique variables.

pyscf.scf.hf_symm module¶

Non-relativistic restricted Hartree-Fock with point group symmetry.

The symmetry are not handled in a separate data structure. Note that during the SCF iteration, the orbitals are grouped in terms of symmetry irreps. But the orbitals in the result are sorted based on the orbital energies. Function symm.label_orb_symm can be used to detect the symmetry of the molecular orbitals.

class pyscf.scf.hf_symm.HF1e(mol)¶

Bases: pyscf.scf.hf_symm.SymAdaptedROHF

scf(*args)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

pyscf.scf.hf_symm.RHF¶: alias of pyscf.scf.hf_symm.SymAdaptedRHF

pyscf.scf.hf_symm.ROHF¶: alias of pyscf.scf.hf_symm.SymAdaptedROHF

class pyscf.scf.hf_symm.SymAdaptedRHF(mol)¶

Bases: pyscf.scf.hf.RHF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for symmetry allowed RHF:

irrep_nelecdict: Specify the number of electrons for particular irrep {‘ir_name’:int,…}. For the irreps not listed in this dict, the program will choose the occupancy based on the orbital energies.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
-76.016789472074251
>>> mf.get_irrep_nelec()
{'A1': 6, 'A2': 0, 'B1': 2, 'B2': 2}
>>> mf.irrep_nelec = {'A2': 2}
>>> mf.scf()
-72.768201804695622
>>> mf.get_irrep_nelec()
{'A1': 6, 'A2': 2, 'B1': 2, 'B2': 0}

CASCI(*args, **kwargs)¶

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354

CASSCF(*args, **kwargs)¶

CASCI

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
CASSCF

Extra attributes for CASSCF:

conv_tolfloat
Converge threshold. Default is 1e-7

conv_tol_gradfloat
Converge threshold for CI gradients and orbital rotation gradients. Default is 1e-4

max_stepsizefloat
The step size for orbital rotation. Small step (0.005 - 0.05) is prefered. Default is 0.03.

max_cycle_macroint
Max number of macro iterations. Default is 50.

max_cycle_microint
Max number of micro iterations in each macro iteration. Depending on systems, increasing this value might reduce the total macro iterations. Generally, 2 - 5 steps should be enough. Default is 3.

ah_level_shiftfloat, for AH solver.
Level shift for the Davidson diagonalization in AH solver. Default is 1e-8.

ah_conv_tolfloat, for AH solver.
converge threshold for AH solver. Default is 1e-12.

ah_max_cyclefloat, for AH solver.
Max number of iterations allowd in AH solver. Default is 30.

ah_lindepfloat, for AH solver.
Linear dependence threshold for AH solver. Default is 1e-14.

ah_start_tolflat, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 0.2.

ah_start_cycleint, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 2.

ah_conv_tol, ah_max_cycle, ah_lindep, ah_start_tol and ah_start_cycle can affect the accuracy and performance of CASSCF solver. Lower ah_conv_tol and ah_lindep might improve the accuracy of CASSCF optimization, but decrease the performance.
>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()[0]
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()[0]
-109.044401887945668
chkfilestr
Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.

ci_response_spaceint
subspace size to solve the CI vector response. Default is 3.

callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

scale_restorationfloat
When a step of orbital rotation moves out of trust region, the orbital optimization will be restored to previous state and the step size of the orbital rotation needs to be reduced. scale_restoration controls how much to scale down the step size.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is enabled, the active segment of mo_coeff is transformed to natural orbitals.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134

analyze(verbose=None, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Occupancy for each irreps; Mulliken population analysis

build(mol=None)¶

canonicalize(mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the Fock matrix in occupied, open, virtual subspaces separatedly (without change occupancy).

eig(h, s)¶: Solve generalized eigenvalue problem, for each irrep. The eigenvalues and eigenvectors are not sorted to ascending order. Instead, they are grouped based on irreps.

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_irrep_nelec(mol=None, mo_coeff=None, mo_occ=None, s=None)¶

Electron numbers for each irreducible representation.

Args:

molan instance of Mole: To provide irrep_id, and spin-adapted basis
mo_coeff2D ndarray: Regular orbital coefficients, without grouping for irreps
mo_occ1D ndarray: Regular occupancy, without grouping for irreps

Returns:

irrep_nelecdict: The number of electrons for each irrep {‘ir_name’:int,…}.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
-76.016789472074251
>>> scf.hf_symm.get_irrep_nelec(mol, mf.mo_coeff, mf.mo_occ)
{'A1': 6, 'A2': 0, 'B1': 2, 'B2': 2}

get_occ(mo_energy=None, mo_coeff=None)¶: We assumed mo_energy are grouped by symmetry irreps, (see function self.eig). The orbitals are sorted after SCF.

get_orbsym(mo_coeff=None, s=None)¶

get_wfnsym(mo_coeff=None, mo_occ=None)¶

property orbsym¶

property wfnsym¶

class pyscf.scf.hf_symm.SymAdaptedROHF(mol)¶

Bases: pyscf.scf.rohf.ROHF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for symmetry allowed ROHF:

irrep_nelecdict: Specify the number of alpha/beta electrons for particular irrep {‘ir_name’:(int,int), …}. For the irreps not listed in these dicts, the program will choose the occupancy based on the orbital energies.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, charge=1, spin=1, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
-75.619358861084052
>>> mf.get_irrep_nelec()
{'A1': (3, 3), 'A2': (0, 0), 'B1': (1, 1), 'B2': (1, 0)}
>>> mf.irrep_nelec = {'B1': (1, 0)}
>>> mf.scf()
-75.425669486776457
>>> mf.get_irrep_nelec()
{'A1': (3, 3), 'A2': (0, 0), 'B1': (1, 0), 'B2': (1, 1)}

CASCI(*args, **kwargs)¶

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354

CASSCF(*args, **kwargs)¶

CASCI

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
CASSCF

Extra attributes for CASSCF:

conv_tolfloat
Converge threshold. Default is 1e-7

conv_tol_gradfloat
Converge threshold for CI gradients and orbital rotation gradients. Default is 1e-4

max_stepsizefloat
The step size for orbital rotation. Small step (0.005 - 0.05) is prefered. Default is 0.03.

max_cycle_macroint
Max number of macro iterations. Default is 50.

max_cycle_microint
Max number of micro iterations in each macro iteration. Depending on systems, increasing this value might reduce the total macro iterations. Generally, 2 - 5 steps should be enough. Default is 3.

ah_level_shiftfloat, for AH solver.
Level shift for the Davidson diagonalization in AH solver. Default is 1e-8.

ah_conv_tolfloat, for AH solver.
converge threshold for AH solver. Default is 1e-12.

ah_max_cyclefloat, for AH solver.
Max number of iterations allowd in AH solver. Default is 30.

ah_lindepfloat, for AH solver.
Linear dependence threshold for AH solver. Default is 1e-14.

ah_start_tolflat, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 0.2.

ah_start_cycleint, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 2.

ah_conv_tol, ah_max_cycle, ah_lindep, ah_start_tol and ah_start_cycle can affect the accuracy and performance of CASSCF solver. Lower ah_conv_tol and ah_lindep might improve the accuracy of CASSCF optimization, but decrease the performance.
>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()[0]
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()[0]
-109.044401887945668
chkfilestr
Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.

ci_response_spaceint
subspace size to solve the CI vector response. Default is 3.

callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

scale_restorationfloat
When a step of orbital rotation moves out of trust region, the orbital optimization will be restored to previous state and the step size of the orbital rotation needs to be reduced. scale_restoration controls how much to scale down the step size.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is enabled, the active segment of mo_coeff is transformed to natural orbitals.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134

TDA = None¶

TDHF = None¶

analyze(verbose=None, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis

build(mol=None)¶

canonicalize(mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the Fock matrix in occupied, open, virtual subspaces separatedly (without change occupancy).

dump_flags(verbose=None)¶

eig(fock, s)¶: Solve generalized eigenvalue problem, for each irrep. The eigenvalues and eigenvectors are not sorted to ascending order. Instead, they are grouped based on irreps.

get_grad(mo_coeff, mo_occ, fock=None)¶: ROHF gradients is the off-diagonal block [co + cv + ov], where [ cc co cv ] [ oc oo ov ] [ vc vo vv ]

get_irrep_nelec(mol=None, mo_coeff=None, mo_occ=None, s=None)¶

get_occ(mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital. NOTE the occupancies are not assigned based on the orbital energy ordering. The first N orbitals are assigned to be occupied orbitals.

Examples:

>>> mol = gto.M(atom='H 0 0 0; O 0 0 1.1', spin=1)
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 2, 2, 1, 0])

get_orbsym(mo_coeff=None, s=None)¶

get_wfnsym(mo_coeff=None, mo_occ=None)¶

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)¶: One-particle densit matrix. mo_occ is a 1D array, with occupancy 1 or 2.

property orbsym¶

property wfnsym¶

pyscf.scf.hf_symm.analyze(mf, verbose=5, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Occupancy for each irreps; Mulliken population analysis

pyscf.scf.hf_symm.canonicalize(mf, mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the Fock matrix in occupied, open, virtual subspaces separatedly (without change occupancy).

pyscf.scf.hf_symm.check_irrep_nelec(mol, irrep_nelec, nelec)¶

pyscf.scf.hf_symm.eig(mf, h, s)¶: Solve generalized eigenvalue problem, for each irrep. The eigenvalues and eigenvectors are not sorted to ascending order. Instead, they are grouped based on irreps.

pyscf.scf.hf_symm.get_irrep_nelec(mol, mo_coeff, mo_occ, s=None)¶

Electron numbers for each irreducible representation.

Args:

molan instance of Mole: To provide irrep_id, and spin-adapted basis
mo_coeff2D ndarray: Regular orbital coefficients, without grouping for irreps
mo_occ1D ndarray: Regular occupancy, without grouping for irreps

Returns:

irrep_nelecdict: The number of electrons for each irrep {‘ir_name’:int,…}.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
-76.016789472074251
>>> scf.hf_symm.get_irrep_nelec(mol, mf.mo_coeff, mf.mo_occ)
{'A1': 6, 'A2': 0, 'B1': 2, 'B2': 2}

pyscf.scf.hf_symm.get_orbsym(mol, mo_coeff, s=None, check=False)¶

pyscf.scf.hf_symm.get_wfnsym(mf, mo_coeff=None, mo_occ=None)¶

pyscf.scf.hf_symm.so2ao_mo_coeff(so, irrep_mo_coeff)¶: Transfer the basis of MO coefficients, from spin-adapted basis to AO basis

pyscf.scf.jk module¶

General JK contraction function for * arbitrary integrals * 4 different molecules * multiple density matrices * arbitrary basis subset for the 4 indices

pyscf.scf.jk.get_jk(mols, dms, scripts=['ijkl,ji->kl'], intor='int2e_sph', aosym='s1', comp=None, hermi=0, shls_slice=None, verbose=2, vhfopt=None)¶

Compute J/K matrices for the given density matrix

Args:

mols : an instance of Mole or a list of Mole objects

dmsndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether the returned J (K) matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
intorstr: 2-electron integral name. See getints() for the complete list of available 2-electron integral names
aosymint or str: Permutation symmetry for the AO integrals

4 or ‘4’ or ‘s4’: 4-fold symmetry (default)

‘2ij’ or ‘s2ij’ : symmetry between i, j in (ij|kl)

‘2kl’ or ‘s2kl’ : symmetry between k, l in (ij|kl)

1 or ‘1’ or ‘s1’: no symmetry

‘a4ij’ : 4-fold symmetry with anti-symmetry between i, j in (ij|kl)

‘a4kl’ : 4-fold symmetry with anti-symmetry between k, l in (ij|kl)

‘a2ij’ : anti-symmetry between i, j in (ij|kl)

‘a2kl’ : anti-symmetry between k, l in (ij|kl)
compint: Components of the integrals, e.g. cint2e_ip_sph has 3 components.
scriptsstring or a list of strings: Contraction description (following numpy.einsum convention) based on letters [ijkl]. Each script will be one-to-one applied to each entry of dms. So it must have the same number of elements as the dms, len(scripts) == len(dms).
shls_slice8-element list: (ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)

Returns:

Depending on the number of density matrices, the function returns one J/K matrix or a list of J/K matrices (the same number of entries as the input dms). Each JK matrices may be a 2D array or 3D array if the AO integral has multiple components.

Examples:

>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
>>> nao = mol.nao_nr()
>>> dm = numpy.random.random((nao,nao))
>>> # Default, Coulomb matrix
>>> vj = get_jk(mol, dm)
>>> # Coulomb matrix with 8-fold permutation symmetry for AO integrals
>>> vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
>>> # Exchange matrix with 8-fold permutation symmetry for AO integrals
>>> vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
>>> # Compute coulomb and exchange matrices together
>>> vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'), aosym='s8')
>>> # Analytical gradients for coulomb matrix
>>> j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='int2e_ip1_sph', aosym='s2kl', comp=3)

>>> # contraction across two molecules
>>> mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
>>> nao1 = mol1.nao_nr()
>>> dm1 = numpy.random.random((nao1,nao1))
>>> # Coulomb interaction between two molecules, note 4-fold symmetry can be applied
>>> jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
>>> ecoul = numpy.einsum('ij,ij', jcross, dm1)
>>> # Exchange interaction between two molecules, no symmetry can be used
>>> kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
>>> ex = numpy.einsum('ij,ji', kcross, dm1)

>>> # Analytical gradients for coulomb matrix between two molecules
>>> jcros1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3)
>>> # Analytical gradients for coulomb interaction between 1s density and the other molecule
>>> jpart1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3,
...                 shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))

pyscf.scf.jk.jk_build(mols, dms, scripts=['ijkl,ji->kl'], intor='int2e_sph', aosym='s1', comp=None, hermi=0, shls_slice=None, verbose=2, vhfopt=None)¶

Compute J/K matrices for the given density matrix

Args:

mols : an instance of Mole or a list of Mole objects

dmsndarray or list of ndarrays: A density matrix or a list of density matrices

Kwargs:

hermiint: Whether the returned J (K) matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
intorstr: 2-electron integral name. See getints() for the complete list of available 2-electron integral names
aosymint or str: Permutation symmetry for the AO integrals

4 or ‘4’ or ‘s4’: 4-fold symmetry (default)

‘2ij’ or ‘s2ij’ : symmetry between i, j in (ij|kl)

‘2kl’ or ‘s2kl’ : symmetry between k, l in (ij|kl)

1 or ‘1’ or ‘s1’: no symmetry

‘a4ij’ : 4-fold symmetry with anti-symmetry between i, j in (ij|kl)

‘a4kl’ : 4-fold symmetry with anti-symmetry between k, l in (ij|kl)

‘a2ij’ : anti-symmetry between i, j in (ij|kl)

‘a2kl’ : anti-symmetry between k, l in (ij|kl)
compint: Components of the integrals, e.g. cint2e_ip_sph has 3 components.
scriptsstring or a list of strings: Contraction description (following numpy.einsum convention) based on letters [ijkl]. Each script will be one-to-one applied to each entry of dms. So it must have the same number of elements as the dms, len(scripts) == len(dms).
shls_slice8-element list: (ish_start, ish_end, jsh_start, jsh_end, ksh_start, ksh_end, lsh_start, lsh_end)

Returns:

Depending on the number of density matrices, the function returns one J/K matrix or a list of J/K matrices (the same number of entries as the input dms). Each JK matrices may be a 2D array or 3D array if the AO integral has multiple components.

Examples:

>>> from pyscf import gto
>>> mol = gto.M(atom='H 0 -.5 0; H 0 .5 0', basis='cc-pvdz')
>>> nao = mol.nao_nr()
>>> dm = numpy.random.random((nao,nao))
>>> # Default, Coulomb matrix
>>> vj = get_jk(mol, dm)
>>> # Coulomb matrix with 8-fold permutation symmetry for AO integrals
>>> vj = get_jk(mol, dm, 'ijkl,ji->kl', aosym='s8')
>>> # Exchange matrix with 8-fold permutation symmetry for AO integrals
>>> vk = get_jk(mol, dm, 'ijkl,jk->il', aosym='s8')
>>> # Compute coulomb and exchange matrices together
>>> vj, vk = get_jk(mol, (dm,dm), ('ijkl,ji->kl','ijkl,li->kj'), aosym='s8')
>>> # Analytical gradients for coulomb matrix
>>> j1 = get_jk(mol, dm, 'ijkl,lk->ij', intor='int2e_ip1_sph', aosym='s2kl', comp=3)

>>> # contraction across two molecules
>>> mol1 = gto.M(atom='He 2 0 0', basis='6-31g')
>>> nao1 = mol1.nao_nr()
>>> dm1 = numpy.random.random((nao1,nao1))
>>> # Coulomb interaction between two molecules, note 4-fold symmetry can be applied
>>> jcross = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', aosym='s4')
>>> ecoul = numpy.einsum('ij,ij', jcross, dm1)
>>> # Exchange interaction between two molecules, no symmetry can be used
>>> kcross = get_jk((mol1,mol,mol,mol1), dm, scripts='ijkl,jk->il')
>>> ex = numpy.einsum('ij,ji', kcross, dm1)

>>> # Analytical gradients for coulomb matrix between two molecules
>>> jcros1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3)
>>> # Analytical gradients for coulomb interaction between 1s density and the other molecule
>>> jpart1 = get_jk((mol1,mol1,mol,mol), dm, scripts='ijkl,lk->ij', intor='int2e_ip1_sph', comp=3,
...                 shls_slice=(0,1,0,1,0,mol.nbas,0,mol.nbas))

pyscf.scf.newton_ah module¶

pyscf.scf.rohf module¶

Restricted Open-shell Hartree-Fock

class pyscf.scf.rohf.HF1e(mol)¶

Bases: pyscf.scf.rohf.ROHF

scf(*args)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

class pyscf.scf.rohf.ROHF(mol)¶

Bases: pyscf.scf.hf.RHF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

CASCI(*args, **kwargs)¶

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354

CASSCF(*args, **kwargs)¶

CASCI

Args:

mf_or_molSCF object or Mole object: SCF or Mole to define the problem size.
ncasint: Number of active orbitals.
nelecasint or a pair of int: Number of electrons in active space.

Kwargs:

ncoreint: Number of doubly occupied core orbitals. If not presented, this parameter can be automatically determined.

Attributes:

verboseint

Print level. Default value equals to Mole.verbose.

max_memoryfloat or int

Allowed memory in MB. Default value equals to Mole.max_memory.

ncasint

Active space size.

nelecastuple of int

Active (nelec_alpha, nelec_beta)

ncoreint or tuple of int

Core electron number. In UHF-CASSCF, it’s a tuple to indicate the different core eletron numbers.

natorbbool

Whether to transform natural orbitals in active space. Note: when CASCI/CASSCF are combined with DMRG solver or selected CI solver, enabling this parameter may slightly change the total energy. False by default.

canonicalizationbool

Whether to canonicalize orbitals in core and external space against the general Fock matrix. The orbitals in active space are NOT transformed by default. To get the natural orbitals in active space, the attribute .natorb needs to be enabled. True by default.

sorting_mo_energybool

Whether to sort the orbitals based on the diagonal elements of the general Fock matrix. Default is False.

fcisolveran instance of FCISolver

The pyscf.fci module provides several FCISolver for different scenario. Generally, fci.direct_spin1.FCISolver can be used for all RHF-CASSCF. However, a proper FCISolver can provide better performance and better numerical stability. One can either use fci.solver() function to pick the FCISolver by the program or manually assigen the FCISolver to this attribute, e.g.

>>> from pyscf import fci
>>> mc = mcscf.CASSCF(mf, 4, 4)
>>> mc.fcisolver = fci.solver(mol, singlet=True)
>>> mc.fcisolver = fci.direct_spin1.FCISolver(mol)

You can control FCISolver by setting e.g.:

>>> mc.fcisolver.max_cycle = 30
>>> mc.fcisolver.conv_tol = 1e-7

For more details of the parameter for FCISolver, See fci.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
When canonicalization is specified, the orbitals are canonical orbitals which make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is specified, the active segment of the mo_coeff is natural orbitls.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

mo_occndarray
Occupation numbers of natural orbitals if natorb is specified.

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASCI(mf, 6, 6)
>>> mc.kernel()[0]
-108.980200816243354
CASSCF

Extra attributes for CASSCF:

conv_tolfloat
Converge threshold. Default is 1e-7

conv_tol_gradfloat
Converge threshold for CI gradients and orbital rotation gradients. Default is 1e-4

max_stepsizefloat
The step size for orbital rotation. Small step (0.005 - 0.05) is prefered. Default is 0.03.

max_cycle_macroint
Max number of macro iterations. Default is 50.

max_cycle_microint
Max number of micro iterations in each macro iteration. Depending on systems, increasing this value might reduce the total macro iterations. Generally, 2 - 5 steps should be enough. Default is 3.

ah_level_shiftfloat, for AH solver.
Level shift for the Davidson diagonalization in AH solver. Default is 1e-8.

ah_conv_tolfloat, for AH solver.
converge threshold for AH solver. Default is 1e-12.

ah_max_cyclefloat, for AH solver.
Max number of iterations allowd in AH solver. Default is 30.

ah_lindepfloat, for AH solver.
Linear dependence threshold for AH solver. Default is 1e-14.

ah_start_tolflat, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 0.2.

ah_start_cycleint, for AH solver.
In AH solver, the orbital rotation is started without completely solving the AH problem. This value is to control the start point. Default is 2.

ah_conv_tol, ah_max_cycle, ah_lindep, ah_start_tol and ah_start_cycle can affect the accuracy and performance of CASSCF solver. Lower ah_conv_tol and ah_lindep might improve the accuracy of CASSCF optimization, but decrease the performance.
>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.conv_tol = 1e-10
>>> mc.ah_conv_tol = 1e-5
>>> mc.kernel()[0]
-109.044401898486001
>>> mc.ah_conv_tol = 1e-10
>>> mc.kernel()[0]
-109.044401887945668
chkfilestr
Checkpoint file to save the intermediate orbitals during the CASSCF optimization. Default is the checkpoint file of mean field object.

ci_response_spaceint
subspace size to solve the CI vector response. Default is 3.

callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

scale_restorationfloat
When a step of orbital rotation moves out of trust region, the orbital optimization will be restored to previous state and the step size of the orbital rotation needs to be reduced. scale_restoration controls how much to scale down the step size.

Saved results

e_totfloat
Total MCSCF energy (electronic energy plus nuclear repulsion)

e_casfloat
CAS space FCI energy

cindarray
CAS space FCI coefficients

mo_coeffndarray
Optimized CASSCF orbitals coefficients. When canonicalization is specified, the returned orbitals make the general Fock matrix (Fock operator on top of MCSCF 1-particle density matrix) diagonalized within each subspace (core, active, external). If natorb (natural orbitals in active space) is enabled, the active segment of mo_coeff is transformed to natural orbitals.

mo_energyndarray
Diagonal elements of general Fock matrix (in mo_coeff representation).

Examples:

>>> from pyscf import gto, scf, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> mc = mcscf.CASSCF(mf, 6, 6)
>>> mc.kernel()[0]
-109.044401882238134

CISD = None¶

DFMP2 = None¶

EFG(*args, **kwargs)¶

Gradients(*args, **kwargs)¶: Non-relativistic ROHF gradients

MP2 = None¶

TDA = None¶

TDHF = None¶

analyze(verbose=None, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis

canonicalize(mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the Fock matrix within occupied, open, virtual subspaces separatedly (without change occupancy).

check_sanity()¶: Check input of class/object attributes, check whether a class method is overwritten. It does not check the attributes which are prefixed with “_”. The return value of method set is the object itself. This allows a series of functions/methods to be executed in pipe.

dump_flags(verbose=None)¶

eig(fock, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

energy_elec(dm=None, h1e=None, vhf=None)¶

Electronic part of Hartree-Fock energy, for given core hamiltonian and HF potential

… math:

E = \sum_{ij}h_{ij} \gamma_{ji}
  + \frac{1}{2}\sum_{ijkl} \gamma_{ji}\gamma_{lk} \langle ik||jl\rangle

Note this function has side effects which cause mf.scf_summary updated.

Args:

mf : an instance of SCF class

Kwargs:

dm2D ndarray: one-partical density matrix
h1e2D ndarray: Core hamiltonian
vhf2D ndarray: HF potential

Returns:

Hartree-Fock electronic energy and the Coulomb energy

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> mf = scf.RHF(mol)
>>> mf.scf()
>>> dm = mf.make_rdm1()
>>> scf.hf.energy_elec(mf, dm)
(-1.5176090667746334, 0.60917167853723675)
>>> mf.energy_elec(dm)
(-1.5176090667746334, 0.60917167853723675)

gen_response(mo_coeff=None, mo_occ=None, with_j=True, hermi=0, max_memory=None)¶: Generate a function to compute the product of UHF response function and UHF density matrices.

get_fock(h1e=None, s1e=None, vhf=None, dm=None, cycle=- 1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None)¶: Build fock matrix based on Roothaan’s effective fock. See also get_roothaan_fock()

get_grad(mo_coeff, mo_occ, fock=None)¶: ROHF gradients is the off-diagonal block [co + cv + ov], where [ cc co cv ] [ oc oo ov ] [ vc vo vv ]

get_occ(mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital. NOTE the occupancies are not assigned based on the orbital energy ordering. The first N orbitals are assigned to be occupied orbitals.

Examples:

>>> mol = gto.M(atom='H 0 0 0; O 0 0 1.1', spin=1)
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 2, 2, 1, 0])

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)¶

Unrestricted Hartree-Fock potential matrix of alpha and beta spins, for the given density matrix

\[\begin{split}V_{ij}^\alpha &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\alpha \\ V_{ij}^\beta &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\beta\end{split}\]

Args:

mol : an instance of Mole

dma list of ndarrays: A list of density matrices, stored as (alpha,alpha,…,beta,beta,…)

Kwargs:

dm_lastndarray or a list of ndarrays or 0: The density matrix baseline. When it is not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_lastndarray or a list of ndarrays or 0: The reference HF potential matrix.
hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

\(V_{hf} = (V^\alpha, V^\beta)\). \(V^\alpha\) (and \(V^\beta\)) can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dmsa = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dmsb = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dms = numpy.vstack((dmsa,dmsb))
>>> dms.shape
(6, 2, 2)
>>> vhfa, vhfb = scf.uhf.get_veff(mol, dms, hermi=0)
>>> vhfa.shape
(3, 2, 2)
>>> vhfb.shape
(3, 2, 2)

init_guess_by_1e(mol=None)¶

Generate initial guess density matrix from core hamiltonian

Returns:: Density matrix, 2D ndarray

init_guess_by_atom(mol=None)¶

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:: Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)¶

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:: Density matrix, 2D ndarray

init_guess_by_huckel(mol=None)¶

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:: Density matrix, 2D ndarray

init_guess_by_minao(mol=None)¶

Generate initial guess density matrix based on ANO basis, then project the density matrix to the basis set defined by mol

Returns:: Density matrix, 2D ndarray

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> scf.hf.init_guess_by_minao(mol)
array([[ 0.94758917,  0.09227308],
       [ 0.09227308,  0.94758917]])

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)¶: One-particle densit matrix. mo_occ is a 1D array, with occupancy 1 or 2.

property nelec¶

property nelectron_alpha¶

nuc_grad_method()¶: Hook to create object for analytical nuclear gradients.

spin_square(mo_coeff=None, s=None)¶: Spin square and multiplicity of RHF determinant

stability(internal=True, external=False, verbose=None)¶

ROHF/ROKS stability analysis.

See also pyscf.scf.stability.rohf_stability function.

Kwargs:

internalbool: Internal stability, within the RHF optimization space.
externalbool: External stability. It is not available in current version.

Returns:

The return value includes two set of orbitals which are more close to the required stable condition.

pyscf.scf.rohf.analyze(mf, verbose=5, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis

pyscf.scf.rohf.canonicalize(mf, mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the Fock matrix within occupied, open, virtual subspaces separatedly (without change occupancy).

pyscf.scf.rohf.energy_elec(mf, dm=None, h1e=None, vhf=None)¶

pyscf.scf.rohf.get_fock(mf, h1e=None, s1e=None, vhf=None, dm=None, cycle=- 1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None)¶: Build fock matrix based on Roothaan’s effective fock. See also get_roothaan_fock()

pyscf.scf.rohf.get_grad(mo_coeff, mo_occ, fock)¶: ROHF gradients is the off-diagonal block [co + cv + ov], where [ cc co cv ] [ oc oo ov ] [ vc vo vv ]

pyscf.scf.rohf.get_occ(mf, mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital. NOTE the occupancies are not assigned based on the orbital energy ordering. The first N orbitals are assigned to be occupied orbitals.

Examples:

>>> mol = gto.M(atom='H 0 0 0; O 0 0 1.1', spin=1)
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 2, 2, 1, 0])

pyscf.scf.rohf.get_roothaan_fock(focka_fockb, dma_dmb, s)¶

Roothaan’s effective fock. Ref. http://www-theor.ch.cam.ac.uk/people/ross/thesis/node15.html

space	closed	open	virtual
closed	Fc	Fb	Fc
open	Fb	Fc	Fa
virtual	Fc	Fa	Fc

where Fc = (Fa + Fb) / 2

Returns:: Roothaan effective Fock matrix

pyscf.scf.rohf.init_guess_by_atom(mol)¶

pyscf.scf.rohf.init_guess_by_minao(mol)¶

pyscf.scf.rohf.make_rdm1(mo_coeff, mo_occ, **kwargs)¶: One-particle densit matrix. mo_occ is a 1D array, with occupancy 1 or 2.

pyscf.scf.stability module¶

Wave Function Stability Analysis

Ref. JCP 66, 3045 (1977); DOI:10.1063/1.434318 JCP 104, 9047 (1996); DOI:10.1063/1.471637

See also tddft/rhf.py and scf/newton_ah.py

pyscf.scf.stability.ghf_stability(mf, verbose=None)¶

pyscf.scf.stability.rhf_external(mf, with_symmetry=True, verbose=None)¶

pyscf.scf.stability.rhf_internal(mf, with_symmetry=True, verbose=None)¶

pyscf.scf.stability.rhf_stability(mf, internal=True, external=False, verbose=None)¶

Stability analysis for RHF/RKS method.

Args:

mf : RHF or RKS object

Kwargs:

internalbool: Internal stability, within the RHF space.
externalbool: External stability. Including the RHF -> UHF and real -> complex stability analysis.

Returns:

New orbitals that are more close to the stable condition. The return value includes two set of orbitals. The first corresponds to the internal stability and the second corresponds to the external stability.

pyscf.scf.stability.rohf_external(mf, with_symmetry=True, verbose=None)¶

pyscf.scf.stability.rohf_internal(mf, with_symmetry=True, verbose=None)¶

pyscf.scf.stability.rohf_stability(mf, internal=True, external=False, verbose=None)¶

Stability analysis for ROHF/ROKS method.

Args:

mf : ROHF or ROKS object

Kwargs:

internalbool: Internal stability, within the RHF space.
externalbool: External stability. It is not available in current version.

Returns:

The return value includes two set of orbitals which are more close to the required stable condition.

pyscf.scf.stability.uhf_external(mf, with_symmetry=True, verbose=None)¶

pyscf.scf.stability.uhf_internal(mf, with_symmetry=True, verbose=None)¶

pyscf.scf.stability.uhf_stability(mf, internal=True, external=False, verbose=None)¶

Stability analysis for RHF/RKS method.

Args:

mf : UHF or UKS object

Kwargs:

internalbool: Internal stability, within the UHF space.
externalbool: External stability. Including the UHF -> GHF and real -> complex stability analysis.

Returns:

New orbitals that are more close to the stable condition. The return value includes two set of orbitals. The first corresponds to the internal stability and the second corresponds to the external stability.

pyscf.scf.stability_slow module¶

Wave Function Stability Analysis

Ref. JCP, 66, 3045 (1977); DOI:10.1063/1.434318 JCP 104, 9047 (1996); DOI:10.1063/1.471637

pyscf.scf.stability_slow.rhf_external(mf, verbose=None)¶

pyscf.scf.stability_slow.rhf_internal(mf, verbose=None)¶

pyscf.scf.stability_slow.rhf_stability(mf, internal=True, external=False, verbose=None)¶

pyscf.scf.stability_slow.uhf_external(mf, verbose=None)¶

pyscf.scf.stability_slow.uhf_internal(mf, verbose=None)¶

pyscf.scf.stability_slow.uhf_stability(mf, internal=True, external=False, verbose=None)¶

pyscf.scf.ucphf module¶

Unrestricted coupled pertubed Hartree-Fock solver

pyscf.scf.ucphf.kernel(fvind, mo_energy, mo_occ, h1, s1=None, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶

Args:

fvindfunction: Given density matrix, compute (ij|kl)D_{lk}*2 - (ij|kl)D_{jk}

pyscf.scf.ucphf.solve(fvind, mo_energy, mo_occ, h1, s1=None, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶

Args:

fvindfunction: Given density matrix, compute (ij|kl)D_{lk}*2 - (ij|kl)D_{jk}

pyscf.scf.ucphf.solve_nos1(fvind, mo_energy, mo_occ, h1, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶: For field independent basis. First order overlap matrix is zero

pyscf.scf.ucphf.solve_withs1(fvind, mo_energy, mo_occ, h1, s1, max_cycle=20, tol=1e-09, hermi=False, verbose=2)¶: For field dependent basis. First order overlap matrix is non-zero. The first order orbitals are set to C^1_{ij} = -1/2 S1 e1 = h1 - s1*e0 + (e0_j-e0_i)*c1 + vhf[c1]

pyscf.scf.uhf module¶

class pyscf.scf.uhf.HF1e(mol)¶

Bases: pyscf.scf.uhf.UHF

scf(*args)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

spin_square(mo_coeff=None, s=None)¶

Spin square and multiplicity of UHF determinant

\[S^2 = \frac{1}{2}(S_+ S_- + S_- S_+) + S_z^2\]

where \(S_+ = \sum_i S_{i+}\) is effective for all beta occupied orbitals; \(S_- = \sum_i S_{i-}\) is effective for all alpha occupied orbitals.

There are two possibilities for \(S_+ S_-\)
1. same electron \(S_+ S_- = \sum_i s_{i+} s_{i-}\),
\[\sum_i \langle UHF|s_{i+} s_{i-}|UHF\rangle = \sum_{pq}\langle p|s_+s_-|q\rangle \gamma_{qp} = n_\alpha\]

2) different electrons \(S_+ S_- = \sum s_{i+} s_{j-}, (i\neq j)\). There are in total \(n(n-1)\) terms. As a two-particle operator,

\[\langle S_+ S_- \rangle = \langle ij|s_+ s_-|ij\rangle - \langle ij|s_+ s_-|ji\rangle = -\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle\]
Similarly, for \(S_- S_+\)
1. same electron
\[\sum_i \langle s_{i-} s_{i+}\rangle = n_\beta\]
1. different electrons
\[\langle S_- S_+ \rangle = -\langle i^\beta|j^\alpha\rangle \langle j^\alpha|i^\beta\rangle\]
For \(S_z^2\)
1. same electron
\[\langle s_z^2\rangle = \frac{1}{4}(n_\alpha + n_\beta)\]
1. different electrons
\[\begin{split}&\frac{1}{2}\sum_{ij}(\langle ij|2s_{z1}s_{z2}|ij\rangle -\langle ij|2s_{z1}s_{z2}|ji\rangle) \\ &=\frac{1}{4}(\langle i^\alpha|i^\alpha\rangle \langle j^\alpha|j^\alpha\rangle - \langle i^\alpha|i^\alpha\rangle \langle j^\beta|j^\beta\rangle - \langle i^\beta|i^\beta\rangle \langle j^\alpha|j^\alpha\rangle + \langle i^\beta|i^\beta\rangle \langle j^\beta|j^\beta\rangle) \\ &-\frac{1}{4}(\langle i^\alpha|j^\alpha\rangle \langle j^\alpha|i^\alpha\rangle + \langle i^\beta|j^\beta\rangle\langle j^\beta|i^\beta\rangle) \\ &=\frac{1}{4}(n_\alpha^2 - n_\alpha n_\beta - n_\beta n_\alpha + n_\beta^2) -\frac{1}{4}(n_\alpha + n_\beta) \\ &=\frac{1}{4}((n_\alpha-n_\beta)^2 - (n_\alpha+n_\beta))\end{split}\]

In total

\[\begin{split}\langle S^2\rangle &= \frac{1}{2} (n_\alpha-\sum_{ij}\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle +n_\beta -\sum_{ij}\langle i^\beta|j^\alpha\rangle\langle j^\alpha|i^\beta\rangle) + \frac{1}{4}(n_\alpha-n_\beta)^2 \\\end{split}\]

Args:

moa list of 2 ndarrays: Occupied alpha and occupied beta orbitals

Kwargs:

sndarray: AO overlap

Returns:

A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> mo = (mf.mo_coeff[0][:,mf.mo_occ[0]>0], mf.mo_coeff[1][:,mf.mo_occ[1]>0])
>>> print('S^2 = %.7f, 2S+1 = %.7f' % spin_square(mo, mol.intor('int1e_ovlp_sph')))
S^2 = 0.7570150, 2S+1 = 2.0070027

class pyscf.scf.uhf.UHF(mol)¶

Bases: pyscf.scf.hf.SCF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for UHF:

nelec(int, int): If given, freeze the number of (alpha,beta) electrons to the given value.
level_shiftnumber or two-element list: level shift (in Eh) for alpha and beta Fock if two-element list is given.
init_guess_breaksymlogical: If given, overwrite BREAKSYM.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> print('S^2 = %.7f, 2S+1 = %.7f' % mf.spin_square())
S^2 = 0.7570150, 2S+1 = 2.0070027

CASCI = None¶

CASSCF = None¶

CISD(*args, **kwargs)¶

DFMP2 = None¶

EFG(*args, **kwargs)¶

Gradients(*args, **kwargs)¶: Non-relativistic unrestricted Hartree-Fock gradients

Hessian(*args, **kwargs)¶: Non-relativistic UHF hessian

MP2(*args, **kwargs)¶

NMR(*args, **kwargs)¶

NSR(*args, **kwargs)¶: Nuclear-spin rotation tensors for UHF

Polarizability(*args, **kwargs)¶

RotationalGTensor(*args, **kwargs)¶: Rotational g-tensors for UHF

SSC(*args, **kwargs)¶

SpinSpinCoupling(*args, **kwargs)¶

TDA(*args, **kwargs)¶

TDHF(*args, **kwargs)¶

analyze(verbose=None, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

canonicalize(mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the UHF Fock matrix within occupied, virtual subspaces separatedly (without change occupancy).

convert_from_(mf)¶: Create UHF object based on the RHF/ROHF object

det_ovlp(mo1, mo2, occ1, occ2, ovlp=None)¶

Calculate the overlap between two different determinants. It is the product of single values of molecular orbital overlap matrix.

\[S_{12} = \langle \Psi_A | \Psi_B \rangle = (\mathrm{det}\mathbf{U}) (\mathrm{det}\mathbf{V^\dagger}) \prod\limits_{i=1}\limits^{2N} \lambda_{ii}\]

where \(\mathbf{U}, \mathbf{V}, \lambda\) are unitary matrices and single values generated by single value decomposition(SVD) of the overlap matrix \(\mathbf{O}\) which is the overlap matrix of two sets of molecular orbitals:

\[\mathbf{U}^\dagger \mathbf{O} \mathbf{V} = \mathbf{\Lambda}\]

Args:

mo1, mo22D ndarrays: Molecualr orbital coefficients
occ1, occ2: 2D ndarrays: occupation numbers

Return:

A list: the product of single values: float: x_a, x_b: 1D ndarrays \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\) They are used to calculate asymmetric density matrix

dump_flags(verbose=None)¶

eig(fock, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

energy_elec(dm=None, h1e=None, vhf=None)¶

Electronic energy of Unrestricted Hartree-Fock

Note this function has side effects which cause mf.scf_summary updated.

Returns:: Hartree-Fock electronic energy and the 2-electron part contribution

gen_response(mo_coeff=None, mo_occ=None, with_j=True, hermi=0, max_memory=None)¶: Generate a function to compute the product of UHF response function and UHF density matrices.

get_fock(h1e=None, s1e=None, vhf=None, dm=None, cycle=- 1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None)¶

F = h^{core} + V^{HF}

Special treatment (damping, DIIS, or level shift) will be applied to the Fock matrix if diis and cycle is specified (The two parameters are passed to get_fock function during the SCF iteration)

Kwargs:

h1e2D ndarray: Core hamiltonian
s1e2D ndarray: Overlap matrix, for DIIS
vhf2D ndarray: HF potential matrix
dm2D ndarray: Density matrix, for DIIS
cycleint: Then present SCF iteration step, for DIIS
diisan object of SCF.DIIS class: DIIS object to hold intermediate Fock and error vectors
diis_start_cycleint: The step to start DIIS. Default is 0.
level_shift_factorfloat or int: Level shift (in AU) for virtual space. Default is 0.

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_jk(mol=None, dm=None, hermi=1, with_j=True, with_k=True, omega=None)¶

Coulomb (J) and exchange (K)

Args:

dma list of 2D arrays or a list of 3D arrays: (alpha_dm, beta_dm) or (alpha_dms, beta_dms)

get_occ(mo_energy=None, mo_coeff=None)¶

Label the occupancies for each orbital

Kwargs:

mo_energy1D ndarray: Obital energies
mo_coeff2D ndarray: Obital coefficients

Examples:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> energy = numpy.array([-10., -1., 1, -2., 0, -3])
>>> mf.get_occ(energy)
array([2, 2, 0, 2, 2, 2])

get_veff(mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1)¶

Unrestricted Hartree-Fock potential matrix of alpha and beta spins, for the given density matrix

\[\begin{split}V_{ij}^\alpha &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\alpha \\ V_{ij}^\beta &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\beta\end{split}\]

Args:

mol : an instance of Mole

dma list of ndarrays: A list of density matrices, stored as (alpha,alpha,…,beta,beta,…)

Kwargs:

dm_lastndarray or a list of ndarrays or 0: The density matrix baseline. When it is not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_lastndarray or a list of ndarrays or 0: The reference HF potential matrix.
hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

\(V_{hf} = (V^\alpha, V^\beta)\). \(V^\alpha\) (and \(V^\beta\)) can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dmsa = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dmsb = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dms = numpy.vstack((dmsa,dmsb))
>>> dms.shape
(6, 2, 2)
>>> vhfa, vhfb = scf.uhf.get_veff(mol, dms, hermi=0)
>>> vhfa.shape
(3, 2, 2)
>>> vhfb.shape
(3, 2, 2)

init_guess_by_1e(mol=None, breaksym=True)¶

Generate initial guess density matrix from core hamiltonian

Returns:: Density matrix, 2D ndarray

init_guess_by_atom(mol=None, breaksym=True)¶

Generate initial guess density matrix from superposition of atomic HF density matrix. The atomic HF is occupancy averaged RHF

Returns:: Density matrix, 2D ndarray

init_guess_by_chkfile(chkfile=None, project=None)¶

Read the HF results from checkpoint file, then project it to the basis defined by mol

Returns:: Density matrix, 2D ndarray

init_guess_by_huckel(mol=None, breaksym=True)¶

Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089

Returns:: Density matrix, 2D ndarray

init_guess_by_minao(mol=None, breaksym=True)¶: Initial guess in terms of the overlap to minimal basis.

make_asym_dm(mo1, mo2, occ1, occ2, x)¶

One-particle asymmetric density matrix

Args:

mo1, mo22D ndarrays: Molecualr orbital coefficients
occ1, occ2: 2D ndarrays: Occupation numbers
x: 2D ndarrays: \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\). See also det_ovlp()

Return:

A list of 2D ndarrays for alpha and beta spin

Examples:

>>> mf1 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.3', basis='ccpvdz')).run()
>>> mf2 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.4', basis='ccpvdz')).run()
>>> s = gto.intor_cross('int1e_ovlp_sph', mf1.mol, mf2.mol)
>>> det, x = det_ovlp(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, s)
>>> adm = make_asym_dm(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, x)
>>> adm.shape
(2, 19, 19)

make_rdm1(mo_coeff=None, mo_occ=None, **kwargs)¶

One-particle density matrix

Returns:: A list of 2D ndarrays for alpha and beta spins

mulliken_meta(mol=None, dm=None, verbose=5, pre_orth_method='ANO', s=None)¶

Mulliken population analysis, based on meta-Lowdin AOs. In the meta-lowdin, the AOs are grouped in three sets: core, valence and Rydberg, the orthogonalization are carreid out within each subsets.

Args:

mol : an instance of Mole

dmndarray or 2-item list of ndarray: Density matrix. ROHF dm is a 2-item list of 2D array

Kwargs:

verbose : int or instance of lib.logger.Logger

pre_orth_methodstr: Pre-orthogonalization, which localized GTOs for each atom. To obtain the occupied and unoccupied atomic shells, there are three methods

‘ano’ : Project GTOs to ANO basis

‘minao’ : Project GTOs to MINAO basis

‘scf’ : Symmetry-averaged fractional occupation atomic RHF

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

mulliken_meta_spin(mol=None, dm=None, verbose=5, pre_orth_method='ANO', s=None)¶

mulliken_pop(mol=None, dm=None, s=None, verbose=5)¶

Mulliken population analysis

\[M_{ij} = D_{ij} S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

Returns:

A list : pop, charges

popnparray: Mulliken population on each atomic orbitals
chargesnparray: Mulliken charges

mulliken_spin_pop(mol=None, dm=None, s=None, verbose=5)¶

property nelec¶

property nelectron_alpha¶

nuc_grad_method()¶: Hook to create object for analytical nuclear gradients.

spin_square(mo_coeff=None, s=None)¶

Spin square and multiplicity of UHF determinant

\[S^2 = \frac{1}{2}(S_+ S_- + S_- S_+) + S_z^2\]

where \(S_+ = \sum_i S_{i+}\) is effective for all beta occupied orbitals; \(S_- = \sum_i S_{i-}\) is effective for all alpha occupied orbitals.

There are two possibilities for \(S_+ S_-\)
1. same electron \(S_+ S_- = \sum_i s_{i+} s_{i-}\),
\[\sum_i \langle UHF|s_{i+} s_{i-}|UHF\rangle = \sum_{pq}\langle p|s_+s_-|q\rangle \gamma_{qp} = n_\alpha\]

2) different electrons \(S_+ S_- = \sum s_{i+} s_{j-}, (i\neq j)\). There are in total \(n(n-1)\) terms. As a two-particle operator,

\[\langle S_+ S_- \rangle = \langle ij|s_+ s_-|ij\rangle - \langle ij|s_+ s_-|ji\rangle = -\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle\]
Similarly, for \(S_- S_+\)
1. same electron
\[\sum_i \langle s_{i-} s_{i+}\rangle = n_\beta\]
1. different electrons
\[\langle S_- S_+ \rangle = -\langle i^\beta|j^\alpha\rangle \langle j^\alpha|i^\beta\rangle\]
For \(S_z^2\)
1. same electron
\[\langle s_z^2\rangle = \frac{1}{4}(n_\alpha + n_\beta)\]
1. different electrons
\[\begin{split}&\frac{1}{2}\sum_{ij}(\langle ij|2s_{z1}s_{z2}|ij\rangle -\langle ij|2s_{z1}s_{z2}|ji\rangle) \\ &=\frac{1}{4}(\langle i^\alpha|i^\alpha\rangle \langle j^\alpha|j^\alpha\rangle - \langle i^\alpha|i^\alpha\rangle \langle j^\beta|j^\beta\rangle - \langle i^\beta|i^\beta\rangle \langle j^\alpha|j^\alpha\rangle + \langle i^\beta|i^\beta\rangle \langle j^\beta|j^\beta\rangle) \\ &-\frac{1}{4}(\langle i^\alpha|j^\alpha\rangle \langle j^\alpha|i^\alpha\rangle + \langle i^\beta|j^\beta\rangle\langle j^\beta|i^\beta\rangle) \\ &=\frac{1}{4}(n_\alpha^2 - n_\alpha n_\beta - n_\beta n_\alpha + n_\beta^2) -\frac{1}{4}(n_\alpha + n_\beta) \\ &=\frac{1}{4}((n_\alpha-n_\beta)^2 - (n_\alpha+n_\beta))\end{split}\]

In total

\[\begin{split}\langle S^2\rangle &= \frac{1}{2} (n_\alpha-\sum_{ij}\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle +n_\beta -\sum_{ij}\langle i^\beta|j^\alpha\rangle\langle j^\alpha|i^\beta\rangle) + \frac{1}{4}(n_\alpha-n_\beta)^2 \\\end{split}\]

Args:

moa list of 2 ndarrays: Occupied alpha and occupied beta orbitals

Kwargs:

sndarray: AO overlap

Returns:

A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> mo = (mf.mo_coeff[0][:,mf.mo_occ[0]>0], mf.mo_coeff[1][:,mf.mo_occ[1]>0])
>>> print('S^2 = %.7f, 2S+1 = %.7f' % spin_square(mo, mol.intor('int1e_ovlp_sph')))
S^2 = 0.7570150, 2S+1 = 2.0070027

stability(internal=True, external=False, verbose=None)¶

Stability analysis for RHF/RKS method.

See also pyscf.scf.stability.uhf_stability function.

Args:

mf : UHF or UKS object

Kwargs:

internalbool: Internal stability, within the UHF space.
externalbool: External stability. Including the UHF -> GHF and real -> complex stability analysis.

Returns:

New orbitals that are more close to the stable condition. The return value includes two set of orbitals. The first corresponds to the internal stability and the second corresponds to the external stability.

pyscf.scf.uhf.analyze(mf, verbose=5, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Dipole moment; Spin density for AOs and atoms;

pyscf.scf.uhf.canonicalize(mf, mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the UHF Fock matrix within occupied, virtual subspaces separatedly (without change occupancy).

pyscf.scf.uhf.det_ovlp(mo1, mo2, occ1, occ2, ovlp)¶

Calculate the overlap between two different determinants. It is the product of single values of molecular orbital overlap matrix.

\[S_{12} = \langle \Psi_A | \Psi_B \rangle = (\mathrm{det}\mathbf{U}) (\mathrm{det}\mathbf{V^\dagger}) \prod\limits_{i=1}\limits^{2N} \lambda_{ii}\]

where \(\mathbf{U}, \mathbf{V}, \lambda\) are unitary matrices and single values generated by single value decomposition(SVD) of the overlap matrix \(\mathbf{O}\) which is the overlap matrix of two sets of molecular orbitals:

\[\mathbf{U}^\dagger \mathbf{O} \mathbf{V} = \mathbf{\Lambda}\]

Args:

mo1, mo22D ndarrays: Molecualr orbital coefficients
occ1, occ2: 2D ndarrays: occupation numbers

Return:

A list: the product of single values: float: x_a, x_b: 1D ndarrays \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\) They are used to calculate asymmetric density matrix

pyscf.scf.uhf.energy_elec(mf, dm=None, h1e=None, vhf=None)¶

Electronic energy of Unrestricted Hartree-Fock

Note this function has side effects which cause mf.scf_summary updated.

Returns:: Hartree-Fock electronic energy and the 2-electron part contribution

pyscf.scf.uhf.get_fock(mf, h1e=None, s1e=None, vhf=None, dm=None, cycle=- 1, diis=None, diis_start_cycle=None, level_shift_factor=None, damp_factor=None)¶

pyscf.scf.uhf.get_grad(mo_coeff, mo_occ, fock_ao)¶: UHF Gradients

pyscf.scf.uhf.get_init_guess(mol, key='minao')¶

pyscf.scf.uhf.get_occ(mf, mo_energy=None, mo_coeff=None)¶

pyscf.scf.uhf.get_veff(mol, dm, dm_last=0, vhf_last=0, hermi=1, vhfopt=None)¶

Unrestricted Hartree-Fock potential matrix of alpha and beta spins, for the given density matrix

\[\begin{split}V_{ij}^\alpha &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\alpha \\ V_{ij}^\beta &= \sum_{kl} (ij|kl)(\gamma_{lk}^\alpha+\gamma_{lk}^\beta) - \sum_{kl} (il|kj)\gamma_{lk}^\beta\end{split}\]

Args:

mol : an instance of Mole

dma list of ndarrays: A list of density matrices, stored as (alpha,alpha,…,beta,beta,…)

Kwargs:

dm_lastndarray or a list of ndarrays or 0: The density matrix baseline. When it is not 0, this function computes the increment of HF potential w.r.t. the reference HF potential matrix.
vhf_lastndarray or a list of ndarrays or 0: The reference HF potential matrix.
hermiint: Whether J, K matrix is hermitian

0 : no hermitian or symmetric

1 : hermitian

2 : anti-hermitian
vhfopt :: A class which holds precomputed quantities to optimize the computation of J, K matrices

Returns:

\(V_{hf} = (V^\alpha, V^\beta)\). \(V^\alpha\) (and \(V^\beta\)) can be a list matrices, corresponding to the input density matrices.

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1')
>>> dmsa = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dmsb = numpy.random.random((3,mol.nao_nr(),mol.nao_nr()))
>>> dms = numpy.vstack((dmsa,dmsb))
>>> dms.shape
(6, 2, 2)
>>> vhfa, vhfb = scf.uhf.get_veff(mol, dms, hermi=0)
>>> vhfa.shape
(3, 2, 2)
>>> vhfb.shape
(3, 2, 2)

pyscf.scf.uhf.init_guess_by_1e(mol, breaksym=True)¶

pyscf.scf.uhf.init_guess_by_atom(mol, breaksym=True)¶

pyscf.scf.uhf.init_guess_by_chkfile(mol, chkfile_name, project=None)¶

Read SCF chkfile and make the density matrix for UHF initial guess.

Kwargs:

projectNone or bool

Whether to project chkfile’s orbitals to the new basis. Note when the geometry of the chkfile and the given molecule are very different, this projection can produce very poor initial guess. In PES scanning, it is recommended to swith off project.

If project is set to None, the projection is only applied when the basis sets of the chkfile’s molecule are different to the basis sets of the given molecule (regardless whether the geometry of the two molecules are different). Note the basis sets are considered to be different if the two molecules are derived from the same molecule with different ordering of atoms.

pyscf.scf.uhf.init_guess_by_huckel(mol, breaksym=True)¶

pyscf.scf.uhf.init_guess_by_minao(mol, breaksym=True)¶

Generate initial guess density matrix based on ANO basis, then project the density matrix to the basis set defined by mol

Returns:: Density matrices, a list of 2D ndarrays for alpha and beta spins

pyscf.scf.uhf.make_asym_dm(mo1, mo2, occ1, occ2, x)¶

One-particle asymmetric density matrix

Args:

mo1, mo22D ndarrays: Molecualr orbital coefficients
occ1, occ2: 2D ndarrays: Occupation numbers
x: 2D ndarrays: \(\mathbf{U} \mathbf{\Lambda}^{-1} \mathbf{V}^\dagger\). See also det_ovlp()

Return:

A list of 2D ndarrays for alpha and beta spin

Examples:

>>> mf1 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.3', basis='ccpvdz')).run()
>>> mf2 = scf.UHF(gto.M(atom='H 0 0 0; F 0 0 1.4', basis='ccpvdz')).run()
>>> s = gto.intor_cross('int1e_ovlp_sph', mf1.mol, mf2.mol)
>>> det, x = det_ovlp(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, s)
>>> adm = make_asym_dm(mf1.mo_coeff, mf1.mo_occ, mf2.mo_coeff, mf2.mo_occ, x)
>>> adm.shape
(2, 19, 19)

pyscf.scf.uhf.make_rdm1(mo_coeff, mo_occ, **kwargs)¶

One-particle density matrix

Returns:: A list of 2D ndarrays for alpha and beta spins

pyscf.scf.uhf.mulliken_meta(mol, dm_ao, verbose=5, pre_orth_method='ANO', s=None)¶: Mulliken population analysis, based on meta-Lowdin AOs.

pyscf.scf.uhf.mulliken_meta_spin(mol, dm_ao, verbose=5, pre_orth_method='ANO', s=None)¶: Mulliken spin population analysis, based on meta-Lowdin AOs.

pyscf.scf.uhf.mulliken_pop(mol, dm, s=None, verbose=5)¶: Mulliken population analysis

pyscf.scf.uhf.mulliken_pop_meta_lowdin_ao(mol, dm_ao, verbose=5, pre_orth_method='ANO', s=None)¶: Mulliken population analysis, based on meta-Lowdin AOs.

pyscf.scf.uhf.mulliken_spin_pop(mol, dm, s=None, verbose=5)¶

Mulliken spin density analysis

See Eq. 80 in https://arxiv.org/pdf/1206.2234.pdf and the surrounding text for more details.

\[M_{ij} = (D^a_{ij} - D^b_{ij}) S_{ji}\]

Mulliken charges

\[\delta_i = \sum_j M_{ij}\]

Returns:

A list : spin_pop, Ms

spin_popnparray: Mulliken spin density on each atomic orbitals
Msnparray: Mulliken spin density on each atom

pyscf.scf.uhf.mulliken_spin_pop_meta_lowdin_ao(mol, dm_ao, verbose=5, pre_orth_method='ANO', s=None)¶: Mulliken spin population analysis, based on meta-Lowdin AOs.

pyscf.scf.uhf.spin_square(mo, s=1)¶

Spin square and multiplicity of UHF determinant

\[S^2 = \frac{1}{2}(S_+ S_- + S_- S_+) + S_z^2\]

where \(S_+ = \sum_i S_{i+}\) is effective for all beta occupied orbitals; \(S_- = \sum_i S_{i-}\) is effective for all alpha occupied orbitals.

There are two possibilities for \(S_+ S_-\)
1. same electron \(S_+ S_- = \sum_i s_{i+} s_{i-}\),
\[\sum_i \langle UHF|s_{i+} s_{i-}|UHF\rangle = \sum_{pq}\langle p|s_+s_-|q\rangle \gamma_{qp} = n_\alpha\]

2) different electrons \(S_+ S_- = \sum s_{i+} s_{j-}, (i\neq j)\). There are in total \(n(n-1)\) terms. As a two-particle operator,

\[\langle S_+ S_- \rangle = \langle ij|s_+ s_-|ij\rangle - \langle ij|s_+ s_-|ji\rangle = -\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle\]
Similarly, for \(S_- S_+\)
1. same electron
\[\sum_i \langle s_{i-} s_{i+}\rangle = n_\beta\]
1. different electrons
\[\langle S_- S_+ \rangle = -\langle i^\beta|j^\alpha\rangle \langle j^\alpha|i^\beta\rangle\]
For \(S_z^2\)
1. same electron
\[\langle s_z^2\rangle = \frac{1}{4}(n_\alpha + n_\beta)\]
1. different electrons
\[\begin{split}&\frac{1}{2}\sum_{ij}(\langle ij|2s_{z1}s_{z2}|ij\rangle -\langle ij|2s_{z1}s_{z2}|ji\rangle) \\ &=\frac{1}{4}(\langle i^\alpha|i^\alpha\rangle \langle j^\alpha|j^\alpha\rangle - \langle i^\alpha|i^\alpha\rangle \langle j^\beta|j^\beta\rangle - \langle i^\beta|i^\beta\rangle \langle j^\alpha|j^\alpha\rangle + \langle i^\beta|i^\beta\rangle \langle j^\beta|j^\beta\rangle) \\ &-\frac{1}{4}(\langle i^\alpha|j^\alpha\rangle \langle j^\alpha|i^\alpha\rangle + \langle i^\beta|j^\beta\rangle\langle j^\beta|i^\beta\rangle) \\ &=\frac{1}{4}(n_\alpha^2 - n_\alpha n_\beta - n_\beta n_\alpha + n_\beta^2) -\frac{1}{4}(n_\alpha + n_\beta) \\ &=\frac{1}{4}((n_\alpha-n_\beta)^2 - (n_\alpha+n_\beta))\end{split}\]

In total

\[\begin{split}\langle S^2\rangle &= \frac{1}{2} (n_\alpha-\sum_{ij}\langle i^\alpha|j^\beta\rangle \langle j^\beta|i^\alpha\rangle +n_\beta -\sum_{ij}\langle i^\beta|j^\alpha\rangle\langle j^\alpha|i^\beta\rangle) + \frac{1}{4}(n_\alpha-n_\beta)^2 \\\end{split}\]

Args:

moa list of 2 ndarrays: Occupied alpha and occupied beta orbitals

Kwargs:

sndarray: AO overlap

Returns:

A list of two floats. The first is the expectation value of S^2. The second is the corresponding 2S+1

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> mo = (mf.mo_coeff[0][:,mf.mo_occ[0]>0], mf.mo_coeff[1][:,mf.mo_occ[1]>0])
>>> print('S^2 = %.7f, 2S+1 = %.7f' % spin_square(mo, mol.intor('int1e_ovlp_sph')))
S^2 = 0.7570150, 2S+1 = 2.0070027

pyscf.scf.uhf_symm module¶

Non-relativistic unrestricted Hartree-Fock with point group symmetry.

class pyscf.scf.uhf_symm.HF1e(mol)¶

Bases: pyscf.scf.uhf_symm.SymAdaptedUHF

scf(*args)¶

SCF main driver

Kwargs:

dm0ndarray: If given, it will be used as the initial guess density matrix

Examples:

>>> import numpy
>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; F 0 0 1.1')
>>> mf = scf.hf.SCF(mol)
>>> dm_guess = numpy.eye(mol.nao_nr())
>>> mf.kernel(dm_guess)
converged SCF energy = -98.5521904482821
-98.552190448282104

class pyscf.scf.uhf_symm.SymAdaptedUHF(mol)¶

Bases: pyscf.scf.uhf.UHF

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for UHF:

nelec(int, int): If given, freeze the number of (alpha,beta) electrons to the given value.
level_shiftnumber or two-element list: level shift (in Eh) for alpha and beta Fock if two-element list is given.
init_guess_breaksymlogical: If given, overwrite BREAKSYM.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> print('S^2 = %.7f, 2S+1 = %.7f' % mf.spin_square())
S^2 = 0.7570150, 2S+1 = 2.0070027

Attributes for symmetry allowed UHF:

irrep_nelecdict: Specify the number of alpha/beta electrons for particular irrep {‘ir_name’:(int,int), …}. For the irreps not listed in these dicts, the program will choose the occupancy based on the orbital energies.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, charge=1, spin=1, verbose=0)
>>> mf = scf.RHF(mol)
>>> mf.scf()
-75.623975516256692
>>> mf.get_irrep_nelec()
{'A1': (3, 3), 'A2': (0, 0), 'B1': (1, 1), 'B2': (1, 0)}
>>> mf.irrep_nelec = {'B1': (1, 0)}
>>> mf.scf()
-75.429189192031131
>>> mf.get_irrep_nelec()
{'A1': (3, 3), 'A2': (0, 0), 'B1': (1, 0), 'B2': (1, 1)}

CASCI = None¶

CASSCF = None¶

analyze(verbose=None, with_meta_lowdin=True, **kwargs)¶: Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment.

build(mol=None)¶

canonicalize(mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the UHF Fock matrix in occupied, virtual subspaces separatedly (without change occupancy).

dump_flags(verbose=None)¶

eig(h, s)¶: Solver for generalized eigenvalue problem

\[HC = SCE\]

get_grad(mo_coeff, mo_occ, fock=None)¶

RHF orbital gradients

Args:

mo_coeff2D ndarray: Obital coefficients
mo_occ1D ndarray: Orbital occupancy
fock_ao2D ndarray: Fock matrix in AO representation

Returns:

Gradients in MO representation. It’s a num_occ*num_vir vector.

get_irrep_nelec(mol=None, mo_coeff=None, mo_occ=None, s=None)¶

Alpha/beta electron numbers for each irreducible representation.

Args:

molan instance of Mole: To provide irrep_id, and spin-adapted basis
mo_occa list of 1D ndarray: Regular occupancy, without grouping for irreps
mo_coeffa list of 2D ndarray: Regular orbital coefficients, without grouping for irreps

Returns:

irrep_nelecdict: The number of alpha/beta electrons for each irrep {‘ir_name’:(int,int), …}.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
-75.623975516256721
>>> scf.uhf_symm.get_irrep_nelec(mol, mf.mo_coeff, mf.mo_occ)
{'A1': (3, 3), 'A2': (0, 0), 'B1': (1, 1), 'B2': (1, 0)}

get_occ(mo_energy=None, mo_coeff=None)¶: We assumed mo_energy are grouped by symmetry irreps, (see function self.eig). The orbitals are sorted after SCF.

get_orbsym(mo_coeff=None, s=None)¶

get_wfnsym(mo_coeff=None, mo_occ=None)¶

property orbsym¶

property wfnsym¶

pyscf.scf.uhf_symm.UHF¶: alias of pyscf.scf.uhf_symm.SymAdaptedUHF

pyscf.scf.uhf_symm.analyze(mf, verbose=5, with_meta_lowdin=True, **kwargs)¶

pyscf.scf.uhf_symm.canonicalize(mf, mo_coeff, mo_occ, fock=None)¶: Canonicalization diagonalizes the UHF Fock matrix in occupied, virtual subspaces separatedly (without change occupancy).

pyscf.scf.uhf_symm.get_irrep_nelec(mol, mo_coeff, mo_occ, s=None)¶

Alpha/beta electron numbers for each irreducible representation.

Args:

molan instance of Mole: To provide irrep_id, and spin-adapted basis
mo_occa list of 1D ndarray: Regular occupancy, without grouping for irreps
mo_coeffa list of 2D ndarray: Regular orbital coefficients, without grouping for irreps

Returns:

irrep_nelecdict: The number of alpha/beta electrons for each irrep {‘ir_name’:(int,int), …}.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', symmetry=True, charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.scf()
-75.623975516256721
>>> scf.uhf_symm.get_irrep_nelec(mol, mf.mo_coeff, mf.mo_occ)
{'A1': (3, 3), 'A2': (0, 0), 'B1': (1, 1), 'B2': (1, 0)}

pyscf.scf.uhf_symm.get_orbsym(mol, mo_coeff, s=None, check=False)¶

pyscf.scf.uhf_symm.get_wfnsym(mf, mo_coeff=None, mo_occ=None)¶

pyscf.scf.x2c module¶

Module contents¶

Hartree-Fock¶

Simple usage:

>>> from pyscf import gto, scf
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1')
>>> mf = scf.RHF(mol).run()

scf.RHF() returns an instance of SCF class. There are some parameters to control the SCF method.

verboseint
Print level. Default value equals to Mole.verbose

max_memoryfloat or int
Allowed memory in MB. Default value equals to Mole.max_memory

chkfilestr
checkpoint file to save MOs, orbital energies etc.

conv_tolfloat
converge threshold. Default is 1e-10

max_cycleint
max number of iterations. Default is 50

init_guessstr
initial guess method. It can be one of ‘minao’, ‘atom’, ‘1e’, ‘chkfile’. Default is ‘minao’

DIISclass listed in scf.diis
Default is diis.SCF_DIIS. Set it to None/False to turn off DIIS.

diisbool
whether to do DIIS. Default is True.

diis_spaceint
DIIS space size. By default, 8 Fock matrices and errors vector are stored.

diis_start_cycleint
The step to start DIIS. Default is 0.

level_shift_factorfloat or int
Level shift (in AU) for virtual space. Default is 0.

direct_scfbool
Direct SCF is used by default.

direct_scf_tolfloat
Direct SCF cutoff threshold. Default is 1e-13.

callbackfunction
callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

conv_checkbool
An extra cycle to check convergence after SCF iterations.

nelec(int,int), for UHF/ROHF class
freeze the number of (alpha,beta) electrons.

irrep_nelecdict, for symmetry- RHF/ROHF/UHF class only
to indicate the number of electrons for each irreps. In RHF, give {‘ir_name’:int, …} ; In ROHF/UHF, give {‘ir_name’:(int,int), …} . It is effective when Mole.symmetry is set True.

auxbasisstr, for density fitting SCF only
Auxiliary basis for density fitting.
>>> mf = scf.density_fit(scf.UHF(mol))
>>> mf.scf()
Density fitting can be applied to all non-relativistic HF class.
with_ssssbool, for Dirac-Hartree-Fock only
If False, ignore small component integrals (SS|SS). Default is True.

with_gauntbool, for Dirac-Hartree-Fock only
If False, ignore Gaunt interaction. Default is False.

Saved results

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

pyscf.scf.DHF(mol, *args)¶

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for Dirac-Hartree-Fock

with_ssssbool, for Dirac-Hartree-Fock only: If False, ignore small component integrals (SS|SS). Default is True.
with_gauntbool, for Dirac-Hartree-Fock only: Default is False.
with_breitbool, for Dirac-Hartree-Fock only: Gaunt + gauge term. Default is False.

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1', basis='ccpvdz', verbose=0)
>>> mf = scf.RHF(mol)
>>> e0 = mf.scf()
>>> mf = scf.DHF(mol)
>>> e1 = mf.scf()
>>> print('Relativistic effects = %.12f' % (e1-e0))
Relativistic effects = -0.000008854205

pyscf.scf.DKS(mol, *args)¶

pyscf.scf.GHF(mol, *args)¶

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for GHF method: GHF orbital coefficients are 2D array. Let nao be the number of spatial AOs, mo_coeff[:nao] are the coefficients of AO with alpha spin; mo_coeff[nao:nao*2] are the coefficients of AO with beta spin.

pyscf.scf.GKS(mol, *args)¶

pyscf.scf.HF(mol, *args)¶

A wrap function to create SCF class (RHF or UHF).

SCF base class. non-relativistic RHF.

Attributes:

verboseint
Print level. Default value equals to Mole.verbose

max_memoryfloat or int
Allowed memory in MB. Default equals to Mole.max_memory

chkfilestr
checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.

conv_tolfloat
converge threshold. Default is 1e-9

conv_tol_gradfloat
gradients converge threshold. Default is sqrt(conv_tol)

max_cycleint
max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.

init_guessstr
initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’

DIISDIIS class
The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.

diisboolean or object of DIIS class defined in scf.diis.
Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.

diis_spaceint
DIIS space size. By default, 8 Fock matrices and errors vector are stored.

diis_start_cycleint
The step to start DIIS. Default is 1.

diis_file: ‘str’
File to store DIIS vectors and error vectors.

level_shiftfloat or int
Level shift (in AU) for virtual space. Default is 0.

direct_scfbool
Direct SCF is used by default.

direct_scf_tolfloat
Direct SCF cutoff threshold. Default is 1e-13.

callbackfunction(envs_dict) => None
callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.

conv_checkbool
An extra cycle to check convergence after SCF iterations.

check_convergencefunction(envs) => bool
A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:
>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

pyscf.scf.KS(mol, *args)¶

pyscf.scf.RHF(mol, *args)¶

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

pyscf.scf.RKS(mol, *args)¶

pyscf.scf.ROHF(mol, *args)¶

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

pyscf.scf.ROKS(mol, *args)¶

pyscf.scf.UHF(mol, *args)¶

SCF base class. non-relativistic RHF.

Attributes:

verboseint: Print level. Default value equals to Mole.verbose
max_memoryfloat or int: Allowed memory in MB. Default equals to Mole.max_memory
chkfilestr: checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False.
conv_tolfloat: converge threshold. Default is 1e-9
conv_tol_gradfloat: gradients converge threshold. Default is sqrt(conv_tol)
max_cycleint: max number of iterations. If max_cycle <= 0, SCF iteration will be skiped and the kernel function will compute only the total energy based on the intial guess. Default value is 50.
init_guessstr: initial guess method. It can be one of ‘minao’, ‘atom’, ‘huckel’, ‘hcore’, ‘1e’, ‘chkfile’. Default is ‘minao’
DIISDIIS class: The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS.
diisboolean or object of DIIS class defined in scf.diis.: Default is the object associated to the attribute self.DIIS. Set it to None/False to turn off DIIS. Note if this attribute is inialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS informations (vector basis and error vector) will be held inside this object. When kernel function is called again, the old states (vector basis and error vector) will be reused.
diis_spaceint: DIIS space size. By default, 8 Fock matrices and errors vector are stored.
diis_start_cycleint: The step to start DIIS. Default is 1.
diis_file: ‘str’: File to store DIIS vectors and error vectors.
level_shiftfloat or int: Level shift (in AU) for virtual space. Default is 0.
direct_scfbool: Direct SCF is used by default.
direct_scf_tolfloat: Direct SCF cutoff threshold. Default is 1e-13.
callbackfunction(envs_dict) => None: callback function takes one dict as the argument which is generated by the builtin function locals(), so that the callback function can access all local variables in the current envrionment.
conv_checkbool: An extra cycle to check convergence after SCF iterations.
check_convergencefunction(envs) => bool: A hook for overloading convergence criteria in SCF iterations.

Saved results:

convergedbool
SCF converged or not

e_totfloat
Total HF energy (electronic energy plus nuclear repulsion)

mo_energy :
Orbital energies

mo_occ
Orbital occupancy

mo_coeff
Orbital coefficients

Examples:

>>> mol = gto.M(atom='H 0 0 0; H 0 0 1.1', basis='cc-pvdz')
>>> mf = scf.hf.SCF(mol)
>>> mf.verbose = 0
>>> mf.level_shift = .4
>>> mf.scf()
-1.0811707843775884

Attributes for UHF:

nelec(int, int): If given, freeze the number of (alpha,beta) electrons to the given value.
level_shiftnumber or two-element list: level shift (in Eh) for alpha and beta Fock if two-element list is given.
init_guess_breaksymlogical: If given, overwrite BREAKSYM.

Examples:

>>> mol = gto.M(atom='O 0 0 0; H 0 0 1; H 0 1 0', basis='ccpvdz', charge=1, spin=1, verbose=0)
>>> mf = scf.UHF(mol)
>>> mf.kernel()
-75.623975516256706
>>> print('S^2 = %.7f, 2S+1 = %.7f' % mf.spin_square())
S^2 = 0.7570150, 2S+1 = 2.0070027

pyscf.scf.UKS(mol, *args)¶

pyscf.scf.X2C(mol, *args)¶: X2C UHF (in testing)

pyscf.scf.density_fit(mf, auxbasis=None, with_df=None, only_dfj=False)¶

pyscf.scf.newton(mf)¶

pyscf.scf.sfx2c(mf)¶

pyscf.scf.sfx2c1e(mf)¶