Source code for pyscf.scf.hf

#!/usr/bin/env python
# Copyright 2014-2020 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Author: Qiming Sun <osirpt.sun@gmail.com>
#

'''
Hartree-Fock
'''

import sys
import tempfile

from functools import reduce
import numpy
import scipy.linalg
import h5py
from pyscf import gto
from pyscf import lib
from pyscf.lib import logger
from pyscf.scf import diis
from pyscf.scf import _vhf
from pyscf.scf import chkfile
from pyscf.data import nist
from pyscf import __config__


WITH_META_LOWDIN = getattr(__config__, 'scf_analyze_with_meta_lowdin', True)
PRE_ORTH_METHOD = getattr(__config__, 'scf_analyze_pre_orth_method', 'ANO')
MO_BASE = getattr(__config__, 'MO_BASE', 1)
TIGHT_GRAD_CONV_TOL = getattr(__config__, 'scf_hf_kernel_tight_grad_conv_tol', True)
MUTE_CHKFILE = getattr(__config__, 'scf_hf_SCF_mute_chkfile', False)

[docs] def 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: mf : an 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_tol : float converge threshold. conv_tol_grad : float gradients converge threshold. dump_chk : bool Whether to save SCF intermediate results in the checkpoint file dm0 : ndarray Initial guess density matrix. If not given (the default), the kernel takes the density matrix generated by ``mf.get_init_guess``. callback : function(envs_dict) => None callback function takes one dict as the argument which is generated by the builtin function :func:`locals`, so that the callback function can access all local variables in the current environment. Returns: A list : scf_conv, e_tot, mo_energy, mo_coeff, mo_occ scf_conv : bool True means SCF converged e_tot : float Hartree-Fock energy of last iteration mo_energy : 1D float array Orbital energies. Depending the eig function provided by mf object, the orbital energies may NOT be sorted. mo_coeff : 2D array Orbital coefficients. mo_occ : 1D 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 ''' if 'init_dm' in kwargs: raise RuntimeError(''' You see this error message because of the API updates in pyscf v0.11. Keyword argument "init_dm" is replaced by "dm0"''') cput0 = (logger.process_clock(), logger.perf_counter()) if conv_tol_grad is None: conv_tol_grad = numpy.sqrt(conv_tol) logger.info(mf, 'Set gradient conv threshold to %g', conv_tol_grad) mol = mf.mol if dm0 is None: dm = mf.get_init_guess(mol, mf.init_guess) else: dm = dm0 h1e = mf.get_hcore(mol) vhf = mf.get_veff(mol, dm) e_tot = mf.energy_tot(dm, h1e, vhf) logger.info(mf, 'init E= %.15g', e_tot) scf_conv = False mo_energy = mo_coeff = mo_occ = None s1e = mf.get_ovlp(mol) cond = lib.cond(s1e) logger.debug(mf, 'cond(S) = %s', cond) if numpy.max(cond)*1e-17 > conv_tol: logger.warn(mf, 'Singularity detected in overlap matrix (condition number = %4.3g). ' 'SCF may be inaccurate and hard to converge.', numpy.max(cond)) # Skip SCF iterations. Compute only the total energy of the initial density if mf.max_cycle <= 0: fock = mf.get_fock(h1e, s1e, vhf, dm) # = h1e + vhf, no DIIS mo_energy, mo_coeff = mf.eig(fock, s1e) mo_occ = mf.get_occ(mo_energy, mo_coeff) return scf_conv, e_tot, mo_energy, mo_coeff, mo_occ if isinstance(mf.diis, lib.diis.DIIS): mf_diis = mf.diis elif mf.diis: assert issubclass(mf.DIIS, lib.diis.DIIS) mf_diis = mf.DIIS(mf, mf.diis_file) mf_diis.space = mf.diis_space mf_diis.rollback = mf.diis_space_rollback # We get the used orthonormalized AO basis from any old eigendecomposition. # Since the ingredients for the Fock matrix has already been built, we can # just go ahead and use it to determine the orthonormal basis vectors. fock = mf.get_fock(h1e, s1e, vhf, dm) _, mf_diis.Corth = mf.eig(fock, s1e) else: mf_diis = None if dump_chk and mf.chkfile: # Explicit overwrite the mol object in chkfile # Note in pbc.scf, mf.mol == mf.cell, cell is saved under key "mol" chkfile.save_mol(mol, mf.chkfile) # A preprocessing hook before the SCF iteration mf.pre_kernel(locals()) cput1 = logger.timer(mf, 'initialize scf', *cput0) for cycle in range(mf.max_cycle): dm_last = dm last_hf_e = e_tot fock = mf.get_fock(h1e, s1e, vhf, dm, cycle, mf_diis) mo_energy, mo_coeff = mf.eig(fock, s1e) mo_occ = mf.get_occ(mo_energy, mo_coeff) dm = mf.make_rdm1(mo_coeff, mo_occ) vhf = mf.get_veff(mol, dm, dm_last, vhf) e_tot = mf.energy_tot(dm, h1e, vhf) # Here Fock matrix is h1e + vhf, without DIIS. Calling get_fock # instead of the statement "fock = h1e + vhf" because Fock matrix may # be modified in some methods. fock = mf.get_fock(h1e, s1e, vhf, dm) # = h1e + vhf, no DIIS norm_gorb = numpy.linalg.norm(mf.get_grad(mo_coeff, mo_occ, fock)) if not TIGHT_GRAD_CONV_TOL: norm_gorb = norm_gorb / numpy.sqrt(norm_gorb.size) norm_ddm = numpy.linalg.norm(dm-dm_last) logger.info(mf, 'cycle= %d E= %.15g delta_E= %4.3g |g|= %4.3g |ddm|= %4.3g', cycle+1, e_tot, e_tot-last_hf_e, norm_gorb, norm_ddm) if callable(mf.check_convergence): scf_conv = mf.check_convergence(locals()) elif abs(e_tot-last_hf_e) < conv_tol and norm_gorb < conv_tol_grad: scf_conv = True if dump_chk: mf.dump_chk(locals()) if callable(callback): callback(locals()) cput1 = logger.timer(mf, 'cycle= %d'%(cycle+1), *cput1) if scf_conv: break if scf_conv and conv_check: # An extra diagonalization, to remove level shift #fock = mf.get_fock(h1e, s1e, vhf, dm) # = h1e + vhf mo_energy, mo_coeff = mf.eig(fock, s1e) mo_occ = mf.get_occ(mo_energy, mo_coeff) dm, dm_last = mf.make_rdm1(mo_coeff, mo_occ), dm vhf = mf.get_veff(mol, dm, dm_last, vhf) e_tot, last_hf_e = mf.energy_tot(dm, h1e, vhf), e_tot fock = mf.get_fock(h1e, s1e, vhf, dm) norm_gorb = numpy.linalg.norm(mf.get_grad(mo_coeff, mo_occ, fock)) if not TIGHT_GRAD_CONV_TOL: norm_gorb = norm_gorb / numpy.sqrt(norm_gorb.size) norm_ddm = numpy.linalg.norm(dm-dm_last) conv_tol = conv_tol * 10 conv_tol_grad = conv_tol_grad * 3 if callable(mf.check_convergence): scf_conv = mf.check_convergence(locals()) elif abs(e_tot-last_hf_e) < conv_tol or norm_gorb < conv_tol_grad: scf_conv = True logger.info(mf, 'Extra cycle E= %.15g delta_E= %4.3g |g|= %4.3g |ddm|= %4.3g', e_tot, e_tot-last_hf_e, norm_gorb, norm_ddm) if dump_chk: mf.dump_chk(locals()) logger.timer(mf, 'scf_cycle', *cput0) # A post-processing hook before return mf.post_kernel(locals()) return scf_conv, e_tot, mo_energy, mo_coeff, mo_occ
[docs] def energy_elec(mf, dm=None, h1e=None, vhf=None): r'''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: dm : 2D ndarray one-partical density matrix h1e : 2D ndarray Core hamiltonian vhf : 2D 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) ''' if dm is None: dm = mf.make_rdm1() if h1e is None: h1e = mf.get_hcore() if vhf is None: vhf = mf.get_veff(mf.mol, dm) e1 = numpy.einsum('ij,ji->', h1e, dm).real e_coul = numpy.einsum('ij,ji->', vhf, dm).real * .5 mf.scf_summary['e1'] = e1 mf.scf_summary['e2'] = e_coul logger.debug(mf, 'E1 = %s E_coul = %s', e1, e_coul) return e1+e_coul, e_coul
[docs] def energy_tot(mf, dm=None, h1e=None, vhf=None): r'''Total Hartree-Fock energy, electronic part plus nuclear repulstion See :func:`scf.hf.energy_elec` for the electron part Note this function has side effects which cause mf.scf_summary updated. ''' nuc = mf.energy_nuc() e_tot = mf.energy_elec(dm, h1e, vhf)[0] + nuc mf.scf_summary['nuc'] = nuc.real return e_tot
[docs] def 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]]) ''' h = mol.intor_symmetric('int1e_kin') if mol._pseudo: # Although mol._pseudo for GTH PP is only available in Cell, GTH PP # may exist if mol is converted from cell object. from pyscf.gto import pp_int h += pp_int.get_gth_pp(mol) else: h+= mol.intor_symmetric('int1e_nuc') if len(mol._ecpbas) > 0: h += mol.intor_symmetric('ECPscalar') return h
[docs] def get_ovlp(mol): '''Overlap matrix ''' return mol.intor_symmetric('int1e_ovlp')
[docs] def 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]]) ''' from pyscf.scf import atom_hf from pyscf.scf import addons def minao_basis(symb, nelec_ecp): occ = [] basis_ano = [] if gto.is_ghost_atom(symb): return occ, basis_ano stdsymb = gto.mole._std_symbol(symb) basis_add = gto.basis.load('ano', stdsymb) # coreshl defines the core shells to be removed in the initial guess coreshl = gto.ecp.core_configuration(nelec_ecp, atom_symbol=stdsymb) # coreshl = (0,0,0,0) # it keeps all core electrons in the initial guess for l in range(4): ndocc, frac = atom_hf.frac_occ(stdsymb, l) if ndocc >= coreshl[l]: degen = l * 2 + 1 occ_l = [2, ]*(ndocc-coreshl[l]) + [frac, ] occ.append(numpy.repeat(occ_l, degen)) basis_ano.append([l] + [b[:1] + b[1+coreshl[l]:ndocc+2] for b in basis_add[l][1:]]) else: logger.debug(mol, '*** ECP incorporates partially occupied ' 'shell of l = %d for atom %s ***', l, symb) occ = numpy.hstack(occ) if nelec_ecp > 0: if symb in mol._basis: input_basis = mol._basis[symb] elif stdsymb in mol._basis: input_basis = mol._basis[stdsymb] else: raise KeyError(symb) basis4ecp = [[] for i in range(4)] for bas in input_basis: l = bas[0] if l < 4: basis4ecp[l].append(bas) occ4ecp = [] for l in range(4): nbas_l = sum((len(bas[1]) - 1) for bas in basis4ecp[l]) ndocc, frac = atom_hf.frac_occ(stdsymb, l) ndocc -= coreshl[l] assert ndocc <= nbas_l if nbas_l > 0: occ_l = numpy.zeros(nbas_l) occ_l[:ndocc] = 2 if frac > 0: occ_l[ndocc] = frac occ4ecp.append(numpy.repeat(occ_l, l * 2 + 1)) occ4ecp = numpy.hstack(occ4ecp) basis4ecp = lib.flatten(basis4ecp) # Compared to ANO valence basis, to check whether the ECP basis set has # reasonable AO-character contraction. The ANO valence AO should have # significant overlap to ECP basis if the ECP basis has AO-character. atm1 = gto.Mole() atm2 = gto.Mole() atom = [[symb, (0.,0.,0.)]] atm1._atm, atm1._bas, atm1._env = atm1.make_env(atom, {symb:basis4ecp}, []) atm2._atm, atm2._bas, atm2._env = atm2.make_env(atom, {symb:basis_ano}, []) atm1._built = True atm2._built = True s12 = gto.intor_cross('int1e_ovlp', atm1, atm2) if abs(numpy.linalg.det(s12[occ4ecp>0][:,occ>0])) > .1: occ, basis_ano = occ4ecp, basis4ecp else: logger.debug(mol, 'Density of valence part of ANO basis ' 'will be used as initial guess for %s', symb) return occ, basis_ano # Issue 548 if any(gto.charge(mol.atom_symbol(ia)) > 96 for ia in range(mol.natm)): logger.info(mol, 'MINAO initial guess is not available for super-heavy ' 'elements. "atom" initial guess is used.') return init_guess_by_atom(mol) nelec_ecp_dic = dict([(mol.atom_symbol(ia), mol.atom_nelec_core(ia)) for ia in range(mol.natm)]) basis = {} occdic = {} for symb, nelec_ecp in nelec_ecp_dic.items(): occ_add, basis_add = minao_basis(symb, nelec_ecp) occdic[symb] = occ_add basis[symb] = basis_add occ = [] new_atom = [] for ia in range(mol.natm): symb = mol.atom_symbol(ia) if not gto.is_ghost_atom(symb): occ.append(occdic[symb]) new_atom.append(mol._atom[ia]) occ = numpy.hstack(occ) pmol = gto.Mole() pmol._atm, pmol._bas, pmol._env = pmol.make_env(new_atom, basis, []) pmol._built = True #: dm = addons.project_dm_nr2nr(pmol, numpy.diag(occ), mol) mo = addons.project_mo_nr2nr(pmol, numpy.eye(pmol.nao), mol) dm = lib.dot(mo*occ, mo.conj().T) # normalize eletron number # s = mol.intor_symmetric('int1e_ovlp') # dm *= mol.nelectron / (dm*s).sum() return lib.tag_array(dm, mo_coeff=mo, mo_occ=occ)
[docs] def init_guess_by_1e(mol): '''Generate initial guess density matrix from core hamiltonian Returns: Density matrix, 2D ndarray ''' mf = RHF(mol) return mf.init_guess_by_1e(mol)
[docs] def 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 ''' from pyscf.scf import atom_hf atm_scf = atom_hf.get_atm_nrhf(mol) aoslice = mol.aoslice_by_atom() atm_dms = [] mo_coeff = [] mo_occ = [] for ia in range(mol.natm): symb = mol.atom_symbol(ia) if symb not in atm_scf: symb = mol.atom_pure_symbol(ia) if symb in atm_scf: e_hf, e, c, occ = atm_scf[symb] else: # symb's basis is not specified in the input nao_atm = aoslice[ia,3] - aoslice[ia,2] c = numpy.zeros((nao_atm, nao_atm)) occ = numpy.zeros(nao_atm) atm_dms.append(numpy.dot(c*occ, c.conj().T)) mo_coeff.append(c) mo_occ.append(occ) dm = scipy.linalg.block_diag(*atm_dms) mo_coeff = scipy.linalg.block_diag(*mo_coeff) mo_occ = numpy.hstack(occ) if mol.cart: cart2sph = mol.cart2sph_coeff(normalized='sp') dm = reduce(lib.dot, (cart2sph, dm, cart2sph.T)) mo_coeff = lib.dot(cart2sph, mo_coeff) for k, v in atm_scf.items(): logger.debug1(mol, 'Atom %s, E = %.12g', k, v[0]) return lib.tag_array(dm, mo_coeff=mo_coeff, mo_occ=mo_occ)
[docs] def 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 ''' mo_energy, mo_coeff = _init_guess_huckel_orbitals(mol, updated_rule = False) mo_occ = get_occ(SCF(mol), mo_energy, mo_coeff) return make_rdm1(mo_coeff, mo_occ)
[docs] def init_guess_by_mod_huckel(mol): '''Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089 In contrast to init_guess_by_huckel, this routine employs the updated GWH rule from doi:10.1021/ja00480a005 to form the guess. Returns: Density matrix, 2D ndarray ''' mo_energy, mo_coeff = _init_guess_huckel_orbitals(mol, updated_rule = True) mo_occ = get_occ(SCF(mol), mo_energy, mo_coeff) return make_rdm1(mo_coeff, mo_occ)
[docs] def Kgwh(Ei, Ej, updated_rule=False): '''Computes the generalized Wolfsberg-Helmholtz parameter''' # GWH parameter value k = 1.75 if updated_rule: '''Updated scheme from J. Am. Chem. Soc. 100, 3686 (1978); doi:10.1021/ja00480a005''' Delta = (Ei-Ej)/(Ei+Ej) return k + Delta**2 + Delta**4 * (1 - k) else: '''Original rule''' return k
def _init_guess_huckel_orbitals(mol, updated_rule = False): '''Generate initial guess density matrix from a Huckel calculation based on occupancy averaged atomic RHF calculations, doi:10.1021/acs.jctc.8b01089 Arguments: mol, the molecule updated_rule, boolean triggering use of the updated GWH rule from doi:10.1021/ja00480a005 Returns: An 1D array for Huckel orbital energies and an 2D array for orbital coefficients ''' from pyscf.scf import atom_hf atm_scf = atom_hf.get_atm_nrhf(mol) # Run atomic SCF calculations to get orbital energies, coefficients and occupations at_e = [] at_c = [] at_occ = [] for ia in range(mol.natm): symb = mol.atom_symbol(ia) if symb not in atm_scf: symb = mol.atom_pure_symbol(ia) e_hf, e, c, occ = atm_scf[symb] at_c.append(c) at_e.append(e) at_occ.append(occ) # Count number of occupied orbitals nocc = 0 for ia in range(mol.natm): for iorb in range(len(at_occ[ia])): if (at_occ[ia][iorb]>0.0): nocc=nocc+1 # Number of basis functions nbf = mol.nao_nr() # Collect AO coefficients and energies orb_E = numpy.zeros(nocc) orb_C = numpy.zeros((nbf,nocc)) # Atomic basis info aoslice = mol.aoslice_by_atom() # Atomic cartesian mappings atcart2sph = None if mol.cart: atcart2sph = [] molcart2sph = mol.cart2sph_coeff(normalized='sp') for ia in range(mol.natm): # First and last bf index abeg = aoslice[ia, 2] aend = aoslice[ia, 3] # Atomic slice atsph = molcart2sph[abeg:aend,:] # Find the columns with nonzero entries on the atom colnorm = numpy.asarray([numpy.linalg.norm(atsph[:,i]) for i in range(atsph.shape[1])]) atcart2sph.append(atsph[:,colnorm!=0.0]) iocc = 0 for ia in range(mol.natm): # First and last bf index abeg = aoslice[ia, 2] aend = aoslice[ia, 3] for iorb in range(len(at_occ[ia])): if (at_occ[ia][iorb]>0.0): if mol.cart: orb_C[abeg:aend,iocc] = numpy.dot(at_c[ia][:,iorb], atcart2sph[ia].T) else: orb_C[abeg:aend,iocc] = at_c[ia][:,iorb] orb_E[iocc] = at_e[ia][iorb] iocc=iocc+1 # Overlap matrix S = get_ovlp(mol) # Atomic orbital overlap orb_S = orb_C.transpose().dot(S).dot(orb_C) # Build Huckel matrix orb_H = numpy.zeros((nocc,nocc)) for io in range(nocc): # Diagonal is just the orbital energies orb_H[io,io] = orb_E[io] for jo in range(io): # Off-diagonal is given by GWH approximation orb_H[io,jo] = 0.5*Kgwh(orb_E[io],orb_E[jo],updated_rule=updated_rule)*orb_S[io,jo]*(orb_E[io]+orb_E[jo]) orb_H[jo,io] = orb_H[io,jo] # Energies and coefficients in the minimal orbital basis mo_E, atmo_C = eig(orb_H, orb_S) # and in the AO basis mo_C = orb_C.dot(atmo_C) return mo_E, mo_C
[docs] def 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 ''' from pyscf.scf import uhf dm = uhf.init_guess_by_chkfile(mol, chkfile_name, project) return dm[0] + dm[1]
[docs] def get_init_guess(mol, key='minao'): '''Generate density matrix for initial guess Kwargs: key : str One of 'minao', 'atom', 'huckel', 'hcore', '1e', 'chkfile'. ''' return RHF(mol).get_init_guess(mol, key)
# eigenvalue of d is 1
[docs] def level_shift(s, d, f, factor): r'''Apply level shift :math:`\Delta` to virtual orbitals .. math:: :nowrap: \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 ''' dm_vir = s - reduce(numpy.dot, (s, d, s)) return f + dm_vir * factor
[docs] def damping(s, d, f, factor): #dm_vir = s - reduce(numpy.dot, (s,d,s)) #sinv = numpy.linalg.inv(s) #f0 = reduce(numpy.dot, (dm_vir, sinv, f, d, s)) dm_vir = numpy.eye(s.shape[0]) - numpy.dot(s, d) f0 = reduce(numpy.dot, (dm_vir, f, d, s)) f0 = (f0+f0.conj().T) * (factor/(factor+1.)) return f - f0
# full density matrix for RHF
[docs] def make_rdm1(mo_coeff, mo_occ, **kwargs): '''One-particle density matrix in AO representation Args: mo_coeff : 2D ndarray Orbital coefficients. Each column is one orbital. mo_occ : 1D ndarray Occupancy Returns: One-particle density matrix, 2D ndarray ''' mocc = mo_coeff[:,mo_occ>0] # DO NOT make tag_array for dm1 here because this DM array may be modified and # passed to functions like get_jk, get_vxc. These functions may take the tags # (mo_coeff, mo_occ) to compute the potential if tags were found in the DM # array and modifications to DM array may be ignored. dm = numpy.dot(mocc*mo_occ[mo_occ>0], mocc.conj().T) return lib.tag_array(dm, mo_coeff=mo_coeff, mo_occ=mo_occ)
[docs] def make_rdm2(mo_coeff, mo_occ, **kwargs): '''Two-particle density matrix in AO representation Args: mo_coeff : 2D ndarray Orbital coefficients. Each column is one orbital. mo_occ : 1D ndarray Occupancy Returns: Two-particle density matrix, 4D ndarray ''' dm1 = make_rdm1(mo_coeff, mo_occ, **kwargs) dm2 = (numpy.einsum('ij,kl->ijkl', dm1, dm1) - numpy.einsum('ij,kl->iklj', dm1, dm1)/2) return dm2
################################################ # for general DM # hermi = 0 : arbitrary # hermi = 1 : hermitian # hermi = 2 : anti-hermitian ################################################
[docs] def 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: eri : ndarray 8-fold or 4-fold ERIs or complex integral array with N^4 elements (N is the number of orbitals) dm : ndarray or list of ndarrays A density matrix or a list of density matrices Kwargs: hermi : int 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) ''' dm = numpy.asarray(dm) nao = dm.shape[-1] if eri.dtype == numpy.complex128 or eri.size == nao**4: eri = eri.reshape((nao,)*4) dms = dm.reshape(-1,nao,nao) vj = vk = None if with_j: vj = numpy.einsum('ijkl,xji->xkl', eri, dms) vj = vj.reshape(dm.shape) if with_k: vk = numpy.einsum('ijkl,xjk->xil', eri, dms) vk = vk.reshape(dm.shape) else: vj, vk = _vhf.incore(eri, dm.real, hermi, with_j, with_k) if dm.dtype == numpy.complex128: vs = _vhf.incore(eri, dm.imag, 0, with_j, with_k) if with_j: vj = vj + vs[0] * 1j if with_k: vk = vk + vs[1] * 1j return vj, vk
[docs] def 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 :class:`Mole` dm : ndarray or list of ndarrays A density matrix or a list of density matrices Kwargs: hermi : int 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_j : boolean Whether to compute J matrices with_k : boolean Whether to compute K matrices omega : float 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) ''' dm = numpy.asarray(dm, order='C') dm_shape = dm.shape dm_dtype = dm.dtype nao = dm_shape[-1] if dm_dtype == numpy.complex128: dm = numpy.vstack((dm.real, dm.imag)).reshape(-1,nao,nao) hermi = 0 with mol.with_range_coulomb(omega): vj, vk = _vhf.direct(dm, mol._atm, mol._bas, mol._env, vhfopt, hermi, mol.cart, with_j, with_k) if dm_dtype == numpy.complex128: if with_j: vj = vj.reshape((2,) + dm_shape) vj = vj[0] + vj[1] * 1j if with_k: vk = vk.reshape((2,) + dm_shape) vk = vk[0] + vk[1] * 1j else: if with_j: vj = vj.reshape(dm_shape) if with_k: vk = vk.reshape(dm_shape) return vj, vk
[docs] def 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 :class:`Mole` dm : ndarray or list of ndarrays A density matrix or a list of density matrices Kwargs: dm_last : ndarray 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_last : ndarray or a list of ndarrays or 0 The reference HF potential matrix. hermi : int 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 ''' if dm_last is None: vj, vk = get_jk(mol, numpy.asarray(dm), hermi, vhfopt) return vj - vk * .5 else: ddm = numpy.asarray(dm) - numpy.asarray(dm_last) vj, vk = get_jk(mol, ddm, hermi, vhfopt) return vj - vk * .5 + numpy.asarray(vhf_last)
[docs] def 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: h1e : 2D ndarray Core hamiltonian s1e : 2D ndarray Overlap matrix, for DIIS vhf : 2D ndarray HF potential matrix dm : 2D ndarray Density matrix, for DIIS cycle : int Then present SCF iteration step, for DIIS diis : an object of :attr:`SCF.DIIS` class DIIS object to hold intermediate Fock and error vectors diis_start_cycle : int The step to start DIIS. Default is 0. level_shift_factor : float or int Level shift (in AU) for virtual space. Default is 0. ''' if h1e is None: h1e = mf.get_hcore() if vhf is None: vhf = mf.get_veff(mf.mol, dm) f = h1e + vhf if cycle < 0 and diis is None: # Not inside the SCF iteration return f if diis_start_cycle is None: diis_start_cycle = mf.diis_start_cycle if level_shift_factor is None: level_shift_factor = mf.level_shift if damp_factor is None: damp_factor = mf.damp if s1e is None: s1e = mf.get_ovlp() if dm is None: dm = mf.make_rdm1() if 0 <= cycle < diis_start_cycle-1 and abs(damp_factor) > 1e-4: f = damping(s1e, dm*.5, f, damp_factor) if diis is not None and cycle >= diis_start_cycle: f = diis.update(s1e, dm, f, mf, h1e, vhf) if abs(level_shift_factor) > 1e-4: f = level_shift(s1e, dm*.5, f, level_shift_factor) return f
[docs] def get_occ(mf, mo_energy=None, mo_coeff=None): '''Label the occupancies for each orbital Kwargs: mo_energy : 1D ndarray Obital energies mo_coeff : 2D 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]) ''' if mo_energy is None: mo_energy = mf.mo_energy e_idx = numpy.argsort(mo_energy) e_sort = mo_energy[e_idx] nmo = mo_energy.size mo_occ = numpy.zeros(nmo) nocc = mf.mol.nelectron // 2 mo_occ[e_idx[:nocc]] = 2 if mf.verbose >= logger.INFO and nocc < nmo: if e_sort[nocc-1]+1e-3 > e_sort[nocc]: logger.warn(mf, 'HOMO %.15g == LUMO %.15g', e_sort[nocc-1], e_sort[nocc]) else: logger.info(mf, ' HOMO = %.15g LUMO = %.15g', e_sort[nocc-1], e_sort[nocc]) if mf.verbose >= logger.DEBUG: numpy.set_printoptions(threshold=nmo) logger.debug(mf, ' mo_energy =\n%s', mo_energy) numpy.set_printoptions(threshold=1000) return mo_occ
[docs] def get_grad(mo_coeff, mo_occ, fock_ao): '''RHF orbital gradients Args: mo_coeff : 2D ndarray Obital coefficients mo_occ : 1D ndarray Orbital occupancy fock_ao : 2D ndarray Fock matrix in AO representation Returns: Gradients in MO representation. It's a num_occ*num_vir vector. ''' occidx = mo_occ > 0 viridx = ~occidx g = reduce(numpy.dot, (mo_coeff[:,viridx].conj().T, fock_ao, mo_coeff[:,occidx])) * 2 return g.ravel()
[docs] def analyze(mf, verbose=logger.DEBUG, with_meta_lowdin=WITH_META_LOWDIN, **kwargs): '''Analyze the given SCF object: print orbital energies, occupancies; print orbital coefficients; Mulliken population analysis; Diople moment. ''' from pyscf.lo import orth from pyscf.tools import dump_mat mo_energy = mf.mo_energy mo_occ = mf.mo_occ mo_coeff = mf.mo_coeff log = logger.new_logger(mf, verbose) if log.verbose >= logger.NOTE: mf.dump_scf_summary(log) log.note('**** MO energy ****') for i,c in enumerate(mo_occ): log.note('MO #%-3d energy= %-18.15g occ= %g', i+MO_BASE, mo_energy[i], c) ovlp_ao = mf.get_ovlp() if verbose >= logger.DEBUG: label = mf.mol.ao_labels() if with_meta_lowdin: log.debug(' ** MO coefficients (expansion on meta-Lowdin AOs) **') orth_coeff = orth.orth_ao(mf.mol, 'meta_lowdin', s=ovlp_ao) c = reduce(numpy.dot, (orth_coeff.conj().T, ovlp_ao, mo_coeff)) else: log.debug(' ** MO coefficients (expansion on AOs) **') c = mo_coeff dump_mat.dump_rec(mf.stdout, c, label, start=MO_BASE, **kwargs) dm = mf.make_rdm1(mo_coeff, mo_occ) if with_meta_lowdin: return (mf.mulliken_meta(mf.mol, dm, s=ovlp_ao, verbose=log), mf.dip_moment(mf.mol, dm, verbose=log)) else: return (mf.mulliken_pop(mf.mol, dm, s=ovlp_ao, verbose=log), mf.dip_moment(mf.mol, dm, verbose=log))
[docs] def dump_scf_summary(mf, verbose=logger.DEBUG): if not mf.scf_summary: return log = logger.new_logger(mf, verbose) summary = mf.scf_summary def write(fmt, key): if key in summary: log.info(fmt, summary[key]) log.info('**** SCF Summaries ****') log.info('Total Energy = %24.15f', mf.e_tot) write('Nuclear Repulsion Energy = %24.15f', 'nuc') write('One-electron Energy = %24.15f', 'e1') write('Two-electron Energy = %24.15f', 'e2') write('Two-electron Coulomb Energy = %24.15f', 'coul') write('DFT Exchange-Correlation Energy = %24.15f', 'exc') write('Empirical Dispersion Energy = %24.15f', 'dispersion') write('PCM Polarization Energy = %24.15f', 'epcm') write('EFP Energy = %24.15f', 'efp') if getattr(mf, 'entropy', None): log.info('(Electronic) Entropy %24.15f', mf.entropy) log.info('(Electronic) Zero Point Energy %24.15f', mf.e_zero) log.info('Free Energy = %24.15f', mf.e_free)
[docs] def mulliken_pop(mol, dm, s=None, verbose=logger.DEBUG): r'''Mulliken population analysis .. math:: M_{ij} = D_{ij} S_{ji} Mulliken charges .. math:: \delta_i = \sum_j M_{ij} Returns: A list : pop, charges pop : nparray Mulliken population on each atomic orbitals charges : nparray Mulliken charges ''' if s is None: s = get_ovlp(mol) log = logger.new_logger(mol, verbose) if isinstance(dm, numpy.ndarray) and dm.ndim == 2: pop = numpy.einsum('ij,ji->i', dm, s).real else: # ROHF pop = numpy.einsum('ij,ji->i', dm[0]+dm[1], s).real log.info(' ** Mulliken pop **') for i, s in enumerate(mol.ao_labels()): log.info('pop of %-14s %10.5f', s, pop[i]) log.note(' ** Mulliken atomic charges **') chg = numpy.zeros(mol.natm) for i, s in enumerate(mol.ao_labels(fmt=None)): chg[s[0]] += pop[i] chg = mol.atom_charges() - chg for ia in range(mol.natm): symb = mol.atom_symbol(ia) log.note('charge of %3d%s = %10.5f', ia, symb, chg[ia]) return pop, chg
[docs] def mulliken_meta(mol, dm, verbose=logger.DEBUG, pre_orth_method=PRE_ORTH_METHOD, 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 carried out within each subsets. Args: mol : an instance of :class:`Mole` dm : ndarray or 2-item list of ndarray Density matrix. ROHF dm is a 2-item list of 2D array Kwargs: verbose : int or instance of :class:`lib.logger.Logger` pre_orth_method : str 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 pop : nparray Mulliken population on each atomic orbitals charges : nparray Mulliken charges ''' from pyscf.lo import orth if s is None: s = get_ovlp(mol) log = logger.new_logger(mol, verbose) orth_coeff = orth.orth_ao(mol, 'meta_lowdin', pre_orth_method, s=s) c_inv = numpy.dot(orth_coeff.conj().T, s) if isinstance(dm, numpy.ndarray) and dm.ndim == 2: dm = reduce(numpy.dot, (c_inv, dm, c_inv.T.conj())) else: # ROHF dm = reduce(numpy.dot, (c_inv, dm[0]+dm[1], c_inv.T.conj())) log.info(' ** Mulliken pop on meta-lowdin orthogonal AOs **') return mulliken_pop(mol, dm, numpy.eye(orth_coeff.shape[0]), log)
mulliken_pop_meta_lowdin_ao = mulliken_meta
[docs] def eig(h, s): '''Solver for generalized eigenvalue problem .. math:: HC = SCE ''' e, c = scipy.linalg.eigh(h, s) idx = numpy.argmax(abs(c.real), axis=0) c[:,c[idx,numpy.arange(len(e))].real<0] *= -1 return e, c
[docs] def canonicalize(mf, mo_coeff, mo_occ, fock=None): '''Canonicalization diagonalizes the Fock matrix within occupied, open, virtual subspaces separatedly (without change occupancy). ''' if fock is None: dm = mf.make_rdm1(mo_coeff, mo_occ) fock = mf.get_fock(dm=dm) coreidx = mo_occ == 2 viridx = mo_occ == 0 openidx = ~(coreidx | viridx) mo = numpy.empty_like(mo_coeff) mo_e = numpy.empty(mo_occ.size) for idx in (coreidx, openidx, viridx): if numpy.count_nonzero(idx) > 0: orb = mo_coeff[:,idx] f1 = reduce(numpy.dot, (orb.conj().T, fock, orb)) e, c = scipy.linalg.eigh(f1) mo[:,idx] = numpy.dot(orb, c) mo_e[idx] = e return mo_e, mo
[docs] def dip_moment(mol, dm, unit='Debye', verbose=logger.NOTE, **kwargs): r''' Dipole moment calculation .. math:: \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 where :math:`\mu_x, \mu_y, \mu_z` are the x, y and z components of dipole moment Args: mol: an instance of :class:`Mole` dm : a 2D ndarrays density matrices Return: A list: the dipole moment on x, y and z component ''' log = logger.new_logger(mol, verbose) if 'unit_symbol' in kwargs: # pragma: no cover log.warn('Kwarg "unit_symbol" was deprecated. It was replaced by kwarg ' 'unit since PySCF-1.5.') unit = kwargs['unit_symbol'] if not (isinstance(dm, numpy.ndarray) and dm.ndim == 2): # UHF density matrices dm = dm[0] + dm[1] with mol.with_common_orig((0,0,0)): ao_dip = mol.intor_symmetric('int1e_r', comp=3) el_dip = numpy.einsum('xij,ji->x', ao_dip, dm).real charges = mol.atom_charges() coords = mol.atom_coords() nucl_dip = numpy.einsum('i,ix->x', charges, coords) mol_dip = nucl_dip - el_dip if unit.upper() == 'DEBYE': mol_dip *= nist.AU2DEBYE log.note('Dipole moment(X, Y, Z, Debye): %8.5f, %8.5f, %8.5f', *mol_dip) else: log.note('Dipole moment(X, Y, Z, A.U.): %8.5f, %8.5f, %8.5f', *mol_dip) return mol_dip
[docs] def uniq_var_indices(mo_occ): ''' Indices of the unique variables for the orbital-gradients (or orbital-rotation) matrix. ''' occidxa = mo_occ>0 occidxb = mo_occ==2 viridxa = ~occidxa viridxb = ~occidxb mask = (viridxa[:,None] & occidxa) | (viridxb[:,None] & occidxb) return mask
[docs] def pack_uniq_var(x, mo_occ): ''' Extract the unique variables from the full orbital-gradients (or orbital-rotation) matrix ''' idx = uniq_var_indices(mo_occ) return x[idx]
[docs] def unpack_uniq_var(dx, mo_occ): ''' Fill the full orbital-gradients (or orbital-rotation) matrix with the unique variables. ''' nmo = len(mo_occ) idx = uniq_var_indices(mo_occ) x1 = numpy.zeros((nmo,nmo), dtype=dx.dtype) x1[idx] = dx return x1 - x1.conj().T
[docs] def 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 ''' if isinstance(mf, lib.SinglePointScanner): return mf logger.info(mf, 'Create scanner for %s', mf.__class__) name = mf.__class__.__name__ + SCF_Scanner.__name_mixin__ return lib.set_class(SCF_Scanner(mf), (SCF_Scanner, mf.__class__), name)
[docs] class SCF_Scanner(lib.SinglePointScanner): def __init__(self, mf_obj): self.__dict__.update(mf_obj.__dict__) self._last_mol_fp = mf_obj.mol.ao_loc def __call__(self, mol_or_geom, **kwargs): if isinstance(mol_or_geom, gto.MoleBase): mol = mol_or_geom else: mol = self.mol.set_geom_(mol_or_geom, inplace=False) # Cleanup intermediates associated to the previous mol object self.reset(mol) if 'dm0' in kwargs: dm0 = kwargs.pop('dm0') elif self.mo_coeff is None: dm0 = None elif self.chkfile and h5py.is_hdf5(self.chkfile): dm0 = self.from_chk(self.chkfile) else: dm0 = None # dm0 form last calculation cannot be used in the current # calculation if a completely different system is given. # Obviously, the systems are very different if the number of # basis functions are different. # TODO: A robust check should include more comparison on # various attributes between current `mol` and the `mol` in # last calculation. if numpy.array_equal(self._last_mol_fp, mol.ao_loc): dm0 = self.make_rdm1() self.mo_coeff = None # To avoid last mo_coeff being used by SOSCF e_tot = self.kernel(dm0=dm0, **kwargs) self._last_mol_fp = mol.ao_loc return e_tot
[docs] class SCF(lib.StreamObject): '''SCF base class. non-relativistic RHF. Attributes: verbose : int Print level. Default value equals to :class:`Mole.verbose` max_memory : float or int Allowed memory in MB. Default equals to :class:`Mole.max_memory` chkfile : str checkpoint file to save MOs, orbital energies etc. Writing to chkfile can be disabled if this attribute is set to None or False. conv_tol : float converge threshold. Default is 1e-9 conv_tol_grad : float gradients converge threshold. Default is sqrt(conv_tol) max_cycle : int max number of iterations. If max_cycle <= 0, SCF iteration will be skipped and the kernel function will compute only the total energy based on the initial guess. Default value is 50. init_guess : str initial guess method. It can be one of 'minao', 'atom', 'huckel', 'hcore', '1e', 'chkfile'. Default is 'minao' DIIS : DIIS class The class to generate diis object. It can be one of diis.SCF_DIIS, diis.ADIIS, diis.EDIIS. diis : boolean or object of DIIS class defined in :mod:`scf.diis`. Default is the object associated to the attribute :attr:`self.DIIS`. Set it to None/False to turn off DIIS. Note if this attribute is initialized as a DIIS object, the SCF driver will use this object in the iteration. The DIIS information (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_space : int DIIS space size. By default, 8 Fock matrices and errors vector are stored. diis_start_cycle : int The step to start DIIS. Default is 1. diis_file: 'str' File to store DIIS vectors and error vectors. level_shift : float or int Level shift (in AU) for virtual space. Default is 0. direct_scf : bool Direct SCF is used by default. direct_scf_tol : float Direct SCF cutoff threshold. Default is 1e-13. callback : function(envs_dict) => None callback function takes one dict as the argument which is generated by the builtin function :func:`locals`, so that the callback function can access all local variables in the current environment. conv_check : bool An extra cycle to check convergence after SCF iterations. check_convergence : function(envs) => bool A hook for overloading convergence criteria in SCF iterations. Saved results: converged : bool SCF converged or not e_tot : float 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 ''' conv_tol = getattr(__config__, 'scf_hf_SCF_conv_tol', 1e-9) conv_tol_grad = getattr(__config__, 'scf_hf_SCF_conv_tol_grad', None) max_cycle = getattr(__config__, 'scf_hf_SCF_max_cycle', 50) init_guess = getattr(__config__, 'scf_hf_SCF_init_guess', 'minao') # To avoid diis pollution from previous run, self.diis should not be # initialized as DIIS instance here DIIS = diis.SCF_DIIS diis = getattr(__config__, 'scf_hf_SCF_diis', True) diis_space = getattr(__config__, 'scf_hf_SCF_diis_space', 8) # need > 0 if initial DM is numpy.zeros array diis_start_cycle = getattr(__config__, 'scf_hf_SCF_diis_start_cycle', 1) diis_file = None diis_space_rollback = 0 damp = getattr(__config__, 'scf_hf_SCF_damp', 0) level_shift = getattr(__config__, 'scf_hf_SCF_level_shift', 0) direct_scf = getattr(__config__, 'scf_hf_SCF_direct_scf', True) direct_scf_tol = getattr(__config__, 'scf_hf_SCF_direct_scf_tol', 1e-13) conv_check = getattr(__config__, 'scf_hf_SCF_conv_check', True) callback = None _keys = set(( 'conv_tol', 'conv_tol_grad', 'max_cycle', 'init_guess', 'DIIS', 'diis', 'diis_space', 'diis_start_cycle', 'diis_file', 'diis_space_rollback', 'damp', 'level_shift', 'direct_scf', 'direct_scf_tol', 'conv_check', 'callback', 'mol', 'chkfile', 'mo_energy', 'mo_coeff', 'mo_occ', 'e_tot', 'converged', 'scf_summary', 'opt', )) def __init__(self, mol): if not mol._built: sys.stderr.write('Warning: %s must be initialized before calling SCF.\n' 'Initialize %s in %s\n' % (mol, mol, self)) mol.build() self.mol = mol self.verbose = mol.verbose self.max_memory = mol.max_memory self.stdout = mol.stdout # If chkfile is muted, SCF intermediates will not be dumped anywhere. if MUTE_CHKFILE: self.chkfile = None else: # the chkfile will be removed automatically, to save the chkfile, assign a # filename to self.chkfile self._chkfile = tempfile.NamedTemporaryFile(dir=lib.param.TMPDIR) self.chkfile = self._chkfile.name ################################################## # don't modify the following attributes, they are not input options self.mo_energy = None self.mo_coeff = None self.mo_occ = None self.e_tot = 0 self.converged = False self.scf_summary = {} self._opt = {None: None} self._eri = None # Note: self._eri requires large amount of memory
[docs] def build(self, mol=None): if mol is None: mol = self.mol if self.verbose >= logger.WARN: self.check_sanity() return self
@property def opt(self): return self._opt[None] @opt.setter def opt(self, x): self._opt[None] = x
[docs] def dump_flags(self, verbose=None): log = logger.new_logger(self, verbose) if log.verbose < logger.INFO: return self log.info('\n') log.info('******** %s ********', self.__class__) log.info('method = %s', self.__class__.__name__) log.info('initial guess = %s', self.init_guess) log.info('damping factor = %g', self.damp) log.info('level_shift factor = %s', self.level_shift) if isinstance(self.diis, lib.diis.DIIS): log.info('DIIS = %s', self.diis) log.info('diis_start_cycle = %d', self.diis_start_cycle) log.info('diis_space = %d', self.diis.space) elif self.diis: log.info('DIIS = %s', self.DIIS) log.info('diis_start_cycle = %d', self.diis_start_cycle) log.info('diis_space = %d', self.diis_space) else: log.info('DIIS disabled') log.info('SCF conv_tol = %g', self.conv_tol) log.info('SCF conv_tol_grad = %s', self.conv_tol_grad) log.info('SCF max_cycles = %d', self.max_cycle) log.info('direct_scf = %s', self.direct_scf) if self.direct_scf: log.info('direct_scf_tol = %g', self.direct_scf_tol) if self.chkfile: log.info('chkfile to save SCF result = %s', self.chkfile) log.info('max_memory %d MB (current use %d MB)', self.max_memory, lib.current_memory()[0]) return self
def _eigh(self, h, s): return eig(h, s)
[docs] @lib.with_doc(eig.__doc__) def eig(self, h, s): # An intermediate call to self._eigh so that the modification to eig function # can be applied on different level. Different SCF modules like RHF/UHF # redefine only the eig solver and leave the other modifications (like removing # linear dependence, sorting eigenvalues) to low level ._eigh return self._eigh(h, s)
[docs] def get_hcore(self, mol=None): if mol is None: mol = self.mol return get_hcore(mol)
[docs] def get_ovlp(self, mol=None): if mol is None: mol = self.mol return get_ovlp(mol)
get_fock = get_fock get_occ = get_occ
[docs] @lib.with_doc(get_grad.__doc__) def get_grad(self, mo_coeff, mo_occ, fock=None): if fock is None: dm1 = self.make_rdm1(mo_coeff, mo_occ) fock = self.get_hcore(self.mol) + self.get_veff(self.mol, dm1) return get_grad(mo_coeff, mo_occ, fock)
[docs] def dump_chk(self, envs): if self.chkfile: chkfile.dump_scf(self.mol, self.chkfile, envs['e_tot'], envs['mo_energy'], envs['mo_coeff'], envs['mo_occ'], overwrite_mol=False) return self
[docs] @lib.with_doc(init_guess_by_minao.__doc__) def init_guess_by_minao(self, mol=None): if mol is None: mol = self.mol logger.info(self, 'Initial guess from minao.') return init_guess_by_minao(mol)
[docs] @lib.with_doc(init_guess_by_atom.__doc__) def init_guess_by_atom(self, mol=None): if mol is None: mol = self.mol logger.info(self, 'Initial guess from superposition of atomic densities.') return init_guess_by_atom(mol)
[docs] @lib.with_doc(init_guess_by_huckel.__doc__) def init_guess_by_huckel(self, mol=None): if mol is None: mol = self.mol logger.info(self, 'Initial guess from on-the-fly Huckel, doi:10.1021/acs.jctc.8b01089.') mo_energy, mo_coeff = _init_guess_huckel_orbitals(mol, updated_rule=False) mo_occ = self.get_occ(mo_energy, mo_coeff) return self.make_rdm1(mo_coeff, mo_occ)
[docs] @lib.with_doc(init_guess_by_mod_huckel.__doc__) def init_guess_by_mod_huckel(self, updated_rule, mol=None): if mol is None: mol = self.mol logger.info(self, '''Initial guess from on-the-fly Huckel, doi:10.1021/acs.jctc.8b01089, employing the updated GWH rule from doi:10.1021/ja00480a005.''') mo_energy, mo_coeff = _init_guess_huckel_orbitals(mol, updated_rule=True) mo_occ = self.get_occ(mo_energy, mo_coeff) return self.make_rdm1(mo_coeff, mo_occ)
[docs] @lib.with_doc(init_guess_by_1e.__doc__) def init_guess_by_1e(self, mol=None): if mol is None: mol = self.mol logger.info(self, 'Initial guess from hcore.') h1e = self.get_hcore(mol) s1e = self.get_ovlp(mol) mo_energy, mo_coeff = self.eig(h1e, s1e) mo_occ = self.get_occ(mo_energy, mo_coeff) return self.make_rdm1(mo_coeff, mo_occ)
[docs] @lib.with_doc(init_guess_by_chkfile.__doc__) def init_guess_by_chkfile(self, chkfile=None, project=None): if chkfile is None: chkfile = self.chkfile return init_guess_by_chkfile(self.mol, chkfile, project=project)
[docs] def from_chk(self, chkfile=None, project=None): return self.init_guess_by_chkfile(chkfile, project)
from_chk.__doc__ = init_guess_by_chkfile.__doc__
[docs] def get_init_guess(self, mol=None, key='minao'): if not isinstance(key, str): return key key = key.lower() if mol is None: mol = self.mol if key == '1e' or key == 'hcore': dm = self.init_guess_by_1e(mol) elif key == 'huckel': dm = self.init_guess_by_huckel(mol) elif key == 'mod_huckel': dm = self.init_guess_by_mod_huckel(mol) elif getattr(mol, 'natm', 0) == 0: logger.info(self, 'No atom found in mol. Use 1e initial guess') dm = self.init_guess_by_1e(mol) elif key == 'atom': dm = self.init_guess_by_atom(mol) elif key == 'vsap' and hasattr(self, 'init_guess_by_vsap'): # Only available for DFT objects dm = self.init_guess_by_vsap(mol) elif key[:3] == 'chk': try: dm = self.init_guess_by_chkfile() except (IOError, KeyError): logger.warn(self, 'Fail in reading %s. Use MINAO initial guess', self.chkfile) dm = self.init_guess_by_minao(mol) else: dm = self.init_guess_by_minao(mol) return dm
make_rdm1 = lib.module_method(make_rdm1, absences=['mo_coeff', 'mo_occ']) make_rdm2 = lib.module_method(make_rdm2, absences=['mo_coeff', 'mo_occ']) energy_elec = energy_elec energy_tot = energy_tot
[docs] def energy_nuc(self): return self.mol.energy_nuc()
# A hook for overloading convergence criteria in SCF iterations. Assigning # a function # f(envs) => bool # to check_convergence can overwrite the default convergence criteria check_convergence = None
[docs] def scf(self, dm0=None, **kwargs): '''SCF main driver Kwargs: dm0 : ndarray 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 ''' cput0 = (logger.process_clock(), logger.perf_counter()) self.dump_flags() self.build(self.mol) if self.max_cycle > 0 or self.mo_coeff is None: self.converged, self.e_tot, \ self.mo_energy, self.mo_coeff, self.mo_occ = \ kernel(self, self.conv_tol, self.conv_tol_grad, dm0=dm0, callback=self.callback, conv_check=self.conv_check, **kwargs) else: # Avoid to update SCF orbitals in the non-SCF initialization # (issue #495). But run regular SCF for initial guess if SCF was # not initialized. self.e_tot = kernel(self, self.conv_tol, self.conv_tol_grad, dm0=dm0, callback=self.callback, conv_check=self.conv_check, **kwargs)[1] logger.timer(self, 'SCF', *cput0) self._finalize() return self.e_tot
kernel = lib.alias(scf, alias_name='kernel') def _finalize(self): '''Hook for dumping results and clearing up the object.''' if self.converged: logger.note(self, 'converged SCF energy = %.15g', self.e_tot) else: logger.note(self, 'SCF not converged.') logger.note(self, 'SCF energy = %.15g', self.e_tot) return self
[docs] def init_direct_scf(self, mol=None): if mol is None: mol = self.mol # Integrals < direct_scf_tol may be set to 0 in int2e. # Higher accuracy is required for Schwartz inequality prescreening. cpu0 = (logger.process_clock(), logger.perf_counter()) opt = _vhf._VHFOpt(mol, 'int2e', 'CVHFnrs8_prescreen', 'CVHFnr_int2e_q_cond', 'CVHFnr_dm_cond', self.direct_scf_tol) logger.timer(self, 'init_direct_scf', *cpu0) return opt
[docs] @lib.with_doc(get_jk.__doc__) def get_jk(self, mol=None, dm=None, hermi=1, with_j=True, with_k=True, omega=None): if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() cpu0 = (logger.process_clock(), logger.perf_counter()) if self.direct_scf and self._opt.get(omega) is None: # Be careful that opt has to be initialized with a proper setting of # omega. opt of regular ERI and SR ERI are incompatible since cint 5.4.0 with mol.with_range_coulomb(omega): self._opt[omega] = self.init_direct_scf(mol) vhfopt = self._opt.get(omega) if with_j and with_k: vj, vk = get_jk(mol, dm, hermi, vhfopt, with_j, with_k, omega) else: if with_j: prescreen = 'CVHFnrs8_vj_prescreen' else: prescreen = 'CVHFnrs8_vk_prescreen' with lib.temporary_env(vhfopt, prescreen=prescreen): vj, vk = get_jk(mol, dm, hermi, vhfopt, with_j, with_k, omega) logger.timer(self, 'vj and vk', *cpu0) return vj, vk
[docs] def get_j(self, mol=None, dm=None, hermi=1, omega=None): '''Compute J matrices for all input density matrices ''' return self.get_jk(mol, dm, hermi, with_k=False, omega=omega)[0]
[docs] def get_k(self, mol=None, dm=None, hermi=1, omega=None): '''Compute K matrices for all input density matrices ''' return self.get_jk(mol, dm, hermi, with_j=False, omega=omega)[1]
[docs] @lib.with_doc(get_veff.__doc__) def get_veff(self, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1): # Be carefule with the effects of :attr:`SCF.direct_scf` on this function if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() if self.direct_scf: ddm = numpy.asarray(dm) - dm_last vj, vk = self.get_jk(mol, ddm, hermi=hermi) return vhf_last + vj - vk * .5 else: vj, vk = self.get_jk(mol, dm, hermi=hermi) return vj - vk * .5
[docs] @lib.with_doc(analyze.__doc__) def analyze(self, verbose=None, with_meta_lowdin=WITH_META_LOWDIN, **kwargs): if verbose is None: verbose = self.verbose return analyze(self, verbose, with_meta_lowdin, **kwargs)
dump_scf_summary = dump_scf_summary
[docs] @lib.with_doc(mulliken_pop.__doc__) def mulliken_pop(self, mol=None, dm=None, s=None, verbose=logger.DEBUG): if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() if s is None: s = self.get_ovlp(mol) return mulliken_pop(mol, dm, s=s, verbose=verbose)
[docs] @lib.with_doc(mulliken_meta.__doc__) def mulliken_meta(self, mol=None, dm=None, verbose=logger.DEBUG, pre_orth_method=PRE_ORTH_METHOD, s=None): if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() if s is None: s = self.get_ovlp(mol) return mulliken_meta(mol, dm, s=s, verbose=verbose, pre_orth_method=pre_orth_method)
[docs] def pop(self, *args, **kwargs): return self.mulliken_meta(*args, **kwargs)
pop.__doc__ = mulliken_meta.__doc__ mulliken_pop_meta_lowdin_ao = pop canonicalize = canonicalize
[docs] @lib.with_doc(dip_moment.__doc__) def dip_moment(self, mol=None, dm=None, unit='Debye', verbose=logger.NOTE, **kwargs): if mol is None: mol = self.mol if dm is None: dm =self.make_rdm1() return dip_moment(mol, dm, unit, verbose=verbose, **kwargs)
def _is_mem_enough(self): nbf = self.mol.nao_nr() return nbf**4/1e6+lib.current_memory()[0] < self.max_memory*.95
[docs] def density_fit(self, auxbasis=None, with_df=None, only_dfj=False): import pyscf.df.df_jk return pyscf.df.df_jk.density_fit(self, auxbasis, with_df, only_dfj)
[docs] def sfx2c1e(self): import pyscf.x2c.sfx2c1e return pyscf.x2c.sfx2c1e.sfx2c1e(self)
x2c1e = sfx2c1e x2c = x2c1e
[docs] def newton(self): '''Create an SOSCF object based on the mean-field object''' from pyscf.soscf import newton_ah return newton_ah.newton(self)
[docs] def remove_soscf(self): '''Remove the SOSCF decorator''' from pyscf.soscf import newton_ah if not isinstance(self, newton_ah._CIAH_SOSCF): return self return self.undo_soscf()
[docs] def stability(self): raise NotImplementedError
[docs] def nuc_grad_method(self): # pragma: no cover '''Hook to create object for analytical nuclear gradients.''' raise NotImplementedError
[docs] def update_(self, chkfile=None): '''Read attributes from the chkfile then replace the attributes of current object. It's an alias of function update_from_chk_. ''' from pyscf.scf import chkfile as chkmod if chkfile is None: chkfile = self.chkfile chk_scf = chkmod.load(chkfile, 'scf') nao = self.mol.nao mo = chk_scf['mo_coeff'] if isinstance(mo, numpy.ndarray): # RHF mo_nao = mo.shape[-2] elif isinstance(mo[0], numpy.ndarray): # UHF mo_nao = mo[0].shape[-2] else: # KUHF mo_nao = mo[0][0].shape[-2] if mo_nao not in (nao, nao*2): logger.warn(self, 'Current mol is inconsistent with SCF object in ' 'chkfile %s', chkfile) self.__dict__.update(chk_scf) return self
update_from_chk = update_from_chk_ = update = update_ as_scanner = as_scanner
[docs] def reset(self, mol=None): '''Reset mol and relevant attributes associated to the old mol object''' if mol is not None: self.mol = mol self._opt = {None: None} self._eri = None return self
[docs] def apply(self, fn, *args, **kwargs): if callable(fn): return lib.StreamObject.apply(self, fn, *args, **kwargs) elif isinstance(fn, str): from pyscf import mp, cc, ci, mcscf, tdscf for mod in (mp, cc, ci, mcscf, tdscf): method = getattr(mod, fn.upper(), None) if method is not None and callable(method): if self.mo_coeff is None: logger.warn(self, 'SCF object must be initialized ' 'before calling post-SCF methods.\n' 'Initialize %s for %s', self, mod) self.kernel() return method(self, *args, **kwargs) raise ValueError('Unknown method %s' % fn) else: raise TypeError('First argument of .apply method must be a ' 'function/class or a name (string) of a method.')
[docs] def to_rhf(self): '''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. ''' from pyscf.scf import addons return addons.convert_to_rhf(self)
[docs] def to_uhf(self): '''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. ''' from pyscf.scf import addons return addons.convert_to_uhf(self)
[docs] def to_ghf(self): '''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. ''' from pyscf.scf import addons return addons.convert_to_ghf(self)
[docs] def to_rks(self, 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. ''' return self.to_rhf().to_ks(xc)
[docs] def to_uks(self, 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. ''' return self.to_uhf().to_ks(xc)
[docs] def to_gks(self, 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. ''' return self.to_ghf().to_ks(xc)
[docs] def convert_from_(self, mf): '''Convert the abinput mean-field object to the associated KS object. ''' raise NotImplementedError
[docs] def to_ks(self, xc='HF'): '''Convert the input mean-field object to the associated 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 mean-field object. ''' raise NotImplementedError
def _transfer_attrs_(self, dst): '''This helper function transfers attributes from one SCF object to another SCF object. It is invoked by to_ks and to_hf methods. ''' loc_dic = self.__dict__ keys = dst.__dict__.keys() & loc_dic.keys() dst.__dict__.update({k: loc_dic[k] for k in keys}) dst.converged = False return dst
class KohnShamDFT: '''A mock DFT base class The base class KohnShamDFT is defined in the dft.rks module. This class can be used to verify if an SCF object is a Hartree-Fock method or a DFT method. It should be overwritten by the actual KohnShamDFT class when loading dft module. '''
[docs] class RHF(SCF): __doc__ = SCF.__doc__
[docs] def check_sanity(self): mol = self.mol if mol.nelectron != 1 and mol.spin != 0: logger.warn(self, 'Invalid number of electrons %d for RHF method.', mol.nelectron) return SCF.check_sanity(self)
[docs] def get_init_guess(self, mol=None, key='minao'): dm = SCF.get_init_guess(self, mol, key) if self.verbose >= logger.DEBUG1: s = self.get_ovlp() nelec = numpy.einsum('ij,ji', dm, s).real logger.debug1(self, 'Nelec from initial guess = %s', nelec) return dm
[docs] @lib.with_doc(get_jk.__doc__) def get_jk(self, mol=None, dm=None, hermi=1, with_j=True, with_k=True, omega=None): # Note the incore version, which initializes an _eri array in memory. if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() if (not omega and (self._eri is not None or mol.incore_anyway or self._is_mem_enough())): if self._eri is None: self._eri = mol.intor('int2e', aosym='s8') vj, vk = dot_eri_dm(self._eri, dm, hermi, with_j, with_k) else: vj, vk = SCF.get_jk(self, mol, dm, hermi, with_j, with_k, omega) return vj, vk
[docs] @lib.with_doc(get_veff.__doc__) def get_veff(self, mol=None, dm=None, dm_last=0, vhf_last=0, hermi=1): if mol is None: mol = self.mol if dm is None: dm = self.make_rdm1() if self._eri is not None or not self.direct_scf: vj, vk = self.get_jk(mol, dm, hermi) vhf = vj - vk * .5 else: ddm = numpy.asarray(dm) - numpy.asarray(dm_last) vj, vk = self.get_jk(mol, ddm, hermi) vhf = vj - vk * .5 vhf += numpy.asarray(vhf_last) return vhf
[docs] def convert_from_(self, mf): '''Convert the input mean-field object to RHF/ROHF''' tgt = mf.to_rhf() self.__dict__.update(tgt.__dict__) return self
[docs] def spin_square(self, mo_coeff=None, s=None): # pragma: no cover '''Spin square and multiplicity of RHF determinant''' return 0, 1
[docs] def stability(self, internal=getattr(__config__, 'scf_stability_internal', True), external=getattr(__config__, 'scf_stability_external', False), verbose=None, return_status=False): ''' RHF/RKS stability analysis. See also pyscf.scf.stability.rhf_stability function. Kwargs: internal : bool Internal stability, within the RHF optimization space. external : bool External stability. Including the RHF -> UHF and real -> complex stability analysis. return_status: bool Whether to return `stable_i` and `stable_e` Returns: If return_status is False (default), the return value includes two set of orbitals, which are more close to the stable condition. The first corresponds to the internal stability and the second corresponds to the external stability. Else, another two boolean variables (indicating current status: stable or unstable) are returned. The first corresponds to the internal stability and the second corresponds to the external stability. ''' from pyscf.scf.stability import rhf_stability return rhf_stability(self, internal, external, verbose, return_status)
[docs] def nuc_grad_method(self): from pyscf.grad import rhf return rhf.Gradients(self)
[docs] def to_ks(self, xc='HF'): '''Convert to RKS object. ''' from pyscf import dft return self._transfer_attrs_(dft.RKS(self.mol, xc=xc))
def _hf1e_scf(mf, *args): logger.info(mf, '\n') logger.info(mf, '******** 1 electron system ********') mf.converged = True h1e = mf.get_hcore(mf.mol) s1e = mf.get_ovlp(mf.mol) mf.mo_energy, mf.mo_coeff = mf.eig(h1e, s1e) mf.mo_occ = mf.get_occ(mf.mo_energy, mf.mo_coeff) mf.e_tot = mf.mo_energy[mf.mo_occ>0][0].real + mf.mol.energy_nuc() mf._finalize() return mf.e_tot del (WITH_META_LOWDIN, PRE_ORTH_METHOD) if __name__ == '__main__': from pyscf import scf mol = gto.Mole() mol.verbose = 5 mol.output = None mol.atom = [['He', (0, 0, 0)], ] mol.basis = 'ccpvdz' mol.build(0, 0) ############## # SCF result method = scf.RHF(mol).x2c().density_fit().newton() method.init_guess = '1e' energy = method.scf() print(energy)