#!/usr/bin/env python
# Copyright 2014-2022 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>
#
'''
CASSCF analytical nuclear gradients
Ref.
J. Comput. Chem., 5, 589
MRH: copied from pyscf.grad.casscf.py on 12/07/2019
Contains my modifications for SA-CASSCF gradients
1. Generalized Fock has nonzero i->a and u->a
2. Memory footprint for differentiated eris bugfix
'''
import inspect
import time
from functools import reduce
from itertools import product
import numpy
from scipy import linalg
from pyscf import gto
from pyscf import lib
from pyscf import ao2mo
from pyscf.lib import logger
from pyscf.grad import casci as casci_grad
from pyscf.grad import rhf as rhf_grad
from pyscf.grad.mp2 import _shell_prange
from pyscf.df.grad import rhf as dfrhf_grad
from pyscf.df.grad.casdm2_util import (solve_df_rdm2, grad_elec_dferi,
grad_elec_auxresponse_dferi)
from pyscf.mcscf.addons import StateAverageMCSCFSolver
[docs]
def grad_elec(mc_grad, mo_coeff=None, ci=None, atmlst=None, verbose=None):
mc = mc_grad.base
with_df = mc.with_df
if mo_coeff is None: mo_coeff = mc.mo_coeff
if ci is None: ci = mc.ci
if mc.frozen is not None:
raise NotImplementedError
time0 = logger.process_clock(), logger.perf_counter()
log = logger.new_logger(mc_grad, verbose)
mol = mc_grad.mol
ncore = mc.ncore
ncas = mc.ncas
nocc = ncore + ncas
nelecas = mc.nelecas
nao, nmo = mo_coeff.shape
# Necessary kludge because gfock isn't zero in occ-virt space in SA-CASSCf
# Among many other potential applications!
if hasattr (mc, '_tag_gfock_ov_nonzero'):
if mc._tag_gfock_ov_nonzero:
nocc = nmo
mo_occ = mo_coeff[:,:nocc]
mo_core = mo_coeff[:,:ncore]
mo_cas = mo_coeff[:,ncore:ncore+ncas]
casdm1, casdm2 = mc.fcisolver.make_rdm12(ci, ncas, nelecas)
# gfock = Generalized Fock, Adv. Chem. Phys., 69, 63
dm_core = numpy.dot(mo_core, mo_core.T) * 2
dm_cas = reduce(numpy.dot, (mo_cas, casdm1, mo_cas.T))
# MRH flag: this is one of my kludges
# It would be better to just pass the ERIS object used in orbital optimization
# But I am too lazy at the moment
aapa = with_df.ao2mo ((mo_cas, mo_cas, mo_occ, mo_cas), compact=False)
aapa = aapa.reshape(ncas,ncas,nocc,ncas)
vj, vk = mc._scf.get_jk(mol, (dm_core, dm_cas))
h1 = mc.get_hcore()
vhf_c = vj[0] - vk[0] * .5
vhf_a = vj[1] - vk[1] * .5
gfock = numpy.zeros ((nocc, nocc))
gfock[:,:ncore] = reduce(numpy.dot, (mo_occ.T, h1 + vhf_c + vhf_a, mo_core)) * 2
gfock[:,ncore:ncore+ncas] = reduce(numpy.dot, (mo_occ.T, h1 + vhf_c, mo_cas, casdm1))
gfock[:,ncore:ncore+ncas] += numpy.einsum('uviw,vuwt->it', aapa, casdm2)
dme0 = reduce(numpy.dot, (mo_occ, (gfock+gfock.T)*.5, mo_occ.T))
aapa = vj = vk = vhf_c = vhf_a = h1 = gfock = None
dm1 = dm_core + dm_cas
vj, vk = mc_grad.get_jk(mol, (dm_core, dm_cas))
vhf1c, vhf1a = vj - vk * .5
hcore_deriv = mc_grad.hcore_generator(mol)
s1 = mc_grad.get_ovlp(mol)
dfcasdm2 = casdm2 = solve_df_rdm2 (mc_grad, mo_cas=mo_cas, casdm2=casdm2)
if atmlst is None:
atmlst = range(mol.natm)
aoslices = mol.aoslice_by_atom()
de = grad_elec_dferi (mc_grad, mo_cas=mo_cas, dfcasdm2=dfcasdm2, atmlst=atmlst,
max_memory=mc_grad.max_memory)[0]
if mc_grad.auxbasis_response:
de_aux = vj.aux - vk.aux * .5
de_aux = de_aux.sum ((0,1)) - de_aux[1,1]
de_aux += grad_elec_auxresponse_dferi (mc_grad, mo_cas=mo_cas, dfcasdm2=dfcasdm2,
atmlst=atmlst, max_memory=mc_grad.max_memory)[0]
de += de_aux
dfcasdm2 = casdm2 = None
for k, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
h1ao = hcore_deriv(ia)
de[k] += numpy.einsum('xij,ij->x', h1ao, dm1)
de[k] -= numpy.einsum('xij,ij->x', s1[:,p0:p1], dme0[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1c[:,p0:p1], dm1[p0:p1]) * 2
de[k] += numpy.einsum('xij,ij->x', vhf1a[:,p0:p1], dm_core[p0:p1]) * 2
log.timer('CASSCF nuclear gradients', *time0)
return de
[docs]
def as_scanner(mcscf_grad):
'''Generating a nuclear gradients scanner/solver (for geometry optimizer).
The returned solver is a function. This function requires one argument
"mol" as input and returns energy and first order nuclear derivatives.
The solver will automatically use the results of last calculation as the
initial guess of the new calculation. All parameters assigned in the
nuc-grad object and 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, mcscf
>>> mol = gto.M(atom='N 0 0 0; N 0 0 1.1', verbose=0)
>>> mc_grad_scanner = mcscf.CASSCF(scf.RHF(mol), 4, 4).nuc_grad_method().as_scanner()
>>> etot, grad = mc_grad_scanner(gto.M(atom='N 0 0 0; N 0 0 1.1'))
>>> etot, grad = mc_grad_scanner(gto.M(atom='N 0 0 0; N 0 0 1.5'))
'''
if isinstance(mcscf_grad, lib.GradScanner):
return mcscf_grad
logger.info(mcscf_grad, 'Create scanner for %s', mcscf_grad.__class__)
name = mcscf_grad.__class__.__name__ + CASSCF_GradScanner.__name_mixin__
return lib.set_class(CASSCF_GradScanner(mcscf_grad),
(CASSCF_GradScanner, mcscf_grad.__class__), name)
[docs]
class CASSCF_GradScanner(lib.GradScanner):
def __init__(self, g):
lib.GradScanner.__init__(self, g)
def __call__(self, mol_or_geom, **kwargs):
if isinstance(mol_or_geom, gto.MoleBase):
assert mol_or_geom.__class__ == gto.Mole
mol = mol_or_geom
else:
mol = self.mol.set_geom_(mol_or_geom, inplace=False)
mc_scanner = self.base
e_tot = mc_scanner(mol)
if isinstance(mc_scanner, StateAverageMCSCFSolver):
e_tot = mc_scanner.e_average
self.mol = mol
de = self.kernel(**kwargs)
return e_tot, de
[docs]
class Gradients(casci_grad.Gradients):
'''Non-relativistic restricted Hartree-Fock gradients'''
_keys = {'with_df', 'auxbasis_response'}
def __init__(self, mc):
self.with_df = mc.with_df
self.auxbasis_response = True
casci_grad.Gradients.__init__(self, mc)
grad_elec = grad_elec
[docs]
def get_jk (self, mol=None, dm=None, hermi=0):
if mol is None: mol = self.mol
if dm is None: dm = self.base.make_rdm1()
cpu0 = (logger.process_clock(), logger.perf_counter())
vj, vk = dfrhf_grad.get_jk(self, mol, dm)
logger.timer(self, 'vj and vk', *cpu0)
return vj, vk
[docs]
def kernel (self, mo_coeff=None, ci=None, atmlst=None, verbose=None):
log = logger.new_logger(self, verbose)
if atmlst is None:
atmlst = self.atmlst
else:
self.atmlst = atmlst
if self.verbose >= logger.WARN:
self.check_sanity()
if self.verbose >= logger.INFO:
self.dump_flags()
de = self.grad_elec(mo_coeff, ci, atmlst, log)
self.de = de = de + self.grad_nuc(atmlst=atmlst)
if self.mol.symmetry:
self.de = self.symmetrize(self.de, atmlst)
self._finalize()
return self.de
def _finalize(self):
if self.verbose >= logger.NOTE:
logger.note(self, '--------------- %s gradients ---------------',
self.base.__class__.__name__)
self._write(self.mol, self.de, self.atmlst)
logger.note(self, '----------------------------------------------')
as_scanner = as_scanner
Grad = Gradients
#from pyscf import mcscf
#mcscf.mc1step.CASSCF.Gradients = lib.class_as_method(Gradients)
if __name__ == '__main__':
from pyscf import scf
from pyscf import mcscf
from pyscf import df
#from pyscf.grad import numeric
mol = gto.Mole()
mol.atom = 'N 0 0 0; N 0 0 1.2; H 1 1 0; H 1 1 1.2'
mol.basis = '631g'
mol.build()
aux = df.aug_etb (mol)
mf = scf.RHF(mol).density_fit (auxbasis=aux).run()
mc = mcscf.CASSCF(mf, 4, 4).run()
mc.conv_tol = 1e-10
de = Gradients (mc).kernel()
#de_num = numeric.Gradients (mc).kernel ()
#print(lib.finger(de) - 0.019602220578635747)
#print(lib.finger(de) - lib.finger (de_num))
mol = gto.Mole()
mol.verbose = 0
mol.atom = 'N 0 0 0; N 0 0 1.2'
mol.basis = 'sto3g'
mol.build()
mf = scf.RHF(mol).density_fit (auxbasis=aux).run()
mc = mcscf.CASSCF(mf, 4, 4)
mc.conv_tol = 1e-10
mc.kernel ()
de = Gradients (mc).kernel()
mcs = mc.as_scanner()
mol.set_geom_('N 0 0 0; N 0 0 1.201')
e1 = mcs(mol)
mol.set_geom_('N 0 0 0; N 0 0 1.199')
e2 = mcs(mol)
print(de[1,2], (e1-e2)/0.002*lib.param.BOHR)