#!/usr/bin/env python
# Copyright 2021-2022 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>
#
import numpy
from pyscf import lib
from pyscf import symm
from pyscf.tdscf import ghf
from pyscf.scf import ghf_symm
from pyscf.scf import _response_functions # noqa
from pyscf.data import nist
from pyscf.dft.rks import KohnShamDFT
from pyscf import __config__
[docs]
class TDA(ghf.TDA):
pass
[docs]
class TDDFT(ghf.TDHF):
pass
RPA = TDGKS = TDDFT
[docs]
class CasidaTDDFT(TDDFT, TDA):
'''Solve the Casida TDDFT formula (A-B)(A+B)(X+Y) = (X+Y)w^2
'''
init_guess = TDA.init_guess
[docs]
def gen_vind(self, mf=None):
if mf is None:
mf = self._scf
wfnsym = self.wfnsym
mol = mf.mol
mo_coeff = mf.mo_coeff
assert mo_coeff.dtype == numpy.double
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
nao, nmo = mo_coeff.shape
occidx = numpy.where(mo_occ==1)[0]
viridx = numpy.where(mo_occ==0)[0]
nocc = len(occidx)
nvir = len(viridx)
orbv = mo_coeff[:,viridx]
orbo = mo_coeff[:,occidx]
if wfnsym is not None and mol.symmetry:
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mol.groupname, wfnsym)
wfnsym = wfnsym % 10 # convert to D2h subgroup
orbsym = ghf_symm.get_orbsym(mol, mo_coeff)
orbsym_in_d2h = numpy.asarray(orbsym) % 10 # convert to D2h irreps
sym_forbid = (orbsym_in_d2h[occidx,None] ^ orbsym_in_d2h[viridx]) != wfnsym
e_ia = (mo_energy[viridx].reshape(-1,1) - mo_energy[occidx]).T
if wfnsym is not None and mol.symmetry:
e_ia[sym_forbid] = 0
d_ia = numpy.sqrt(e_ia)
ed_ia = e_ia * d_ia
hdiag = e_ia.ravel() ** 2
vresp = mf.gen_response(mo_coeff, mo_occ, hermi=1)
def vind(zs):
zs = numpy.asarray(zs).reshape(-1,nocc,nvir)
if wfnsym is not None and mol.symmetry:
zs = numpy.copy(zs)
zs[:,sym_forbid] = 0
dmov = lib.einsum('xov,qv,po->xpq', zs*d_ia, orbv, orbo)
# +cc for A+B because K_{ai,jb} in A == K_{ai,bj} in B
dmov = dmov + dmov.transpose(0,2,1)
v1ao = vresp(dmov)
v1ov = lib.einsum('xpq,po,qv->xov', v1ao, orbo, orbv)
# numpy.sqrt(e_ia) * (e_ia*d_ia*z + v1ov)
v1ov += numpy.einsum('xov,ov->xov', zs, ed_ia)
v1ov *= d_ia
if wfnsym is not None and mol.symmetry:
v1ov[:,sym_forbid] = 0
return v1ov.reshape(v1ov.shape[0],-1)
return vind, hdiag
[docs]
def kernel(self, x0=None, nstates=None):
'''TDDFT diagonalization solver
'''
cpu0 = (lib.logger.process_clock(), lib.logger.perf_counter())
mf = self._scf
if mf._numint.libxc.is_hybrid_xc(mf.xc):
raise RuntimeError('%s cannot be used with hybrid functional'
% self.__class__)
self.check_sanity()
self.dump_flags()
if nstates is None:
nstates = self.nstates
else:
self.nstates = nstates
log = lib.logger.Logger(self.stdout, self.verbose)
vind, hdiag = self.gen_vind(self._scf)
precond = self.get_precond(hdiag)
def pickeig(w, v, nroots, envs):
idx = numpy.where(w > self.positive_eig_threshold)[0]
return w[idx], v[:,idx], idx
if x0 is None:
x0 = self.init_guess(self._scf, self.nstates)
self.converged, w2, x1 = \
lib.davidson1(vind, x0, precond,
tol=self.conv_tol,
nroots=nstates, lindep=self.lindep,
max_cycle=self.max_cycle,
max_space=self.max_space, pick=pickeig,
verbose=log)
mo_energy = self._scf.mo_energy
mo_occ = self._scf.mo_occ
occidx = numpy.where(mo_occ==1)[0]
viridx = numpy.where(mo_occ==0)[0]
e_ia = (mo_energy[viridx,None] - mo_energy[occidx]).T
e_ia = numpy.sqrt(e_ia)
def norm_xy(w, z):
zp = e_ia * z.reshape(e_ia.shape)
zm = w/e_ia * z.reshape(e_ia.shape)
x = (zp + zm) * .5
y = (zp - zm) * .5
norm = lib.norm(x)**2 - lib.norm(y)**2
norm = numpy.sqrt(1./norm)
return (x*norm, y*norm)
idx = numpy.where(w2 > self.positive_eig_threshold)[0]
self.e = numpy.sqrt(w2[idx])
self.xy = [norm_xy(self.e[i], x1[i]) for i in idx]
if self.chkfile:
lib.chkfile.save(self.chkfile, 'tddft/e', self.e)
lib.chkfile.save(self.chkfile, 'tddft/xy', self.xy)
log.timer('TDDFT', *cpu0)
self._finalize()
return self.e, self.xy
[docs]
def nuc_grad_method(self):
raise NotImplementedError
TDDFTNoHybrid = CasidaTDDFT
[docs]
def tddft(mf):
'''Driver to create TDDFT or CasidaTDDFT object'''
if (not mf._numint.libxc.is_hybrid_xc(mf.xc) and
# Casida formula can be applied for real orbitals only
mf.mo_coeff.dtype == numpy.double and mf.collinear[0] != 'm'):
return CasidaTDDFT(mf)
else:
return TDDFT(mf)
from pyscf import dft
dft.gks.GKS.TDA = dft.gks_symm.GKS.TDA = lib.class_as_method(TDA)
dft.gks.GKS.TDHF = dft.gks_symm.GKS.TDHF = None
dft.gks.GKS.TDDFTNoHybrid = dft.gks_symm.GKS.TDDFTNoHybrid = lib.class_as_method(TDDFTNoHybrid)
dft.gks.GKS.CasidaTDDFT = dft.gks_symm.GKS.CasidaTDDFT = lib.class_as_method(CasidaTDDFT)
dft.gks.GKS.TDDFT = dft.gks_symm.GKS.TDDFT = tddft