#!/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>
#
# Ref:
# Chem Phys Lett, 256, 454
# J. Mol. Struct. THEOCHEM, 914, 3
#
import numpy
from pyscf import lib
from pyscf import symm
from pyscf.tdscf import rhf
from pyscf.tdscf._lr_eig import eigh as lr_eigh
from pyscf.dft.rks import KohnShamDFT
from pyscf import __config__
[docs]
class TDA(rhf.TDA):
[docs]
def nuc_grad_method(self):
from pyscf.grad import tdrks
return tdrks.Gradients(self)
[docs]
class TDDFT(rhf.TDHF):
[docs]
def nuc_grad_method(self):
from pyscf.grad import tdrks
return tdrks.Gradients(self)
RPA = TDRKS = 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
singlet = self.singlet
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==2)[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
sym_forbid = rhf._get_x_sym_table(mf) != 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(singlet=singlet, hermi=1)
def vind(zs):
zs = numpy.asarray(zs).reshape(-1,nocc,nvir)
# *2 for double occupancy
dmov = lib.einsum('xov,ov,po,qv->xpq', zs, d_ia*2, orbo, orbv.conj())
# +cc for A+B and K_{ai,jb} in A == K_{ai,bj} in B
dmov = dmov + dmov.conj().transpose(0,2,1)
v1ao = vresp(dmov)
v1ov = lib.einsum('xpq,po,qv->xov', v1ao, orbo.conj(), orbv)
# numpy.sqrt(e_ia) * (e_ia*d_ia*z + v1ov)
v1ov += numpy.einsum('xov,ov->xov', zs, ed_ia)
v1ov *= d_ia
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())
mol = self.mol
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
x0sym = None
if x0 is None:
x0, x0sym = self.init_guess(
self._scf, self.nstates, return_symmetry=True)
elif mol.symmetry:
x_sym = rhf._get_x_sym_table(mf).ravel()
x0sym = [rhf._guess_wfnsym_id(self, x_sym, x) for x in x0]
self.converged, w2, x1 = lr_eigh(
vind, x0, precond, tol_residual=self.conv_tol, lindep=self.lindep,
nroots=nstates, x0sym=x0sym, pick=pickeig, max_cycle=self.max_cycle,
max_memory=self.max_memory, verbose=log)
mo_energy = self._scf.mo_energy
mo_occ = self._scf.mo_occ
occidx = numpy.where(mo_occ==2)[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(.5/norm) # normalize to 0.5 for alpha spin
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):
from pyscf.grad import tdrks
return tdrks.Gradients(self)
TDDFTNoHybrid = CasidaTDDFT
[docs]
class dRPA(TDDFTNoHybrid):
def __init__(self, mf):
if not isinstance(mf, KohnShamDFT):
raise RuntimeError("direct RPA can only be applied with DFT; for HF+dRPA, use .xc='hf'")
mf = mf.to_rks()
# commit fc8d1967995b7e033b60d4428ddcca87aac78e4f handles xc='' .
# xc='0*LDA' is equivalent to xc=''
#mf.xc = '0.0*LDA'
mf.xc = ''
TDDFTNoHybrid.__init__(self, mf)
TDH = dRPA
[docs]
class dTDA(TDA):
def __init__(self, mf):
if not isinstance(mf, KohnShamDFT):
raise RuntimeError("direct TDA can only be applied with DFT; for HF+dTDA, use .xc='hf'")
mf = mf.to_rks()
# commit fc8d1967995b7e033b60d4428ddcca87aac78e4f handles xc='' .
# xc='0*LDA' is equivalent to xc=''
#mf.xc = '0.0*LDA'
mf.xc = ''
TDA.__init__(self, mf)
[docs]
def tddft(mf):
'''Driver to create TDDFT or CasidaTDDFT object'''
if mf._numint.libxc.is_hybrid_xc(mf.xc):
return TDDFT(mf)
else:
return CasidaTDDFT(mf)
from pyscf import dft
dft.rks.RKS.TDA = dft.rks_symm.RKS.TDA = lib.class_as_method(TDA)
dft.rks.RKS.TDHF = dft.rks_symm.RKS.TDHF = None
#dft.rks.RKS.TDDFT = dft.rks_symm.RKS.TDDFT = lib.class_as_method(TDDFT)
dft.rks.RKS.TDDFTNoHybrid = dft.rks_symm.RKS.TDDFTNoHybrid = lib.class_as_method(TDDFTNoHybrid)
dft.rks.RKS.CasidaTDDFT = dft.rks_symm.RKS.CasidaTDDFT = lib.class_as_method(CasidaTDDFT)
dft.rks.RKS.TDDFT = dft.rks_symm.RKS.TDDFT = tddft
dft.rks.RKS.dTDA = dft.rks_symm.RKS.dTDA = lib.class_as_method(dTDA)
dft.rks.RKS.dRPA = dft.rks_symm.RKS.dRPA = lib.class_as_method(dRPA)
dft.roks.ROKS.TDA = dft.rks_symm.ROKS.TDA = None
dft.roks.ROKS.TDHF = dft.rks_symm.ROKS.TDHF = None
dft.roks.ROKS.TDDFT = dft.rks_symm.ROKS.TDDFT = None
dft.roks.ROKS.TDDFTNoHybrid = dft.rks_symm.ROKS.TDDFTNoHybrid = None
dft.roks.ROKS.dTDA = dft.rks_symm.ROKS.dTDA = None
dft.roks.ROKS.dRPA = dft.rks_symm.ROKS.dRPA = None
