#!/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>
#
# Ref:
# Chem Phys Lett, 256, 454
# J. Mol. Struct. THEOCHEM, 914, 3
# Recent Advances in Density Functional Methods, Chapter 5, M. E. Casida
#
from functools import reduce
import numpy
from pyscf import lib
from pyscf import scf
from pyscf import ao2mo
from pyscf import symm
from pyscf.lib import logger
from pyscf.tdscf import rhf
from pyscf.tdscf._lr_eig import eigh as lr_eigh, eig as lr_eig
from pyscf.scf import ghf_symm
from pyscf import __config__
OUTPUT_THRESHOLD = getattr(__config__, 'tdscf_rhf_get_nto_threshold', 0.3)
REAL_EIG_THRESHOLD = getattr(__config__, 'tdscf_rhf_TDDFT_pick_eig_threshold', 1e-4)
[docs]
def gen_tda_operation(mf, fock_ao=None, wfnsym=None):
'''A x
Kwargs:
wfnsym : int or str
Point group symmetry irrep symbol or ID for excited CIS wavefunction.
'''
mol = mf.mol
mo_coeff = mf.mo_coeff
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
sym_forbid = _get_x_sym_table(mf) != wfnsym
if fock_ao is None:
e_ia = hdiag = mo_energy[viridx] - mo_energy[occidx,None]
else:
fock = reduce(numpy.dot, (mo_coeff.conj().T, fock_ao, mo_coeff))
foo = fock[occidx[:,None],occidx]
fvv = fock[viridx[:,None],viridx]
hdiag = fvv.diagonal() - foo.diagonal()[:,None]
if wfnsym is not None and mol.symmetry:
hdiag[sym_forbid] = 0
hdiag = hdiag.ravel().real
mo_coeff = numpy.asarray(numpy.hstack((orbo,orbv)), order='F')
vresp = mf.gen_response(hermi=0)
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, orbv.conj(), orbo)
v1ao = vresp(dmov)
v1ov = lib.einsum('xpq,po,qv->xov', v1ao, orbo.conj(), orbv)
if fock_ao is None:
v1ov += numpy.einsum('xia,ia->xia', zs, e_ia)
else:
v1ov += lib.einsum('xqs,sp->xqp', zs, fvv)
v1ov -= lib.einsum('xpr,sp->xsr', zs, foo)
if wfnsym is not None and mol.symmetry:
v1ov[:,sym_forbid] = 0
return v1ov.reshape(v1ov.shape[0],-1)
return vind, hdiag
gen_tda_hop = gen_tda_operation
def _get_x_sym_table(mf):
'''Irrep (up to D2h symmetry) of each coefficient in X[nocc,nvir]'''
mol = mf.mol
mo_occ = mf.mo_occ
orbsym = ghf_symm.get_orbsym(mol, mf.mo_coeff)
orbsym = numpy.asarray(orbsym) % 10 # convert to D2h irreps
return orbsym[mo_occ==1,None] ^ orbsym[mo_occ==0]
[docs]
def get_ab(mf, mo_energy=None, mo_coeff=None, mo_occ=None):
r'''A and B matrices for TDDFT response function.
A[i,a,j,b] = \delta_{ab}\delta_{ij}(E_a - E_i) + (ia||bj)
B[i,a,j,b] = (ia||jb)
'''
if mo_energy is None: mo_energy = mf.mo_energy
if mo_coeff is None: mo_coeff = mf.mo_coeff
if mo_occ is None: mo_occ = mf.mo_occ
mol = mf.mol
nmo = mo_occ.size
nao = mol.nao
occidx = numpy.where(mo_occ==1)[0]
viridx = numpy.where(mo_occ==0)[0]
orbv = mo_coeff[:,viridx]
orbo = mo_coeff[:,occidx]
nvir = orbv.shape[1]
nocc = orbo.shape[1]
mo = numpy.hstack((orbo,orbv))
moa = mo[:nao].copy()
mob = mo[nao:].copy()
orboa = orbo[:nao]
orbob = orbo[nao:]
nmo = nocc + nvir
e_ia = lib.direct_sum('a-i->ia', mo_energy[viridx], mo_energy[occidx])
a = numpy.diag(e_ia.ravel()).reshape(nocc,nvir,nocc,nvir).astype(mo_coeff.dtype)
b = numpy.zeros_like(a)
def add_hf_(a, b, hyb=1):
if mo_coeff.dtype == numpy.double:
eri_mo = ao2mo.general(mol, [orboa,moa,moa,moa], compact=False)
eri_mo += ao2mo.general(mol, [orbob,mob,mob,mob], compact=False)
eri_mo += ao2mo.general(mol, [orboa,moa,mob,mob], compact=False)
eri_mo += ao2mo.general(mol, [orbob,mob,moa,moa], compact=False)
eri_mo = eri_mo.reshape(nocc,nmo,nmo,nmo)
else:
eri_ao = mol.intor('int2e').reshape([nao]*4)
eri_mo_a = lib.einsum('pqrs,pi,qj->ijrs', eri_ao, orboa.conj(), moa)
eri_mo_a+= lib.einsum('pqrs,pi,qj->ijrs', eri_ao, orbob.conj(), mob)
eri_mo = lib.einsum('ijrs,rk,sl->ijkl', eri_mo_a, moa.conj(), moa)
eri_mo+= lib.einsum('ijrs,rk,sl->ijkl', eri_mo_a, mob.conj(), mob)
a += numpy.einsum('iabj->iajb', eri_mo[:nocc,nocc:,nocc:,:nocc])
a -= numpy.einsum('ijba->iajb', eri_mo[:nocc,:nocc,nocc:,nocc:]) * hyb
b += numpy.einsum('iajb->iajb', eri_mo[:nocc,nocc:,:nocc,nocc:])
b -= numpy.einsum('jaib->iajb', eri_mo[:nocc,nocc:,:nocc,nocc:]) * hyb
return a, b
if isinstance(mf, scf.hf.KohnShamDFT):
from pyscf.dft import xc_deriv
ni = mf._numint
ni.libxc.test_deriv_order(mf.xc, 2, raise_error=True)
if mf.do_nlc():
raise NotImplementedError('DKS-TDDFT NLC functional')
if not mf.collinear:
raise NotImplementedError
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, mol.spin)
assert omega == 0.
a, b = add_hf_(a, b, hyb)
if ni.collinear[0] == 'm': # mcol
a = a.astype(numpy.complex128)
b = b.astype(numpy.complex128)
xctype = ni._xc_type(mf.xc)
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.8-mem_now)
def get_mo_value(ao):
if ao.ndim == 2:
mo_a = lib.einsum('rp,pi->ri', ao, moa)
mo_b = lib.einsum('rp,pi->ri', ao, mob)
return mo_a[:,:nocc], mo_a[:,nocc:], mo_b[:,:nocc], mo_b[:,nocc:]
else:
mo_a = lib.einsum('xrp,pi->xri', ao, moa)
mo_b = lib.einsum('xrp,pi->xri', ao, mob)
return mo_a[:,:,:nocc], mo_a[:,:,nocc:], mo_b[:,:,:nocc], mo_b[:,:,nocc:]
def ud2tm(aa, ab, ba, bb):
return numpy.stack([aa + bb, # rho
ba + ab, # mx
(ba - ab) * 1j, # my
aa - bb]) # mz
if xctype == 'LDA':
ao_deriv = 0
for ao, mask, weight, coords \
in ni.block_loop(mol, mf.grids, nao, ao_deriv, max_memory):
if ni.collinear[0] == 'm':
rho = ni.eval_rho(mol, ao, dm0, mask, xctype, hermi=1, with_lapl=False)
eval_xc = ni.mcfun_eval_xc_adapter(mf.xc)
fxc = eval_xc(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = weight * fxc.reshape(4,4,-1)
wr, wmx, wmy, wmz = weight * fxc.reshape(4,4,-1)
mo_oa, mo_va, mo_ob, mo_vb = get_mo_value(ao)
rho_ov_aa = numpy.einsum('ri,ra->ria', mo_oa.conj(), mo_va)
rho_ov_ab = numpy.einsum('ri,ra->ria', mo_oa.conj(), mo_vb)
rho_ov_ba = numpy.einsum('ri,ra->ria', mo_ob.conj(), mo_va)
rho_ov_bb = numpy.einsum('ri,ra->ria', mo_ob.conj(), mo_vb)
rho_ov = ud2tm(rho_ov_aa, rho_ov_ab, rho_ov_ba, rho_ov_bb)
rho_vo = rho_ov.conj()
w_ov = numpy.einsum('tsr,tria->sria', wfxc, rho_ov)
a += lib.einsum('sria,srjb->iajb', w_ov, rho_vo)
b += lib.einsum('sria,srjb->iajb', w_ov, rho_ov)
elif ni.collinear[0] == 'c':
rho = ni.eval_rho(mol, ao, dm0, mask, xctype, hermi=1, with_lapl=False)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2)[2]
wv_a, wv_b = weight * fxc.reshape(2,2,-1)
mo_oa, mo_va, mo_ob, mo_vb = get_mo_value(ao)
rho_ov_a = numpy.einsum('ri,ra->ria', mo_oa.conj(), mo_va)
rho_ov_b = numpy.einsum('ri,ra->ria', mo_ob.conj(), mo_vb)
rho_vo_a = rho_ov_a.conj()
rho_vo_b = rho_ov_b.conj()
w_ov = wv_a[:,:,None,None] * rho_ov_a
w_ov += wv_b[:,:,None,None] * rho_ov_b
wa_ov, wb_ov = w_ov
a += lib.einsum('ria,rjb->iajb', wa_ov, rho_vo_a)
a += lib.einsum('ria,rjb->iajb', wb_ov, rho_vo_b)
b += lib.einsum('ria,rjb->iajb', wa_ov, rho_ov_a)
b += lib.einsum('ria,rjb->iajb', wb_ov, rho_ov_b)
else:
raise NotImplementedError(ni.collinear)
elif xctype == 'GGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, mf.grids, nao, ao_deriv, max_memory):
if ni.collinear[0] == 'm':
rho = ni.eval_rho(mol, ao, dm0, mask, xctype, hermi=1, with_lapl=False)
eval_xc = ni.mcfun_eval_xc_adapter(mf.xc)
fxc = eval_xc(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = weight * fxc
wr, wmx, wmy, wmz = weight * fxc
mo_oa, mo_va, mo_ob, mo_vb = get_mo_value(ao)
rho_ov_aa = numpy.einsum('ri,xra->xria', mo_oa[0].conj(), mo_va)
rho_ov_ab = numpy.einsum('ri,xra->xria', mo_oa[0].conj(), mo_vb)
rho_ov_ba = numpy.einsum('ri,xra->xria', mo_ob[0].conj(), mo_va)
rho_ov_bb = numpy.einsum('ri,xra->xria', mo_ob[0].conj(), mo_vb)
rho_ov_aa[1:4] += numpy.einsum('xri,ra->xria', mo_oa[1:4].conj(), mo_va[0])
rho_ov_ab[1:4] += numpy.einsum('xri,ra->xria', mo_oa[1:4].conj(), mo_vb[0])
rho_ov_ba[1:4] += numpy.einsum('xri,ra->xria', mo_ob[1:4].conj(), mo_va[0])
rho_ov_bb[1:4] += numpy.einsum('xri,ra->xria', mo_ob[1:4].conj(), mo_vb[0])
rho_ov = ud2tm(rho_ov_aa, rho_ov_ab, rho_ov_ba, rho_ov_bb)
rho_vo = rho_ov.conj()
w_ov = numpy.einsum('txsyr,txria->syria', wfxc, rho_ov)
a += lib.einsum('syria,syrjb->iajb', w_ov, rho_vo)
b += lib.einsum('syria,syrjb->iajb', w_ov, rho_ov)
elif ni.collinear[0] == 'c':
rho = ni.eval_rho(mol, ao, dm0, mask, xctype, hermi=1, with_lapl=False)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2)[2]
wv_a, wv_b = weight * fxc
mo_oa, mo_va, mo_ob, mo_vb = get_mo_value(ao)
rho_ov_a = numpy.einsum('xri,ra->xria', mo_oa.conj(), mo_va[0])
rho_ov_b = numpy.einsum('xri,ra->xria', mo_ob.conj(), mo_vb[0])
rho_ov_a[1:4] += numpy.einsum('ri,xra->xria', mo_oa[0].conj(), mo_va[1:4])
rho_ov_b[1:4] += numpy.einsum('ri,xra->xria', mo_ob[0].conj(), mo_vb[1:4])
rho_vo_a = rho_ov_a.conj()
rho_vo_b = rho_ov_b.conj()
w_ov = numpy.einsum('xsyr,xria->syria', wv_a, rho_ov_a)
w_ov += numpy.einsum('xsyr,xria->syria', wv_b, rho_ov_b)
wa_ov, wb_ov = w_ov
a += lib.einsum('xria,xrjb->iajb', wa_ov, rho_vo_a)
a += lib.einsum('xria,xrjb->iajb', wb_ov, rho_vo_b)
b += lib.einsum('xria,xrjb->iajb', wa_ov, rho_ov_a)
b += lib.einsum('xria,xrjb->iajb', wb_ov, rho_ov_b)
else:
raise NotImplementedError(ni.collinear)
elif xctype == 'HF':
pass
elif xctype == 'NLC':
raise NotImplementedError('NLC')
elif xctype == 'MGGA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, mf.grids, nao, ao_deriv, max_memory):
if ni.collinear[0] == 'm':
rho = ni.eval_rho(mol, ao, dm0, mask, xctype, hermi=1, with_lapl=False)
eval_xc = ni.mcfun_eval_xc_adapter(mf.xc)
fxc = eval_xc(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = weight * fxc
wr, wmx, wmy, wmz = weight * fxc
mo_oa, mo_va, mo_ob, mo_vb = get_mo_value(ao)
rho_ov_aa = numpy.einsum('ri,xra->xria', mo_oa[0].conj(), mo_va)
rho_ov_ab = numpy.einsum('ri,xra->xria', mo_oa[0].conj(), mo_vb)
rho_ov_ba = numpy.einsum('ri,xra->xria', mo_ob[0].conj(), mo_va)
rho_ov_bb = numpy.einsum('ri,xra->xria', mo_ob[0].conj(), mo_vb)
rho_ov_aa[1:4] += numpy.einsum('xri,ra->xria', mo_oa[1:4].conj(), mo_va[0])
rho_ov_ab[1:4] += numpy.einsum('xri,ra->xria', mo_oa[1:4].conj(), mo_vb[0])
rho_ov_ba[1:4] += numpy.einsum('xri,ra->xria', mo_ob[1:4].conj(), mo_va[0])
rho_ov_bb[1:4] += numpy.einsum('xri,ra->xria', mo_ob[1:4].conj(), mo_vb[0])
tau_ov_aa = numpy.einsum('xri,xra->ria', mo_oa[1:4].conj(), mo_va[1:4]) * .5
tau_ov_ab = numpy.einsum('xri,xra->ria', mo_oa[1:4].conj(), mo_vb[1:4]) * .5
tau_ov_ba = numpy.einsum('xri,xra->ria', mo_ob[1:4].conj(), mo_va[1:4]) * .5
tau_ov_bb = numpy.einsum('xri,xra->ria', mo_ob[1:4].conj(), mo_vb[1:4]) * .5
rho_ov_aa = numpy.vstack([rho_ov_aa, tau_ov_aa[numpy.newaxis]])
rho_ov_ab = numpy.vstack([rho_ov_ab, tau_ov_ab[numpy.newaxis]])
rho_ov_ba = numpy.vstack([rho_ov_ba, tau_ov_ba[numpy.newaxis]])
rho_ov_bb = numpy.vstack([rho_ov_bb, tau_ov_bb[numpy.newaxis]])
rho_ov = ud2tm(rho_ov_aa, rho_ov_ab, rho_ov_ba, rho_ov_bb)
rho_vo = rho_ov.conj()
w_ov = numpy.einsum('txsyr,txria->syria', wfxc, rho_ov)
a += lib.einsum('syria,syrjb->iajb', w_ov, rho_vo)
b += lib.einsum('syria,syrjb->iajb', w_ov, rho_ov)
elif ni.collinear[0] == 'c':
rho = ni.eval_rho(mol, ao, dm0, mask, xctype, hermi=1, with_lapl=False)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2)[2]
wv_a, wv_b = weight * fxc
mo_oa, mo_va, mo_ob, mo_vb = get_mo_value(ao)
rho_ov_a = numpy.einsum('xri,ra->xria', mo_oa.conj(), mo_va[0])
rho_ov_b = numpy.einsum('xri,ra->xria', mo_ob.conj(), mo_vb[0])
rho_ov_a[1:4] += numpy.einsum('ri,xra->xria', mo_oa[0].conj(), mo_va[1:4])
rho_ov_b[1:4] += numpy.einsum('ri,xra->xria', mo_ob[0].conj(), mo_vb[1:4])
tau_ov_a = numpy.einsum('xri,xra->ria', mo_oa[1:4].conj(), mo_va[1:4]) * .5
tau_ov_b = numpy.einsum('xri,xra->ria', mo_ob[1:4].conj(), mo_vb[1:4]) * .5
rho_ov_a = numpy.vstack([rho_ov_a, tau_ov_a[numpy.newaxis]])
rho_ov_b = numpy.vstack([rho_ov_b, tau_ov_b[numpy.newaxis]])
rho_vo_a = rho_ov_a.conj()
rho_vo_b = rho_ov_b.conj()
w_ov = numpy.einsum('xsyr,xria->syria', wv_a, rho_ov_a)
w_ov += numpy.einsum('xsyr,xria->syria', wv_b, rho_ov_b)
wa_ov, wb_ov = w_ov
a += lib.einsum('xria,xrjb->iajb', wa_ov, rho_vo_a)
a += lib.einsum('xria,xrjb->iajb', wb_ov, rho_vo_b)
b += lib.einsum('xria,xrjb->iajb', wa_ov, rho_ov_a)
b += lib.einsum('xria,xrjb->iajb', wb_ov, rho_ov_b)
else:
raise NotImplementedError(ni.collinear)
else:
a, b = add_hf_(a, b)
return a, b
[docs]
def get_nto(tdobj, state=1, threshold=OUTPUT_THRESHOLD, verbose=None):
raise NotImplementedError('get_nto')
[docs]
def analyze(tdobj, verbose=None):
raise NotImplementedError('analyze')
def _contract_multipole(tdobj, ints, hermi=True, xy=None):
raise NotImplementedError
[docs]
class TDBase(rhf.TDBase):
[docs]
@lib.with_doc(get_ab.__doc__)
def get_ab(self, mf=None):
if mf is None: mf = self._scf
return get_ab(mf)
analyze = analyze
get_nto = get_nto
_contract_multipole = _contract_multipole # needed by transition dipoles
[docs]
def nuc_grad_method(self):
raise NotImplementedError
[docs]
@lib.with_doc(rhf.TDA.__doc__)
class TDA(TDBase):
singlet = None
[docs]
def gen_vind(self, mf=None):
'''Generate function to compute Ax'''
if mf is None:
mf = self._scf
return gen_tda_hop(mf, wfnsym=self.wfnsym)
[docs]
def init_guess(self, mf, nstates=None, wfnsym=None, return_symmetry=False):
if nstates is None: nstates = self.nstates
if wfnsym is None: wfnsym = self.wfnsym
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
occidx = numpy.where(mo_occ==1)[0]
viridx = numpy.where(mo_occ==0)[0]
e_ia = (mo_energy[viridx] - mo_energy[occidx,None]).ravel()
nov = e_ia.size
nstates = min(nstates, nov)
if (wfnsym is not None or return_symmetry) and mf.mol.symmetry:
x_sym = _get_x_sym_table(mf).ravel()
if wfnsym is not None:
if isinstance(wfnsym, str):
wfnsym = symm.irrep_name2id(mf.mol.groupname, wfnsym)
wfnsym = wfnsym % 10 # convert to D2h subgroup
e_ia[x_sym != wfnsym] = 1e99
nov_allowed = numpy.count_nonzero(x_sym == wfnsym)
nstates = min(nstates, nov_allowed)
e_threshold = numpy.partition(e_ia, nstates-1)[nstates-1]
e_threshold += self.deg_eia_thresh
idx = numpy.where(e_ia <= e_threshold)[0]
x0 = numpy.zeros((idx.size, nov))
for i, j in enumerate(idx):
x0[i, j] = 1 # Koopmans' excitations
if return_symmetry:
if mf.mol.symmetry:
x0sym = x_sym[idx]
else:
x0sym = None
return x0, x0sym
else:
return x0
[docs]
def kernel(self, x0=None, nstates=None):
'''TDA diagonalization solver
'''
cpu0 = (logger.process_clock(), logger.perf_counter())
self.check_sanity()
self.dump_flags()
if nstates is None:
nstates = self.nstates
else:
self.nstates = nstates
mol = self.mol
log = 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 = _get_x_sym_table(self._scf).ravel()
x0sym = [rhf._guess_wfnsym_id(self, x_sym, x) for x in x0]
self.converged, self.e, 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)
nocc = (self._scf.mo_occ>0).sum()
nmo = self._scf.mo_occ.size
nvir = nmo - nocc
self.xy = [(xi.reshape(nocc,nvir), 0) for xi in x1]
if self.chkfile:
lib.chkfile.save(self.chkfile, 'tddft/e', self.e)
lib.chkfile.save(self.chkfile, 'tddft/xy', self.xy)
log.timer('TDA', *cpu0)
self._finalize()
return self.e, self.xy
CIS = TDA
[docs]
def gen_tdhf_operation(mf, fock_ao=None, wfnsym=None):
'''Generate function to compute
[ A B ][X]
[-B* -A*][Y]
'''
mol = mf.mol
mo_coeff = mf.mo_coeff
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
sym_forbid = _get_x_sym_table(mf) != wfnsym
assert fock_ao is None
e_ia = hdiag = mo_energy[viridx] - mo_energy[occidx,None]
if wfnsym is not None and mol.symmetry:
hdiag[sym_forbid] = 0
hdiag = numpy.hstack((hdiag.ravel(), -hdiag.ravel())).real
mo_coeff = numpy.asarray(numpy.hstack((orbo,orbv)), order='F')
vresp = mf.gen_response(hermi=0)
def vind(xys):
xys = numpy.asarray(xys).reshape(-1,2,nocc,nvir)
if wfnsym is not None and mol.symmetry:
# shape(nz,2,nocc,nvir): 2 ~ X,Y
xys = numpy.copy(xys)
xys[:,:,sym_forbid] = 0
xs, ys = xys.transpose(1,0,2,3)
dms = lib.einsum('xov,qv,po->xpq', xs, orbv.conj(), orbo)
dms += lib.einsum('xov,pv,qo->xpq', ys, orbv, orbo.conj())
v1ao = vresp(dms) # = <mb||nj> Xjb + <mj||nb> Yjb
# A ~= <ib||aj>, B = <ij||ab>
# AX + BY
# = <ib||aj> Xjb + <ij||ab> Yjb
# = (<mb||nj> Xjb + <mj||nb> Yjb) Cmi* Cna
v1ov = lib.einsum('xpq,po,qv->xov', v1ao, orbo.conj(), orbv)
# (B*)X + (A*)Y
# = <ab||ij> Xjb + <aj||ib> Yjb
# = (<mb||nj> Xjb + <mj||nb> Yjb) Cma* Cni
v1vo = lib.einsum('xpq,qo,pv->xov', v1ao, orbo, orbv.conj())
v1ov += numpy.einsum('xia,ia->xia', xs, e_ia) # AX
v1vo += numpy.einsum('xia,ia->xia', ys, e_ia.conj()) # (A*)Y
if wfnsym is not None and mol.symmetry:
v1ov[:,sym_forbid] = 0
v1vo[:,sym_forbid] = 0
# (AX, (-A*)Y)
nz = xys.shape[0]
hx = numpy.hstack((v1ov.reshape(nz,-1), -v1vo.reshape(nz,-1)))
return hx
return vind, hdiag
[docs]
class TDHF(TDBase):
singlet = None
[docs]
@lib.with_doc(gen_tdhf_operation.__doc__)
def gen_vind(self, mf=None):
if mf is None:
mf = self._scf
return gen_tdhf_operation(mf, wfnsym=self.wfnsym)
[docs]
def init_guess(self, mf, nstates=None, wfnsym=None, return_symmetry=False):
if return_symmetry:
x0, x0sym = TDA.init_guess(self, mf, nstates, wfnsym, return_symmetry)
y0 = numpy.zeros_like(x0)
return numpy.hstack([x0, y0]), x0sym
else:
x0 = TDA.init_guess(self, mf, nstates, wfnsym, return_symmetry)
y0 = numpy.zeros_like(x0)
return numpy.hstack([x0, y0])
[docs]
def kernel(self, x0=None, nstates=None):
'''TDHF diagonalization with non-Hermitian eigenvalue solver
'''
cpu0 = (logger.process_clock(), logger.perf_counter())
self.check_sanity()
self.dump_flags()
if nstates is None:
nstates = self.nstates
else:
self.nstates = nstates
mol = self.mol
log = logger.Logger(self.stdout, self.verbose)
vind, hdiag = self.gen_vind(self._scf)
precond = self.get_precond(hdiag)
ensure_real = self._scf.mo_coeff.dtype == numpy.double
def pickeig(w, v, nroots, envs):
realidx = numpy.where((abs(w.imag) < REAL_EIG_THRESHOLD) &
(w.real > self.positive_eig_threshold))[0]
# FIXME: Should the amplitudes be real? It also affects x2c-tdscf
return lib.linalg_helper._eigs_cmplx2real(w, v, realidx, ensure_real)
x0sym = None
if x0 is None:
x0, x0sym = self.init_guess(
self._scf, self.nstates, return_symmetry=True)
elif mol.symmetry:
x_sym = y_sym = _get_x_sym_table(self._scf).ravel()
x_sym = numpy.append(x_sym, y_sym)
x0sym = [rhf._guess_wfnsym_id(self, x_sym, x) for x in x0]
self.converged, w, x1 = lr_eig(
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)
nocc = (self._scf.mo_occ>0).sum()
nmo = self._scf.mo_occ.size
nvir = nmo - nocc
self.e = w
def norm_xy(z):
x, y = z.reshape(2,nocc,nvir)
norm = lib.norm(x)**2 - lib.norm(y)**2
norm = numpy.sqrt(1./norm)
return x*norm, y*norm
self.xy = [norm_xy(z) for z in x1]
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
RPA = TDGHF = TDHF
scf.ghf.GHF.TDA = lib.class_as_method(TDA)
scf.ghf.GHF.TDHF = lib.class_as_method(TDHF)
