#!/usr/bin/env python
# Copyright 2014-2021 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
#
from functools import reduce
import numpy
from pyscf import lib
from pyscf.lib import linalg_helper
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.pbc import scf
from pyscf.pbc.tdscf.rhf import TDBase
from pyscf.pbc.scf import _response_functions # noqa
from pyscf.pbc.lib.kpts_helper import is_gamma_point, get_kconserv_ria, conj_mapping
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
from pyscf.pbc import df as pbcdf
from pyscf.data import nist
from pyscf import __config__
REAL_EIG_THRESHOLD = getattr(__config__, 'pbc_tdscf_rhf_TDDFT_pick_eig_threshold', 1e-3)
[docs]
def get_ab(mf, kshift=0):
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)
Ref: Chem Phys Lett, 256, 454
Kwargs:
kshift : integer
The index of the k-point that represents the transition between
k-points in the excitation coefficients.
'''
cell = mf.cell
mo_energy = scf.addons.mo_energy_with_exxdiv_none(mf)
mo = numpy.asarray(mf.mo_coeff)
mo_occ = numpy.asarray(mf.mo_occ)
kpts = mf.kpts
nkpts, nao, nmo = mo.shape
noccs = numpy.count_nonzero(mo_occ==2, axis=1)
nocc = noccs[0]
nvir = nmo - nocc
assert all(noccs == nocc)
orbo = mo[:,:,:nocc]
orbv = mo[:,:,nocc:]
kconserv = get_kconserv_ria(cell, kpts)[kshift]
e_ia = numpy.asarray(_get_e_ia(mo_energy, mo_occ, kconserv)).astype(mo.dtype)
a = numpy.diag(e_ia.ravel()).reshape(nkpts,nocc,nvir,nkpts,nocc,nvir)
b = numpy.zeros_like(a)
weight = 1./nkpts
def add_hf_(a, b, hyb=1):
eri = mf.with_df.ao2mo_7d([orbo,mo,mo,mo], kpts)
eri *= weight
eri = eri.reshape(nkpts,nkpts,nkpts,nocc,nmo,nmo,nmo)
for ki, ka in enumerate(kconserv):
for kj, kb in enumerate(kconserv):
a[ki,:,:,kj] += numpy.einsum('iabj->iajb', eri[ki,ka,kb,:nocc,nocc:,nocc:,:nocc]) * 2
a[ki,:,:,kj] -= numpy.einsum('ijba->iajb', eri[ki,kj,kb,:nocc,:nocc,nocc:,nocc:]) * hyb
for kb, kj in enumerate(kconserv):
b[ki,:,:,kj] += numpy.einsum('iajb->iajb', eri[ki,ka,kj,:nocc,nocc:,:nocc,nocc:]) * 2
b[ki,:,:,kj] -= numpy.einsum('ibja->iajb', eri[ki,kb,kj,:nocc,nocc:,:nocc,nocc:]) * hyb
if isinstance(mf, scf.hf.KohnShamDFT):
assert kshift == 0
ni = mf._numint
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, cell.spin)
add_hf_(a, b, hyb)
if omega != 0: # For RSH
raise NotImplementedError
xctype = ni._xc_type(mf.xc)
dm0 = mf.make_rdm1(mo, mo_occ)
make_rho = ni._gen_rho_evaluator(cell, dm0, hermi=1, with_lapl=False)[0]
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.8-mem_now)
cmap = conj_mapping(cell, kpts)
if xctype == 'LDA':
ao_deriv = 0
for ao, _, mask, weight, coords \
in ni.block_loop(cell, mf.grids, nao, ao_deriv, kpts, None, max_memory):
rho = make_rho(0, ao, mask, xctype)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = fxc[0,0] * weight
rho_o = lib.einsum('krp,kpi->kri', ao, orbo)
rho_v = lib.einsum('krp,kpi->kri', ao, orbv)
rho_ov = numpy.einsum('kri,kra->kria', rho_o, rho_v)
w_ov = numpy.einsum('kria,r->kria', rho_ov, wfxc) * (2/nkpts)
rho_vo = rho_ov.conj()[cmap]
a += lib.einsum('kria,lrjb->kialjb', w_ov, rho_vo)
b += lib.einsum('kria,lrjb->kialjb', w_ov, rho_ov)
elif xctype == 'GGA':
ao_deriv = 1
for ao, _, mask, weight, coords \
in ni.block_loop(cell, mf.grids, nao, ao_deriv, kpts, None, max_memory):
rho = make_rho(0, ao, mask, xctype)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = fxc * weight
rho_o = lib.einsum('kxrp,kpi->kxri', ao, orbo)
rho_v = lib.einsum('kxrp,kpi->kxri', ao, orbv)
rho_ov = numpy.einsum('kxri,kra->kxria', rho_o, rho_v[:,0])
rho_ov[:,1:4] += numpy.einsum('kri,kxra->kxria', rho_o[:,0], rho_v[:,1:4])
w_ov = numpy.einsum('xyr,kxria->kyria', wfxc, rho_ov) * (2/nkpts)
rho_vo = rho_ov.conj()[cmap]
a += lib.einsum('kxria,lxrjb->kialjb', w_ov, rho_vo)
b += lib.einsum('kxria,lxrjb->kialjb', w_ov, rho_ov)
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(cell, mf.grids, nao, ao_deriv, kpts, None, max_memory):
rho = make_rho(0, ao, mask, xctype)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = fxc * weight
rho_o = lib.einsum('kxrp,kpi->kxri', ao, orbo)
rho_v = lib.einsum('kxrp,kpi->kxri', ao, orbv)
rho_ov = numpy.einsum('kxri,kra->kxria', rho_o, rho_v[:,0])
rho_ov[:,1:4] += numpy.einsum('kri,kxra->kxria', rho_o[:,0], rho_v[:,1:4])
tau_ov = numpy.einsum('kxri,kxra->kria', rho_o[:,1:4], rho_v[:,1:4]) * .5
rho_ov = numpy.concatenate([rho_ov, tau_ov[:,numpy.newaxis]], axis=1)
w_ov = numpy.einsum('xyr,kxria->kyria', wfxc, rho_ov) * (2/nkpts)
rho_vo = rho_ov.conj()[cmap]
a += lib.einsum('kxria,lxrjb->kialjb', w_ov, rho_vo)
b += lib.einsum('kxria,lxrjb->kialjb', w_ov, rho_ov)
else:
add_hf_(a, b)
return a, b
[docs]
class KTDBase(TDBase):
'''
Attributes:
kshift_lst : list of integers
Each element in the list is the index of the k-point that
represents the transition between k-points in the excitation
coefficients.
'''
conv_tol = getattr(__config__, 'pbc_tdscf_rhf_TDA_conv_tol', 1e-4)
_keys = {'kshift_lst'}
def __init__(self, mf, kshift_lst=None):
assert isinstance(mf, scf.khf.KSCF)
TDBase.__init__(self, mf)
warn_pbc2d_eri(mf)
if kshift_lst is None: kshift_lst = [0]
self.kshift_lst = kshift_lst
[docs]
def dump_flags(self, verbose=None):
log = logger.new_logger(self, verbose)
log.info('\n')
log.info('******** %s for %s ********',
self.__class__, self._scf.__class__)
if self.singlet is None:
log.info('nstates = %d', self.nstates)
elif self.singlet:
log.info('nstates = %d singlet', self.nstates)
else:
log.info('nstates = %d triplet', self.nstates)
log.info('deg_eia_thresh = %.3e', self.deg_eia_thresh)
log.info('kshift_lst = %s', self.kshift_lst)
log.info('wfnsym = %s', self.wfnsym)
log.info('conv_tol = %g', self.conv_tol)
log.info('eigh lindep = %g', self.lindep)
log.info('eigh level_shift = %g', self.level_shift)
log.info('eigh max_cycle = %d', self.max_cycle)
log.info('chkfile = %s', self.chkfile)
log.info('max_memory %d MB (current use %d MB)',
self.max_memory, lib.current_memory()[0])
if not self._scf.converged:
log.warn('Ground state SCF is not converged')
log.info('\n')
[docs]
def check_sanity(self):
TDBase.check_sanity(self)
mf = self._scf
if any(k != 0 for k in self.kshift_lst):
if mf.rsjk is not None or not isinstance(mf.with_df, pbcdf.df.DF):
logger.error(self, 'Solutions with non-zero kshift for %s are '
'only supported by GDF/RSDF')
raise NotImplementedError
def _finalize(self):
'''Hook for dumping results and clearing up the object.'''
for k,kshift in enumerate(self.kshift_lst):
if not all(self.converged[k]):
logger.note(self, 'kshift = %d TD-SCF states %s not converged.',
kshift, [i for i, x in enumerate(self.converged[k]) if not x])
logger.note(self, 'kshift = %d Excited State energies (eV)\n%s',
kshift, self.e[k] * nist.HARTREE2EV)
return self
get_nto = lib.invalid_method('get_nto')
[docs]
class TDA(KTDBase):
[docs]
@lib.with_doc(get_ab.__doc__)
def get_ab(self, mf=None, kshift=0):
if mf is None: mf = self._scf
return get_ab(mf, kshift)
[docs]
def gen_vind(self, mf, kshift=0):
'''Compute Ax
Kwargs:
kshift : integer
The index of the k-point that represents the transition between
k-points in the excitation coefficients.
'''
singlet = self.singlet
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ)
nao, nmo = mo_coeff[0].shape
occidx = [numpy.where(mo_occ[k]==2)[0] for k in range(nkpts)]
viridx = [numpy.where(mo_occ[k]==0)[0] for k in range(nkpts)]
orbo = [mo_coeff[k][:,occidx[k]] for k in range(nkpts)]
orbv = [mo_coeff[k][:,viridx[k]] for k in range(nkpts)]
e_ia = _get_e_ia(scf.addons.mo_energy_with_exxdiv_none(mf), mo_occ, kconserv)
hdiag = numpy.hstack([x.ravel() for x in e_ia])
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = mf.gen_response(singlet=singlet, hermi=0, max_memory=max_memory)
def vind(zs):
nz = len(zs)
z1s = [_unpack(z, mo_occ, kconserv) for z in zs]
dmov = numpy.empty((nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
for k, kp in enumerate(kconserv):
# *2 for double occupancy
dm1 = z1s[i][k] * 2
dmov[i,k] = reduce(numpy.dot, (orbo[k], dm1, orbv[kp].conj().T))
with lib.temporary_env(mf, exxdiv=None):
v1ao = vresp(dmov, kshift)
v1s = []
for i in range(nz):
dm1 = z1s[i]
v1 = []
for k, kp in enumerate(kconserv):
v1vo = reduce(numpy.dot, (orbo[k].conj().T, v1ao[i,k], orbv[kp]))
v1vo += e_ia[k] * dm1[k]
v1.append(v1vo.ravel())
v1s.append( numpy.concatenate(v1) )
return lib.asarray(v1s).reshape(nz,-1)
return vind, hdiag
[docs]
def init_guess(self, mf, kshift, nstates=None):
if nstates is None: nstates = self.nstates
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
e_ia = numpy.concatenate( [x.reshape(-1) for x in
_get_e_ia(mo_energy, mo_occ, kconserv)] )
nov = e_ia.size
nstates = min(nstates, nov)
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
return x0
[docs]
def kernel(self, x0=None):
'''TDA diagonalization solver
Args:
x0: list of init guess arrays for each k-shift specified in :attr:`self.kshift_lst`
[x0_1, x0_2, ..., x0_nshift]
x0_i ~ (nstates, nkpts*nocc*nvir)
'''
cpu0 = (logger.process_clock(), logger.perf_counter())
self.check_sanity()
self.dump_flags()
log = logger.new_logger(self)
mf = self._scf
mo_occ = mf.mo_occ
def pickeig(w, v, nroots, envs):
idx = numpy.where(w > self.positive_eig_threshold)[0]
return w[idx], v[:,idx], idx
log = logger.Logger(self.stdout, self.verbose)
self.converged = []
self.e = []
self.xy = []
for i,kshift in enumerate(self.kshift_lst):
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
vind, hdiag = self.gen_vind(self._scf, kshift)
precond = self.get_precond(hdiag)
if x0 is None:
x0k = self.init_guess(self._scf, kshift, self.nstates)
else:
x0k = x0[i]
converged, e, x1 = lr_eigh(
vind, x0k, precond, tol_residual=self.conv_tol, lindep=self.lindep,
nroots=self.nstates, pick=pickeig, max_cycle=self.max_cycle,
max_memory=self.max_memory, verbose=log)
self.converged.append( converged )
self.e.append( e )
# 1/sqrt(2) because self.x is for alpha excitation amplitude and 2(X^+*X) = 1
self.xy.append( [(_unpack(xi*numpy.sqrt(.5), mo_occ, kconserv), 0) for xi in x1] )
log.timer(self.__class__.__name__, *cpu0)
self._finalize()
return self.e, self.xy
CIS = KTDA = TDA
[docs]
class TDHF(KTDBase):
[docs]
@lib.with_doc(get_ab.__doc__)
def get_ab(self, mf=None, kshift=0):
if mf is None: mf = self._scf
return get_ab(mf, kshift)
[docs]
def gen_vind(self, mf, kshift=0):
'''
[ A B ][X]
[-B* -A*][Y]
'''
assert kshift == 0
singlet = self.singlet
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ)
nao, nmo = mo_coeff[0].shape
occidx = [numpy.where(mo_occ[k]==2)[0] for k in range(nkpts)]
viridx = [numpy.where(mo_occ[k]==0)[0] for k in range(nkpts)]
orbo = [mo_coeff[k][:,occidx[k]] for k in range(nkpts)]
orbv = [mo_coeff[k][:,viridx[k]] for k in range(nkpts)]
kconserv = numpy.arange(nkpts)
e_ia = _get_e_ia(scf.addons.mo_energy_with_exxdiv_none(mf), mo_occ, kconserv)
hdiag = numpy.hstack([x.ravel() for x in e_ia])
tot_x = hdiag.size
hdiag = numpy.hstack((hdiag, -hdiag))
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = mf.gen_response(singlet=singlet, hermi=0, max_memory=max_memory)
def vind(xys):
nz = len(xys)
z1xs = [_unpack(xy[:tot_x], mo_occ, kconserv) for xy in xys]
z1ys = [_unpack(xy[tot_x:], mo_occ, kconserv) for xy in xys]
dmov = numpy.zeros((nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
for k in range(nkpts):
# *2 for double occupancy
dmx = z1xs[i][k] * 2
dmy = z1ys[i][k] * 2
dmov[i,k] += reduce(numpy.dot, (orbo[k], dmx , orbv[k].T.conj()))
dmov[i,k] += reduce(numpy.dot, (orbv[k], dmy.T, orbo[k].T.conj()))
with lib.temporary_env(mf, exxdiv=None):
v1ao = vresp(dmov, kshift) # = <mb||nj> Xjb + <mj||nb> Yjb
v1s = []
for i in range(nz):
dmx = z1xs[i]
dmy = z1ys[i]
v1xs = [0] * nkpts
v1ys = [0] * nkpts
for k in range(nkpts):
# AX + BY
# = <ib||aj> Xjb + <ij||ab> Yjb
# = (<mb||nj> Xjb + <mj||nb> Yjb) Cmi* Cna
v1x = reduce(numpy.dot, (orbo[k].T.conj(), v1ao[i,k], orbv[k]))
# (B*)X + (A*)Y
# = <ab||ij> Xjb + <aj||ib> Yjb
# = (<mb||nj> Xjb + <mj||nb> Yjb) Cma* Cni
v1y = reduce(numpy.dot, (orbv[k].T.conj(), v1ao[i,k], orbo[k])).T
v1x += e_ia[k] * dmx[k]
v1y += e_ia[k].conj() * dmy[k]
v1xs[k] += v1x.ravel()
v1ys[k] -= v1y.ravel()
v1s.append( numpy.concatenate(v1xs + v1ys) )
return lib.asarray(v1s).reshape(nz,-1)
return vind, hdiag
[docs]
def init_guess(self, mf, kshift, nstates=None):
x0 = TDA.init_guess(self, mf, kshift, nstates)
y0 = numpy.zeros_like(x0)
return numpy.hstack([x0, y0])
get_precond = rhf.TDHF.get_precond
[docs]
def kernel(self, x0=None):
'''TDHF diagonalization with non-Hermitian eigenvalue solver
'''
cpu0 = (logger.process_clock(), logger.perf_counter())
self.check_sanity()
self.dump_flags()
log = logger.new_logger(self)
mf = self._scf
mo_occ = mf.mo_occ
real_system = (is_gamma_point(self._scf.kpts) and
self._scf.mo_coeff[0].dtype == numpy.double)
if any(k != 0 for k in self.kshift_lst):
# It's not clear how to define the Y matrix for kshift!=0 .
# When the A tensor is constructed against the X(kshift) matrix,
# the diagonal terms e_ia are calculated as e_i[k] - e_k[k+kshift].
# Given the k-conserve relation in the A tensor, the j-b indices in
# the A tensor should follow j[k'], b[k'+kshift]. This leads to the
# j-b indices in the B tensor being defined as (j[k'+shift], b[k']).
# To form the square A-B-B-A matrix, the diagonal terms for the
# -A* part need to be constructed as e_i[k+kshift] - e_a[k], which
# conflict to the diagonal terms of the A tensor.
raise RuntimeError('kshift != 0 for TDHF')
# We only need positive eigenvalues
def pickeig(w, v, nroots, envs):
realidx = numpy.where((abs(w.imag) < REAL_EIG_THRESHOLD) &
(w.real > self.positive_eig_threshold))[0]
return lib.linalg_helper._eigs_cmplx2real(w, v, realidx, real_system)
log = logger.Logger(self.stdout, self.verbose)
def norm_xy(z, kconserv):
x, y = z.reshape(2,-1)
norm = 2*(lib.norm(x)**2 - lib.norm(y)**2)
norm = 1/numpy.sqrt(norm)
x *= norm
y *= norm
return _unpack(x, mo_occ, kconserv), _unpack(y, mo_occ, kconserv)
self.converged = []
self.e = []
self.xy = []
for i,kshift in enumerate(self.kshift_lst):
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
vind, hdiag = self.gen_vind(self._scf, kshift)
precond = self.get_precond(hdiag)
if x0 is None:
x0k = self.init_guess(self._scf, kshift, self.nstates)
else:
x0k = x0[i]
converged, e, x1 = lr_eig(
vind, x0k, precond, tol_residual=self.conv_tol, lindep=self.lindep,
nroots=self.nstates, pick=pickeig, max_cycle=self.max_cycle,
max_memory=self.max_memory, verbose=log)
self.converged.append( converged )
self.e.append( e )
self.xy.append( [norm_xy(z, kconserv) for z in x1] )
log.timer(self.__class__.__name__, *cpu0)
self._finalize()
return self.e, self.xy
RPA = KTDHF = TDHF
def _get_e_ia(mo_energy, mo_occ, kconserv=None):
e_ia = []
nkpts = len(mo_occ)
if kconserv is None: kconserv = numpy.arange(nkpts)
for k in range(nkpts):
kp = kconserv[k]
moeocc = mo_energy[k][mo_occ[k] > 1e-6]
moevir = mo_energy[kp][mo_occ[kp] < 1e-6]
e_ia.append( -moeocc[:,None] + moevir )
return e_ia
def _unpack(vo, mo_occ, kconserv):
z = []
p1 = 0
no_kpts = [numpy.count_nonzero(occ) for occ in mo_occ]
for k, no in enumerate(no_kpts):
kp = kconserv[k]
nv = mo_occ[kp].size - no_kpts[kp]
p0, p1 = p1, p1 + no * nv
z.append(vo[p0:p1].reshape(no,nv))
return z
scf.khf.KRHF.TDA = lib.class_as_method(KTDA)
scf.khf.KRHF.TDHF = lib.class_as_method(KTDHF)
scf.krohf.KROHF.TDA = None
scf.krohf.KROHF.TDHF = None
