#!/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>
#
from functools import reduce
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.tdscf import uhf
from pyscf.pbc import scf
from pyscf.pbc.tdscf.krhf import KTDBase, _get_e_ia, purify_krlyov_heff
from pyscf.pbc.lib.kpts_helper import gamma_point
from pyscf.pbc.scf import _response_functions # noqa
from pyscf import __config__
REAL_EIG_THRESHOLD = getattr(__config__, 'pbc_tdscf_uhf_TDDFT_pick_eig_threshold', 1e-3)
[docs]
class TDA(KTDBase):
conv_tol = getattr(__config__, 'pbc_tdscf_rhf_TDA_conv_tol', 1e-6)
[docs]
def gen_vind(self, mf, kshift):
'''Compute Ax'''
kconserv = self.kconserv[kshift]
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ[0])
nao, nmo = mo_coeff[0][0].shape
occidxa = [numpy.where(mo_occ[0][k]> 0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k]> 0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k]==0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k]==0)[0] for k in range(nkpts)]
orboa = [mo_coeff[0][k][:,occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:,occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][kconserv[k]][:,viridxa[kconserv[k]]] for k in range(nkpts)]
orbvb = [mo_coeff[1][kconserv[k]][:,viridxb[kconserv[k]]] for k in range(nkpts)]
moe = scf.addons.mo_energy_with_exxdiv_none(mf)
e_ia_a = _get_e_ia(moe[0], mo_occ[0], kconserv)
e_ia_b = _get_e_ia(moe[1], mo_occ[1], kconserv)
hdiag = numpy.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = mf.gen_response(hermi=0, max_memory=max_memory)
def vind(zs):
nz = len(zs)
zs = [_unpack(z, mo_occ, kconserv) for z in zs]
dmov = numpy.empty((2,nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
dm1a, dm1b = zs[i]
for k in range(nkpts):
dmov[0,i,k] = reduce(numpy.dot, (orboa[k], dm1a[k], orbva[k].conj().T))
dmov[1,i,k] = reduce(numpy.dot, (orbob[k], dm1b[k], orbvb[k].conj().T))
with lib.temporary_env(mf, exxdiv=None):
dmov = dmov.reshape(2,nz,nkpts,nao,nao)
v1ao = vresp(dmov, kshift)
v1ao = v1ao.reshape(2,nz,nkpts,nao,nao)
v1s = []
for i in range(nz):
dm1a, dm1b = zs[i]
v1as = []
v1bs = []
for k in range(nkpts):
v1a = reduce(numpy.dot, (orboa[k].conj().T, v1ao[0,i,k], orbva[k]))
v1b = reduce(numpy.dot, (orbob[k].conj().T, v1ao[1,i,k], orbvb[k]))
v1a += e_ia_a[k] * dm1a[k]
v1b += e_ia_b[k] * dm1b[k]
v1as.append(v1a.ravel())
v1bs.append(v1b.ravel())
v1s.append( numpy.concatenate(v1as + v1bs) )
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 = self.kconserv[kshift]
e_ia_a = _get_e_ia(mo_energy[0], mo_occ[0], kconserv)
e_ia_b = _get_e_ia(mo_energy[1], mo_occ[1], kconserv)
e_ia = numpy.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
nov = e_ia.size
nstates = min(nstates, nov)
e_threshold = numpy.sort(e_ia)[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
'''
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)
precision = self.cell.precision * 1e-2
hermi = 1
self.converged = []
self.e = []
self.xy = []
for i,kshift in enumerate(self.kshift_lst):
kconserv = self.kconserv[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 = \
lib.davidson1(vind, x0k, precond,
tol=self.conv_tol,
max_cycle=self.max_cycle,
nroots=self.nstates,
lindep=self.lindep,
max_space=self.max_space, pick=pickeig,
fill_heff=purify_krlyov_heff(precision, hermi, log),
verbose=self.verbose)
self.converged.append( converged )
self.e.append( e )
self.xy.append( [(_unpack(xi, mo_occ, kconserv), # (X_alpha, X_beta)
(0, 0)) # (Y_alpha, Y_beta)
for xi in x1] )
#TODO: analyze CIS wfn point group symmetry
log.timer(self.__class__.__name__, *cpu0)
self._finalize()
return self.e, self.xy
CIS = KTDA = TDA
[docs]
class TDHF(TDA):
[docs]
def gen_vind(self, mf, kshift):
kconserv = self.kconserv[kshift]
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ[0])
nao, nmo = mo_coeff[0][0].shape
occidxa = [numpy.where(mo_occ[0][k]> 0)[0] for k in range(nkpts)]
occidxb = [numpy.where(mo_occ[1][k]> 0)[0] for k in range(nkpts)]
viridxa = [numpy.where(mo_occ[0][k]==0)[0] for k in range(nkpts)]
viridxb = [numpy.where(mo_occ[1][k]==0)[0] for k in range(nkpts)]
orboa = [mo_coeff[0][k][:,occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:,occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][kconserv[k]][:,viridxa[kconserv[k]]] for k in range(nkpts)]
orbvb = [mo_coeff[1][kconserv[k]][:,viridxb[kconserv[k]]] for k in range(nkpts)]
moe = scf.addons.mo_energy_with_exxdiv_none(mf)
e_ia_a = _get_e_ia(moe[0], mo_occ[0], kconserv)
e_ia_b = _get_e_ia(moe[1], mo_occ[1], kconserv)
hdiag = numpy.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
hdiag = numpy.hstack((hdiag, -hdiag))
tot_x_a = sum(x.size for x in e_ia_a)
tot_x_b = sum(x.size for x in e_ia_b)
tot_x = tot_x_a + tot_x_b
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = mf.gen_response(hermi=0, max_memory=max_memory)
def vind(xys):
nz = len(xys)
x1s = [_unpack(x[:tot_x], mo_occ, kconserv) for x in xys]
y1s = [_unpack(x[tot_x:], mo_occ, kconserv) for x in xys]
dmov = numpy.empty((2,nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
for k in range(nkpts):
dmx = reduce(numpy.dot, (orboa[k], xa[k] , orbva[k].conj().T))
dmy = reduce(numpy.dot, (orbva[k], ya[k].T, orboa[k].conj().T))
dmov[0,i,k] = dmx + dmy # AX + BY
dmx = reduce(numpy.dot, (orbob[k], xb[k] , orbvb[k].conj().T))
dmy = reduce(numpy.dot, (orbvb[k], yb[k].T, orbob[k].conj().T))
dmov[1,i,k] = dmx + dmy # AX + BY
with lib.temporary_env(mf, exxdiv=None):
dmov = dmov.reshape(2,nz,nkpts,nao,nao)
v1ao = vresp(dmov, kshift)
v1ao = v1ao.reshape(2,nz,nkpts,nao,nao)
v1s = []
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
v1xsa = []
v1xsb = []
v1ysa = []
v1ysb = []
for k in range(nkpts):
v1xa = reduce(numpy.dot, (orboa[k].conj().T, v1ao[0,i,k], orbva[k]))
v1xb = reduce(numpy.dot, (orbob[k].conj().T, v1ao[1,i,k], orbvb[k]))
v1ya = reduce(numpy.dot, (orbva[k].conj().T, v1ao[0,i,k], orboa[k])).T
v1yb = reduce(numpy.dot, (orbvb[k].conj().T, v1ao[1,i,k], orbob[k])).T
v1xa+= e_ia_a[k] * xa[k]
v1xb+= e_ia_b[k] * xb[k]
v1ya+= e_ia_a[k] * ya[k]
v1yb+= e_ia_b[k] * yb[k]
v1xsa.append(v1xa.ravel())
v1xsb.append(v1xb.ravel())
v1ysa.append(-v1ya.ravel())
v1ysb.append(-v1yb.ravel())
v1s.append( numpy.concatenate(v1xsa + v1xsb + v1ysa + v1ysb) )
return numpy.hstack(v1s).reshape(nz,-1)
return vind, hdiag
[docs]
def init_guess(self, mf, kshift, nstates=None, wfnsym=None):
x0 = TDA.init_guess(self, mf, kshift, nstates)
y0 = numpy.zeros_like(x0)
return numpy.asarray(numpy.block([[x0, y0], [y0, x0.conj()]]))
[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 = (gamma_point(self._scf.kpts) and
self._scf.mo_coeff[0][0].dtype == numpy.double)
# 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)
precision = self.cell.precision * 1e-2
self.converged = []
self.e = []
self.xy = []
for i,kshift in enumerate(self.kshift_lst):
kconserv = self.kconserv[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, w, x1 = \
lib.davidson_nosym1(vind, x0k, precond,
tol=self.conv_tol,
max_cycle=self.max_cycle,
nroots=self.nstates,
lindep=self.lindep,
max_space=self.max_space, pick=pickeig,
fill_heff=purify_krlyov_heff(precision, 0, log),
verbose=self.verbose)
self.converged.append( converged )
e = []
xy = []
for i, z in enumerate(x1):
xs, ys = z.reshape(2,-1)
norm = lib.norm(xs)**2 - lib.norm(ys)**2
if norm > 0:
norm = 1/numpy.sqrt(norm)
xs *= norm
ys *= norm
e.append(w[i])
xy.append((_unpack(xs, mo_occ, kconserv), _unpack(ys, mo_occ, kconserv)))
self.e.append( numpy.array(e) )
self.xy.append( xy )
log.timer(self.__class__.__name__, *cpu0)
self._finalize()
return self.e, self.xy
RPA = KTDHF = TDHF
def _unpack(vo, mo_occ, kconserv):
za = []
zb = []
p1 = 0
for k, occ in enumerate(mo_occ[0]):
no = numpy.count_nonzero(occ > 0)
no1 = numpy.count_nonzero(mo_occ[0][kconserv[k]] > 0)
nv = occ.size - no1
p0, p1 = p1, p1 + no * nv
za.append(vo[p0:p1].reshape(no,nv))
for k, occ in enumerate(mo_occ[1]):
no = numpy.count_nonzero(occ > 0)
no1 = numpy.count_nonzero(mo_occ[1][kconserv[k]] > 0)
nv = occ.size - no1
p0, p1 = p1, p1 + no * nv
zb.append(vo[p0:p1].reshape(no,nv))
return za, zb
scf.kuhf.KUHF.TDA = lib.class_as_method(KTDA)
scf.kuhf.KUHF.TDHF = lib.class_as_method(KTDHF)
if __name__ == '__main__':
from pyscf.pbc import gto
from pyscf.pbc import scf
from pyscf.pbc import df
cell = gto.Cell()
cell.unit = 'B'
cell.atom = '''
C 0. 0. 0.
C 1.68506879 1.68506879 1.68506879
'''
cell.a = '''
0. 3.37013758 3.37013758
3.37013758 0. 3.37013758
3.37013758 3.37013758 0.
'''
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.mesh = [37]*3
cell.build()
mf = scf.KUHF(cell, cell.make_kpts([2,1,1])).set(exxdiv=None)
# mf.with_df = df.DF(cell, cell.make_kpts([2,1,1]))
# mf.with_df.auxbasis = 'weigend'
# mf.with_df._cderi = 'eri3d-df.h5'
# mf.with_df.build(with_j3c=False)
mf.run()
td = TDA(mf)
td.verbose = 5
td.nstates = 5
print(td.kernel()[0][0] * 27.2114)
td = TDHF(mf)
td.verbose = 5
td.nstates = 5
print(td.kernel()[0][0] * 27.2114)
cell.spin = 2
mf = scf.KUHF(cell, cell.make_kpts([2,1,1])).set(exxdiv=None)
mf.run()
td = TDA(mf)
td.verbose = 5
td.nstates = 5
print(td.kernel()[0][0] * 27.2114)
td = TDHF(mf)
td.verbose = 5
td.nstates = 5
print(td.kernel()[0][0] * 27.2114)