#!/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
#
from functools import reduce
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.tdscf import rhf
from pyscf.pbc.scf import _response_functions # noqa
from pyscf.pbc.lib.kpts_helper import gamma_point
from pyscf import __config__
REAL_EIG_THRESHOLD = getattr(__config__, 'pbc_tdscf_rhf_TDDFT_pick_eig_threshold', 1e-3)
POSTIVE_EIG_THRESHOLD = getattr(__config__, 'pbc_tdscf_rhf_TDDFT_positive_eig_threshold', 1e-3)
[docs]class TDA(rhf.TDA):
#FIXME: numerically unstable with small mesh?
#TODO: Add a warning message for small mesh.
conv_tol = getattr(__config__, 'pbc_tdscf_rhf_TDA_conv_tol', 1e-6)
def __init__(self, mf):
from pyscf.pbc import scf
assert(isinstance(mf, scf.khf.KSCF))
self.cell = mf.cell
rhf.TDA.__init__(self, mf)
from pyscf.pbc.df.df_ao2mo import warn_pbc2d_eri
warn_pbc2d_eri(mf)
[docs] def gen_vind(self, mf):
singlet = self.singlet
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
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(mo_energy, mo_occ)
# FIXME: hdiag corresponds to the orbital energy with the exxdiv
# correction. The integrals in A, B matrices do not have the
# contribution from the exxdiv. Should the exchange correction be
# removed from hdiag?
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) for z in zs]
dmov = numpy.empty((nz,nkpts,nao,nao), dtype=numpy.complex128)
for i in range(nz):
for k in range(nkpts):
# *2 for double occupancy
dm1 = z1s[i][k] * 2
dmov[i,k] = reduce(numpy.dot, (orbo[k], dm1, orbv[k].conj().T))
with lib.temporary_env(mf, exxdiv=None):
v1ao = vresp(dmov)
v1s = []
for i in range(nz):
dm1 = z1s[i]
for k in range(nkpts):
v1vo = reduce(numpy.dot, (orbo[k].conj().T, v1ao[i,k], orbv[k]))
v1vo += e_ia[k] * dm1[k]
v1s.append(v1vo.ravel())
return lib.asarray(v1s).reshape(nz,-1)
return vind, hdiag
def init_guess(self, mf, nstates=None):
if nstates is None: nstates = self.nstates
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
e_ia = numpy.hstack([x.ravel() for x in _get_e_ia(mo_energy, mo_occ)])
nov = e_ia.size
nroot = min(nstates, nov)
x0 = numpy.zeros((nroot, nov))
idx = numpy.argsort(e_ia.ravel())
for i in range(nroot):
x0[i,idx[i]] = 1 # lowest excitations
return x0
[docs] def kernel(self, x0=None):
'''TDA diagonalization solver
'''
self.check_sanity()
self.dump_flags()
vind, hdiag = self.gen_vind(self._scf)
precond = self.get_precond(hdiag)
if x0 is None:
x0 = self.init_guess(self._scf, self.nstates)
self.converged, self.e, x1 = \
lib.davidson1(vind, x0, precond,
tol=self.conv_tol,
nroots=self.nstates, lindep=self.lindep,
max_space=self.max_space,
verbose=self.verbose)
mo_occ = self._scf.mo_occ
# 1/sqrt(2) because self.x is for alpha excitation amplitude and 2(X^+*X) = 1
self.xy = [(_unpack(xi*numpy.sqrt(.5), mo_occ), 0) for xi in x1]
return self.e, self.xy
CIS = KTDA = TDA
[docs]class TDHF(TDA):
[docs] def gen_vind(self, mf):
'''
[ A B ][X]
[-B* -A*][Y]
'''
singlet = self.singlet
mo_coeff = mf.mo_coeff
mo_energy = mf.mo_energy
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(mo_energy, mo_occ)
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) for xy in xys]
z1ys = [_unpack(xy[tot_x:], mo_occ) for xy in xys]
dmov = numpy.empty((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)
v1s = []
for i in range(nz):
dmx = z1xs[i]
dmy = z1ys[i]
v1xs = []
v1ys = []
for k in range(nkpts):
v1x = reduce(numpy.dot, (orbo[k].T.conj(), v1ao[i,k], orbv[k]))
v1y = reduce(numpy.dot, (orbv[k].T.conj(), v1ao[i,k], orbo[k])).T
v1x+= e_ia[k] * dmx[k]
v1y+= e_ia[k] * dmy[k]
v1xs.append(v1x.ravel())
v1ys.append(-v1y.ravel())
v1s += v1xs + v1ys
return lib.asarray(v1s).reshape(nz,-1)
return vind, hdiag
def init_guess(self, mf, nstates=None):
x0 = TDA.init_guess(self, mf, nstates)
y0 = numpy.zeros_like(x0)
return numpy.hstack((x0,y0))
[docs] def kernel(self, x0=None):
'''TDHF diagonalization with non-Hermitian eigenvalue solver
'''
logger.warn(self, 'PBC-TDDFT is an experimental feature. '
'It is numerically sensitive to the accuracy of integrals '
'(relating to cell.precision).')
self.check_sanity()
self.dump_flags()
vind, hdiag = self.gen_vind(self._scf)
precond = self.get_precond(hdiag)
if x0 is None:
x0 = self.init_guess(self._scf, self.nstates)
real_system = (gamma_point(self._scf.kpts) and
self._scf.mo_coeff[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 > POSTIVE_EIG_THRESHOLD))[0]
return lib.linalg_helper._eigs_cmplx2real(w, v, realidx, real_system)
self.converged, w, x1 = \
lib.davidson_nosym1(vind, x0, precond,
tol=self.conv_tol,
nroots=self.nstates, lindep=self.lindep,
max_space=self.max_space, pick=pickeig,
verbose=self.verbose)
mo_occ = self._scf.mo_occ
self.e = w
def norm_xy(z):
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), _unpack(y, mo_occ)
self.xy = [norm_xy(z) for z in x1]
return self.e, self.xy
RPA = KTDHF = TDHF
def _get_e_ia(mo_energy, mo_occ):
e_ia = []
for k, occ in enumerate(mo_occ):
occidx = occ > 0
viridx = occ == 0
e_ia.append(mo_energy[k][viridx] - mo_energy[k][occidx,None])
return e_ia
def _unpack(vo, mo_occ):
z = []
p1 = 0
for k, occ in enumerate(mo_occ):
no = numpy.count_nonzero(occ > 0)
nv = occ.size - no
p0, p1 = p1, p1 + no * nv
z.append(vo[p0:p1].reshape(no,nv))
return z
from pyscf.pbc import scf
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
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 = [25]*3
cell.build()
mf = scf.KRHF(cell, cell.make_kpts([2,1,1])).set(exxdiv=None)
#mf.with_df = df.MDF(cell, cell.make_kpts([2,1,1]))
#mf.with_df.auxbasis = 'weigend'
#mf.with_df._cderi = 'eri3d-mdf.h5'
#mf.with_df.build(with_j3c=False)
mf.run()
#mesh=9 -8.65192427146353
#mesh=12 -8.65192352289817
#mesh=15 -8.6519235231529
#MDF mesh=5 -8.6519301815144
td = TDA(mf)
td.verbose = 5
print(td.kernel()[0] * 27.2114)
#mesh=9 [ 6.0073749 6.09315355 6.3479901 ]
#mesh=12 [ 6.00253282 6.09317929 6.34799109]
#mesh=15 [ 6.00253396 6.09317949 6.34799109]
#MDF mesh=5 [ 6.09317489 6.09318265 6.34798637]
# from pyscf.pbc import tools
# scell = tools.super_cell(cell, [2,1,1])
# mf = scf.RHF(scell).run()
# td = rhf.TDA(mf)
# td.verbose = 5
# print(td.kernel()[0] * 27.2114)
td = TDHF(mf)
td.verbose = 5
print(td.kernel()[0] * 27.2114)
#mesh=9 [ 6.03860914 6.21664545 8.20305225]
#mesh=12 [ 6.03868259 6.03860343 6.2167623 ]
#mesh=15 [ 6.03861321 6.03861324 6.21675868]
#MDF mesh=5 [ 6.03861693 6.03861775 6.21675694]