#!/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>
#
'''
Unrestricted coupled pertubed Hartree-Fock solver
'''
import numpy
from pyscf import lib
from pyscf.lib import logger
[docs]
def solve(fvind, mo_energy, mo_occ, h1, s1=None,
max_cycle=20, tol=1e-9, hermi=False, verbose=logger.WARN):
'''
Args:
fvind : function
Given density matrix, compute (ij|kl)D_{lk}*2 - (ij|kl)D_{jk}
'''
if s1 is None:
return solve_nos1(fvind, mo_energy, mo_occ, h1,
max_cycle, tol, hermi, verbose)
else:
return solve_withs1(fvind, mo_energy, mo_occ, h1, s1,
max_cycle, tol, hermi, verbose)
kernel = solve
# h1 shape is (:,nvir,nocc)
[docs]
def solve_nos1(fvind, mo_energy, mo_occ, h1,
max_cycle=20, tol=1e-9, hermi=False, verbose=logger.WARN):
'''For field independent basis. First order overlap matrix is zero'''
log = logger.new_logger(verbose=verbose)
t0 = (logger.process_clock(), logger.perf_counter())
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
viridxa = ~occidxa
viridxb = ~occidxb
nocca = numpy.count_nonzero(occidxa)
noccb = numpy.count_nonzero(occidxb)
nvira = mo_occ[0].size - nocca
nvirb = mo_occ[1].size - noccb
e_ai = numpy.hstack(((mo_energy[0][viridxa,None]-mo_energy[0][occidxa]).ravel(),
(mo_energy[1][viridxb,None]-mo_energy[1][occidxb]).ravel()))
e_ai = 1 / e_ai
mo1base = numpy.hstack((h1[0].reshape(-1,nvira*nocca),
h1[1].reshape(-1,nvirb*noccb)))
mo1base *= -e_ai
def vind_vo(mo1):
v = fvind(mo1.reshape(mo1base.shape)).reshape(mo1base.shape)
v *= e_ai
return v.ravel()
mo1 = lib.krylov(vind_vo, mo1base.ravel(),
tol=tol, max_cycle=max_cycle, hermi=hermi, verbose=log)
log.timer('krylov solver in CPHF', *t0)
if isinstance(h1[0], numpy.ndarray) and h1[0].ndim == 2:
mo1 = (mo1[:nocca*nvira].reshape(nvira,nocca),
mo1[nocca*nvira:].reshape(nvirb,noccb))
else:
mo1 = mo1.reshape(mo1base.shape)
mo1_a = mo1[:,:nvira*nocca].reshape(-1,nvira,nocca)
mo1_b = mo1[:,nvira*nocca:].reshape(-1,nvirb,noccb)
mo1 = (mo1_a, mo1_b)
return mo1, None
# h1 shape is (:,nvir+nocc,nocc)
[docs]
def solve_withs1(fvind, mo_energy, mo_occ, h1, s1,
max_cycle=20, tol=1e-9, hermi=False, verbose=logger.WARN):
'''For field dependent basis. First order overlap matrix is non-zero.
The first order orbitals are set to
C^1_{ij} = -1/2 S1
e1 = h1 - s1*e0 + (e0_j-e0_i)*c1 + vhf[c1]
'''
log = logger.new_logger(verbose=verbose)
t0 = (logger.process_clock(), logger.perf_counter())
occidxa = mo_occ[0] > 0
occidxb = mo_occ[1] > 0
viridxa = ~occidxa
viridxb = ~occidxb
nocca = numpy.count_nonzero(occidxa)
noccb = numpy.count_nonzero(occidxb)
nmoa, nmob = mo_occ[0].size, mo_occ[1].size
eai_a = mo_energy[0][viridxa,None] - mo_energy[0][occidxa]
eai_b = mo_energy[1][viridxb,None] - mo_energy[1][occidxb]
s1_a = s1[0].reshape(-1,nmoa,nocca)
nset = s1_a.shape[0]
s1_b = s1[1].reshape(nset,nmob,noccb)
hs_a = mo1base_a = h1[0].reshape(nset,nmoa,nocca) - s1_a * mo_energy[0][occidxa]
hs_b = mo1base_b = h1[1].reshape(nset,nmob,noccb) - s1_b * mo_energy[1][occidxb]
mo_e1_a = hs_a[:,occidxa].copy()
mo_e1_b = hs_b[:,occidxb].copy()
mo1base_a[:,viridxa]/= -eai_a
mo1base_b[:,viridxb]/= -eai_b
mo1base_a[:,occidxa] = -s1_a[:,occidxa] * .5
mo1base_b[:,occidxb] = -s1_b[:,occidxb] * .5
eai_a = 1. / eai_a
eai_b = 1. / eai_b
mo1base = numpy.hstack((mo1base_a.reshape(nset,-1), mo1base_b.reshape(nset,-1)))
def vind_vo(mo1):
v = fvind(mo1).reshape(mo1base.shape)
v1a = v[:,:nmoa*nocca].reshape(nset,nmoa,nocca)
v1b = v[:,nmoa*nocca:].reshape(nset,nmob,noccb)
v1a[:,viridxa] *= eai_a
v1b[:,viridxb] *= eai_b
v1a[:,occidxa] = 0
v1b[:,occidxb] = 0
return v.ravel()
mo1 = lib.krylov(vind_vo, mo1base.ravel(),
tol=tol, max_cycle=max_cycle, hermi=hermi, verbose=log)
log.timer('krylov solver in CPHF', *t0)
v1mo = fvind(mo1).reshape(mo1base.shape)
v1a = v1mo[:,:nmoa*nocca].reshape(nset,nmoa,nocca)
v1b = v1mo[:,nmoa*nocca:].reshape(nset,nmob,noccb)
mo1 = mo1.reshape(mo1base.shape)
mo1_a = mo1[:,:nmoa*nocca].reshape(nset,nmoa,nocca)
mo1_b = mo1[:,nmoa*nocca:].reshape(nset,nmob,noccb)
mo1_a[:,viridxa] = mo1base_a[:,viridxa] - v1a[:,viridxa] * eai_a
mo1_b[:,viridxb] = mo1base_b[:,viridxb] - v1b[:,viridxb] * eai_b
mo_e1_a += mo1_a[:,occidxa] * (mo_energy[0][occidxa,None] - mo_energy[0][occidxa])
mo_e1_b += mo1_b[:,occidxb] * (mo_energy[1][occidxb,None] - mo_energy[1][occidxb])
mo_e1_a += v1mo[:,:nmoa*nocca].reshape(nset,nmoa,nocca)[:,occidxa]
mo_e1_b += v1mo[:,nmoa*nocca:].reshape(nset,nmob,noccb)[:,occidxb]
if isinstance(h1[0], numpy.ndarray) and h1[0].ndim == 2:
mo1_a, mo1_b = mo1_a[0], mo1_b[0]
mo_e1_a, mo_e1_b = mo_e1_a[0], mo_e1_b[0]
return (mo1_a, mo1_b), (mo_e1_a, mo_e1_b)