#!/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: Xing Zhang <zhangxing.nju@gmail.com>
#
'''
Restricted coupled pertubed Hartree-Fock solver
Modified from pyscf.scf.cphf
'''
import numpy as np
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}
Kwargs:
hermi : boolean
Whether the matrix defined by fvind is Hermitian or not.
'''
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())
nkpt = len(h1)
moloc = np.zeros([nkpt+1], dtype=int)
for k in range(nkpt):
moloc[k+1] = moloc[k] + h1[k].size
occidx = []
viridx = []
for k in range(nkpt):
occidx.append(mo_occ[k] > 0)
viridx.append(mo_occ[k] == 0)
e_a = [mo_energy[k][viridx[k]] for k in range(nkpt)]
e_i = [mo_energy[k][occidx[k]] for k in range(nkpt)]
e_ai = [1 / lib.direct_sum('a-i->ai', e_a[k], e_i[k]) for k in range(nkpt)]
mo1base = []
for k in range(nkpt):
mo1base.append((h1[k] * -e_ai[k]).ravel())
mo1base = np.hstack(mo1base)
def vind_vo(mo1):
mo1 = mo1.flatten()
tmp = []
for k in range(nkpt):
tmp.append(mo1[moloc[k]:moloc[k+1]].reshape(h1[k].shape))
v = fvind(tmp)
for k in range(nkpt):
v[k] *= e_ai[k]
v[k] = v[k].ravel()
return np.hstack(v)
_mo1 = lib.krylov(vind_vo, mo1base,
tol=tol, max_cycle=max_cycle, hermi=hermi, verbose=log).flatten()
log.timer('krylov solver in CPHF', *t0)
mo1 = []
for k in range(nkpt):
mo1.append(_mo1[moloc[k]:moloc[k+1]].reshape(h1[k].shape))
return mo1, None
# h1 shape is (:,nocc+nvir,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]
Kwargs:
hermi : boolean
Whether the matrix defined by fvind is Hermitian or not.
Returns:
First order orbital coefficients (in MO basis) and first order orbital
energy matrix
'''
log = logger.new_logger(verbose=verbose)
t0 = (logger.process_clock(), logger.perf_counter())
nkpt = len(h1)
ncomp = h1[0].shape[0]
occidx = []
viridx = []
for k in range(nkpt):
occidx.append(mo_occ[k] > 0)
viridx.append(mo_occ[k] == 0)
e_a = [mo_energy[k][viridx[k]] for k in range(nkpt)]
e_i = [mo_energy[k][occidx[k]] for k in range(nkpt)]
e_ai = [1 / lib.direct_sum('a-i->ai', e_a[k], e_i[k]) for k in range(nkpt)]
nocc = np.zeros([nkpt], dtype=int)
nvir = np.zeros([nkpt], dtype=int)
nmo = np.zeros([nkpt], dtype=int)
moloc = np.zeros([nkpt+1], dtype=int)
for k in range(nkpt):
nvir_k, nocc_k = e_ai[k].shape
nmo_k = nvir_k + nocc_k
nvir[k] = nvir_k
nocc[k] = nocc_k
nmo[k] = nmo_k
moloc[k+1] = moloc[k] + nmo_k * nocc_k * ncomp
mo1base = []
_mo1base = []
mo_e1 = []
for k in range(nkpt):
mo1base.append(h1[k] - s1[k] * e_i[k])
mo_e1.append(mo1base[k][:,occidx[k],:].copy())
mo1base[k][:,viridx[k]] *= -e_ai[k]
mo1base[k][:,occidx[k]] = -s1[k][:,occidx[k]] * .5
_mo1base.append(mo1base[k].ravel())
_mo1base = np.hstack(_mo1base)
def vind_vo(mo1):
mo1 = mo1.ravel()
tmp = []
for k in range(nkpt):
tmp.append(mo1[moloc[k]:moloc[k+1]].reshape(-1,nmo[k],nocc[k]))
v = fvind(tmp)
for k in range(nkpt):
v[k][:,viridx[k],:] *= e_ai[k]
v[k][:,occidx[k],:] = 0
v[k] = v[k].ravel()
return np.hstack(v)
_mo1 = lib.krylov(vind_vo, _mo1base,
tol=tol, max_cycle=max_cycle, hermi=hermi, verbose=log)
mo1 = []
for k in range(nkpt):
mo1.append(_mo1[moloc[k]:moloc[k+1]].reshape(-1,nmo[k],nocc[k]))
log.timer('krylov solver in CPHF', *t0)
v1mo = fvind(mo1)
for k in range(nkpt):
mo1[k][:,viridx[k]] = mo1base[k][:,viridx[k]] - \
v1mo[k][:,viridx[k]]*e_ai[k]
# mo_e1 has the same symmetry as the first order Fock matrix (hermitian or
# anti-hermitian). mo_e1 = v1mo + u1*lib.direct_sum('i-j->ij',e_i,e_i)
for k in range(nkpt):
mo_e1[k] += mo1[k][:,occidx[k]] * lib.direct_sum('i-j->ij', e_i[k], e_i[k])
mo_e1[k] += v1mo[k][:,occidx[k]]
return mo1, mo_e1