#!/usr/bin/env python
# Copyright 2014-2019 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>
#
'''
Non-relativistic UHF analytical Hessian
'''
from functools import reduce
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.scf import ucphf
from pyscf.hessian import rhf as rhf_hess
_get_jk = rhf_hess._get_jk
_make_vhfopt = rhf_hess._make_vhfopt
# import _response_functions to load gen_response methods in SCF class
from pyscf.scf import _response_functions # noqa
# import pyscf.grad.uhf to activate nuc_grad_method method
from pyscf.grad import uhf # noqa
[docs]
def hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None,
mo1=None, mo_e1=None, h1ao=None,
atmlst=None, max_memory=4000, verbose=None):
log = logger.new_logger(hessobj, verbose)
time0 = t1 = (logger.process_clock(), logger.perf_counter())
mol = hessobj.mol
mf = hessobj.base
if mo_energy is None: mo_energy = mf.mo_energy
if mo_occ is None: mo_occ = mf.mo_occ
if mo_coeff is None: mo_coeff = mf.mo_coeff
if atmlst is None: atmlst = range(mol.natm)
de2 = hessobj.partial_hess_elec(mo_energy, mo_coeff, mo_occ, atmlst,
max_memory, log)
if h1ao is None:
h1ao = hessobj.make_h1(mo_coeff, mo_occ, None, atmlst, log)
t1 = log.timer_debug1('making H1', *time0)
if mo1 is None or mo_e1 is None:
mo1, mo_e1 = hessobj.solve_mo1(mo_energy, mo_coeff, mo_occ, h1ao,
None, atmlst, max_memory, log)
t1 = log.timer_debug1('solving MO1', *t1)
h1aoa, h1aob = h1ao
mo1a, mo1b = mo1
mo_e1a, mo_e1b = mo_e1
nao, nmo = mo_coeff[0].shape
mocca = mo_coeff[0][:,mo_occ[0]>0]
moccb = mo_coeff[1][:,mo_occ[1]>0]
mo_ea = mo_energy[0][mo_occ[0]>0]
mo_eb = mo_energy[1][mo_occ[1]>0]
s1a = -mol.intor('int1e_ipovlp', comp=3)
aoslices = mol.aoslice_by_atom()
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
s1ao = numpy.zeros((3,nao,nao))
s1ao[:,p0:p1] += s1a[:,p0:p1]
s1ao[:,:,p0:p1] += s1a[:,p0:p1].transpose(0,2,1)
s1ooa = numpy.einsum('xpq,pi,qj->xij', s1ao, mocca, mocca)
s1oob = numpy.einsum('xpq,pi,qj->xij', s1ao, moccb, moccb)
for j0, ja in enumerate(atmlst[:i0+1]):
q0, q1 = aoslices[ja][2:]
dm1a = numpy.einsum('ypi,qi->ypq', mo1a[ja], mocca)
dm1b = numpy.einsum('ypi,qi->ypq', mo1b[ja], moccb)
de2[i0,j0] += numpy.einsum('xpq,ypq->xy', h1aoa[ia], dm1a) * 2
de2[i0,j0] += numpy.einsum('xpq,ypq->xy', h1aob[ia], dm1b) * 2
dm1a = numpy.einsum('ypi,qi,i->ypq', mo1a[ja], mocca, mo_ea)
dm1b = numpy.einsum('ypi,qi,i->ypq', mo1b[ja], moccb, mo_eb)
de2[i0,j0] -= numpy.einsum('xpq,ypq->xy', s1ao, dm1a) * 2
de2[i0,j0] -= numpy.einsum('xpq,ypq->xy', s1ao, dm1b) * 2
de2[i0,j0] -= numpy.einsum('xpq,ypq->xy', s1ooa, mo_e1a[ja])
de2[i0,j0] -= numpy.einsum('xpq,ypq->xy', s1oob, mo_e1b[ja])
for j0 in range(i0):
de2[j0,i0] = de2[i0,j0].T
log.timer('UHF hessian', *time0)
return de2
[docs]
def partial_hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None,
atmlst=None, max_memory=4000, verbose=None):
e1, ej, ek = _partial_hess_ejk(hessobj, mo_energy, mo_coeff, mo_occ,
atmlst, max_memory, verbose, True)
return e1 + ej - ek # (A,B,dR_A,dR_B)
def _partial_hess_ejk(hessobj, mo_energy=None, mo_coeff=None, mo_occ=None,
atmlst=None, max_memory=4000, verbose=None, with_k=True):
log = logger.new_logger(hessobj, verbose)
time0 = t1 = (logger.process_clock(), logger.perf_counter())
mol = hessobj.mol
mf = hessobj.base
if mo_energy is None: mo_energy = mf.mo_energy
if mo_occ is None: mo_occ = mf.mo_occ
if mo_coeff is None: mo_coeff = mf.mo_coeff
if atmlst is None: atmlst = range(mol.natm)
nao, nmo = mo_coeff[0].shape
mocca = mo_coeff[0][:,mo_occ[0]>0]
moccb = mo_coeff[1][:,mo_occ[1]>0]
dm0a = numpy.dot(mocca, mocca.T)
dm0b = numpy.dot(moccb, moccb.T)
dm0 = dm0a + dm0b
# Energy weighted density matrix
mo_ea = mo_energy[0][mo_occ[0]>0]
mo_eb = mo_energy[1][mo_occ[1]>0]
dme0 = numpy.einsum('pi,qi,i->pq', mocca, mocca, mo_ea)
dme0+= numpy.einsum('pi,qi,i->pq', moccb, moccb, mo_eb)
hcore_deriv = hessobj.hcore_generator(mol)
s1aa, s1ab, s1a = rhf_hess.get_ovlp(mol)
vj1_diag, vk1a_diag, vk1b_diag = \
_get_jk(mol, 'int2e_ipip1', 9, 's2kl',
['lk->s1ij', dm0,
'jk->s1il', dm0a, 'jk->s1il', dm0b],
vhfopt=_make_vhfopt(mol, dm0, 'ipip1', 'int2e_ipip1ipip2'))
vj1_diag = vj1_diag.reshape(3,3,nao,nao)
vk1a_diag = vk1a_diag.reshape(3,3,nao,nao)
vk1b_diag = vk1b_diag.reshape(3,3,nao,nao)
t1 = log.timer_debug1('contracting int2e_ipip1', *t1)
ip1ip2_opt = _make_vhfopt(mol, dm0, 'ip1ip2', 'int2e_ip1ip2')
ipvip1_opt = _make_vhfopt(mol, dm0, 'ipvip1', 'int2e_ipvip1ipvip2')
aoslices = mol.aoslice_by_atom()
natm = len(atmlst)
e1 = numpy.zeros((natm, natm, 3, 3)) # (A,B,dR_A,dR_B)
ej = numpy.zeros((natm, natm, 3, 3))
ek = numpy.zeros((natm, natm, 3, 3))
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1) + (0, mol.nbas)*3
vj1, vk1a, vk1b, vk2a, vk2b = \
_get_jk(mol, 'int2e_ip1ip2', 9, 's1',
['ji->s1kl', dm0 [:,p0:p1],
'li->s1kj', dm0a[:,p0:p1], 'li->s1kj', dm0b[:,p0:p1],
'lj->s1ki', dm0a , 'lj->s1ki', dm0b ],
shls_slice=shls_slice, vhfopt=ip1ip2_opt)
vk1a[:,:,p0:p1] += vk2a
vk1b[:,:,p0:p1] += vk2b
t1 = log.timer_debug1('contracting int2e_ip1ip2 for atom %d'%ia, *t1)
vj2, vk2a, vk2b = \
_get_jk(mol, 'int2e_ipvip1', 9, 's2kl',
['lk->s1ij', dm0 ,
'li->s1kj', dm0a[:,p0:p1], 'li->s1kj', dm0b[:,p0:p1]],
shls_slice=shls_slice, vhfopt=ipvip1_opt)
vj1[:,:,p0:p1] += vj2.transpose(0,2,1) * .5
vk1a += vk2a.transpose(0,2,1)
vk1b += vk2b.transpose(0,2,1)
t1 = log.timer_debug1('contracting int2e_ipvip1 for atom %d'%ia, *t1)
vj1 = vj1.reshape(3,3,nao,nao)
vk1a = vk1a.reshape(3,3,nao,nao)
vk1b = vk1b.reshape(3,3,nao,nao)
ej[i0,i0] += numpy.einsum('xypq,pq->xy', vj1_diag[:,:,p0:p1], dm0[p0:p1])*2
ek[i0,i0] += numpy.einsum('xypq,pq->xy', vk1a_diag[:,:,p0:p1], dm0a[p0:p1])*2
ek[i0,i0] += numpy.einsum('xypq,pq->xy', vk1b_diag[:,:,p0:p1], dm0b[p0:p1])*2
e1[i0,i0] -= numpy.einsum('xypq,pq->xy', s1aa[:,:,p0:p1], dme0[p0:p1])*2
for j0, ja in enumerate(atmlst[:i0+1]):
q0, q1 = aoslices[ja][2:]
ej[i0,j0] += numpy.einsum('xypq,pq->xy', vj1[:,:,q0:q1], dm0[q0:q1])*4
ek[i0,j0] += numpy.einsum('xypq,pq->xy', vk1a[:,:,q0:q1], dm0a[q0:q1])*2
ek[i0,j0] += numpy.einsum('xypq,pq->xy', vk1b[:,:,q0:q1], dm0b[q0:q1])*2
e1[i0,j0] -= numpy.einsum('xypq,pq->xy', s1ab[:,:,p0:p1,q0:q1], dme0[p0:p1,q0:q1])*2
h1ao = hcore_deriv(ia, ja)
e1[i0,j0] += numpy.einsum('xypq,pq->xy', h1ao, dm0)
for j0 in range(i0):
e1[j0,i0] = e1[i0,j0].T
ej[j0,i0] = ej[i0,j0].T
ek[j0,i0] = ek[i0,j0].T
log.timer('UHF partial hessian', *time0)
return e1, ej, ek
[docs]
def make_h1(hessobj, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None):
mol = hessobj.mol
if atmlst is None:
atmlst = range(mol.natm)
nao, nmo = mo_coeff[0].shape
mocca = mo_coeff[0][:,mo_occ[0]>0]
moccb = mo_coeff[1][:,mo_occ[1]>0]
dm0a = numpy.dot(mocca, mocca.T)
dm0b = numpy.dot(moccb, moccb.T)
hcore_deriv = hessobj.base.nuc_grad_method().hcore_generator(mol)
aoslices = mol.aoslice_by_atom()
h1aoa = [None] * mol.natm
h1aob = [None] * mol.natm
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1) + (0, mol.nbas)*3
vj1a, vj1b, vj2a, vj2b, vk1a, vk1b, vk2a, vk2b = \
_get_jk(mol, 'int2e_ip1', 3, 's2kl',
['ji->s2kl', -dm0a[:,p0:p1], 'ji->s2kl', -dm0b[:,p0:p1],
'lk->s1ij', -dm0a , 'lk->s1ij', -dm0b ,
'li->s1kj', -dm0a[:,p0:p1], 'li->s1kj', -dm0b[:,p0:p1],
'jk->s1il', -dm0a , 'jk->s1il', -dm0b ],
shls_slice=shls_slice)
vj1 = vj1a + vj1b
vj2 = vj2a + vj2b
vhfa = vj1 - vk1a
vhfb = vj1 - vk1b
vhfa[:,p0:p1] += vj2 - vk2a
vhfb[:,p0:p1] += vj2 - vk2b
h1 = hcore_deriv(ia)
h1aoa[ia] = h1 + vhfa + vhfa.transpose(0,2,1)
h1aob[ia] = h1 + vhfb + vhfb.transpose(0,2,1)
return (h1aoa,h1aob)
[docs]
def solve_mo1(mf, mo_energy, mo_coeff, mo_occ, h1ao,
fx=None, atmlst=None, max_memory=4000, verbose=None,
max_cycle=50, level_shift=0):
mol = mf.mol
if atmlst is None: atmlst = range(mol.natm)
nao, nmo = mo_coeff[0].shape
mocca = mo_coeff[0][:,mo_occ[0]>0]
moccb = mo_coeff[1][:,mo_occ[1]>0]
nocca = mocca.shape[1]
noccb = moccb.shape[1]
if fx is None:
fx = gen_vind(mf, mo_coeff, mo_occ)
s1a = -mol.intor('int1e_ipovlp', comp=3)
h1aoa, h1aob = h1ao
def _ao2mo(mat, mo_coeff, mocc):
return numpy.asarray([reduce(numpy.dot, (mo_coeff.T, x, mocc)) for x in mat])
mem_now = lib.current_memory()[0]
max_memory = max(2000, max_memory*.9-mem_now)
blksize = max(2, int(max_memory*1e6/8 / (nao*(nocca+noccb)*3*6)))
mo1sa = [None] * mol.natm
mo1sb = [None] * mol.natm
e1sa = [None] * mol.natm
e1sb = [None] * mol.natm
aoslices = mol.aoslice_by_atom()
for ia0, ia1 in lib.prange(0, len(atmlst), blksize):
s1voa = []
s1vob = []
h1voa = []
h1vob = []
for i0 in range(ia0, ia1):
ia = atmlst[i0]
shl0, shl1, p0, p1 = aoslices[ia]
s1ao = numpy.zeros((3,nao,nao))
s1ao[:,p0:p1] += s1a[:,p0:p1]
s1ao[:,:,p0:p1] += s1a[:,p0:p1].transpose(0,2,1)
s1voa.append(_ao2mo(s1ao, mo_coeff[0], mocca))
s1vob.append(_ao2mo(s1ao, mo_coeff[1], moccb))
h1voa.append(_ao2mo(h1aoa[ia], mo_coeff[0], mocca))
h1vob.append(_ao2mo(h1aob[ia], mo_coeff[1], moccb))
h1vo = (numpy.vstack(h1voa), numpy.vstack(h1vob))
s1vo = (numpy.vstack(s1voa), numpy.vstack(s1vob))
tol = mf.conv_tol_cpscf * (ia1 - ia0)
mo1, e1 = ucphf.solve(fx, mo_energy, mo_occ, h1vo, s1vo,
max_cycle=max_cycle, level_shift=level_shift, tol=tol)
mo1a = numpy.einsum('pq,xqi->xpi', mo_coeff[0], mo1[0]).reshape(-1,3,nao,nocca)
mo1b = numpy.einsum('pq,xqi->xpi', mo_coeff[1], mo1[1]).reshape(-1,3,nao,noccb)
e1a = e1[0].reshape(-1,3,nocca,nocca)
e1b = e1[1].reshape(-1,3,noccb,noccb)
for k in range(ia1-ia0):
ia = atmlst[k+ia0]
mo1sa[ia] = mo1a[k]
mo1sb[ia] = mo1b[k]
e1sa[ia] = e1a[k].reshape(3,nocca,nocca)
e1sb[ia] = e1b[k].reshape(3,noccb,noccb)
mo1 = e1 = mo1a = mo1b = e1a = e1b = None
return (mo1sa,mo1sb), (e1sa,e1sb)
[docs]
def gen_vind(mf, mo_coeff, mo_occ):
nao, nmoa = mo_coeff[0].shape
nmob = mo_coeff[1].shape[1]
mocca = mo_coeff[0][:,mo_occ[0]>0]
moccb = mo_coeff[1][:,mo_occ[1]>0]
nocca = mocca.shape[1]
noccb = moccb.shape[1]
vresp = mf.gen_response(mo_coeff, mo_occ, hermi=1)
def fx(mo1):
mo1 = mo1.reshape(-1,nmoa*nocca+nmob*noccb)
nset = len(mo1)
dm1 = numpy.empty((2,nset,nao,nao))
for i, x in enumerate(mo1):
xa = x[:nmoa*nocca].reshape(nmoa,nocca)
xb = x[nmoa*nocca:].reshape(nmob,noccb)
dma = reduce(numpy.dot, (mo_coeff[0], xa, mocca.T))
dmb = reduce(numpy.dot, (mo_coeff[1], xb, moccb.T))
dm1[0,i] = dma + dma.T
dm1[1,i] = dmb + dmb.T
v1 = vresp(dm1)
v1vo = numpy.empty_like(mo1)
for i in range(nset):
v1vo[i,:nmoa*nocca] = reduce(numpy.dot, (mo_coeff[0].T, v1[0,i], mocca)).ravel()
v1vo[i,nmoa*nocca:] = reduce(numpy.dot, (mo_coeff[1].T, v1[1,i], moccb)).ravel()
return v1vo
return fx
[docs]
def gen_hop(hobj, mo_energy=None, mo_coeff=None, mo_occ=None, verbose=None):
log = logger.new_logger(hobj, verbose)
mol = hobj.mol
mf = hobj.base
if mo_energy is None: mo_energy = mf.mo_energy
if mo_occ is None: mo_occ = mf.mo_occ
if mo_coeff is None: mo_coeff = mf.mo_coeff
natm = mol.natm
nao, nmo = mo_coeff[0].shape
mocca = mo_coeff[0][:,mo_occ[0]>0]
moccb = mo_coeff[1][:,mo_occ[1]>0]
mo_ea = mo_energy[0][mo_occ[0]>0]
mo_eb = mo_energy[1][mo_occ[1]>0]
nocca = mocca.shape[1]
noccb = moccb.shape[1]
atmlst = range(natm)
max_memory = max(2000, hobj.max_memory - lib.current_memory()[0])
de2 = hobj.partial_hess_elec(mo_energy, mo_coeff, mo_occ, atmlst,
max_memory, log)
de2 += hobj.hess_nuc()
h1ao_cache = hobj.make_h1(mo_coeff, mo_occ, None, atmlst, log)
h1aoa_cache, h1aob_cache = h1ao_cache
aoslices = mol.aoslice_by_atom()
s1a = -mol.intor('int1e_ipovlp', comp=3)
fvind = gen_vind(mf, mo_coeff, mo_occ)
def h_op(x):
x = x.reshape(natm,3)
hx = numpy.einsum('abxy,ax->by', de2, x)
h1aoa = 0
h1aob = 0
s1ao = 0
for ia in range(natm):
shl0, shl1, p0, p1 = aoslices[ia]
h1aoa += numpy.einsum('x,xij->ij', x[ia], h1aoa_cache[ia])
h1aob += numpy.einsum('x,xij->ij', x[ia], h1aob_cache[ia])
s1ao_i = numpy.zeros((3,nao,nao))
s1ao_i[:,p0:p1] += s1a[:,p0:p1]
s1ao_i[:,:,p0:p1] += s1a[:,p0:p1].transpose(0,2,1)
s1ao += numpy.einsum('x,xij->ij', x[ia], s1ao_i)
s1voa = reduce(numpy.dot, (mo_coeff[0].T, s1ao, mocca))
s1vob = reduce(numpy.dot, (mo_coeff[1].T, s1ao, moccb))
h1voa = reduce(numpy.dot, (mo_coeff[0].T, h1aoa, mocca))
h1vob = reduce(numpy.dot, (mo_coeff[1].T, h1aob, moccb))
mo1, mo_e1 = ucphf.solve(fvind, mo_energy, mo_occ,
(h1voa,h1vob), (s1voa,s1vob))
mo1a = numpy.dot(mo_coeff[0], mo1[0])
mo1b = numpy.dot(mo_coeff[1], mo1[1])
mo_e1a = mo_e1[0].reshape(nocca,nocca)
mo_e1b = mo_e1[1].reshape(noccb,noccb)
dm1a = numpy.einsum('pi,qi->pq', mo1a, mocca)
dm1b = numpy.einsum('pi,qi->pq', mo1b, moccb)
dme1a = numpy.einsum('pi,qi,i->pq', mo1a, mocca, mo_ea)
dme1a = dme1a + dme1a.T + reduce(numpy.dot, (mocca, mo_e1a, mocca.T))
dme1b = numpy.einsum('pi,qi,i->pq', mo1b, moccb, mo_eb)
dme1b = dme1b + dme1b.T + reduce(numpy.dot, (moccb, mo_e1b, moccb.T))
dme1 = dme1a + dme1b
for ja in range(natm):
q0, q1 = aoslices[ja][2:]
hx[ja] += numpy.einsum('xpq,pq->x', h1aoa_cache[ja], dm1a) * 2
hx[ja] += numpy.einsum('xpq,pq->x', h1aob_cache[ja], dm1b) * 2
hx[ja] -= numpy.einsum('xpq,pq->x', s1a[:,q0:q1], dme1[q0:q1])
hx[ja] -= numpy.einsum('xpq,qp->x', s1a[:,q0:q1], dme1[:,q0:q1])
return hx.ravel()
hdiag = numpy.einsum('aaxx->ax', de2).ravel()
return h_op, hdiag
[docs]
class Hessian(rhf_hess.HessianBase):
'''Non-relativistic UHF hessian'''
partial_hess_elec = partial_hess_elec
hess_elec = hess_elec
make_h1 = make_h1
gen_hop = gen_hop
[docs]
def solve_mo1(self, mo_energy, mo_coeff, mo_occ, h1ao,
fx=None, atmlst=None, max_memory=4000, verbose=None):
return solve_mo1(self.base, mo_energy, mo_coeff, mo_occ, h1ao,
fx, atmlst, max_memory, verbose,
max_cycle=self.max_cycle, level_shift=self.level_shift)
from pyscf import scf
scf.uhf.UHF.Hessian = lib.class_as_method(Hessian)
