#!/usr/bin/env python
#
# This code was copied from the data generation program of Tencent Alchemy
# project (https://github.com/tencent-alchemy).
#
#
# Copyright 2019 Tencent America LLC. 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 UKS analytical Hessian
'''
import numpy
from pyscf import lib
from pyscf.lib import logger
from pyscf.hessian import uks as uks_hess
from pyscf.df.hessian import uhf as df_uhf_hess
[docs]
def partial_hess_elec(hessobj, mo_energy=None, mo_coeff=None, mo_occ=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
ni = mf._numint
if mf.do_nlc():
raise NotImplementedError('RKS Hessian for NLC functional')
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)
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin)
hybrid = ni.libxc.is_hybrid_xc(mf.xc)
de2, ej, ek = df_uhf_hess._partial_hess_ejk(hessobj, mo_energy, mo_coeff, mo_occ,
atmlst, max_memory, verbose,
with_k=hybrid)
de2 += ej - hyb * ek # (A,B,dR_A,dR_B)
if hybrid and omega != 0:
with hessobj.base.with_df.range_coulomb(omega):
ek_lr = df_uhf_hess._partial_hess_ejk(
hessobj, mo_energy, mo_coeff, mo_occ, atmlst, max_memory, verbose)[2]
de2 -= ek_lr * (alpha - hyb)
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.9-mem_now)
veffa_diag, veffb_diag = uks_hess._get_vxc_diag(hessobj, mo_coeff, mo_occ, max_memory)
t1 = log.timer_debug1('contracting int2e_ipip1', *t1)
aoslices = mol.aoslice_by_atom()
vxca, vxcb = uks_hess._get_vxc_deriv2(hessobj, mo_coeff, mo_occ, max_memory)
for i0, ia in enumerate(atmlst):
shl0, shl1, p0, p1 = aoslices[ia]
veffa = vxca[ia]
veffb = vxcb[ia]
de2[i0,i0] += numpy.einsum('xypq,pq->xy', veffa_diag[:,:,p0:p1], dm0a[p0:p1])*2
de2[i0,i0] += numpy.einsum('xypq,pq->xy', veffb_diag[:,:,p0:p1], dm0b[p0:p1])*2
for j0, ja in enumerate(atmlst[:i0+1]):
q0, q1 = aoslices[ja][2:]
de2[i0,j0] += numpy.einsum('xypq,pq->xy', veffa[:,:,q0:q1], dm0a[q0:q1])*2
de2[i0,j0] += numpy.einsum('xypq,pq->xy', veffb[:,:,q0:q1], dm0b[q0:q1])*2
for j0 in range(i0):
de2[j0,i0] = de2[i0,j0].T
log.timer('UKS partial hessian', *time0)
return de2
[docs]
def make_h1(hessobj, mo_coeff, mo_occ, chkfile=None, atmlst=None, verbose=None):
mol = hessobj.mol
mf = hessobj.base
ni = mf._numint
ni.libxc.test_deriv_order(mf.xc, 2, raise_error=True)
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin)
hybrid = ni.libxc.is_hybrid_xc(mf.xc)
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.9-mem_now)
h1aoa, h1aob = uks_hess._get_vxc_deriv1(hessobj, mo_coeff, mo_occ, max_memory)
for ia, h1, vj1, vk1 in df_uhf_hess._gen_jk(
hessobj, mo_coeff, mo_occ, chkfile, atmlst, verbose, with_k=hybrid):
f1 = h1 + vj1
h1aoa[ia] += f1
h1aob[ia] += f1
if hybrid:
vk1a, vk1b = vk1
h1aoa[ia] -= hyb * vk1a
h1aob[ia] -= hyb * vk1b
if hybrid and omega != 0:
with hessobj.base.with_df.range_coulomb(omega):
for ia, h1, vj1, vk1 in df_uhf_hess._gen_jk(
hessobj, mo_coeff, mo_occ, chkfile, atmlst, verbose):
vk1a, vk1b = vk1
h1aoa[ia] -= (alpha - hyb) * vk1a
h1aob[ia] -= (alpha - hyb) * vk1b
return h1aoa, h1aob
[docs]
class Hessian(uks_hess.Hessian):
'''Non-relativistic RKS hessian'''
def __init__(self, mf):
uks_hess.Hessian.__init__(self, mf)
auxbasis_response = 1
partial_hess_elec = partial_hess_elec
make_h1 = make_h1
if __name__ == '__main__':
from pyscf import gto
from pyscf import dft
#dft.numint.NumInt.libxc = dft.xcfun
xc_code = 'b3lyp'
mol = gto.Mole()
mol.verbose = 0
mol.output = None
mol.atom = [
[1 , (1. , 0. , 0.000)],
[1 , (0. , 1. , 0.000)],
[1 , (0. , -1.517 , 1.177)],
[1 , (0. , 1.517 , 1.177)],
]
mol.basis = '631g'
mol.unit = 'B'
mol.spin = 2
mol.build()
mf = dft.RKS(mol).density_fit()
mf.grids.level = 4
mf.grids.prune = False
mf.xc = xc_code
mf.conv_tol = 1e-14
mf.kernel()
n3 = mol.natm * 3
hobj = Hessian(mf)
e2 = hobj.kernel().transpose(0,2,1,3).reshape(n3,n3)
print(lib.finger(e2) - 0.0091658598954866277)
