#!/usr/bin/env python
# Copyright 2014-2018 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>
#
import numpy as np
from pyscf import lib
from pyscf.tdscf import uhf
from pyscf.pbc.tdscf import rhf as td_rhf
from pyscf.pbc.tdscf.rhf import TDBase
[docs]
def get_ab(mf):
r'''A and B matrices for TDDFT response function.
A[i,a,j,b] = \delta_{ab}\delta_{ij}(E_a - E_i) + (ia||bj)
B[i,a,j,b] = (ia||jb)
Spin symmetry is considered in the returned A, B lists. List A has three
items: (A_aaaa, A_aabb, A_bbbb). A_bbaa = A_aabb.transpose(2,3,0,1).
B has three items: (B_aaaa, B_aabb, B_bbbb).
B_bbaa = B_aabb.transpose(2,3,0,1).
'''
cell = mf.cell
nao = cell.nao_nr()
mo_energy = scf.addons.mo_energy_with_exxdiv_none(mf)
mo = np.asarray(mf.mo_coeff)
mo_occ = np.asarray(mf.mo_occ)
kpt = mf.kpt
occidx_a = np.where(mo_occ[0]==1)[0]
viridx_a = np.where(mo_occ[0]==0)[0]
occidx_b = np.where(mo_occ[1]==1)[0]
viridx_b = np.where(mo_occ[1]==0)[0]
orbo_a = mo[0][:,occidx_a]
orbv_a = mo[0][:,viridx_a]
orbo_b = mo[1][:,occidx_b]
orbv_b = mo[1][:,viridx_b]
nocc_a = orbo_a.shape[1]
nvir_a = orbv_a.shape[1]
nocc_b = orbo_b.shape[1]
nvir_b = orbv_b.shape[1]
mo_a = np.hstack((orbo_a,orbv_a))
mo_b = np.hstack((orbo_b,orbv_b))
nmo_a = nocc_a + nvir_a
nmo_b = nocc_b + nvir_b
e_ia_a = (mo_energy[0][viridx_a,None] - mo_energy[0][occidx_a]).T
e_ia_b = (mo_energy[1][viridx_b,None] - mo_energy[1][occidx_b]).T
a_aa = np.diag(e_ia_a.ravel()).reshape(nocc_a,nvir_a,nocc_a,nvir_a)
a_bb = np.diag(e_ia_b.ravel()).reshape(nocc_b,nvir_b,nocc_b,nvir_b)
a_ab = np.zeros((nocc_a,nvir_a,nocc_b,nvir_b))
b_aa = np.zeros_like(a_aa)
b_ab = np.zeros_like(a_ab)
b_bb = np.zeros_like(a_bb)
a = (a_aa, a_ab, a_bb)
b = (b_aa, b_ab, b_bb)
def add_hf_(a, b, hyb=1):
eri_aa = mf.with_df.ao2mo([orbo_a,mo_a,mo_a,mo_a], kpt, compact=False)
eri_ab = mf.with_df.ao2mo([orbo_a,mo_a,mo_b,mo_b], kpt, compact=False)
eri_bb = mf.with_df.ao2mo([orbo_b,mo_b,mo_b,mo_b], kpt, compact=False)
eri_aa = eri_aa.reshape(nocc_a,nmo_a,nmo_a,nmo_a)
eri_ab = eri_ab.reshape(nocc_a,nmo_a,nmo_b,nmo_b)
eri_bb = eri_bb.reshape(nocc_b,nmo_b,nmo_b,nmo_b)
a_aa, a_ab, a_bb = a
b_aa, b_ab, b_bb = b
a_aa += np.einsum('iabj->iajb', eri_aa[:nocc_a,nocc_a:,nocc_a:,:nocc_a])
a_aa -= np.einsum('ijba->iajb', eri_aa[:nocc_a,:nocc_a,nocc_a:,nocc_a:]) * hyb
b_aa += np.einsum('iajb->iajb', eri_aa[:nocc_a,nocc_a:,:nocc_a,nocc_a:])
b_aa -= np.einsum('jaib->iajb', eri_aa[:nocc_a,nocc_a:,:nocc_a,nocc_a:]) * hyb
a_bb += np.einsum('iabj->iajb', eri_bb[:nocc_b,nocc_b:,nocc_b:,:nocc_b])
a_bb -= np.einsum('ijba->iajb', eri_bb[:nocc_b,:nocc_b,nocc_b:,nocc_b:]) * hyb
b_bb += np.einsum('iajb->iajb', eri_bb[:nocc_b,nocc_b:,:nocc_b,nocc_b:])
b_bb -= np.einsum('jaib->iajb', eri_bb[:nocc_b,nocc_b:,:nocc_b,nocc_b:]) * hyb
a_ab += np.einsum('iabj->iajb', eri_ab[:nocc_a,nocc_a:,nocc_b:,:nocc_b])
b_ab += np.einsum('iajb->iajb', eri_ab[:nocc_a,nocc_a:,:nocc_b,nocc_b:])
if isinstance(mf, scf.hf.KohnShamDFT):
ni = mf._numint
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, cell.spin)
add_hf_(a, b, hyb)
if omega != 0: # For RSH
raise NotImplementedError
xctype = ni._xc_type(mf.xc)
dm0 = mf.make_rdm1(mo, mo_occ)
make_rho = ni._gen_rho_evaluator(cell, dm0, hermi=1, with_lapl=False)[0]
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.8-mem_now)
if xctype == 'LDA':
ao_deriv = 0
for ao, _, mask, weight, coords \
in ni.block_loop(cell, mf.grids, nao, ao_deriv, kpt, None, max_memory):
rho0a = make_rho(0, ao, mask, xctype)
rho0b = make_rho(1, ao, mask, xctype)
rho = (rho0a, rho0b)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = fxc[:,0,:,0] * weight
rho_o_a = lib.einsum('rp,pi->ri', ao, orbo_a)
rho_v_a = lib.einsum('rp,pi->ri', ao, orbv_a)
rho_o_b = lib.einsum('rp,pi->ri', ao, orbo_b)
rho_v_b = lib.einsum('rp,pi->ri', ao, orbv_b)
rho_ov_a = np.einsum('ri,ra->ria', rho_o_a, rho_v_a)
rho_ov_b = np.einsum('ri,ra->ria', rho_o_b, rho_v_b)
rho_vo_a = rho_ov_a.conj()
rho_vo_b = rho_ov_b.conj()
w_ov_aa = np.einsum('ria,r->ria', rho_ov_a, wfxc[0,0])
w_ov_ab = np.einsum('ria,r->ria', rho_ov_a, wfxc[0,1])
w_ov_bb = np.einsum('ria,r->ria', rho_ov_b, wfxc[1,1])
a_aa += lib.einsum('ria,rjb->iajb', w_ov_aa, rho_vo_a)
b_aa += lib.einsum('ria,rjb->iajb', w_ov_aa, rho_ov_a)
a_ab += lib.einsum('ria,rjb->iajb', w_ov_ab, rho_vo_b)
b_ab += lib.einsum('ria,rjb->iajb', w_ov_ab, rho_ov_b)
a_bb += lib.einsum('ria,rjb->iajb', w_ov_bb, rho_vo_b)
b_bb += lib.einsum('ria,rjb->iajb', w_ov_bb, rho_ov_b)
elif xctype == 'GGA':
ao_deriv = 1
for ao, _, mask, weight, coords \
in ni.block_loop(cell, mf.grids, nao, ao_deriv, kpt, None, max_memory):
rho0a = make_rho(0, ao, mask, xctype)
rho0b = make_rho(1, ao, mask, xctype)
rho = (rho0a, rho0b)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = fxc * weight
rho_o_a = lib.einsum('xrp,pi->xri', ao, orbo_a)
rho_v_a = lib.einsum('xrp,pi->xri', ao, orbv_a)
rho_o_b = lib.einsum('xrp,pi->xri', ao, orbo_b)
rho_v_b = lib.einsum('xrp,pi->xri', ao, orbv_b)
rho_ov_a = np.einsum('xri,ra->xria', rho_o_a, rho_v_a[0])
rho_ov_b = np.einsum('xri,ra->xria', rho_o_b, rho_v_b[0])
rho_ov_a[1:4] += np.einsum('ri,xra->xria', rho_o_a[0], rho_v_a[1:4])
rho_ov_b[1:4] += np.einsum('ri,xra->xria', rho_o_b[0], rho_v_b[1:4])
rho_vo_a = rho_ov_a.conj()
rho_vo_b = rho_ov_b.conj()
w_ov_aa = np.einsum('xyr,xria->yria', wfxc[0,:,0], rho_ov_a)
w_ov_ab = np.einsum('xyr,xria->yria', wfxc[0,:,1], rho_ov_a)
w_ov_bb = np.einsum('xyr,xria->yria', wfxc[1,:,1], rho_ov_b)
a_aa += lib.einsum('xria,xrjb->iajb', w_ov_aa, rho_vo_a)
b_aa += lib.einsum('xria,xrjb->iajb', w_ov_aa, rho_ov_a)
a_ab += lib.einsum('xria,xrjb->iajb', w_ov_ab, rho_vo_b)
b_ab += lib.einsum('xria,xrjb->iajb', w_ov_ab, rho_ov_b)
a_bb += lib.einsum('xria,xrjb->iajb', w_ov_bb, rho_vo_b)
b_bb += lib.einsum('xria,xrjb->iajb', w_ov_bb, rho_ov_b)
elif xctype == 'HF':
pass
elif xctype == 'NLC':
raise NotImplementedError('NLC')
elif xctype == 'MGGA':
ao_deriv = 1
for ao, _, mask, weight, coords \
in ni.block_loop(cell, mf.grids, nao, ao_deriv, kpt, None, max_memory):
rho0a = make_rho(0, ao, mask, xctype)
rho0b = make_rho(1, ao, mask, xctype)
rho = (rho0a, rho0b)
fxc = ni.eval_xc_eff(mf.xc, rho, deriv=2, xctype=xctype)[2]
wfxc = fxc * weight
rho_oa = lib.einsum('xrp,pi->xri', ao, orbo_a)
rho_ob = lib.einsum('xrp,pi->xri', ao, orbo_b)
rho_va = lib.einsum('xrp,pi->xri', ao, orbv_a)
rho_vb = lib.einsum('xrp,pi->xri', ao, orbv_b)
rho_ov_a = np.einsum('xri,ra->xria', rho_oa, rho_va[0])
rho_ov_b = np.einsum('xri,ra->xria', rho_ob, rho_vb[0])
rho_ov_a[1:4] += np.einsum('ri,xra->xria', rho_oa[0], rho_va[1:4])
rho_ov_b[1:4] += np.einsum('ri,xra->xria', rho_ob[0], rho_vb[1:4])
tau_ov_a = np.einsum('xri,xra->ria', rho_oa[1:4], rho_va[1:4]) * .5
tau_ov_b = np.einsum('xri,xra->ria', rho_ob[1:4], rho_vb[1:4]) * .5
rho_ov_a = np.vstack([rho_ov_a, tau_ov_a[np.newaxis]])
rho_ov_b = np.vstack([rho_ov_b, tau_ov_b[np.newaxis]])
rho_vo_a = rho_ov_a.conj()
rho_vo_b = rho_ov_b.conj()
w_ov_aa = np.einsum('xyr,xria->yria', wfxc[0,:,0], rho_ov_a)
w_ov_ab = np.einsum('xyr,xria->yria', wfxc[0,:,1], rho_ov_a)
w_ov_bb = np.einsum('xyr,xria->yria', wfxc[1,:,1], rho_ov_b)
a_aa += lib.einsum('xria,xrjb->iajb', w_ov_aa, rho_vo_a)
b_aa += lib.einsum('xria,xrjb->iajb', w_ov_aa, rho_ov_a)
a_ab += lib.einsum('xria,xrjb->iajb', w_ov_ab, rho_vo_b)
b_ab += lib.einsum('xria,xrjb->iajb', w_ov_ab, rho_ov_b)
a_bb += lib.einsum('xria,xrjb->iajb', w_ov_bb, rho_vo_b)
b_bb += lib.einsum('xria,xrjb->iajb', w_ov_bb, rho_ov_b)
else:
add_hf_(a, b)
return a, b
[docs]
class TDA(TDBase):
[docs]
def get_ab(self, mf=None):
if mf is None: mf = self._scf
return get_ab(mf)
singlet = None
init_guess = uhf.TDA.init_guess
kernel = uhf.TDA.kernel
_gen_vind = uhf.TDA.gen_vind
gen_vind = td_rhf.TDA.gen_vind
CIS = TDA
[docs]
class TDHF(TDBase):
[docs]
def get_ab(self, mf=None):
if mf is None: mf = self._scf
return get_ab(mf)
singlet = None
init_guess = uhf.TDHF.init_guess
kernel = uhf.TDHF.kernel
_gen_vind = uhf.TDHF.gen_vind
gen_vind = td_rhf.TDA.gen_vind
RPA = TDUHF = TDHF
from pyscf.pbc import scf
scf.uhf.UHF.TDA = lib.class_as_method(TDA)
scf.uhf.UHF.TDHF = lib.class_as_method(TDHF)
