#!/usr/bin/env python
# Copyright 2014-2021 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>
#
from functools import reduce
import numpy as np
from pyscf import lib
from pyscf.lib import logger
from pyscf.tdscf import uhf
from pyscf.tdscf._lr_eig import eigh as lr_eigh, eig as lr_eig
from pyscf.pbc import scf
from pyscf.pbc.tdscf.krhf import KTDBase, _get_e_ia
from pyscf.pbc.lib.kpts_helper import is_gamma_point, get_kconserv_ria, conj_mapping
from pyscf.pbc.scf import _response_functions # noqa
from pyscf import __config__
REAL_EIG_THRESHOLD = getattr(__config__, 'pbc_tdscf_uhf_TDDFT_pick_eig_threshold', 1e-3)
[docs]
def get_ab(mf, kshift=0):
r'''A and B matrices for TDDFT response function.
A[i,a,j,b] = \delta_{ab}\delta_{ij}(E_a - E_i) + (ai||jb)
B[i,a,j,b] = (ai||bj)
Ref: Chem Phys Lett, 256, 454
Kwargs:
kshift : integer
The index of the k-point that represents the transition between
k-points in the excitation coefficients.
'''
cell = mf.cell
mo_energy = scf.addons.mo_energy_with_exxdiv_none(mf)
mo_a, mo_b = mo = np.asarray(mf.mo_coeff)
mo_occ = np.asarray(mf.mo_occ)
kpts = mf.kpts
nkpts, nao, nmo = mo_a.shape
noccs = np.count_nonzero(mo_occ!=0, axis=2)
nocc = noccs[0,0]
nvir = nmo - nocc
assert np.all(noccs == nocc)
nocc_a = nocc_b = nocc
nvir_a = nvir_b = nvir
orbo_a = mo_a[:,:,:nocc]
orbo_b = mo_b[:,:,:nocc]
orbv_a = mo_a[:,:,nocc:]
orbv_b = mo_b[:,:,nocc:]
kconserv = get_kconserv_ria(cell, kpts)[kshift]
e_ia_a = np.asarray(_get_e_ia(mo_energy[0], mo_occ[0], kconserv)).astype(mo.dtype)
e_ia_b = np.asarray(_get_e_ia(mo_energy[1], mo_occ[1], kconserv)).astype(mo.dtype)
a_aa = np.diag(e_ia_a.ravel()).reshape(nkpts,nocc_a,nvir_a,nkpts,nocc_a,nvir_a)
a_bb = np.diag(e_ia_b.ravel()).reshape(nkpts,nocc_b,nvir_b,nkpts,nocc_b,nvir_b)
a_ab = np.zeros((nkpts,nocc_a,nvir_a,nkpts,nocc_b,nvir_b), dtype=a_aa.dtype)
b_aa = np.zeros_like(a_aa)
b_bb = np.zeros_like(a_bb)
b_ab = np.zeros_like(a_ab)
a = (a_aa, a_ab, a_bb)
b = (b_aa, b_ab, b_bb)
weight = 1./nkpts
def add_hf_(a, b, hyb=1):
eri_aa = mf.with_df.ao2mo_7d([mo_a,orbo_a,mo_a,mo_a], kpts)
eri_ab = mf.with_df.ao2mo_7d([mo_a,orbo_a,mo_b,mo_b], kpts)
eri_bb = mf.with_df.ao2mo_7d([mo_b,orbo_b,mo_b,mo_b], kpts)
eri_aa *= weight
eri_ab *= weight
eri_bb *= weight
eri_aa.reshape(nkpts,nkpts,nkpts,nmo,nocc_a,nmo,nmo)
eri_ab.reshape(nkpts,nkpts,nkpts,nmo,nocc_a,nmo,nmo)
eri_bb.reshape(nkpts,nkpts,nkpts,nmo,nocc_b,nmo,nmo)
a_aa, a_ab, a_bb = a
b_aa, b_ab, b_bb = b
for ki, ka in enumerate(kconserv):
for kj, kb in enumerate(kconserv):
a_aa[ki,:,:,kj] += np.einsum('aijb->iajb', eri_aa[ka,ki,kj,nocc_a:,:,:nocc_a,nocc_a:])
a_aa[ki,:,:,kj] -= np.einsum('jiab->iajb', eri_aa[kj,ki,ka,:nocc_a,:,nocc_a:,nocc_a:]) * hyb
a_bb[ki,:,:,kj] += np.einsum('aijb->iajb', eri_bb[ka,ki,kj,nocc_b:,:,:nocc_b,nocc_b:])
a_bb[ki,:,:,kj] -= np.einsum('jiab->iajb', eri_bb[kj,ki,ka,:nocc_b,:,nocc_b:,nocc_b:]) * hyb
a_ab[ki,:,:,kj] += np.einsum('aijb->iajb', eri_ab[ka,ki,kj,nocc_a:,:,:nocc_b,nocc_b:])
for kb, kj in enumerate(kconserv):
b_aa[ki,:,:,kj] += np.einsum('aibj->iajb', eri_aa[ka,ki,kb,nocc_a:,:,nocc_a:,:nocc_a])
b_aa[ki,:,:,kj] -= np.einsum('ajbi->iajb', eri_aa[ka,kj,kb,nocc_a:,:,nocc_a:,:nocc_a]) * hyb
b_bb[ki,:,:,kj] += np.einsum('aibj->iajb', eri_bb[ka,ki,kb,nocc_b:,:,nocc_b:,:nocc_b])
b_bb[ki,:,:,kj] -= np.einsum('ajbi->iajb', eri_bb[ka,kj,kb,nocc_b:,:,nocc_b:,:nocc_b]) * hyb
b_ab[ki,:,:,kj] += np.einsum('aibj->iajb', eri_ab[ka,ki,kb,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)
cmap = conj_mapping(cell, kpts)
if xctype == 'LDA':
ao_deriv = 0
for ao, _, mask, weight, coords \
in ni.block_loop(cell, mf.grids, nao, ao_deriv, kpts, 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('krp,kpi->kri', ao, orbo_a)
rho_v_a = lib.einsum('krp,kpi->kri', ao, orbv_a)
rho_o_b = lib.einsum('krp,kpi->kri', ao, orbo_b)
rho_v_b = lib.einsum('krp,kpi->kri', ao, orbv_b)
rho_ov_a = np.einsum('kri,kra->kria', rho_o_a, rho_v_a)
rho_ov_b = np.einsum('kri,kra->kria', rho_o_b, rho_v_b)
rho_vo_a = rho_ov_a.conj()[cmap]
rho_vo_b = rho_ov_b.conj()[cmap]
w_vo_aa = np.einsum('kria,r->kria', rho_vo_a, wfxc[0,0]) * (1/nkpts)
w_vo_ab = np.einsum('kria,r->kria', rho_vo_a, wfxc[0,1]) * (1/nkpts)
w_vo_bb = np.einsum('kria,r->kria', rho_vo_b, wfxc[1,1]) * (1/nkpts)
a_aa += lib.einsum('kria,lrjb->kialjb', w_vo_aa, rho_ov_a)
b_aa += lib.einsum('kria,lrjb->kialjb', w_vo_aa, rho_vo_a)
a_ab += lib.einsum('kria,lrjb->kialjb', w_vo_ab, rho_ov_b)
b_ab += lib.einsum('kria,lrjb->kialjb', w_vo_ab, rho_vo_b)
a_bb += lib.einsum('kria,lrjb->kialjb', w_vo_bb, rho_ov_b)
b_bb += lib.einsum('kria,lrjb->kialjb', w_vo_bb, rho_vo_b)
elif xctype == 'GGA':
ao_deriv = 1
for ao, _, mask, weight, coords \
in ni.block_loop(cell, mf.grids, nao, ao_deriv, kpts, 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('kxrp,kpi->kxri', ao, orbo_a)
rho_v_a = lib.einsum('kxrp,kpi->kxri', ao, orbv_a)
rho_o_b = lib.einsum('kxrp,kpi->kxri', ao, orbo_b)
rho_v_b = lib.einsum('kxrp,kpi->kxri', ao, orbv_b)
rho_ov_a = np.einsum('kxri,kra->kxria', rho_o_a, rho_v_a[:,0])
rho_ov_b = np.einsum('kxri,kra->kxria', rho_o_b, rho_v_b[:,0])
rho_ov_a[:,1:4] += np.einsum('kri,kxra->kxria', rho_o_a[:,0], rho_v_a[:,1:4])
rho_ov_b[:,1:4] += np.einsum('kri,kxra->kxria', rho_o_b[:,0], rho_v_b[:,1:4])
rho_vo_a = rho_ov_a.conj()[cmap]
rho_vo_b = rho_ov_b.conj()[cmap]
w_vo_aa = np.einsum('xyr,kxria->kyria', wfxc[0,:,0], rho_vo_a) * (1/nkpts)
w_vo_ab = np.einsum('xyr,kxria->kyria', wfxc[0,:,1], rho_vo_a) * (1/nkpts)
w_vo_bb = np.einsum('xyr,kxria->kyria', wfxc[1,:,1], rho_vo_b) * (1/nkpts)
a_aa += lib.einsum('kxria,lxrjb->kialjb', w_vo_aa, rho_ov_a)
b_aa += lib.einsum('kxria,lxrjb->kialjb', w_vo_aa, rho_vo_a)
a_ab += lib.einsum('kxria,lxrjb->kialjb', w_vo_ab, rho_ov_b)
b_ab += lib.einsum('kxria,lxrjb->kialjb', w_vo_ab, rho_vo_b)
a_bb += lib.einsum('kxria,lxrjb->kialjb', w_vo_bb, rho_ov_b)
b_bb += lib.einsum('kxria,lxrjb->kialjb', w_vo_bb, rho_vo_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, kpts, 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('kxrp,kpi->kxri', ao, orbo_a)
rho_o_b = lib.einsum('kxrp,kpi->kxri', ao, orbo_b)
rho_v_a = lib.einsum('kxrp,kpi->kxri', ao, orbv_a)
rho_v_b = lib.einsum('kxrp,kpi->kxri', ao, orbv_b)
rho_ov_a = np.einsum('kxri,kra->kxria', rho_o_a, rho_v_a[:,0])
rho_ov_b = np.einsum('kxri,kra->kxria', 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])
tau_ov_a = np.einsum('kxri,kxra->kria', rho_o_a[:,1:4], rho_v_a[:,1:4]) * .5
tau_ov_b = np.einsum('kxri,kxra->kria', rho_o_b[:,1:4], rho_v_b[:,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()[cmap]
rho_vo_b = rho_ov_b.conj()[cmap]
w_vo_aa = np.einsum('xyr,kxria->kyria', wfxc[0,:,0], rho_vo_a) * (1/nkpts)
w_vo_ab = np.einsum('xyr,kxria->kyria', wfxc[0,:,1], rho_vo_a) * (1/nkpts)
w_vo_bb = np.einsum('xyr,kxria->kyria', wfxc[1,:,1], rho_vo_b) * (1/nkpts)
a_aa += lib.einsum('kxria,lxrjb->kilajb', w_vo_aa, rho_ov_a)
b_aa += lib.einsum('kxria,lxrjb->kilajb', w_vo_aa, rho_vo_a)
a_ab += lib.einsum('kxria,lxrjb->kilajb', w_vo_ab, rho_ov_b)
b_ab += lib.einsum('kxria,lxrjb->kilajb', w_vo_ab, rho_vo_b)
a_bb += lib.einsum('kxria,lxrjb->kilajb', w_vo_bb, rho_ov_b)
b_bb += lib.einsum('kxria,lxrjb->kilajb', w_vo_bb, rho_vo_b)
else:
add_hf_(a, b)
return a, b
[docs]
class TDA(KTDBase):
[docs]
def get_ab(self, mf=None, kshift=0):
if mf is None: mf = self._scf
return get_ab(mf, kshift)
[docs]
def gen_vind(self, mf, kshift=0):
'''Compute Ax
Kwargs:
kshift : integer
The index of the k-point that represents the transition between
k-points in the excitation coefficients.
'''
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ[0])
nao, nmo = mo_coeff[0][0].shape
occidxa = [mo_occ[0][k]> 0 for k in range(nkpts)]
occidxb = [mo_occ[1][k]> 0 for k in range(nkpts)]
viridxa = [mo_occ[0][k]==0 for k in range(nkpts)]
viridxb = [mo_occ[1][k]==0 for k in range(nkpts)]
orboa = [mo_coeff[0][k][:,occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:,occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][k][:,viridxa[k]] for k in range(nkpts)]
orbvb = [mo_coeff[1][k][:,viridxb[k]] for k in range(nkpts)]
dtype = np.result_type(*mo_coeff[0])
moe = scf.addons.mo_energy_with_exxdiv_none(mf)
e_ia_a = _get_e_ia(moe[0], mo_occ[0], kconserv)
e_ia_b = _get_e_ia(moe[1], mo_occ[1], kconserv)
hdiag = np.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = mf.gen_response(hermi=0, max_memory=max_memory)
def vind(zs):
nz = len(zs)
zs = [_unpack(z, mo_occ, kconserv) for z in zs]
dms = np.empty((2,nz,nkpts,nao,nao), dtype=dtype)
for i in range(nz):
dm1a, dm1b = zs[i]
for k, kp in enumerate(kconserv):
dms[0,i,kp] = lib.einsum('ov,pv,qo->pq', dm1a[k], orbva[kp], orboa[k].conj())
dms[1,i,kp] = lib.einsum('ov,pv,qo->pq', dm1b[k], orbvb[kp], orbob[k].conj())
with lib.temporary_env(mf, exxdiv=None):
v1ao = vresp(dms, kshift)
v1ao = v1ao.reshape(2,nz,nkpts,nao,nao)
v1s = []
for i in range(nz):
dm1a, dm1b = zs[i]
v1as = [None] * nkpts
v1bs = [None] * nkpts
for k, kp in enumerate(kconserv):
v1a = lib.einsum('pq,qo,pv->ov', v1ao[0,i,kp], orboa[k], orbva[kp].conj())
v1b = lib.einsum('pq,qo,pv->ov', v1ao[1,i,kp], orbob[k], orbvb[kp].conj())
v1a += e_ia_a[k] * dm1a[k]
v1b += e_ia_b[k] * dm1b[k]
v1as[k] = v1a.ravel()
v1bs[k] = v1b.ravel()
v1s.append( np.concatenate(v1as + v1bs) )
return np.stack(v1s)
return vind, hdiag
[docs]
def init_guess(self, mf, kshift, nstates=None):
if nstates is None: nstates = self.nstates
mo_energy = mf.mo_energy
mo_occ = mf.mo_occ
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
e_ia_a = _get_e_ia(mo_energy[0], mo_occ[0], kconserv)
e_ia_b = _get_e_ia(mo_energy[1], mo_occ[1], kconserv)
e_ia = np.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
nov = e_ia.size
nstates = min(nstates, nov)
e_threshold = np.partition(e_ia, nstates-1)[nstates-1]
e_threshold += self.deg_eia_thresh
idx = np.where(e_ia <= e_threshold)[0]
x0 = np.zeros((idx.size, nov))
for i, j in enumerate(idx):
x0[i, j] = 1 # Koopmans' excitations
return x0
[docs]
def kernel(self, x0=None):
'''TDA diagonalization solver
'''
cpu0 = (logger.process_clock(), logger.perf_counter())
self.check_sanity()
self.dump_flags()
log = logger.new_logger(self)
mf = self._scf
mo_occ = mf.mo_occ
def pickeig(w, v, nroots, envs):
idx = np.where(w > self.positive_eig_threshold)[0]
return w[idx], v[:,idx], idx
log = logger.Logger(self.stdout, self.verbose)
self.converged = []
self.e = []
self.xy = []
for i,kshift in enumerate(self.kshift_lst):
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
vind, hdiag = self.gen_vind(self._scf, kshift)
precond = self.get_precond(hdiag)
if x0 is None:
x0k = self.init_guess(self._scf, kshift, self.nstates)
else:
x0k = x0[i]
converged, e, x1 = lr_eigh(
vind, x0k, precond, tol_residual=self.conv_tol, lindep=self.lindep,
nroots=self.nstates, pick=pickeig, max_cycle=self.max_cycle,
max_memory=self.max_memory, verbose=log)
self.converged.append( converged )
self.e.append( e )
self.xy.append( [(_unpack(xi, mo_occ, kconserv), # (X_alpha, X_beta)
(0, 0)) # (Y_alpha, Y_beta)
for xi in x1] )
#TODO: analyze CIS wfn point group symmetry
log.timer(self.__class__.__name__, *cpu0)
self._finalize()
return self.e, self.xy
CIS = KTDA = TDA
[docs]
class TDHF(KTDBase):
get_ab = TDA.get_ab
[docs]
def gen_vind(self, mf, kshift=0):
assert kshift == 0
mo_coeff = mf.mo_coeff
mo_occ = mf.mo_occ
nkpts = len(mo_occ[0])
nao, nmo = mo_coeff[0][0].shape
occidxa = [mo_occ[0][k]> 0 for k in range(nkpts)]
occidxb = [mo_occ[1][k]> 0 for k in range(nkpts)]
viridxa = [mo_occ[0][k]==0 for k in range(nkpts)]
viridxb = [mo_occ[1][k]==0 for k in range(nkpts)]
orboa = [mo_coeff[0][k][:,occidxa[k]] for k in range(nkpts)]
orbob = [mo_coeff[1][k][:,occidxb[k]] for k in range(nkpts)]
orbva = [mo_coeff[0][k][:,viridxa[k]] for k in range(nkpts)]
orbvb = [mo_coeff[1][k][:,viridxb[k]] for k in range(nkpts)]
dtype = np.result_type(*mo_coeff[0])
kconserv = np.arange(nkpts)
moe = scf.addons.mo_energy_with_exxdiv_none(mf)
e_ia_a = _get_e_ia(moe[0], mo_occ[0], kconserv)
e_ia_b = _get_e_ia(moe[1], mo_occ[1], kconserv)
hdiag = np.hstack([x.ravel() for x in (e_ia_a + e_ia_b)])
tot_x = hdiag.size
hdiag = np.hstack((hdiag, -hdiag))
mem_now = lib.current_memory()[0]
max_memory = max(2000, self.max_memory*.8-mem_now)
vresp = mf.gen_response(hermi=0, max_memory=max_memory)
def vind(xys):
nz = len(xys)
x1s = [_unpack(x[:tot_x], mo_occ, kconserv) for x in xys]
y1s = [_unpack(x[tot_x:], mo_occ, kconserv) for x in xys]
dms = np.empty((2,nz,nkpts,nao,nao), dtype=dtype)
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
for k in range(nkpts):
dms[0,i,k] = lib.einsum('ov,pv,qo->pq', xa[k], orbva[k], orboa[k].conj())
dms[1,i,k] = lib.einsum('ov,pv,qo->pq', xb[k], orbvb[k], orbob[k].conj())
dms[0,i,k] += lib.einsum('ov,qv,po->pq', ya[k], orbva[k].conj(), orboa[k])
dms[1,i,k] += lib.einsum('ov,qv,po->pq', yb[k], orbvb[k].conj(), orbob[k])
with lib.temporary_env(mf, exxdiv=None):
v1ao = vresp(dms, kshift)
v1ao = v1ao.reshape(2,nz,nkpts,nao,nao)
v1s = []
for i in range(nz):
xa, xb = x1s[i]
ya, yb = y1s[i]
v1xsa = [0] * nkpts
v1xsb = [0] * nkpts
v1ysa = [0] * nkpts
v1ysb = [0] * nkpts
for k in range(nkpts):
v1xa = lib.einsum('pq,qo,pv->ov', v1ao[0,i,k], orboa[k], orbva[k].conj())
v1xb = lib.einsum('pq,qo,pv->ov', v1ao[1,i,k], orbob[k], orbvb[k].conj())
v1ya = lib.einsum('pq,po,qv->ov', v1ao[0,i,k], orboa[k].conj(), orbva[k])
v1yb = lib.einsum('pq,po,qv->ov', v1ao[1,i,k], orbob[k].conj(), orbvb[k])
v1xa += e_ia_a[k] * xa[k]
v1xb += e_ia_b[k] * xb[k]
v1ya += e_ia_a[k] * ya[k]
v1yb += e_ia_b[k] * yb[k]
v1xsa[k] += v1xa.ravel()
v1xsb[k] += v1xb.ravel()
v1ysa[k] -= v1ya.ravel()
v1ysb[k] -= v1yb.ravel()
v1s.append( np.concatenate(v1xsa + v1xsb + v1ysa + v1ysb) )
return np.stack(v1s)
return vind, hdiag
[docs]
def init_guess(self, mf, kshift, nstates=None, wfnsym=None):
x0 = TDA.init_guess(self, mf, kshift, nstates)
y0 = np.zeros_like(x0)
return np.hstack([x0, y0])
get_precond = uhf.TDHF.get_precond
[docs]
def kernel(self, x0=None):
'''TDHF diagonalization with non-Hermitian eigenvalue solver
'''
cpu0 = (logger.process_clock(), logger.perf_counter())
self.check_sanity()
self.dump_flags()
log = logger.new_logger(self)
mf = self._scf
mo_occ = mf.mo_occ
real_system = (is_gamma_point(self._scf.kpts) and
self._scf.mo_coeff[0][0].dtype == np.double)
if any(k != 0 for k in self.kshift_lst):
raise RuntimeError('kshift != 0 for TDHF')
# We only need positive eigenvalues
def pickeig(w, v, nroots, envs):
realidx = np.where((abs(w.imag) < REAL_EIG_THRESHOLD) &
(w.real > self.positive_eig_threshold))[0]
return lib.linalg_helper._eigs_cmplx2real(w, v, realidx, real_system)
self.converged = []
self.e = []
self.xy = []
for i,kshift in enumerate(self.kshift_lst):
kconserv = get_kconserv_ria(mf.cell, mf.kpts)[kshift]
vind, hdiag = self.gen_vind(self._scf, kshift)
precond = self.get_precond(hdiag)
if x0 is None:
x0k = self.init_guess(self._scf, kshift, self.nstates)
else:
x0k = x0[i]
converged, w, x1 = lr_eig(
vind, x0k, precond, tol_residual=self.conv_tol, lindep=self.lindep,
nroots=self.nstates, pick=pickeig, max_cycle=self.max_cycle,
max_memory=self.max_memory, verbose=log)
self.converged.append( converged )
e = []
xy = []
for i, z in enumerate(x1):
xs, ys = z.reshape(2,-1)
norm = lib.norm(xs)**2 - lib.norm(ys)**2
if norm < 0:
log.warn('TDDFT amplitudes |X| smaller than |Y|')
norm = abs(norm)**-.5
xs *= norm
ys *= norm
e.append(w[i])
xy.append((_unpack(xs, mo_occ, kconserv), _unpack(ys, mo_occ, kconserv)))
self.e.append( np.array(e) )
self.xy.append( xy )
log.timer(self.__class__.__name__, *cpu0)
self._finalize()
return self.e, self.xy
RPA = KTDHF = TDHF
def _unpack(vo, mo_occ, kconserv):
za = []
zb = []
p1 = 0
no_a_kpts = [np.count_nonzero(occ) for occ in mo_occ[0]]
no_b_kpts = [np.count_nonzero(occ) for occ in mo_occ[1]]
for k, occ in enumerate(mo_occ[0]):
no = no_a_kpts[k]
nv = occ.size - no_a_kpts[kconserv[k]]
p0, p1 = p1, p1 + no * nv
za.append(vo[p0:p1].reshape(no,nv))
for k, occ in enumerate(mo_occ[1]):
no = no_b_kpts[k]
nv = occ.size - no_b_kpts[kconserv[k]]
p0, p1 = p1, p1 + no * nv
zb.append(vo[p0:p1].reshape(no,nv))
return za, zb
scf.kuhf.KUHF.TDA = lib.class_as_method(KTDA)
scf.kuhf.KUHF.TDHF = lib.class_as_method(KTDHF)
