def get_pnucp(mydf, kpts=None):
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = (logger.process_clock(), logger.perf_counter())
nkpts = len(kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao + 1) // 2
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.mesh)
charge = -cell.atom_charges()
kpt_allow = numpy.zeros(3)
coulG = tools.get_coulG(cell, kpt_allow, mesh=mydf.mesh, Gv=Gv)
coulG *= kws
if mydf.eta == 0:
wj = numpy.zeros((nkpts, nao_pair), dtype=numpy.complex128)
SI = cell.get_SI(Gv)
vG = numpy.einsum('i,ix->x', charge, SI) * coulG
wj = numpy.zeros((nkpts, nao_pair), dtype=numpy.complex128)
else:
nuccell = copy.copy(cell)
half_sph_norm = .5 / numpy.sqrt(numpy.pi)
norm = half_sph_norm / mole.gaussian_int(2, mydf.eta)
chg_env = [mydf.eta, norm]
ptr_eta = cell._env.size
ptr_norm = ptr_eta + 1
chg_bas = [[ia, 0, 1, 1, 0, ptr_eta, ptr_norm, 0]
for ia in range(cell.natm)]
nuccell._atm = cell._atm
nuccell._bas = numpy.asarray(chg_bas, dtype=numpy.int32)
nuccell._env = numpy.hstack((cell._env, chg_env))
wj = lib.asarray(mydf._int_nuc_vloc(nuccell, kpts_lst, 'int3c2e_pvp1'))
t1 = log.timer_debug1('pnucp pass1: analytic int', *t1)
aoaux = ft_ao.ft_ao(nuccell, Gv)
vG = numpy.einsum('i,xi->x', charge, aoaux) * coulG
if cell.dimension == 3:
nucbar = sum(
[z / nuccell.bas_exp(i)[0] for i, z in enumerate(charge)])
nucbar *= numpy.pi / cell.vol
ovlp = cell.pbc_intor('int1e_kin', 1, lib.HERMITIAN, kpts_lst)
for k in range(nkpts):
s = lib.pack_tril(ovlp[k])
# *2 due to the factor 1/2 in T
wj[k] -= nucbar * 2 * s
max_memory = max(2000, mydf.max_memory - lib.current_memory()[0])
for aoaoks, p0, p1 in mydf.ft_loop(mydf.mesh,
kpt_allow,
kpts_lst,
max_memory=max_memory,
aosym='s2',
intor='GTO_ft_pdotp'):
for k, aoao in enumerate(aoaoks):
if aft_jk.gamma_point(kpts_lst[k]):
wj[k] += numpy.einsum('k,kx->x', vG[p0:p1].real, aoao.real)
wj[k] += numpy.einsum('k,kx->x', vG[p0:p1].imag, aoao.imag)
else:
wj[k] += numpy.einsum('k,kx->x', vG[p0:p1].conj(), aoao)
t1 = log.timer_debug1('contracting pnucp', *t1)
wj_kpts = []
for k, kpt in enumerate(kpts_lst):
if aft_jk.gamma_point(kpt):
wj_kpts.append(lib.unpack_tril(wj[k].real.copy()))
else:
wj_kpts.append(lib.unpack_tril(wj[k]))
if kpts is None or numpy.shape(kpts) == (3, ):
wj_kpts = wj_kpts[0]
return numpy.asarray(wj_kpts)
def get_pbc_pvxp(cell, kpts=None):
import numpy
import copy
import time
from pyscf import lib
from pyscf.lib import logger
from pyscf.pbc import tools
from pyscf.gto import mole
from pyscf.pbc.df import ft_ao
from pyscf.pbc.df import aft_jk
from pyscf.pbc.df import aft
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
log = logger.Logger(cell.stdout, cell.verbose)
t1 = t0 = (time.clock(), time.time())
mydf = aft.AFTDF(cell, kpts)
mydf.eta = 0.2
ke_guess = aft.estimate_ke_cutoff_for_eta(cell, mydf.eta, cell.precision)
mydf.mesh = tools.cutoff_to_mesh(cell.lattice_vectors(), ke_guess)
log.debug('mydf.mesh %s', mydf.mesh)
nkpts = len(kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao+1) // 2
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.mesh)
charge = -cell.atom_charges() # Apply Koseki effective charge?
kpt_allow = numpy.zeros(3)
coulG = tools.get_coulG(cell, kpt_allow, mesh=mydf.mesh, Gv=Gv)
coulG *= kws
if mydf.eta == 0:
soc_mat = numpy.zeros((nkpts,3,nao*nao), dtype=numpy.complex128)
SI = cell.get_SI(Gv)
vG = numpy.einsum('i,ix->x', charge, SI) * coulG
else:
nuccell = copy.copy(cell)
half_sph_norm = .5/numpy.sqrt(numpy.pi)
norm = half_sph_norm/mole.gaussian_int(2, mydf.eta)
chg_env = [mydf.eta, norm]
ptr_eta = cell._env.size
ptr_norm = ptr_eta + 1
chg_bas = [[ia, 0, 1, 1, 0, ptr_eta, ptr_norm, 0] for ia in range(cell.natm)]
nuccell._atm = cell._atm
nuccell._bas = numpy.asarray(chg_bas, dtype=numpy.int32)
nuccell._env = numpy.hstack((cell._env, chg_env))
soc_mat = mydf._int_nuc_vloc(nuccell, kpts_lst, 'int3c2e_pvxp1_sph',
aosym='s1', comp=3)
soc_mat = numpy.asarray(soc_mat).reshape(nkpts,3,nao**2)
t1 = log.timer_debug1('pnucp pass1: analytic int', *t1)
aoaux = ft_ao.ft_ao(nuccell, Gv)
vG = numpy.einsum('i,xi->x', charge, aoaux) * coulG
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
for aoaoks, p0, p1 in mydf.ft_loop(mydf.mesh, kpt_allow, kpts_lst,
max_memory=max_memory, aosym='s1',
intor='GTO_ft_pxp_sph', comp=3):
for k, aoao in enumerate(aoaoks):
aoao = aoao.reshape(3,-1,nao**2)
if aft_jk.gamma_point(kpts_lst[k]):
soc_mat[k] += numpy.einsum('k,ckx->cx', vG[p0:p1].real, aoao.real)
soc_mat[k] += numpy.einsum('k,ckx->cx', vG[p0:p1].imag, aoao.imag)
else:
soc_mat[k] += numpy.einsum('k,ckx->cx', vG[p0:p1].conj(), aoao)
t1 = log.timer_debug1('contracting pnucp', *t1)
soc_mat_kpts = []
for k, kpt in enumerate(kpts_lst):
if aft_jk.gamma_point(kpt):
soc_mat_kpts.append(soc_mat[k].real.reshape(3,nao,nao))
else:
soc_mat_kpts.append(soc_mat[k].reshape(3,nao,nao))
if kpts is None or numpy.shape(kpts) == (3,):
soc_mat_kpts = soc_mat_kpts[0]
return numpy.asarray(soc_mat_kpts)
def get_pnucp(mydf, kpts=None):
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1, 3))
else:
kpts_lst = numpy.reshape(kpts, (-1, 3))
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
nkpts = len(kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao + 1) // 2
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.gs)
kpt_allow = numpy.zeros(3)
if mydf.eta == 0:
charge = -cell.atom_charges()
#coulG=4*numpy.pi/G^2 is cancelled with (sigma dot p i, sigma dot p j)
SI = cell.get_SI(Gv)
vGR = numpy.einsum('i,ix->x', 4 * numpy.pi * charge, SI.real) * kws
vGI = numpy.einsum('i,ix->x', 4 * numpy.pi * charge, SI.imag) * kws
wjR = numpy.zeros((nkpts, nao_pair))
wjI = numpy.zeros((nkpts, nao_pair))
else:
nuccell = copy.copy(cell)
half_sph_norm = .5 / numpy.sqrt(numpy.pi)
norm = half_sph_norm / mole._gaussian_int(2, mydf.eta)
chg_env = [mydf.eta, norm]
ptr_eta = cell._env.size
ptr_norm = ptr_eta + 1
chg_bas = [[ia, 0, 1, 1, 0, ptr_eta, ptr_norm, 0]
for ia in range(cell.natm)]
nuccell._atm = cell._atm
nuccell._bas = numpy.asarray(chg_bas, dtype=numpy.int32)
nuccell._env = numpy.hstack((cell._env, chg_env))
wj = lib.asarray(
mydf._int_nuc_vloc(nuccell, kpts_lst, 'int3c2e_pvp1_sph'))
wjR = wj.real
wjI = wj.imag
t1 = log.timer_debug1('pnucp pass1: analytic int', *t1)
charge = -cell.atom_charges()
#coulG=4*numpy.pi/G^2 is cancelled with (sigma dot p i, sigma dot p j)
aoaux = ft_ao.ft_ao(nuccell, Gv)
vGR = numpy.einsum('i,xi->x', 4 * numpy.pi * charge, aoaux.real) * kws
vGI = numpy.einsum('i,xi->x', 4 * numpy.pi * charge, aoaux.imag) * kws
max_memory = max(2000, mydf.max_memory - lib.current_memory()[0])
for k, pqkR, pqkI, p0, p1 \
in mydf.ft_loop(mydf.gs, kpt_allow, kpts_lst,
max_memory=max_memory, aosym='s2'):
# rho_ij(G) nuc(-G) / G^2
# = [Re(rho_ij(G)) + Im(rho_ij(G))*1j] [Re(nuc(G)) - Im(nuc(G))*1j] / G^2
if not aft_jk.gamma_point(kpts_lst[k]):
wjI[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkI)
wjI[k] -= numpy.einsum('k,xk->x', vGI[p0:p1], pqkR)
wjR[k] += numpy.einsum('k,xk->x', vGR[p0:p1], pqkR)
wjR[k] += numpy.einsum('k,xk->x', vGI[p0:p1], pqkI)
t1 = log.timer_debug1('contracting Vnuc', *t1)
if mydf.eta != 0 and cell.dimension == 3:
nucbar = sum([z / nuccell.bas_exp(i)[0] for i, z in enumerate(charge)])
nucbar *= numpy.pi / cell.vol * 2
ovlp = cell.pbc_intor('int1e_kin_sph', 1, lib.HERMITIAN, kpts_lst)
for k in range(nkpts):
s = lib.pack_tril(ovlp[k])
wjR[k] -= nucbar * s.real
wjI[k] -= nucbar * s.imag
wj = []
for k, kpt in enumerate(kpts_lst):
if aft_jk.gamma_point(kpt):
wj.append(lib.unpack_tril(wjR[k]))
else:
wj.append(lib.unpack_tril(wjR[k] + wjI[k] * 1j))
if kpts is None or numpy.shape(kpts) == (3, ):
wj = wj[0]
return wj
def get_pnucp(mydf, kpts=None):
cell = mydf.cell
if kpts is None:
kpts_lst = numpy.zeros((1,3))
else:
kpts_lst = numpy.reshape(kpts, (-1,3))
log = logger.Logger(mydf.stdout, mydf.verbose)
t1 = t0 = (time.clock(), time.time())
nkpts = len(kpts_lst)
nao = cell.nao_nr()
nao_pair = nao * (nao+1) // 2
Gv, Gvbase, kws = cell.get_Gv_weights(mydf.mesh)
charge = -cell.atom_charges()
kpt_allow = numpy.zeros(3)
coulG = tools.get_coulG(cell, kpt_allow, mesh=mydf.mesh, Gv=Gv)
coulG *= kws
if mydf.eta == 0:
wj = numpy.zeros((nkpts,nao_pair), dtype=numpy.complex128)
SI = cell.get_SI(Gv)
vG = numpy.einsum('i,ix->x', charge, SI) * coulG
wj = numpy.zeros((nkpts,nao_pair), dtype=numpy.complex128)
else:
nuccell = copy.copy(cell)
half_sph_norm = .5/numpy.sqrt(numpy.pi)
norm = half_sph_norm/mole.gaussian_int(2, mydf.eta)
chg_env = [mydf.eta, norm]
ptr_eta = cell._env.size
ptr_norm = ptr_eta + 1
chg_bas = [[ia, 0, 1, 1, 0, ptr_eta, ptr_norm, 0] for ia in range(cell.natm)]
nuccell._atm = cell._atm
nuccell._bas = numpy.asarray(chg_bas, dtype=numpy.int32)
nuccell._env = numpy.hstack((cell._env, chg_env))
wj = lib.asarray(mydf._int_nuc_vloc(nuccell, kpts_lst, 'int3c2e_pvp1'))
t1 = log.timer_debug1('pnucp pass1: analytic int', *t1)
aoaux = ft_ao.ft_ao(nuccell, Gv)
vG = numpy.einsum('i,xi->x', charge, aoaux) * coulG
if cell.dimension == 3:
nucbar = sum([z/nuccell.bas_exp(i)[0] for i,z in enumerate(charge)])
nucbar *= numpy.pi/cell.vol
ovlp = cell.pbc_intor('int1e_kin', 1, lib.HERMITIAN, kpts_lst)
for k in range(nkpts):
s = lib.pack_tril(ovlp[k])
# *2 due to the factor 1/2 in T
wj[k] -= nucbar*2 * s
max_memory = max(2000, mydf.max_memory-lib.current_memory()[0])
for aoaoks, p0, p1 in mydf.ft_loop(mydf.mesh, kpt_allow, kpts_lst,
max_memory=max_memory, aosym='s2',
intor='GTO_ft_pdotp'):
for k, aoao in enumerate(aoaoks):
if aft_jk.gamma_point(kpts_lst[k]):
wj[k] += numpy.einsum('k,kx->x', vG[p0:p1].real, aoao.real)
wj[k] += numpy.einsum('k,kx->x', vG[p0:p1].imag, aoao.imag)
else:
wj[k] += numpy.einsum('k,kx->x', vG[p0:p1].conj(), aoao)
t1 = log.timer_debug1('contracting pnucp', *t1)
wj_kpts = []
for k, kpt in enumerate(kpts_lst):
if aft_jk.gamma_point(kpt):
wj_kpts.append(lib.unpack_tril(wj[k].real.copy()))
else:
wj_kpts.append(lib.unpack_tril(wj[k]))
if kpts is None or numpy.shape(kpts) == (3,):
wj_kpts = wj_kpts[0]
return numpy.asarray(wj_kpts)