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 _uncontract_mol(mol, xuncontract=False, exp_drop=0.2):
'''mol._basis + uncontracted steep functions'''
pmol = copy.copy(mol)
_bas = []
_env = []
ptr = len(pmol._env)
contr_coeff = []
for ib in range(mol.nbas):
if isinstance(xuncontract, str):
ia = mol.bas_atom(ib)
uncontract_me = ((xuncontract == mol.atom_pure_symbol(ia)) or
(xuncontract == mol.atom_symbol(ia)))
elif isinstance(xuncontract, (tuple, list)):
ia = mol.bas_atom(ib)
uncontract_me = ((mol.atom_pure_symbol(ia) in xuncontract) or
(mol.atom_symbol(ia) in xuncontract) or
(ia in xuncontract))
else:
uncontract_me = xuncontract
nc = mol._bas[ib,mole.NCTR_OF]
l = mol._bas[ib,mole.ANG_OF]
if mol.cart:
degen = (l + 1) * (l + 2) // 2
else:
degen = l * 2 + 1
if uncontract_me:
np = mol._bas[ib,mole.NPRIM_OF]
pexp = mol._bas[ib,mole.PTR_EXP]
# Modfied partially uncontraction to avoid potentially lindep in the
# segment-contracted basis
nkept = (pmol._env[pexp:pexp+np] > exp_drop).sum()
if nkept > nc:
b_coeff = mol.bas_ctr_coeff(ib)
importance = numpy.einsum('ij->i', abs(b_coeff))
idx = numpy.argsort(importance[:nkept])
contracted = numpy.sort(idx[nkept-nc:])
primitive = numpy.sort(idx[:nkept-nc])
# part1: pGTOs that are associated with small coefficients
bs = numpy.empty((nkept-nc,mol._bas.shape[1]), dtype=numpy.int32)
bs[:] = mol._bas[ib]
bs[:,mole.NCTR_OF] = bs[:,mole.NPRIM_OF] = 1
for k, i in enumerate(primitive):
norm = mole.gto_norm(l, mol._env[pexp+i])
_env.append(mol._env[pexp+i])
_env.append(norm)
bs[k,mole.PTR_EXP] = ptr
bs[k,mole.PTR_COEFF] = ptr + 1
ptr += 2
_bas.append(bs)
part1 = numpy.zeros((degen*(nkept-nc),degen*nc))
c = b_coeff[primitive]
for i in range(degen):
part1[i::degen,i::degen] = c
# part2: binding the pGTOs of small exps to the pGTOs of large coefficients
bs = mol._bas[ib].copy()
bs[mole.NPRIM_OF] = np - nkept + nc
idx = numpy.hstack((contracted, numpy.arange(nkept,np)))
exps = mol._env[pexp:pexp+np][idx]
cs = mol._libcint_ctr_coeff(ib)[idx]
ee = mole.gaussian_int(l*2+2, exps[:,None] + exps)
s1 = numpy.einsum('pi,pq,qi->i', cs, ee, cs)
s1 = numpy.sqrt(s1)
cs = numpy.einsum('pi,i->pi', cs, 1/s1)
_env.extend(exps)
_env.extend(cs.T.reshape(-1))
bs[mole.PTR_EXP] = ptr
bs[mole.PTR_COEFF] = ptr + exps.size
ptr += exps.size + cs.size
_bas.append(bs)
part2 = numpy.eye(degen*nc)
for i in range(nc):
part2[i*degen:(i+1)*degen,i*degen:(i+1)*degen] *= s1[i]
contr_coeff.append(numpy.vstack((part1, part2)))
else:
_bas.append(mol._bas[ib])
contr_coeff.append(numpy.eye(degen*nc))
else:
_bas.append(mol._bas[ib])
contr_coeff.append(numpy.eye(degen*nc))
pmol._bas = numpy.asarray(numpy.vstack(_bas), dtype=numpy.int32)
pmol._env = numpy.hstack((mol._env, _env))
return pmol, scipy.linalg.block_diag(*contr_coeff)
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.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)