#!/usr/bin/env python
# Copyright 2014-2019 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.
#
# Authors: Timothy Berkelbach <tim.berkelbach@gmail.com>
# Qiming Sun <osirpt.sun@gmail.com>
#
'''
Non-relativistic Restricted Kohn-Sham for periodic systems with k-point sampling
See Also:
pyscf.pbc.dft.rks.py : Non-relativistic Restricted Kohn-Sham for periodic
systems at a single k-point
'''
import numpy as np
from pyscf import lib
from pyscf.lib import logger
from pyscf.pbc.scf import khf
from pyscf.pbc.dft import gen_grid
from pyscf.pbc.dft import rks
from pyscf.pbc.dft import multigrid
from pyscf import __config__
[docs]
def get_veff(ks, cell=None, dm=None, dm_last=0, vhf_last=0, hermi=1,
kpts=None, kpts_band=None):
'''Coulomb + XC functional
.. note::
This is a replica of pyscf.dft.rks.get_veff with kpts added.
This function will change the ks object.
Args:
ks : an instance of :class:`RKS`
XC functional are controlled by ks.xc attribute. Attribute
ks.grids might be initialized.
dm : ndarray or list of ndarrays
A density matrix or a list of density matrices
Returns:
Veff : (nkpts, nao, nao) or (*, nkpts, nao, nao) ndarray
Veff = J + Vxc.
'''
if cell is None: cell = ks.cell
if dm is None: dm = ks.make_rdm1()
if kpts is None: kpts = ks.kpts
t0 = (logger.process_clock(), logger.perf_counter())
ni = ks._numint
hybrid = ni.libxc.is_hybrid_xc(ks.xc)
if not hybrid and isinstance(ks.with_df, multigrid.MultiGridFFTDF):
if ks.nlc or ni.libxc.is_nlc(ks.xc):
raise NotImplementedError(f'MultiGrid for NLC functional {ks.xc} + {ks.nlc}')
n, exc, vxc = multigrid.nr_rks(ks.with_df, ks.xc, dm, hermi,
kpts, kpts_band,
with_j=True, return_j=False)
logger.debug(ks, 'nelec by numeric integration = %s', n)
t0 = logger.timer(ks, 'vxc', *t0)
return vxc
# ndim = 3 : dm.shape = (nkpts, nao, nao)
ground_state = (isinstance(dm, np.ndarray) and dm.ndim == 3 and
kpts_band is None)
ks.initialize_grids(cell, dm, kpts, ground_state)
if hermi == 2: # because rho = 0
n, exc, vxc = 0, 0, 0
else:
max_memory = ks.max_memory - lib.current_memory()[0]
n, exc, vxc = ni.nr_rks(cell, ks.grids, ks.xc, dm, 0, hermi,
kpts, kpts_band, max_memory=max_memory)
logger.debug(ks, 'nelec by numeric integration = %s', n)
if ks.nlc or ni.libxc.is_nlc(ks.xc):
if ni.libxc.is_nlc(ks.xc):
xc = ks.xc
else:
assert ni.libxc.is_nlc(ks.nlc)
xc = ks.nlc
n, enlc, vnlc = ni.nr_nlc_vxc(cell, ks.nlcgrids, xc, dm, 0, hermi, kpts,
max_memory=max_memory)
exc += enlc
vxc += vnlc
logger.debug(ks, 'nelec with nlc grids = %s', n)
t0 = logger.timer(ks, 'vxc', *t0)
nkpts = len(kpts)
weight = 1. / nkpts
if not hybrid:
vj = ks.get_j(cell, dm, hermi, kpts, kpts_band)
vxc += vj
else:
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(ks.xc, spin=cell.spin)
vj, vk = ks.get_jk(cell, dm, hermi, kpts, kpts_band)
vk *= hyb
if omega != 0:
vklr = ks.get_k(cell, dm, hermi, kpts, kpts_band, omega=omega)
vklr *= (alpha - hyb)
vk += vklr
vxc += vj - vk * .5
if ground_state:
exc -= np.einsum('Kij,Kji', dm, vk).real * .5 * .5 * weight
if ground_state:
ecoul = np.einsum('Kij,Kji', dm, vj).real * .5 * weight
else:
ecoul = None
vxc = lib.tag_array(vxc, ecoul=ecoul, exc=exc, vj=None, vk=None)
return vxc
[docs]
@lib.with_doc(khf.get_rho.__doc__)
def get_rho(mf, dm=None, grids=None, kpts=None):
if dm is None: dm = mf.make_rdm1()
if grids is None: grids = mf.grids
if kpts is None: kpts = mf.kpts
if dm[0].ndim == 3: # the KUKS density matrix
dm = dm[0] + dm[1]
if isinstance(mf.with_df, multigrid.MultiGridFFTDF):
rho = mf.with_df.get_rho(dm, kpts)
else:
rho = mf._numint.get_rho(mf.cell, dm, grids, kpts, mf.max_memory)
return rho
[docs]
def energy_elec(mf, dm_kpts=None, h1e_kpts=None, vhf=None):
if h1e_kpts is None: h1e_kpts = mf.get_hcore(mf.cell, mf.kpts)
if dm_kpts is None: dm_kpts = mf.make_rdm1()
if vhf is None or getattr(vhf, 'ecoul', None) is None:
vhf = mf.get_veff(mf.cell, dm_kpts)
weight = 1./len(h1e_kpts)
e1 = weight * np.einsum('kij,kji', h1e_kpts, dm_kpts)
ecoul = vhf.ecoul
tot_e = e1 + ecoul + vhf.exc
mf.scf_summary['e1'] = e1.real
mf.scf_summary['coul'] = ecoul.real
mf.scf_summary['exc'] = vhf.exc.real
logger.debug(mf, 'E1 = %s Ecoul = %s Exc = %s', e1, ecoul, vhf.exc)
if khf.CHECK_COULOMB_IMAG and abs(ecoul.imag > mf.cell.precision*10):
logger.warn(mf, "Coulomb energy has imaginary part %s. "
"Coulomb integrals (e-e, e-N) may not converge !",
ecoul.imag)
return tot_e.real, vhf.ecoul + vhf.exc
[docs]
class KRKS(rks.KohnShamDFT, khf.KRHF):
'''RKS class adapted for PBCs with k-point sampling.
'''
get_veff = get_veff
energy_elec = energy_elec
get_rho = get_rho
def __init__(self, cell, kpts=np.zeros((1,3)), xc='LDA,VWN',
exxdiv=getattr(__config__, 'pbc_scf_SCF_exxdiv', 'ewald')):
khf.KRHF.__init__(self, cell, kpts, exxdiv=exxdiv)
rks.KohnShamDFT.__init__(self, xc)
[docs]
def dump_flags(self, verbose=None):
khf.KRHF.dump_flags(self, verbose)
rks.KohnShamDFT.dump_flags(self, verbose)
return self
[docs]
def nuc_grad_method(self):
from pyscf.pbc.grad import krks
return krks.Gradients(self)
[docs]
def to_hf(self):
'''Convert to KRHF object.'''
from pyscf.pbc import scf
return self._transfer_attrs_(scf.KRHF(self.cell, self.kpts))
if __name__ == '__main__':
from pyscf.pbc import gto
cell = gto.Cell()
cell.unit = 'A'
cell.atom = 'C 0., 0., 0.; C 0.8917, 0.8917, 0.8917'
cell.a = '''0. 1.7834 1.7834
1.7834 0. 1.7834
1.7834 1.7834 0. '''
cell.basis = 'gth-szv'
cell.pseudo = 'gth-pade'
cell.verbose = 7
cell.output = '/dev/null'
cell.build()
mf = KRKS(cell, cell.make_kpts([2,1,1]))
print(mf.kernel())