#!/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, multigrid
from pyscf.pbc.dft import rks
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
if isinstance(ni, multigrid.MultiGridNumInt):
if ks.do_nlc():
raise NotImplementedError(f'MultiGrid for NLC functional {ks.xc} + {ks.nlc}')
j_in_xc = ni.xc_with_j
else:
ks.initialize_grids(cell, dm, kpts)
j_in_xc = False
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.info(ks, 'nelec by numeric integration = %s', n)
if ks.do_nlc():
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.info(ks, 'nelec with nlc grids = %s', n)
t0 = logger.timer(ks, 'vxc', *t0)
ground_state = kpts_band is None
nkpts = len(kpts)
weight = 1. / nkpts
vj, vk = _get_jk(ks, cell, dm, hermi, kpts, kpts_band, with_j=not j_in_xc)
if j_in_xc:
ecoul = vxc.ecoul
else:
vxc += vj
ecoul = None
if ground_state:
ecoul = np.einsum('Kij,Kji', dm, vj) * .5 * weight
if ni.libxc.is_hybrid_xc(ks.xc):
vxc -= .5 * vk
if ground_state:
exc -= np.einsum('Kij,Kji', dm, vk).real * .25 * weight
vxc = lib.tag_array(vxc, ecoul=ecoul, exc=exc, vj=None, vk=None)
logger.timer(ks, 'veff', *t0)
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]
return mf._numint.get_rho(mf.cell, dm, grids, kpts, mf.max_memory)
[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
exc = vhf.exc
tot_e = e1 + ecoul + exc
mf.scf_summary['e1'] = e1.real
mf.scf_summary['coul'] = ecoul.real
mf.scf_summary['exc'] = exc.real
logger.debug(mf, 'E1 = %s Ecoul = %s Exc = %s', e1, ecoul, 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, ecoul.real + exc.real
[docs]
def gen_response(mf, mo_coeff=None, mo_occ=None, singlet=None, hermi=0,
max_memory=None, with_nlc=True):
assert isinstance(mf, khf.KRHF)
if mo_coeff is None: mo_coeff = mf.mo_coeff
if mo_occ is None: mo_occ = mf.mo_occ
cell = mf.cell
kpts = mf.kpts
ni = mf._numint
hybrid = ni.libxc.is_hybrid_xc(mf.xc)
j_in_xc = getattr(ni, 'xc_with_j', False)
if with_nlc and mf.do_nlc():
raise NotImplementedError
if singlet is None: # for newton solver
spin = 0
else:
spin = 1
rho0, vxc, fxc = ni.cache_xc_kernel(cell, mf.grids, mf.xc, mo_coeff,
mo_occ, spin, kpts)
dm0 = None
if max_memory is None:
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.8-mem_now)
if singlet is None: # Without specify singlet, general case
def vind(dm1, kshift=0):
# The singlet hessian
if hermi == 2:
v1 = np.zeros_like(dm1)
else:
assert kshift == 0
v1 = ni.nr_rks_fxc(cell, mf.grids, mf.xc, dm0, dm1, 0, hermi,
rho0, vxc, fxc, kpts, max_memory=max_memory)
vj, vk = _get_jk(mf, cell, dm1, hermi, kpts, with_j=not j_in_xc,
kshift=kshift)
if not j_in_xc:
v1 += vj
if hybrid:
v1 -= .5 * vk
return v1
elif singlet:
fxc *= .5
def vind(dm1, kshift=0):
if hermi == 2:
v1 = np.zeros_like(dm1)
else:
assert kshift == 0
# nr_rks_fxc_st requires alpha of dm1
v1 = ni.nr_rks_fxc_st(cell, mf.grids, mf.xc, dm0, dm1, hermi,
True, rho0, vxc, fxc, kpts,
max_memory=max_memory)
vj, vk = _get_jk(mf, cell, dm1, hermi, kpts, with_j=not j_in_xc,
kshift=kshift)
if not j_in_xc:
v1 += vj
if hybrid:
v1 -= .5 * vk
return v1
else: # triplet
fxc *= .5
def vind(dm1, kshift=0):
if hermi == 2:
v1 = np.zeros_like(dm1)
else:
assert kshift == 0
# nr_rks_fxc_st requires alpha of dm1
v1 = ni.nr_rks_fxc_st(cell, mf.grids, mf.xc, dm0, dm1, hermi,
False, rho0, vxc, fxc, kpts,
max_memory=max_memory)
vk = _get_jk(mf, cell, dm1, hermi, kpts, with_j=False, kshift=kshift)[1]
if hybrid:
v1 -= .5 * vk
return v1
return vind
def _get_jk(mf, cell, dm, hermi, kpts, kpts_band=None, with_j=True, kshift=0):
'''J and Exx matrix. Note, Exx here is a scaled HF K term.'''
if kshift != 0:
raise NotImplementedError
ni = mf._numint
omega, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=cell.spin)
hybrid = ni.libxc.is_hybrid_xc(mf.xc)
if not hybrid:
if hermi == 2 or not with_j:
vj = 0
else:
vj = mf.get_j(cell, dm, hermi, kpts, kpts_band)
return vj, 0
if omega == 0:
vj, vk = mf.get_jk(cell, dm, hermi, kpts, kpts_band)
vk *= hyb
elif alpha == 0: # LR=0, only SR exchange
vk = mf.get_k(cell, dm, hermi, kpts, kpts_band, omega=-omega)
vk *= hyb
vj = mf.get_j(cell, dm, hermi, kpts, kpts_band)
elif hyb == 0: # SR=0, only LR exchange
vk = mf.get_k(cell, dm, hermi, kpts, kpts_band, omega=omega)
vk *= alpha
vj = mf.get_j(cell, dm, hermi, kpts, kpts_band)
else: # SR and LR exchange with different ratios
vj, vk = mf.get_jk(cell, dm, hermi, kpts, kpts_band)
vk *= hyb
vklr = mf.get_k(cell, dm, hermi, kpts, kpts_band, omega=omega)
vklr *= (alpha - hyb)
vk += vklr
return vj, vk
[docs]
class KRKS(rks.KohnShamDFT, khf.KRHF):
'''RKS class adapted for PBCs with k-point sampling (default: gamma point).
'''
get_veff = get_veff
energy_elec = energy_elec
get_rho = get_rho
gen_response = gen_response
def __init__(self, cell, kpts=None, 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 Gradients(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, df
out = self._transfer_attrs_(scf.KRHF(self.cell, self.kpts))
# Pure functionals only construct J-type integrals. Enable all integrals for KHF.
if (not self._numint.libxc.is_hybrid_xc(self.xc) and
len(self.kpts) > 1 and getattr(self.with_df, '_j_only', False)):
out.with_df._j_only = False
out.with_df.reset()
return out
multigrid_numint = rks.RKS.multigrid_numint
to_gpu = lib.to_gpu
