#!/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: Tianyu Zhu <zhutianyu1991@gmail.com>
#
"""
Spin-unrestricted random phase approximation (direct RPA/dRPA in chemistry)
with N^4 scaling
Method:
Main routines are based on GW-AC method described in:
T. Zhu and G.K.-L. Chan, J. Chem. Theory. Comput. 17, 727-741 (2021)
X. Ren et al., New J. Phys. 14, 053020 (2012)
"""
import numpy as np
from pyscf import lib
from pyscf.lib import logger
from pyscf.ao2mo import _ao2mo
from pyscf import df, scf
from pyscf.mp import dfump2
from pyscf.gw.rpa import RPA
einsum = lib.einsum
[docs]
def make_dielectric_matrix(omega, e_ov, f_ov, eris, blksize=None):
'''
Compute dielectric matrix at a given frequency omega
Args:
omega : float, frequency
e_ov : 1D array (nocc * nvir), orbital energy differences
eris : DF ERI object
Returns:
diel : 2D array (naux, naux), dielectric matrix
'''
assert blksize is not None
nocc, nvir, naux = eris.nocc, eris.nvir, eris.naux
isreal = eris.dtype == np.float64
diel = np.zeros((naux, naux), dtype=eris.dtype)
for s in [0,1]:
chi0 = (2.0 * e_ov[s] * f_ov[s] / (omega ** 2 + e_ov[s] ** 2)).ravel()
for p0,p1 in lib.prange(0, nocc[s]*nvir[s], blksize):
ovL = eris.get_ov_blk(s,p0,p1)
ovL_chi = (ovL.T * chi0[p0:p1]).T
if isreal:
lib.ddot(ovL_chi.T, ovL, c=diel, beta=1)
else:
lib.dot(ovL_chi.T, ovL.conj(), c=diel, beta=1)
ovL = ovL_chi = None
return diel
[docs]
class URPA(dfump2.DFUMP2):
get_e_hf = RPA.get_e_hf
kernel = RPA.kernel
_finalize = RPA._finalize
[docs]
def make_e_ov(self):
'''
Compute orbital energy differences
'''
log = logger.new_logger(self)
split_mo_energy = self.split_mo_energy()
e_ov = [(split_mo_energy[s][1][:,None] - split_mo_energy[s][2]).ravel() for s in [0,1]]
gap = [-e_ov[s].max() for s in [0,1]]
log.info('Lowest orbital energy difference: (% 6.4e, % 6.4e)', gap[0], gap[1])
if (np.min(gap) < 1e-3):
log.warn('RPA code is not well-defined for degenerate systems!')
log.warn('Lowest orbital energy difference: % 6.4e', np.min(gap))
return e_ov
[docs]
def make_f_ov(self):
'''
Compute orbital occupation number differences
'''
split_mo_occ = self.split_mo_occ()
return [(split_mo_occ[s][1][:,None] - split_mo_occ[s][2]).ravel() for s in [0,1]]
[docs]
def make_dielectric_matrix(self, omega, e_ov=None, f_ov=None, eris=None,
max_memory=None, blksize=None):
'''
Args:
omega : float, frequency
e_ov : 1D array (nocc * nvir), orbital energy differences
mo_coeff : (nao, nmo), mean-field mo coefficient
cderi_ov : (naux, nocc, nvir), Cholesky decomposed ERI in OV subspace.
Returns:
diel : 2D array (naux, naux), dielectric matrix
'''
if e_ov is None: e_ov = self.make_e_ov()
if f_ov is None: f_ov = self.make_f_ov()
if eris is None: eris = self.ao2mo()
if max_memory is None: max_memory = self.max_memory
if blksize is None:
mem_avail = max_memory - lib.current_memory()[0]
nocc, nvir, naux = eris.nocc, eris.nvir, eris.naux
dsize = eris.dsize
mem_blk = 2*naux * dsize/1e6 # ovL and ovL*chi0
blksize = max(1, min(max(nocc)*max(nvir), int(np.floor(mem_avail*0.7 / mem_blk))))
else:
blksize = min(blksize, e_ov.size)
diel = make_dielectric_matrix(omega, e_ov, f_ov, eris, blksize=blksize)
return diel
if __name__ == '__main__':
from pyscf import gto, dft
# Closed-shell unrestricted RPA
mol = gto.Mole()
mol.verbose = 0
mol.atom = [
[8 , (0. , 0. , 0.)],
[1 , (0. , -0.7571 , 0.5861)],
[1 , (0. , 0.7571 , 0.5861)]]
mol.basis = 'def2svp'
mol.build()
mol.verbose = 4
mf = dft.UKS(mol)
mf.xc = 'pbe'
mf.kernel()
# Shall be identical to the restricted RPA result
rpa = URPA(mf)
rpa.verbose = 5
rpa.kernel()
print ('RPA e_tot, e_hf, e_corr = ', rpa.e_tot, rpa.e_hf, rpa.e_corr)
assert (abs(rpa.e_corr - -0.307830040357800) < 1e-6)
assert (abs(rpa.e_tot - -76.26651423730257) < 1e-6)
# Open-shell RPA
mol = gto.Mole()
mol.verbose = 0
mol.atom = 'F 0 0 0'
mol.basis = 'def2-svp'
mol.spin = 1
mol.build()
mol.verbose = 4
mf = dft.UKS(mol)
mf.xc = 'pbe0'
mf.kernel()
rpa = URPA(mf)
rpa.verbose = 5
rpa.kernel()
print ('RPA e_tot, e_hf, e_corr = ', rpa.e_tot, rpa.e_hf, rpa.e_corr)
assert (abs(rpa.e_corr - -0.20980646878974454) < 1e-6)
assert (abs(rpa.e_tot - -99.49455969299747) < 1e-6)
