#!/usr/bin/env python
# Copyright 2014-2020 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: Yang Gao <younggao1994@gmail.com>
#
'''
Analytical electron-phonon matrix for restricted kohm sham
'''
import numpy as np
from pyscf import lib
from pyscf.hessian import rks as rks_hess
from pyscf.hessian import rhf as rhf_hess
from pyscf.grad import rks as rks_grad
from pyscf.dft import numint
from pyscf.eph import rhf as rhf_eph
from pyscf.data.nist import MP_ME
CUTOFF_FREQUENCY = rhf_eph.CUTOFF_FREQUENCY
KEEP_IMAG_FREQUENCY = rhf_eph.KEEP_IMAG_FREQUENCY
def _get_vxc_deriv1(hessobj, mo_coeff, mo_occ, max_memory):
"""" This functions is slightly different from hessian.rks._get_vxc_deriv1 in that <\nabla u|Vxc|v> is removed"""
mol = hessobj.mol
mf = hessobj.base
if hessobj.grids is not None:
grids = hessobj.grids
else:
grids = mf.grids
if grids.coords is None:
grids.build(with_non0tab=True)
nao, nmo = mo_coeff.shape
ni = mf._numint
xctype = ni._xc_type(mf.xc)
aoslices = mol.aoslice_by_atom()
shls_slice = (0, mol.nbas)
ao_loc = mol.ao_loc_nr()
dm0 = mf.make_rdm1(mo_coeff, mo_occ)
vmat = np.zeros((mol.natm,3,nao,nao))
max_memory = max(2000, max_memory-vmat.size*8/1e6)
if xctype == 'LDA':
ao_deriv = 1
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[0], mo_coeff, mo_occ, mask, 'LDA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
frr = fxc[0]
ao_dm0 = numint._dot_ao_dm(mol, ao[0], dm0, mask, shls_slice, ao_loc)
for ia in range(mol.natm):
p0, p1 = aoslices[ia][2:]
rho1 = np.einsum('xpi,pi->xp', ao[1:,:,p0:p1], ao_dm0[:,p0:p1])
aow = np.einsum('pi,xp->xpi', ao[0], weight*frr*rho1)
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True)
ao_dm0 = aow = None
for ia in range(mol.natm):
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0,2,1)
elif xctype == 'GGA':
ao_deriv = 2
# v_ip = np.zeros((3,nao,nao))
for ao, mask, weight, coords \
in ni.block_loop(mol, grids, nao, ao_deriv, max_memory):
rho = ni.eval_rho2(mol, ao[:4], mo_coeff, mo_occ, mask, 'GGA')
vxc, fxc = ni.eval_xc(mf.xc, rho, 0, deriv=2)[1:3]
wv = numint._rks_gga_wv0(rho, vxc, weight)
# rks_grad._gga_grad_sum_(v_ip, mol, ao, wv, mask, ao_loc)
ao_dm0 = [numint._dot_ao_dm(mol, ao[i], dm0, mask, shls_slice, ao_loc)
for i in range(4)]
for ia in range(mol.natm):
wv = dR_rho1 = rks_hess._make_dR_rho1(ao, ao_dm0, ia, aoslices, xctype)
wv[0] = numint._rks_gga_wv1(rho, dR_rho1[0], vxc, fxc, weight)
wv[1] = numint._rks_gga_wv1(rho, dR_rho1[1], vxc, fxc, weight)
wv[2] = numint._rks_gga_wv1(rho, dR_rho1[2], vxc, fxc, weight)
aow = np.einsum('npi,Xnp->Xpi', ao[:4], wv)
rks_grad._d1_dot_(vmat[ia], mol, aow, ao[0], mask, ao_loc, True)
ao_dm0 = aow = None
for ia in range(mol.natm):
vmat[ia] = -vmat[ia] - vmat[ia].transpose(0,2,1)
elif xctype == 'MGGA':
raise NotImplementedError('meta-GGA')
return vmat
[docs]
def get_eph(ephobj, mo1, omega, vec, mo_rep):
mol = ephobj.mol
mf = ephobj.base
ni = mf._numint
ni.libxc.test_deriv_order(mf.xc, 2, raise_error=True)
omg, alpha, hyb = ni.rsh_and_hybrid_coeff(mf.xc, spin=mol.spin)
hybrid = ni.libxc.is_hybrid_xc(mf.xc)
vnuc_deriv = ephobj.vnuc_generator(mol)
aoslices = mol.aoslice_by_atom()
vind = rhf_eph.rhf_deriv_generator(mf, mf.mo_coeff, mf.mo_occ)
mocc = mf.mo_coeff[:,mf.mo_occ>0]
dm0 = np.dot(mocc, mocc.T) * 2
natoms = mol.natm
nao = mol.nao_nr()
mem_now = lib.current_memory()[0]
max_memory = max(2000, mf.max_memory*.9-mem_now)
vxc1ao = _get_vxc_deriv1(ephobj, mf.mo_coeff, mf.mo_occ, max_memory)
vcore = []
for ia in range(natoms):
h1 = vnuc_deriv(ia)
v1 = vind(mo1[ia])
shl0, shl1, p0, p1 = aoslices[ia]
shls_slice = (shl0, shl1) + (0, mol.nbas)*3
if hybrid:
vj1, vk1 = \
rhf_hess._get_jk(mol, 'int2e_ip1', 3, 's2kl',
['ji->s2kl', -dm0[:,p0:p1], #vj1
'li->s1kj', -dm0[:,p0:p1]], #vk1
shls_slice=shls_slice)
veff = vj1 - hyb * .5 * vk1
if omg != 0:
with mol.with_range_coulomb(omg):
vk1 = \
rhf_hess._get_jk(mol, 'int2e_ip1', 3, 's2kl',
['li->s1kj', -dm0[:,p0:p1]], # vk1
shls_slice=shls_slice)
veff -= (alpha-hyb) * .5 * vk1
else:
vj1 = rhf_hess._get_jk(mol, 'int2e_ip1', 3, 's2kl',
['ji->s2kl', -dm0[:,p0:p1]], # vj1
shls_slice=shls_slice)
veff = vj1[0]
vtot = h1 + v1 + veff + vxc1ao[ia] + veff.transpose(0,2,1)
vcore.append(vtot)
vcore = np.asarray(vcore).reshape(-1,nao,nao)
mass = mol.atom_mass_list() * MP_ME
vec = rhf_eph._freq_mass_weighted_vec(vec, omega, mass)
mat = np.einsum('xJ,xuv->Juv', vec, vcore, optimize=True)
if mo_rep:
mat = np.einsum('Juv,up,vq->Jpq', mat, mf.mo_coeff.conj(), mf.mo_coeff, optimize=True)
return mat
[docs]
class EPH(rks_hess.Hessian):
'''EPH for restricted DFT
Attributes:
cutoff_frequency : float or int
cutoff frequency in cm-1. Default is 80
keep_imag_frequency : bool
Whether to keep imaginary frequencies in the output. Default is False
Saved results
omega : numpy.ndarray
Vibrational frequencies in au.
vec : numpy.ndarray
Polarization vectors of the vibration modes
eph : numpy.ndarray
Electron phonon matrix eph[j,a,b] (j in nmodes, a,b in norbs)
'''
def __init__(self, scf_method, cutoff_frequency=CUTOFF_FREQUENCY,
keep_imag_frequency=KEEP_IMAG_FREQUENCY):
rks_hess.Hessian.__init__(self, scf_method)
self.cutoff_frequency = cutoff_frequency
self.keep_imag_frequency = keep_imag_frequency
get_mode = rhf_eph.get_mode
get_eph = get_eph
vnuc_generator = rhf_eph.vnuc_generator
kernel = rhf_eph.kernel
if __name__ == '__main__':
from pyscf import gto, dft
mol = gto.M()
mol.atom = [['O', [0.000000000000, 0.000000002577,0.868557119905]],
['H', [0.000000000000,-1.456050381698,2.152719488376]],
['H', [0.000000000000, 1.456050379121,2.152719486067]]]
mol.unit = 'Bohr'
mol.basis = 'sto3g'
mol.verbose=4
mol.build() # this is a pre-computed relaxed geometry
mf = dft.RKS(mol)
mf.grids.level=6
mf.xc = 'b3lyp'
mf.conv_tol = 1e-16
mf.conv_tol_grad = 1e-10
mf.kernel()
grad = mf.nuc_grad_method().kernel()
print("Force on the atoms/au:")
print(grad)
myeph = EPH(mf)
eph, omega = myeph.kernel(mo_rep=True)
print(np.amax(eph))
