Source code for pyscf.dft.sap

# Copyright (c) 2020, Susi Lehtola
# All rights reserved.
#
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# modification, are permitted provided that the following conditions are met:
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# notice, this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright
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# documentation and/or other materials provided with the distribution.
# * Neither the name of the <organization> nor the
# names of its contributors may be used to endorse or promote products
# derived from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
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#
# Routines for the implementation of the superposition of atomic
# potentials guess for electronic structure calculations, see
#
# S. Lehtola, "Assessment of Initial Guesses for Self-Consistent Field
# Calculations. Superposition of Atomic Potentials: Simple yet
# Efficient", J. Chem. Theory Comput. 15, 1593 (2019).
# DOI: 10.1021/acs.jctc.8b01089
#
# This function evaluates the effective charge of a neutral atom,
# given by exchange-only LDA on top of spherically symmetric
# unrestricted Hartree-Fock calculations as described in
#
# S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the
# superposition of atomic potentials initial guess for electronic
# structure calculations in Gaussian basis sets, J. Chem. Phys., in
# press (2020).
#
# The potentials have been calculated for the ground-states of
# spherically symmetric atoms at the non-relativistic level of theory
# as described in
#
# S. Lehtola, "Fully numerical calculations on atoms with fractional
# occupations and range-separated exchange functionals", Phys. Rev. A
# 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516
#
# using accurate finite-element calculations as described in
#
# S. Lehtola, "Fully numerical Hartree-Fock and density functional
# calculations. I. Atoms", Int. J. Quantum Chem. e25945 (2019).
# DOI: 10.1002/qua.25945

import numpy
from pyscf.dft.sap_data import sap_Zeff

[docs] def sap_effective_charge(Z, r): ''' Calculates the effective charge for the superposition of atomic potentials. S. Lehtola, "Assessment of Initial Guesses for Self-Consistent Field Calculations. Superposition of Atomic Potentials: Simple yet Efficient", J. Chem. Theory Comput. 15, 1593 (2019). DOI: 10.1021/acs.jctc.8b01089 This function evaluates the effective charge of a neutral atom, given by exchange-only LDA on top of spherically symmetric unrestricted Hartree-Fock calculations as described in S. Lehtola, L. Visscher, E. Engel, Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets, J. Chem. Phys., in press (2020). The potentials have been calculated for the ground-states of spherically symmetric atoms at the non-relativistic level of theory as described in S. Lehtola, "Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals", Phys. Rev. A 101, 012516 (2020). DOI: 10.1103/PhysRevA.101.012516 using accurate finite-element calculations as described in S. Lehtola, "Fully numerical Hartree-Fock and density functional calculations. I. Atoms", Int. J. Quantum Chem. e25945 (2019). DOI: 10.1002/qua.25945 Input: Z: atomic charge r: distance from nucleus Output: Z(r): screened charge ''' if Z < 1: return 0.0 if Z >= sap_Zeff.shape[1]: raise ValueError('Atoms beyond Og are not supported') if numpy.any(r < 0.0): raise ValueError('Distance cannot be negative') if r.ndim == 0: if r >= sap_Zeff.shape[0]: return 0.0 # Linear interpolation return numpy.interp(r, sap_Zeff[0,:], sap_Zeff[Z,:]) else: v = numpy.interp(r, sap_Zeff[0,:], sap_Zeff[Z,:]) v[r >= sap_Zeff.shape[0]] = 0. return v