Density fitting in periodic systems: application to TDHF in diamond and oxides

TL;DR

This paper introduces a robust density fitting method for Coulomb matrix elements in periodic systems, applied to TDHF calculations in diamond and oxides, improving computational efficiency and accuracy.

Contribution

It develops and implements a new density fitting approach for periodic systems and demonstrates its effectiveness in TDHF calculations for various materials.

Findings

Density fitting coefficients compare well with variational methods.

Good agreement with experiments and BSE calculations after adjustments.

Method enhances TDHF calculations in complex materials.

Abstract

A robust density fitting method for calculating Coulomb matrix elements over Bloch functions based on calculation of two- and three-center matrix elements of the Ewald potential is described and implemented in a Gaussian orbital basis in the Exciton code. The method is tested by comparing Coulomb and exchange energies from density fitting to corresponding energies from SCF HF calculations for diamond, magnesium oxide and bulk Ne. Density fitting coefficients from the robust method are compared to coefficients from a variational method applied to wave function orbital products in bulk Ne. Four center Coulomb matrix elements from density fitting are applied to time dependent Hartree-Fock (TDHF) calculations in diamond, magnesium oxide and anatase and rutile polytypes of titanium dioxide. Shifting virtual states downwards uniformly relative to occupied states and scaling the electron-hole attraction term in the TDHF Hamiltonian by 0.4 yields good agreement with either experiment and/or Bethe-Salpeter equation calculations. This approach mirrors similar 'scissors' adjustments of occupied and virtual states and introduction of a scaled electron-hole attraction term in some time dependent DFT calculations.