Electron energy-loss and inelastic X-ray scattering cross sections from time-dependent density-functional perturbation theory

TL;DR

This paper introduces a generalized Liouville-Lanczos approach within time-dependent density-functional theory to efficiently compute electron energy-loss and inelastic X-ray scattering spectra in periodic solids, significantly reducing computational complexity.

Contribution

The authors develop a new method that avoids virtual orbitals and large matrix manipulations, enabling efficient calculations of spectroscopies over wide frequency ranges for large systems.

Findings

Validated on silicon and aluminum with existing experimental data

Achieves computational efficiency comparable to ground-state calculations

Allows analysis of larger and more complex materials

Abstract

The Liouville-Lanczos approach to linear-response time-dependent density-functional theory is generalized so as to encompass electron energy-loss and inelastic X-ray scattering spectroscopies in periodic solids. The computation of virtual orbitals and the manipulation of large matrices are avoided by adopting a representation of response orbitals borrowed from (time-independent) density-functional perturbation theory and a suitable Lanczos recursion scheme. The latter allows the bulk of the numerical work to be performed at any given transferred momentum only once, for a whole extended frequency range. The numerical complexity of the method is thus greatly reduced, making the computation of the loss function over a wide frequency range at any given transferred momentum only slightly more expensive than a single standard ground-state calculation, and opening the way to computations for systems of unprecedented size and complexity. Our method is validated on the paradigmatic examples of bulk silicon and aluminum, for which both experimental and theoretical results already exist in the literature.