Changes in polarization dictate necessary approximations for modeling electronic de-excitation intensity: an application to X-ray emission

TL;DR

This paper explores various approximation methods for modeling electronic de-excitation intensities in X-ray emission spectroscopy, highlighting the effectiveness of orbital optimization and the limitations of linear-response approaches.

Contribution

It introduces a computationally cheaper single-SCF approach for modeling XES and analyzes the conditions under which different approximations are valid.

Findings

Orbital optimization within a Slater-determinant framework yields accurate XES modeling.

A single self-consistent field approach is typically sufficient for final state modeling.

Change in net dipole moment indicates the validity of linear-response approximations.

Abstract

We systematically investigate the underlying relations among different levels of approximation for simulating electronic de-excitations, with a focus on modeling X-ray emission spectroscopy (XES). Using Fermi's golden rule and explicit modeling of the initial, core-excited state and the final, valence-hole state, we show that XES can be accurately modeled by using orbital optimization for the various final states within a Slater-determinant framework. However, in this paper, we introduce a much cheaper approach reliant only on a single self-consistent field for all the final states, and show that it is typically sufficient. Further approximations reveal that these fundamentally many-body transitions can be reasonably approximated by projections of ground state orbitals, but that the ground state alone is insufficient. Furthermore, except in cases where the core-ionization induces negligible changes in polarization, linear-response approaches within the adiabatic approximation will have difficulty in accurately modeling de-excitation to the core level. Therefore, change in the net dipole moment of the valence electrons can serve as a metric for the validity of the linear-response approximation.