Probing chirality across the electromagnetic spectrum with the full semi-classical light-matter interaction

We present a formulation and implementation of anisotropic and isotropic electronic circular dichroism (ECD) using the full semi-classical light-matter interaction operator within a four-component relativistic framework. Our treatment uniquely accounts for both beyond-first-order light-matter interactions and relativistic effects, enabling us to investigate the ECD response across the electromagnetic spectrum from optical to x-ray wavelengths where relativistic selection rules and spatial field variations gain increasing importance. We consider the isotropic and oriented ECD across the valence transition and sulfur L- and K-edge transitions in the simplest disulfides, H2S2 and (CH3S)(2), and evaluate the influence of the full interaction by comparing to a traditional truncated formulation in the Coulomb gauge (velocity representation). Additionally, we demonstrate that in the relativistic formalism, it is possible to work in the velocity representation, hence keeping order-by-order gauge-origin invariance, contrary to the multipolar gauge, yet being able to distinguish electric and magnetic multipole contributions. Going beyond a first-order treatment in the wave vector is mandatory in the higher-energy end of the soft x-ray region and beyond where the consequent intensity redistribution becomes significant. While the sulfur K-edge absorption spectrum is essentially unaffected by this redistribution, the signed differential counterpart is not: At least third-order contributions are required to describe the differential absorption profile that is otherwise overestimated by a factor of about two. The first-order description deteriorates at higher transition energies (beyond similar to 1000 eV) where it may even fail to predict the sign of individual differential oscillator strengths. (c) 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).