Probing Chirality across the Electromagnetic Spectrum with the Full Semi-classical Light--Matter Interaction

27 October 2021, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


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. The account of both beyond-first-order light--matter interactions and relativistic effects allows 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, 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 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 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.


electronic circular dichroism
X-ray spectroscopy
full light–matter interaction
spin-orbit coupling
circularly polarized light

Supplementary materials

Supplementary Material: Probing Chirality across the Electromagnetic Spectrum with the Full Semi-classical Light–Matter Interaction
Linear and differential absorption spectra and corresponding tabulated oscillator strengths for H2S2. Analysis of structure and origin dependence of the rotational strength tensor.


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.