Martin van Horn, Trond Saue, and Nanna Holmgaard List
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. This allows for an inherently gauge-origin invariant treatment of ECD. By comparison to a formulation based on a truncated interaction in the Coulomb gauge (velocity representation), we investigate the mechanism underlying oriented differential linear absorption across the spectral regions including valence, L- and K -edge transitions and confirm the increasing dominance of the electric-dipole/electric-quadrupole interference term in the center-of-mass frame at higher photon energies. However, going beyond the conventional first-order treatment in the wave vector becomes increasingly important at higher energies, as shown in previous work, inevitable in the higher-energy end of the soft X-ray region. We further compare to the non-relativistic limit to quantify the extent of the breakdown of the electric-dipole/magnetic-dipole selection rule for core transitions in a relativistic domain.