Abstract
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 ∼1000eV) where it may even fail to predict the signof individual differential oscillator strengths.
Highlights
Chirality is fundamental to life on Earth, and the origin of homochirality of natural amino acids and sugars remains an unresolved question.1 Enantiomers of a chiral molecule interact differently with chiral objects, such as chiral receptors or left and right circularly polarized light
We explicitly indicate the results of the full interaction with the superscript “full.” For comparison, we provide the lowest non-vanishing terms in the truncated generalized velocity representation for linear and differential absorption, i.e., zeroth- and first-order in the magnitude of the wave vector, respectively
We have reported the first implementation and application of the anisotropic and isotropic Electronic circular dichroism (ECD) signal using the full semi-classical light–matter interaction operator within a four-component relativistic framework
Summary
Chirality is fundamental to life on Earth, and the origin of homochirality of natural amino acids and sugars remains an unresolved question. Enantiomers of a chiral molecule interact differently with chiral objects, such as chiral receptors or left and right circularly polarized light. An additional aspect arising in the x-ray regime, where the wavelength of the electromagnetic field approaches molecular dimensions, is the importance of higher-order terms in the expansion To address these issues in the context of linear absorption of linearly polarized light, we recently proposed using the full semi-classical light–matter interaction operator in both the non-relativistic and relativistic regimes.. Our implementation accounts for two additional possible contributions: (i) effects of beyond first-order light–matter interactions and (ii) inclusion of relativistic effects, notably spin–orbit coupling that modifies selection rules (in particular, the magnetic transition-dipole selection rule36,37) This allows, for the first time, to realistically examine the ECD response of molecules across the valence and x-ray regimes. Because of its computational tractability, H2S2 has been widely used to benchmark electronic structure methods for the calculation of chiroptical properties. For the same reason, Goulon et al used it to estimate the relative magnitudes of XNCD responses within the first-order truncated interaction and non-relativistic framework, reporting values below the experimental detection limits. Here, we revisit the ECD of the disulfide chromophore across the valence and L- and K-edges, going beyond these approximations
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