Abstract
X-ray processes involve interactions with high-energy photons. For these short wavelengths, the perturbing field cannot be treated as constant, and there is a need to go beyond the electric-dipole approximation. The exact semi-classical light-matter interaction operator offers several advantages compared to the multipole expansion such as improved stability and ease of implementation. Here, the exact operator is used to model x-ray scattering in metal K pre-edges. This is a relativistic two-photon process where absorption is dominated by electric-dipole forbidden transitions. With the restricted active space state-interaction approach, spectra can be calculated even for the multiconfigurational wavefunctions including second-order perturbation. However, as the operator itself depends on the transition energy, the cost for evaluating integrals for hundreds of thousands unique transitions becomes a bottleneck. Here, this is solved by calculating the integrals in a molecular-orbital basis that only runs over the active space, combined with a grouping scheme where the operator is the same for close-lying transitions. This speeds up the calculations of single-photon processes and is critical for the modeling of two-photon scattering processes. The new scheme is used to model Kα resonant inelastic x-ray scattering of iron-porphyrin complexes with relevance to studies of heme enzymes, for which the total computational time is reduced by several orders of magnitude with an effect on transition intensities of 0.1% or less.
Highlights
Simulations of spectroscopic data are a critical tool for validation of calculations against experimental data
All x-ray processes in Fig. 1 will be modeled using both the multipole expansion and the exact operator
The exact operator offers a number of advantages compared to the multipole expansion, including increased stability for small basis sets
Summary
Simulations of spectroscopic data are a critical tool for validation of calculations against experimental data. One example is high-energy photons where the short wavelength means that the electric field changes rapidly over the space of the target This is, in particular, the case for metal K-edge x-ray absorption spectroscopy (XAS). One area where the exact operator is of great value is for simulating the above-mentioned metal K pre-edges.5,9 These spectra provide information about both geometric and 3d-electronic structures.. An electronic structure method that can describe these strongly correlated systems is the multiconfigurational restricted activespace (RAS) approach.24,25 In this framework, multi-photon processes can be described using the the RAS state-interaction (SI) approach.. The spectrum is generated by combining individual transition moments between explicitly calculated initial, intermediate, and final spin–orbit states This approach has previously been used to describe Kα RIXS of iron complexes using a second-order expansion.. Scitation.org/journal/jcp insights into the iron electronic structure in heme systems because the π → π∗ transitions in the porphyrin ligand obscure UV/Vis probes of the metal. L-edge XAS spectra of heme systems have been simulated with RAS, but their RIXS spectra have previously only been modeled using the semi-empirical charge-transfer multiplet model.
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