Multi-reference approach to the calculation of photoelectron spectra including spin-orbit coupling

TL;DR

This paper develops a multi-reference computational method incorporating spin-orbit coupling to accurately calculate X-ray photoelectron spectra of transition metal complexes, addressing the multi-configurational nature of their electronic states.

Contribution

It introduces an efficient algorithm using Restricted Active Space Self-Consistent Field with spin-orbit coupling for photoelectron spectra calculation, improving accuracy for complex systems.

Findings

Good agreement with experimental spectra for water and iron complex

Dyson orbital formalism and sudden approximation compared

Sudden approximation shows deviations from experimental data

Abstract

X-ray photoelectron spectra provide a wealth of information on the electronic structure. The extraction of molecular details requires adequate theoretical methods, which in case of transition metal complexes has to account for effects due to the multi-configurational and spin-mixed nature of the many-electron wave function. Here, the Restricted Active Space Self-Consistent Field method including spin-orbit coupling is used to cope with this challenge and to calculate valence and core photoelectron spectra. The intensities are estimated within the frameworks of the Dyson orbital formalism and the sudden approximation. Thereby, we utilize an efficient computational algorithm that is based on a biorthonormal basis transformation. The approach is applied to the valence photoionization of the gas phase water molecule and to the core ionization spectrum of the $\text{[Fe(H}_2\text{O)}_6\text{]}^{2+}$ complex. The results show good agreement with the experimental data obtained in this work, whereas the sudden approximation demonstrates distinct deviations from experiments.