A Restricted Open ConfigurationInteraction with Singles Method To Calculate Valence-to-CoreResonant X-ray Emission Spectra: A Case Study

摘要

In this work, a new protocol for the calculation of valence-to-core resonant X-ray emission (VtC RXES) spectra is introduced. The approach is based on the previously developed restricted open configuration interaction with singles (ROCIS) method and its parametrized version, based on a ground-state Kohn–Sham determinant (DFT/ROCIS) method. The ROCIS approach has the following features: (1) In the first step approximation, many-particle eigenstates are calculated in which the total spin is retained as a good quantum number. (2) The ground state with total spin S and excited states with spin S′ = S, S ± 1, are obtained. (3) These states have a qualitatively correct multiplet structure. (4) Quasi-degenerate perturbation theory is used to treat the spin–orbit coupling operator variationally at the many-particle level. (5) Transition moments are obtained between the relativistic many-particle states. The method has shown great potential in the field of X-ray spectroscopy, in particular in the field of transition-metal L-edge, which cannot be described correctly with particle–hole theories. In thiswork, the method is extended to the calculation of resonant VtC RXES[alternatively referred to as 1s-VtC resonant inelastic X-ray scattering(RIXS)] spectra. The complete Kramers–Dirac–Heisenergequation is taken into account. Thus, state interference effects aretreated naturally within this protocol. As a first application ofthis protocol, a computational study on the previously reported VtCRXES plane on a molecular managanese(V) complex is performed. Startingfrom conventional X-ray absorption spectra (XAS), we present a systematicstudy that involves calculations and electronic structure analysisof both the XAS and non-resonant and resonant VtC XES spectra. Thevery good agreement between theory and experiment, observed in allcases, allows us to unravel the complicated intensity mechanism ofthese spectroscopic techniques as a synergic function of state polarizationand interference effects. In general, intense features in the RIXSspectra originate from absorption and emission processes that involvenonorthogonal transition moments. We also present a graphical methodto determine the sign of the interference contributions.