Theoretical X‐ray spectroscopy of transition metal compounds

Abstract

X-ray spectroscopy is one of the most powerful tools to access structure and properties of matter in different states of aggregation as it allows to trace atomic and molecular energy levels in course of various physical and chemical processes. Xray spectroscopic techniques probe the local electronic structure of a particular atom in its environment, in contrast to ultraviolet/visible (UV/Vis) spectroscopy, where transitions generally occur between delocalized molecular orbitals. Complementary information is provided by using a combination of different absorption, emission, scattering as well as photo-and autoionization X-ray methods. However, interpretation of the complex experimental spectra and verification of experimental hypotheses is a nontrivial task and powerful first principles theoretical approaches that allow for a systematic investigation of a broad class of systems are needed. Focusing on transition metal compounds, L-edge spectra are of particular relevance as they probe the frontier d-orbitals involved in metal-ligand bonding. Here, neardegeneracy effects in combination with spin-orbit coupling lead to a complicated multiplet energy level structure, which poses a serious challenge to quantum chemical methods. Multiconfigurational self-consistent field (MCSCF) theory has been shown to be capable of providing a rather detailed understanding of experimental X-ray spectroscopy. However, it cannot be considered as a "blackbox" tool and its application requires not only a command of formal theoretical aspects, but also a broad knowledge of already existing applications. Both aspects are covered in this overview.

Solvation and speciation of cobalt(II). A theoretical X-ray absorption and RIXS study

“…The calculations of spectra followed the methodology described in Ref. [2]. The XAS spectrum was calculated according to the Golden Rule expression: (1)…”

“…Thus, the hexaaqua species can be identified even more distinctly in RIXS spectra than in XAS. The SOC is known to play an important role for core-excited states of metal ions [2,6]. In addition, it has been shown to be potentially relevant for the highly excited valence states accessed in RIXS spectroscopy [6].…”

“…X-ray spectroscopy provides a tool for an element-specific investigation of the electronic structure of matter [1,2]. In particular applications to metal ligand interactions continue to attract considerable attention due to their importance for a number of processes in coordination chemistry [3][4][5], (photo)catalysis [6,7], and biochemistry [8].…”

“…Recently, a theoretical protocol based on the RASSCF method [17] has been successfully applied to studies of XAS [9,18], RIXS [5,6,12,19], partial fluorescence yield [10,13], photoelectron [20][21][22], and Auger [23] spectra, for a review see Ref. [2]. This article is organized as follows: In Section 2 we briefly describe the computational protocol for the calculation of XAS and RIXS spectra.…”

Insight into the X‐ray absorption spectra of Cu‐porphyrazines from electronic structure theory

“…[6,[13][14][15][16][17][18] Perhaps the most rigorous approach to the problem is based on the restricted active space configuration interaction (RASCI) ansatz. [19][20][21][22][23][24][25][26][27] Within this approach, the set of molecular orbitals is divided into the internal orbitals that are doubly occupied; the virtual orbitals that are empty; and finally, two sets of active orbitals that are allowed to have a more involved occupation pattern. The first set of active orbitals comprises the transition metal 2p orbitals from which a single electron is promoted into the second set of active orbitals that correspond to a selection of valence orbitals.…”