General Spin Restricted Open-Shell Configuration Interaction Singles (GS-ROCIS): Implementation of Spin–Orbit Coupling and Zeeman Operators for Calculation of Optical and X-ray Absorption and Magnetic Circular Dichroism Spectra of Magnetically Coupled Transition Metal Systems

Abstract

In this paper we present the theory and implementation of the spin–orbit coupling and Zeeman operators in the context of quasi-degenerate perturbation theory into the general spin restricted open-shell configuration interaction singles method. The implementation of the mentioned operators allows for the calculation of magnetic circularly polarized dichroism (MCD), L-edge X-ray absorption spectra (XAS) and X-ray magnetic circularly polarized dichroism (XMCD) spectra. The method was tested on calculating the MCD spectra of isostructural complexes [LCr^III(PyA)₃Ni^II]²⁺, [LCr^III(PyA)₃Zn^II]²⁺and [LGa^III(PyA)₃Ni^II]²⁺, with L = 1,4,7-trimethyl-1,4,7-triazacyclonanane and PyA^– is the monoanion of pyridine-2-aldozime, where it correctly predicts the MCD signs of the lower optical transition of [LCr^III(PyA)₃Ni^II]²⁺and [LGa^III(PyA)₃Ni^II]²⁺. The capabilities of the method in computing L-edge XAS and XMCD spectra were tested on the model complexes [Cu(H₂O)₆]²⁺ and [Cu₂(OAc)₄(H₂O)₂], where it correctly calculates the L_2,3-edge absorption and XMCD spectra, as well as on the antiferromagnetically coupled Cu–Fe dimer [(F₈TPP)Fe(μ-O)Cu(TMPA)]⁺, where it correctly predicts the signs of the L₂ and L₃ edges of the Cu XMCD spectrum. To further illustrate the applicability of the method, the more complex L_2,3-edge XAS and XMCD spectra of thiolate Fe complexes were also calculated.