Advanced aspects of ab initio theoretical optical spectroscopy of transition metal complexes: Multiplets, spin-orbit coupling and resonance Raman intensities

In this review some advanced aspects of the theoretical methods for the calculation of transition metal optical spectra with ab initio methods are discussed. Density functional theory (DFT) based methods are not covered. A brief introduction into the field of complete active space self-consistent field (CASSCF) calculations is provided. These methods allow the correct zeroth order description of arbitrary electron states including singly and doubly excited ligand field or atomic multiplet states. This is followed by a cursory discussion of the treatment of dynamic correlation by using multireference (MR) many body perturbation theory in form of a second order correction to the CASSCF energy (CASPT2). MR based configuration interaction (MRCI) methods are also briefly touched and the spectroscopy oriented CI (SORCI) variant developed in this laboratory is described in some detail. The operators to describe the leading relativistic effects (scalar relativity and spin-orbit coupling (SOC)) are described afterwards. The CASSCF and SORCI methods are first applied to the calculation of the multiplets of the free dipositive and tripositive first-row transition metal ions followed by a discussion of calculations of molecular d-d multiplet states in dipositive and tripositive hexaquo complexes of the first transition row. We then turn to the subject of the treatment of SOC in CASSCF and MRCI based approaches in some detail. The final part of the review provides an introduction into the theory of the resonance Raman effect, the possible quantum chemical calculation of resonance Raman intensities, the implementation of the method into the ORCA electronic structure program system followed by an application to the resonance Raman and absorption spectra of transition metal dithiolene complexes.