Spin-orbit coupling transition metal electronic structure

Transition-metal and rare-earth atoms that contain partially occupied d or f valence subshells also give rise to spectral tine structure, often with very complicated multiplet splitting [2,27,28]. The spin-unpaired valence d or f electrons can undergo spin-orbit coupling with the unpaired core electron (remaining in the orbital from which the photoelectron was removed), producing multiple non-degenerate final states manifested by broad photoelectron peaks [2,27]. 

There remains the possibility of g-values which depart substantially from 2.00 but are isotropic because of cubic symmetry. In practice such conditions are rare for transition metal complexes, as the Jahn-Teller theorem ensures departure from cubic symmetry in the electronic structure. However, for the lanthanoid and actinoid elements, where the spin—orbit coupling constant is very much larger than kT, the Jahn—Teller theorem may not be relevant and effective cubic symmetry certain. For the lanthanoids, g-values often depart considerably from 2.00, although some anisotropy arising from ligand field splittings is common. For the actinoids, direct observation of ESR is less common but there is evidence of a similar situation. 

With the development of current theories of electronic structure, such as multireference ab initio approaches and in particular density-functional theory (DFT), the appealing ligand-field approach became displaced by these approaches theoretically well justified but chemically less transparent and less readily analyzed and interpreted (but see Ref [3] as an exception). In contrast, the parametric strucmre of ligand-field theory and the need of experimental data to allow adjustment of these parameters makes this model a tool for interpretation rather than for predictions of electronic properties of transition-metal complexes. A proposed DFT-supported ligand-field theory (LFDFT) enables one to base the determination of LF parameters solely on DFT calculations from first principle [3-6]. This approach is equally suitable to predict electronic transitions [4] and, with appropriate account of spin-orbit coupling [5], one is able to calculate with satisfactory accuracy g- and A-tensor parameters [6]. 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

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