Spin-orbit coupling theoretical principles

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]. 

In principle, all higher lying states can contribute to the Tj substates via SOC, if the corresponding symmetries fit. However, many of these SOC routes contribute little and can be neglected relative to a few dominating spin-orbit interactions. We will describe fundamentals of the coupling routes from a theoretical point of view and discuss requirements for efficient SOC in organometallic compounds. To make this chapter understandable for the non-specialist, we will start with definitions, which are necessary to fix notations. This will be followed by some relations between orbitals and states. 

From the experimental standpoint, a system such as is well parameterized because there will, in principle, be three spectroscopic transitions from which it will be possible to determine the two NQI parameters, e Qq and q. Other spin systems, such as 0 (/ = S ), S, and Cl (/= 3/1) are more difficult to parameterize because there are fewer spectroscopic transitions than theoretical parameters, but techniques such as double resonance enable one to get the requisite information (Semin et al, 1975 Lucken, 1969b). Simple orbital descriptions of the nuclear quadrupole coupling parameters and orbital hybridization have been reported (Cotton Harris, 1966), and measures of the nuclear quadrupole interaction parameters and their tensor orientation can therefore be applied to solving problems of molecular structure and reactivity. 

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