Darwin terms transition metals

The first-order perturbation theory estimate of relativistic effects (inclusion of the mass-velocity and one-electron Darwin terms as suggested by Cowan and Griffin) is cheap and easy to compute as a property value at the end of a calculation. It is therefore very valuable as a check on the importance of relativistic effects, and should certainly be included in accurate calculations on, for example, transition-metal compounds. For even heavier elements relativistic effective core potentials should be used. 

Molecules that contain heavy elements (in particular 5d transition metals) play an important role in the photochemistry and photophysics of coordination compounds for their luminescent properties as well as for their implication in catalysis and energy/electron transfer processes. Whereas molecular properties and electronic spectroscopy of light molecules can be studied in a non-relativistic quantum chemical model, one has to consider the theory of relativity when dealing with elements that belong to the lower region of the periodic table. As far as transition metal complexes are concerned one has to distinguish between different manifestations of relativity. Important but not directly observable manifestations of relativity are the mass velocity correction and the Darwin correction. These terms lead to the so-called relativistic contraction of the s- and p- shells and to the relativistic expansion of the d- and f- shells. A chemical consequence of this is for instance a destabilisation of the 5d shells with respect to the 3d shells in transition metals. 

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