Overlap populations, transition metal complexes

The X-ray scattering may be expressed directly in terms of a formalism related to the molecular orbitals of a transition metal complex, rather than to the charge distribution on the individual atoms, as is done in the multipole model. In such a formalism the overlap density is directly related to the orbital populations, and does not have to be projected into the one-center functions. 

Even then no practical results have been obtained so far. But in certain cases simplifications are possible, in particular if an atom or fragment of a molecule can be identified which can be treated separately from the remainder of the system. For 3d-transition metal atoms in coordination complexes a major feature of interest is the distribution of the electrons over the d-orbital levels. On the other hand, the overlap between the metal and ligand orbitals is relatively small, and represents a small fraction of the total valence electron density. Therefore, in a first approximation we can describe the d-electron density in terms of the population P j of products of d-orbitals (d ) ... 

The properties of these complexes have been reviewed in great detail [2,21]. A representative structural study [22], illustrating the pseudo-tetrahedral M(C5Hs)3X coordination geometry, is shown in Fig. 23.2. Theoretical studies on the fictitious molecule CpallCH [9] or on CpjUCH j [10] reveal rather small U-C(Cp) overlap populations, but large U-CHj overlap populations (comparable to those in typical transition-metal alkyls). 

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