Overlap populations, transition metal

It has been found that the bond overlap population of metal-metal bond plays an important role on the thermal stability of transition metal nitride. 

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 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. 

Overlap population and thermal stability of transition metal nitrides 3.2.1 Ti-M-N system. 

It has been found for examining empirically the thermal properties of the metal nitrides that the number of valence electrons is more advantageous than the average number of valence electrons per atom. DV-Xa molecular orbital calculations for several metal nitrides reveal that the thermal stability of transition metal nitride is intensely dominated by the bond overlap population of the metal-metal bond. 

Although the electronic requirements of these transition metal systems differ from those of the carbides, the clusters are also trigonally compressed, but to a much greater extent, cf. sect. 2.1. This is consistent with the analysis of overlap populations for the two inequivalent edges of the octahedron in the trigonal field of the complete Y71,2Fe structure, and originates from Y-Y interactions due to a negligible contribution of the Fe 4p orbitals in the HOMO. 

Chemical bonding in several transition metal carbides was theoretically investigated by quasi self consistent augmented-plane-wave (APW) calculations [71-73] and by the extended Hiickel method [74]. These calculation indicated a charge transfer from the early transition metal to the carbon atoms. A crystal orbital overlap population analysis (COOP) revealed strong bonding T—T and T-C... 

The formation of C-C chemical bonds in a variety of solids, including some refractory dicarbides, has been considered by Li and Hoffman (1989) and Wijeyesekera and Hoffman (1984) based on EHT (extended Huckel theory) calculations. To our knowledge, these works are the only ones where the band analogues of bond populations, the so-called crystal orbital overlap populations (COOPs) have been calculated for refractory compounds. The most noticeable result is that, in spite of the evident crudeness of the nonself-consistent semiempirical EHT method, the calculations allow us to understand the nature of the phase transition from cubic to hexagonal structure which occurs in the ZrC, NbC, MoC,... series as the VEC increases. The increase of metal-to-metal bonding when going from cubic (NaCl-type) to hexagonal (WC-type) becomes evident. 

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). 

Fig. 2 Qualitative MO diagram for Fe(CO)j. There are many allowed ligand-field (LF) and metal-ligand charge-transfer (MLCT) transitions that can occur. Selection rules mean that one-photon population of A 2 states is allowed, two-photon population of and states is allowed, while both one- and two- photon population of states is allowed and the spectra may overlap...

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