Complexes extended bonding models

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

Historically, crystal field theory was the first theoretical model (11, 86, 101, 123) used to explain d-d transition energies in metal complexes. Its usefulness is restricted to those complexes whose bonding is largely ionic, and its mqjor deficiency arises from its inability to account for charge transfer transitions. The iterative extended Hiickel and the ab initio, limited basis set, Hartree-Fock calculations are capable of de-... 

In order to investigate electronic structures of the Pt4 cluster complexes, extended Hiickel moleculsir orbital (EHMO) calculations were carried out for a model system, [Pt4(HCOO)8] with D2d S3unmetry, and its quarterly fragment with C2 symmetry (29). The MO studies reasonably justify the presence of Pt—Pt bonds in the cluster core and the regioselective substitution reactivities. 

The MO model can be applied to all types of complex ions, although we will not extend the model to other cases here. In addition, note that in our use of the MO model to describe octahedral complexes, we considered only cr bonding effects to keep the model as simple as possible. For a complete treatment of complex ions, it bonding interactions also would have to be considered. 

The pi back-bonding model of Dewar (29), Chatt, and Duncanson (30) has been widely invoked as an explanation of a variety of features of transition metal complexes. While extended Huckel theory clearly shows such mixing of orbitals, ab initio calculations have found them more elusive (31,32). 

Landis, C. R., Firman, T. K., Cleveland, T, Root, D. M. Extending molecular mechanics methods to the description of transition metal complexes and bond-making and -breaking processes. In Molecular Modeling and Dynamics of Bioinorganic Systems Band, L. Comba, P., Eds. Kluwer Academic Publishers Dordrecht, 1997, p. 49. 

This approach has been successful in rationalizing the melting points, heats of formation and mixing, and various optical and electrical phenomena of tetrahedral semiconductor crystals (e.g., see Ref. 173). It is not clear how far it may be extended to other types of materials in the light of the complexities of bonding which many experiments demonstrate—also few experimental results may be related directly to a fractional ionicity for comparison. Levine, however, has generalized the dielectric model in terms of individual bond properties to several different structures. The critical ionicity ft = 0.785) between octahedral and tetrahedral coordination is not always appropriate for example PbS, PbSe, and PbTe (with rock-salt structures) have ft 0.6, and for LiH (also rock-salt)yi 0.1. This latter value would seem to be in... 

Computer simulations of excess proton conductivity in water have reached a powerful level [8,92,93,102]. Importantly, simulations extend to quantum-mechanical proton dynamic features, so that proton motion can be coupled to details of the molecular environmental dynamics. A recent feature article explored an analytical theory in order to rationalize these complex processes that involve interconversion of proton-bearing clusters and proton transfers [103]. With a simple two-state empirical valence bond model (see below for details), which implements in a classical way the above-mentioned idea of two limiting protonated structures, namely the 11502 and the H30 cluster, it was indeed observed that the two alternative sequences are equivalent with similar life times for both clusters, and that conversions between the two clusters are purely fluctuative. 

Although the bond-valence theory (BVT) is primarily meant to rationalize and predict molecular structures in solids, chemists naturally try to extend structural models to rationalize and predict reactivity. If a model helps us understand why particular equilibrium structures are preferred, for instance, perhaps quantifying the principles underlying the model can help us predict energetic differences between structural states, which are the bases for both thermodynamic and kinetic theory. The BVT is an excellent vehicle for exploring structure-energy relationships, because it is in some respects quantitatively predictive, and boils down complex, multi-body interactions into a single parameter, the bond-valence sum. 

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