Molecular Wave Functions and Valence Bond Theory

1 Molecular Wave Functions and Valence Bond Theory 

The aim of molecular orbital theory is to provide a complete description of the energies of electrons and nuclei in molecules. The principles of the method are simple a partial differential equation is set up, the solutions to which are the allowed energy levels of the system. However, the practice is rather different, and, just as it is impossible (at present) to obtain exact solutions to the wave equations for polyelectronic atoms, so it is not possible to obtain exact solutions for molecular species. Accordingly, the application of molecular orbital theory to molecules is in a regime of successive approximations. Numerous rigorous mathematical methods have been utilised in the effort to obtain ever more accurate solutions to the wave equations. This book is not concerned with the details of the methods which have been used, but only with their results. 

The valence bond model constructs hybrid orbitals which contain various fractions of the character of the pure component orbitals. These hybrid orbitals are constructed such that they possess the correct spatial characteristics for the formation of bonds. The bonding is treated in terms of localised two-electron two-centre interactions between atoms. As applied to first-row transition metals, the valence bond approach considers that the 45, 4p and 3d orbitals are all available for bonding. To obtain an octahedral complex, two 3d, the 45 and the three 4p metal orbitals are mixed to give six spatially-equivalent directed cfisp3 hybrid orbitals, which are oriented with electron density along the principal Cartesian axes (Fig. 1-9). 

Similarly, the bonding in tetrahedral complexes of first row transition-metal ions is considered in terms of four equivalent sp3 hybrid orbitals (which are constructed from the 4s and 4p orbitals of the metal) oriented towards the vertices of a tetrahedron (Fig. 1-10). For a further discussion of the application of the valence bond method to transition-metal complexes, the reader is referred to publications by Pauling.4) The essential feature is that the bonding consists of localised, two-centre two-electron bonds. 

Valence bond theory is somewhat out of favour at present a number of the spectroscopic and magnetic properties of transition-metal complexes are not simply explained by the model. Similarly, there are a number of compounds (with benzene as an organic archetype) which cannot be adequately portrayed by a single two-centre two-electron bonding representation. Valence bond theory explains these compounds in terms of resonance between various forms. This is the origin of the tautomeric forms so frequently encountered in organic chemistry texts. The structures of some common ligands which are represented by a number of resonance forms are shown in Fig. 1-11. 

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