The GVB, VBSCF, and BOVB Methods

Valence-bond theory has been used to describe the electronic structure of transition-metal complex ions, with such concepts as d sp hybridization of the metal orbitals. However, the simple VB treatment of complex ions is not fully satisfactory and has been replaced by ligand-field theory, which is MO theory applied to species whose atoms have d (or f) electrons. 

The classical VB method described in the last section uses AOs that are optimized for individual atoms. Several modem ab initio VB methods have been developed that use orbitals optimized for the molecule. Three such methods are described in this section. 

The Heitler-London VB wave function for ground-state H2 is [Eq. (13.100)] lSa l)lSb 2) + li a(2)lij(l) multiplied by a normalization constant and a spin function. The GVB ground-state H2 wave function replaces this spatial function by /(l)g(2) -f /(2) (1), where the functions /and g are found by minimization of the variational integral. To find/and g, one expands each of them in terms of a basis set of AOs and finds the expansion coefficients by iteratively solving one-electron equations that resemble the equations of the SCF MO method. 

Clearly, the GVB method will give a lower energy than the simple VB wave function. The GVB method allows for the change in the AOs that occurs on molecule formation by solving variationally for/and g. In the VB method, this change is allowed for by adding to the wave function terms that correspond to ionic and other resonance structures. The GVB wave function is thus much simpler than a VB wave function with resonance structures and the calculations are simpler. 

The GVB method gives a of 4.12 eV for ground-state H2, as compared with 3.15 eV 

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