Single Configuration of Non-orthogonal Orbitals

This was first demonstrated for the H2 molecule by Coulson and Fischer (see previous section). Their calculation was repeated by Mueller and Eyring62 who chose for the two basis orbitals f b in equation (55) the functions 

A similar calculation was carried out by Mueller on the HF molecule63 in which the two orbitals f a, i i which participate in the bond are expressed as 

2pa orbital of F which is distorted by the bonding and j b a similarly distorted H Is function. In contrast to the Ha case, the two functions tj a, f b now possess the same symmetry, i.e. they are both invariant under the molecular point group C . This simple function, in which the core orbitals are taken as the Hartree-Fock orbitals for atomic fluorine and all double interchanges between core and valence are neglected, yields a binding energy of 4.48 eV, compared with the experimental value of 6.12 eV,64 and the Hartree-Fock value of 4.38 eV.64 

One is thus led to propose that the N valence electrons in a molecule be described by a single configuration of N distinct non-orthogonal orbitals 

The factor is just a phase factor and is equal to 1. This implies the 

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Table 2 Recent molecular calculations using the single configuration of non-orthogonal orbitals method...

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