Bond index basis functions

The definition (16) doesn t require orthonormalized basis functions, but becomes strictly the same as Armstrong, Perkins and Stewart s bond index, when orthonormalized basis functions are used.(S =5 ) His bond order is... 

As explained in the preceding section, the bond index and the valency have definite physical meanings only when basis functions are orthonormalized. MOPAC satisfies this assumption(6), but general MO methods, including DV-Xa, don t satisfy it. Fortunately basis functions can be orthonormalized after MO calculation without any loss of accuracy, provided that all overlap integrals are known. 

Armstrong, Perkins and Stewart s bond index and valency, which have been used in MOP AC, were extended to general MO methods including DV-Xa, by the way of basis function orthonormalization. 

For a particular homologous series A/ is a specific value that is determined by the character of the functional group(s) of the molecule. Takacs and coworkers (8,9) calculated the Kovats index for paraffins, olefins, cyclic hydrocarbons, and homologs of benzene on the basis of molecular structures. The index was divided into three additive portions atomic index, bond index, and sample stationary-phase index components (see also Reference 2). 

The first Hilbert space definition of bond order was put forward by Wiberg in 1968 and generalized by Armstrong, Perkins, and Stewart in 1973. Ignoring the nonorthogonalities among basis functions, the Wiberg bond index reads... 

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