On the basis of LCAO theory, the following intrinsic definition of bond order is derived:Bijequals;pijSijplus;pijfijgij,whereiandjindex basis functions on different centers,pijis the corresponding chargehyphen;andhyphen;bondhyphen;order matrix element,Sijis the overlap integral,fijis a long range factor, andgijis an atomic hybridization and nonorthogonality factor. The termpijSijis the overlap population and the termpijfijgijis the associated net atomic population; the latter is defined by a reference homopolar bond constructed from normalized hybrids of compositions determined by the LCAO wavefunction. The bond order,Bij, reduces in the appropriate special cases to the Coulson, Mulliken, and Wiberg bond orders. However,Bijis not limited to these cases but is also valid for analysis of any LCAO wavefunction. It may also be combined with a Mulliken population analysis to resolve the total electron population into bonding terms and residual lone pair terms. Similarly, the valence electron population may be resolved into covalence, electrovalence, and free valence. Applications are given to HF, the Group I fluorides, and some organic molecules.
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