A comparative study of Hamilton and overlap population methods for the analysis of chemical bonding

The utility of Hamilton population analysis-a partitioning of the electronic energy of a molecule-is investigated within a one-electron molecular orbital framework of the extended Huckel type. The classical Mulliken overlap population description of the valence electron density in terms of one- and two-center "atom" and "bond" contributions, respectively, provides the starting point for the development of an atom-bond energy partitioning scheme. Within an extended Huckel framework simple analytic relations exist between Hamilton populations and Mulliken overlap populations, permitting a step-by-step comparative study of the techniques. The formalism developed for population analysis of two-orbital interactions is tested by performing Hamilton and overlap population analyses of chemical bonding in the isoelectronic series of main group fluorides BrF5, [TeF5](-), [SbF5](2-) and the tetrahedral P-4 cluster. These molecules were specifically chosen to illustrate the circumstances under which Hamilton and overlap population descriptions of chemical bonding will differ and when they will qualitatively agree. Differences come to the fore when atoms of quite different electronegativity interact, or even in a homonuclear system with disparate atomic basis orbital energies. The significant atomic electronegativity differences in the fluorides result in substantive differences between Hamilton and overlap population descriptions of bonding in these compounds. In contrast the small s-p energy separation in phosphorus results in qualitatively similar Hamilton and overlap population descriptions of P-P bonding in P-4. We argue that Hamilton population analysis, by explicitly including reference to the energies of the individual orbitals, affords a more reliable analysis of orbital interactions in molecules. (C) 2000 American Institute of Physics. [S0021-9606(00)30929-1].