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 electroni c energy of a molecule-is investigated within a one-electron molecular orbi tal framework of the extended Huckel type. The classical Mulliken overlap p opulation description of the valence electron density in terms of one- and two-center "atom" and "bond" contributions, respectively, provides the star ting 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-b y-step comparative study of the techniques. The formalism developed for pop ulation analysis of two-orbital interactions is tested by performing Hamilt on and overlap population analyses of chemical bonding in the isoelectronic series of main group fluorides BrF5, [TeF5](-), [SbF5](2-) and the tetrahe dral P-4 cluster. These molecules were specifically chosen to illustrate th e circumstances under which Hamilton and overlap population descriptions of chemical bonding will differ and when they will qualitatively agree. Diffe rences come to the fore when atoms of quite different electronegativity int eract, or even in a homonuclear system with disparate atomic basis orbital energies. The significant atomic electronegativity differences in the fluor ides result in substantive differences between Hamilton and overlap populat ion descriptions of bonding in these compounds. In contrast the small s-p e nergy separation in phosphorus results in qualitatively similar Hamilton an d overlap population descriptions of P-P bonding in P-4. We argue that Hami lton population analysis, by explicitly including reference to the energies of the individual orbitals, affords a more reliable analysis of orbital in teractions in molecules. (C) 2000 American Institute of Physics. [S0021-960 6(00)30929-1].