Toward a Charge-Density Analysis of the Chemical Bond; The Charge-Density Bond Model

Abstract

Total-charge-density diagrams (ρ diagrams) are presented for the ground states of Li2, N2, F2, HF, and LiF in BMMO (best minimal molecular-orbital) and accurate SCF (self-consistent-field) approximations. On the basis of contour geometry the ρ diagrams are partitioned into regions of localized and delocalized charge density for which approximate average electron populations, called PL and PD, respectively, are computed. The PL are computed as a function of contour value and contour radius and provide a quantitative measure of the degree of charge transfer in the neighborhood of the nuclei attributable to molecule formation. Criteria for binding, nonbinding, and antibinding, following Berlin's treatment of the Hellmann—Feynman electrostatic theorem, are discussed. A positive correlation between the binding energy De and the ratio PD/PL is noted. An alternate approach to interpreting the ρ diagram is introduced, in which charge-density-difference diagrams (Δρ diagrams) are interpreted as bond maps, i.e., diagrams which define regions of localized charge distributions on the corresponding ρ maps. Binding or antibinding character is then determined for each region of the total-density map using Berlin's forces-on-nuclei criteria. Corresponding electron populations for these regions may be computed by integrating the total density over the regional limits defined by the zero contours. A linear relationship between De and the ratios of these populations is noted. The Δρ maps display distinctly different contour patterns for homonuclear and heteronuclear molecules, which characteristic provides a means of differentiating and classifying binding mechanisms in terms of charge-density sharing and charge-density transfer, compatible with conventional bonding concepts. The possible sources of error in calculation and interpretation of the Δρ maps are enumerated and briefly discussed. Although interpretable in terms of orbital theory concepts, accurate ρ diagrams and Δρ diagrams provide an opportunity to interpret chemical phenomena strictly in terms of localized nonintegral intra- and intermolecular electron-charge-density distribution and displacement. In this context orbital theories should be regarded as a means to an end, i.e., computation of a total wavefunction. Explanations in terms of orbitals and single or paired electrons are probably best reserved for particle-type phenomena, e.g., ionization potential, spectroscopic data, etc., while phenomena associated with charge interaction, rearrangement, and displacement (i.e., chemical reactions) are perhaps more appropriately studied in terms of spatially localized aggregates of bulk charge and their associated nonintegral electron populations, interpreted from the ρ diagrams and Δρ diagrams.