# Analysis of charge distributions: Hydrogen fluoride

## Abstract

Electron density maps and their appropriately weighted analogs (e.g., dipole-weighted density map) are found to provide a consistent and useful tool for the analysis and the comparison of atomic and molecular charge distributions obtained with different wavefunctions. Specific applications are made to hydrogen fluoride, for which a series of single-determinant SCF-LCAO-MO wavefunctions permit a study of the changes that occur in the electron density as the Hartree-Fock solution is approached. An examination of alternative basis-set functions of essentially the same size and the same energy shows that significantly different charge distributions can result; this points out the need for a careful selection of basis functions in large scale molecular calculations. It is found also that the charge density fluctuations from one basis set to another can be as large as the effects of chemical binding. Comparisons between density-map and population-analysis results indicate that considerable caution must be used in employing the latter for the interpretation of complicated wavefunctions. Various methods for summarizing wavefunctions in terms of characteristic parameters of the charge distribution are considered. The forces acting on the nuclei are analyzed in relation to the Hellmann-Feynman theorem and a necessary condition on the exact molecular Hartree-Fock solution is obtained. Although none of the presently available wavefunctions for HF and LiF satisfy the condition to a high degree of accuracy, refinements in the wavefunctions are shown to yield improved results.