Some Static and Dynamic Properties of Electron Densities - Bandrauk, Andrew Dieter (My University, 1967)
The electron density approach in conjunction with the Hellmann-Feynman theorem is used for a systematic analysis of binding characteristics of the two isoelectronic molecular series: N₂, CO, BF, and LiF, BeO. Electron density distributions, forces and field gradients corresponding to static properties of electron densities, have been calculated from Hartree-Fock wavefunctions (obtained from the work of other authors) for these molecules. Correlation of these static properties with binding characteristics are presented. Covalent and ionic characteristics are made evident by an analysis of the density distributions, density difference maps obtained by subtracting atomic from molecular distributions, and the forces exerted on nuclei by these distributions. A discussion of the field gradients, as related to quadrupole polarizations of the electron densities, is presented and the relevance of these polarizations to the interpretation of nuclear quadrupole coupling constants is indicated.
Dynamic properties, as reflected by the magnitude of force constants, are analyzed in terms of functionals of the one-electron density. Force constant expressions are derived from the Hellmann-Feynman theorem. Any relation of force constants to field gradients is shown to be not unique as a result of cancellation of static and dynamic electron contributions to the total force constant. The total electronic contribution is shown to arise from a relaxation of density after a displacement of a certain nucleus. Relaxation of density with respect to one nucleus but which remains localized on some other nucleus in a molecule is shown to be equivalent to a field gradient. Thus, such density is separated from other density and its contribution to the force constant is treated as a field gradient. All contributions are computed from polynomial fits of the corresponding forces calculated at a number of internuclear distances. Relaxation density maps for the remaining atomic and overlap densities centered on a specific nucleus are presented. These maps are calculated as the difference between densities of the extended and equilibrium configurations of a molecule. The relaxation densities are correlated to the magnitude of the corresponding electronic force constant components. Thus, for the first time, there is demonstrated the concrete relation between covalent and ionic characteristics of electron densities in molecules and their dynamic properties which result in the magnitude of force constants.
Keywords: chemical physics; static; dynamic properties; electron densities; Hellmann-Feynman theorem