Regularities in nuclear–nuclear potential energy of molecules at equilibrium

Abstract

Regularities in the nuclear–nuclear potential energy Vnn for molecules at equilibrium are exposed. The motivation for the study is afforded by relations between the various energy terms which follow from the simplest form of density functional theory. The first of these relates Vnn to the total electronic kinetic energy T and the electron–electron potential energy Vee by Vnn/T−Vee/T=−1/3. A further relation also follows between Vnn, T, and the electron–nuclear potential energy Ven, namely 2Vnn/T+Ven/T=−7/3, equivalent to a relation suggested previously by Politzer. Attention is then focused on a density functional treatment of tetrahedral and octahedral molecules, in which the model is adopted of smearing the outer nuclei uniformly over a sphere. While the model is too crude to be quantitively useful in calculating the observed properties of these classes of molecules, it is first shown that the above scaling relations are exactly obeyed. Secondly, Vnn is related to T in the model and thirdly Vnn is displayed as a function of the total number of electrons and the charge on the central atom, always at equilibrium. Motivated by the above model, we have studied empirical results for Vnn for tetrahedral and octahedral molecules, and examined T/N, where N is total number of electrons. Also Vnn vs N shows regularities as anticipated from the model. Finally, for light molecules with N?24 we have used selected self-consistent field calculations to (a) verify the scaling relations and (b) demonstrate the relation between Vnn and T/N, and Vnn and N, as for the tetrahedral and octahedral molecules.