On the theoretical foundation of walsh's rules of molecular geometry in terms of the hellmann-feynman theorem

Abstract

A new interpretation of the ordinate in a Walsh diagram for a polyatomic molecule is suggested in terms of the Hellmann-Feynman theorem. This makes use of the fact that in a single-configurational mo wave function the total one-electron density is the sum of individual densities in the occupied orbitals. Walsh-type diagrams have been constructed for three different molecules, water, ammonia and hydrogen peroxide. In H₂O and NH₃ calculation of the force, and thus of the energy, in terms of the valence angle, is made on the assumption that the central (heavy) atom is kept fixed while each of the lighter atoms moves in a plane containing the principal symmetry axis and the relevant bond, in a totally symmetric fashion; for H₂O₂ the two oxygen atoms are kept fixed. The angular correlation diagrams obtained reproduce the general features of those obtained by plotting Hartree-Fock mo energies as functions of the valence angles. The conclusion emerges that the force formulation provides a satisfactory pictorial basis for understanding molecular geometry in terms of the balance between the electron-nucleus attractive forces resulting from the charge densities in the occupied mo's, and the nuclear repulsive forces. However, in the absence of highly accurate charge distributions such an approach is unsuitable for the quantitative prediction of molecular quantities such as valence angles, force constants or energy barriers.