Symmetry, nodal surfaces, and energy ordering of molecular orbitals

Abstract

The relationship between geometrical symmetry and the nodal surfaces of molecular orbitals is explored and the minimum number of nodal regions for MO’s of each species for the common point groups is tabulated. Some old theorems relating the number and nature of the nodal regions of a wavefunction to the rank order of the eigenvalue are reviewed and reproven. Finally, the application of these results to a partial ordering of molecular orbital energies is illustrated. Although some approximations are involved, the conclusions do not depend on nearest neighbor or similar restrictions.