Characterization of molecular orbitals by counting nodal regions.

The number of nodal regions can be used as an index for characterizing molecular orbitals. A computer program has been developed to count the number of nodal regions, based on the labeling and contraction algorithms. This program is applied to the water molecule, the hydrogen sulfide molecule, the hydrogen atomic orbitals, the Rydberg excited states of ethylene, dissociation of carbon monoxide, and CASSCF calculations of formaldehyde. Because the number of nodal regions is independent of the coordinate system, the method is applicable even when the molecular structure changes drastically as in bond rotation or bond elongation. Changes of nodal regions with bond elongation are investigated for carbon monoxide. A prescription for problems arising with basis set expansion techniques is also given. Copyright 2005 Wiley Periodicals, Inc.