Energy localization of approximate molecular orbitals

Energy-localized molecular orbitals (LMO's) obtained from the Edmiston-Ruedenberg (ER) method 2 are useful since they conform to intuitive ideas of chemi· cal bonding. Applications of this method using semi· empirical molecular orbitals are of particular interest since such MO's are at present readily available for a much wider range of molecules than are ab initio orbitals. Trindle and Sinanoglu3a have recently applied the ER localization method to the CND0/23 b molecular orbitals of several molecules; however, some of their results, especially for unsaturated systems, do not agree with the corresponding LMO's obtained from ab initio calculations. 46 In addition, it has been shown7 that the fact that CNDO spherically averages electronrepulsion integrals can lead to an indeterminacy in the resulting LMO's. It is the purpose of this note to demonstrate that the less approximate INDO theory8 is a more appropriate method to use for localization. Since INDO includes distinguishable one-center inte· grals, one would expect this method to give a more reasonable description of the atomic components of a molecule and thus of the canonical and localized orbitals as well.