Localized molecular orbitals for polyatomic molecules. I. A comparison of the Edmiston-Ruedenberg and Boys localization methods
The Edmiston-Ruedenberg (ER) and Boys localization methods are compared for a number of boron hydrides and carboranes. The Boys localization equations are solved explicitly for the two-orbital case and an iterative procedure for the multidimensional case is presented. The Boys analogs of Taylor's [J. Chem. Phys. 48, 2385 (1968)] ER equations are derived and the second-order term is converted into a symmetrized quadratic form which is analogous to the ER equations of Switkes et al. [J. Am. Chem. Soc. 92, 3847 (1970)]. A limited second-derivative test is employed in order to determine the nature of the convergence, and a transformation based on it is defined which successfully resolves structural ambiguities to which the standard two-orbital transformation procedure is subject. The Boys and ER localization methods are in at least qualitative agreement for all molecules except 1,2-C2B4H6, where the Boys localization yields a structure with fractional bonds and no open three-center B-C-B bonding. Previous ER localizations of 1,2-C2B4H6 resulted in two open B-C-B three-center bonds and no fractional bonding.