Localized molecular orbitals for polyatomic molecules. I. A comparison of the Edmiston-Ruedenberg and Boys localization methods

Abstract

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.