Valence and extra-valence orbitals in main group and transition metal bonding

We address the issue first raised by Maseras and Morokuma with regard to the questionable treatment of empty p‐orbitals in the algorithm for natural atomic/bond orbitals (NAOs, NBOs) and associated natural population analysis. We quantify this issue in terms of the numerical error (root‐mean‐square density deviation) resulting from the two alternative treatments of empty p‐sets, leading to distinct NAOs, atomic charges, and idealized Lewis structural representations. Computational application of this criterion to a broad spectrum of main group and transition group species (employing both single‐ and multi‐structure resonance models) reveals the interesting general pattern of (i) relatively insignificant differences for normal‐valent species, where a single resonance structure is usually adequate, but (ii) clear superiority of the standard NAO algorithm for hypervalent species, where multi‐resonance character is pronounced. These comparisons show how the divisive issue of “valence shell expansion” in transition metal bonding is deeply linked to competing conceptual models of hypervalency (viz., “p‐orbital participation” in skeletal hybridization vs. 3c/4e resonance character). The results provide a quantitative measure of superiority both for the standard NAO evaluation of atomic charges as well as the general 3c/4e (A: B‐C ↔ A‐B :C resonance) picture of main‐ and transition‐group hypervalency. © 2006 Wiley Periodicals, Inc. J Comput Chem, 2007