10.2.6 Localized Orbital Bonding Analysis

Localized orbital bonding analysis (LOBA) is a technique developed by Dr. Alex Thom and Eric Sundstrom at Berkeley with Prof. Martin Head-Gordon. ¹²⁶⁶ Thom A. J. W., Sundstrom E. J., Head-Gordon M.
Phys. Chem. Chem. Phys.
(2009), 11, pp. 11297. Link Inspired by the work of Rhee and Head-Gordon, ¹⁰⁸⁸ Rhee Y. M., Head-Gordon M.
J. Am. Chem. Soc.
(2008), 130, pp. 3878. Link it makes use of the fact that the post-SCF localized occupied orbitals of a system provide a large amount of information about the bonding in the system.

While the canonical molecular orbitals can provide information about local reactivity and ionization energies, their delocalized nature makes them rather uninformative when looking at the bonding in larger molecules. Localized orbitals in contrast provide a convenient way to visualize and account for electrons. Transformations of the orbitals within the occupied subspace do not alter the resultant density; if a density can be represented as orbitals localized on individual atoms, then those orbitals can be regarded as non-bonding. If a maximally localized set of orbitals still requires some to be delocalized between atoms, these can be regarded as bonding electrons. A simple example is that of He${}_2$ versus H${}_2$. In the former, the delocalized ${\sigma }_g$ and ${\sigma }_u$ canonical orbitals may be transformed into 1s orbitals on each He atom, and there is no bond between them. This is not possible for the H${}_2$ molecule, and so we can regard there being a bond between the atoms. In cases of multiple bonding, multiple delocalized orbitals are required.

While there are no absolute definitions of bonding and oxidation state, it has been shown that the localized orbitals match the chemically intuitive notions of core, non-bonded, single- and double-bonded electrons, etc. By combining these localized orbitals with population analyses, LOBA allows the nature of the bonding within a molecule to be quickly determined.

In addition, it has been found that by counting localized electrons, the oxidation states of transition metals can be easily found. Owing to polarization caused by ligands, an upper threshold is applied, populations above which are regarded as “localized” on an atom, which has been calibrated to a range of transition metals, recovering standard oxidation states ranging from $-$II to VII.

On a technical note, LOBA can function of both restricted and unrestricted SCF calculations. The figures printed in the bonding analysis count the number of electrons on each atom from that orbital (i.e., up to 1 for unrestricted or singly occupied restricted orbitals, and up to 2 for double occupied restricted.)