Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts

Gerald Knizia J. Chem. Theory Comput. doi:10.1021/ct400687b (Article ASAP)
Contributed by J. Grant Hill.

Readers of Computational Chemistry Highlights are already aware of the power of quantum chemistry in determining/predicting physical observables, but familiar chemical concepts (including the covalent bond!) are, at best, loosely defined in quantum mechanics. This is neatly summarised in Knizia's paper:

"quantum chemistry methods can determine benzene's heat of formation with an accuracy of <2 kJ/mol; but, strictly speaking, they can neither determine the partial charges on benzene's carbon atoms, nor can they show that benzene has twelve localized sigma-bonds and a delocalized pi-system."

 A number of techniques including the quantum theory of atoms in molecules [1], natural bond orbitals [2] and modern valence bond theory [3], to name just a few, have all sought to connect quantum mechanics with concepts known to all chemists, including partial charges, electronegativity, Lewis structures etc. All have been successful to some degree, but often include some assumptions or have complicated programs that require specialist knowledge to run and interpret.

This work by Knizia defines a new method of intrinsic atom orbitals (IAOs) that can exactly express the occupied MOs of an accurate wave function. This is then combined with an orbital localization procedure to construct bond orbitals (IBOs). It is demonstrated that this method is insensitive to basis set size (unlike Mulliken charges), correctly predicts differences in electronegativities, produces the "correct" bond orbitals for some nontrivial cases and can calculate oxidation states of transition-metal complexes (building upon the work of Sit et al.[4]).

This initial implementation of the method shows great promise as an additional tool in the translation of quantum mechanical results into the chemical vernacular, and it will be interesting to observe how it may be applied. My own attraction to the method is due to it combining simplicity of approach with the natural emergence of Lewis structures in the absence of any bias/assumption.

Footnote: The IAO/IBO method will be included in the next public release of the MOLPRO program package, and a sample python implementation will be made available on the author's website (it had not yet been uploaded at the time of writing). Algorithm details are included in an appendix.

References

[1] R. F. W. Bader. A quantum theory of molecular structure and its applications. Chem. Rev. 1991, 91, 893.

[2] E. D. Glendening, C. R. Landis and F. Weinhold. Natural Bond Orbital Methods. WIREs Comput. Mol. Sci. 2012, 2, 1.

[3] J. Gerratt, D. L. Cooper, P. B. Karadakov and M. Raimondi. Modern valence bond theory. Chem. Soc. Rev. 1997, 26, 87; S. Shaik and P. C. Hiberty. A primer on qualitative valence bond theory - a theory coming of age. WIREs Comput. Mol. Sci. 2011, 1, 18.

[4] P. H.-L. Sit, R. Car, M. H. Cohen and A. Selloni. Simple, Unambiguous Theoretical Approach to Oxidation State Determination via First-Principles Calculation. Inorg. Chem. 2011, 50, 10259.