Natural Bond Orbitals

Here is the center for a much more sophisticated treatment of Lewis' bonding model with bonding and lone pairs, the octet rule and much more. Frank Weinhold and colleagues have developed this great computational tool since nearly 30 years at the Department of Chemistry, University of Wisconsin. On the link to the homepage, above, you'll find excellent tutorial material. The NBO program can be called within the Gaussian QC package. For Gamess and other QC programs you have to install an NBO plugin, available at the above link for a nominal fee.

What can NBO's do ?

Many chemists are avoiding QC programs although these are now profusely available for PC's and Mac's or on Linux computers. Assuming satisfactory computer literacy, the reason is that they have not learned to interpret the results of MO computations with so called canonical orbitals. These are delocalized over the whole molecular skeleton and do not reflect the concept of localized electron pair bonds of G.N. Lewis with which all chemists have been educated. There exist several schemes (mentioned elsewhere) for "localizing" transforma-tions of canonical orbitals and thus helping chemists to identify their familiar bonding patterns. The NBO concept and its several subconcepts are by far the most advanced developments in this research field. Are they necessary to understand chemistry?

For my own reflections on chemistry I have not used NBO schemes extensively. Aside from some familiarity with the usual canonical orbitals - having done a lot of molecular spectroscopy! - I feel quite happy with traditional MO theory. The resulting wavefunctions can be linearly combined in a multitude of ways for many different purposes of "better understanding".
However, if you strive for accuracy with ab initio electronic structure systems (ESS) you soon find that the canonical orbitals, you compute, become less understandable. Unfortunately, that applies also to NBO's, which lose their interpretive help the more accurate your computations become!

  Main historical flaw of the "Natural Resonance Theory" concept

In Quantum Chemistry courses students learn that the total ground state electron density must represent the full symmetry group of a molecule (and its Hamiltonian). We know that this is not true in many cases for the structural formula given by the Lewis electron pair bonding model. Since the electron pair bond is an electronic interpretation of Kekulé's unitary bonding concept with a dash for single, two dashes for double "bonds" aso., and, new, double points or dashes for lone pairs, it suffers from the same limitations. Kekulé and his followers had to write two "oscillatory" formulas e.g. for the location of benzene's double bonds, to remedy the obvious failure of his stick or "hook" formula to represent the experimentally proven D6h symmetry. L. Pauling continued this spooky way and called it "resonance". His influence made all organic chemists, to this day, talk about resonance, even "resonance energy", as the energy difference between two spooky formulas. This has been generalized into a quantitative tool by E.D.Glendening & F.Weinhold (& J.K.Badenhoop for part III), J.Comp.Chem. 19,583,610,628(1998), with the name "Natural Resonance Theory". They greatly surpass the older presentations of Pauling and Wheland (and two books by Wheland, 1944, 1955 on "Resonance ..."). The electron-pair formula is used as a schematic of the electron distribution, hence many resonance formulas are necessary to produce some semblance to an MO computation (reminiscent of Rumer symbols in the early days of Valence Bond theory). An example: see citation above, III. part, page 635
The simple CO2 molecule O=C=O needs 4 resonance structures which should circumscribe the
experimentally determined D∞h symmetry of the ground state (formal charges not drawn):

=C=Ö: ↔ :Ö=C=Ö: ↔ :Ö-C≡O: ↔ :O≡C-Ö:

the first two with 24.75%, the other two with 25% weight, each (the first and second formulas have exchanged orthogonal C=O double bonds, rotated by 90° to each other. The weights are heavily dependent on the basis-set used). IMHO this is not satisfactory! The canonical orbitals of MO-theory show two orthogonal ℼ-bonds going all the way from one to the other O nucleus, i.e. delocalized over three "atoms". Since a D∞h symmetry implies cylinder symmetry and an inversion center at the C atom, we immediatly get the correct symmetry (already with the smallest basis-set!). The NBO6 program finds these, too, as 3c-4e "hyper"bonds, not used in the four formulas, above. Hence, the NBO analysis offers broken symmetries (even the center of inversion vanishes!), apparently fixing this by superposition of the four resonanceformulas. Instead of admitting that the 2-electron-2-nuclei dash, the local Lewis electron pair, is just a bad representation in this case, these authors resurrect the ghost of Kekulé to keep an inadequate concept, more than 150 years old (I thank Prof. F. Weinhold for an e-mail exchange on the CO2 problem, May 16, 2018). I'm not convinced that this is good teaching practice! However, that's in the spirit of the powerful community of practising organic chemists, who will be resonating for ever! Of course, this criticism has a history of 100 years, and even contains a controversy between Pauling and Wheland (after 1955), who disagreed on the scientific content of resonance "theory" (google "resonance" in chemistry)! I know from W. Heitler, personal discussion ~1960, that he did not appreciate the concept.