Orbital Theory Doesn’t Have to Suck

When I was in graduate school, I was mystified by the ways in which older graduate students in my synthetic organic chemistry group would invoke orbital interactions with an ease that I had never seen. Physical organic chemistry seemed baked into their brains, as if they were all operating on some kind of mystical shared understanding of organic structure. I used to see scientists in this light often when I was a kid. They knew something that made them clever, and I wanted in!

Organic chemists catch quite a bit of flak for the way we use orbital theory. It seems as though all we do is draw blobs around lone pairs and bonds in Lewis structures (taking care to distinguish between sigma and pi bonds, of course) and call them real. But are they? Or do the physical chemists who yell that “real” molecular orbitals are always delocalized actually have a point?

Let’s just state it plainly: molecular orbital theory is difficult for students. It overlays the weirdness of quantum mechanics on chemical structures, which are expressed in a classical language of their own that’s hard enough to get a grip on. Plus, the upgrade in explanatory power that comes with replacing classical ideas with molecular orbital theory is typically not that great, especially in organic chemistry. Hell, deeply understanding electronegativity plus the language of Lewis structures and curved arrows can get you at least a B in most sophomore organic chemistry courses. As a result, adoption of molecular orbital theory by students is anemic at best. I think this, plus the anxiety over “what will the physical chemists think?!” described above, has caused organic chemistry instructors to shy away from embracing orbital theory in sophomore courses. This approach is misguided for two reasons: (1) molecular orbital theory does provide massive explanatory power when applied the right way, and (2) organic chemists’ “blobs” are just as legitimate as canonical molecular orbitals.

Organickers often use what we might call localized molecular orbitals, which sit on one or between two atoms. The beauty of this system—and the thing you quickly figure out watching an expert use it—is that you can draw orbital shapes right over bonds and lone pairs in structures. The whole system is based a deep faith in the Lewis model of chemical bonding and its artistic products, Lewis structures. There is a deep logic to orbital polarizations and energies within this system consistent with classical notions of where electrons are and are not.

If we replace the philosophical question “are they real” with the more practical question “do they work,” the answer is “absolutely!” This is where natural bond orbital (NBO) theory comes in. The NBO theorist affirms the organicker’s desire to use localized molecular orbitals. “Yes we can!” she says, “subject to a few conditions.” The bottom line is that NBO theory can be used to represent any molecular wave function, as long as we allow:

  • Mixing of atomic orbitals in any proportions (continuous hybridization)
  • Orbital occupancy of any value between 0.0 and 2.0 (trippy, but work with me here)
  • Mixing of hybrids in any proportions to make natural bond orbitals
  • Mixing of natural bond orbitals to make natural localized MOs (real delocalization effects, important to resonance-active molecules)
  • Mixing of NLMOs to make the overall wave function (again, straightforward…and necessary to satisfy the Schrödinger equation)

The second and fourth points are related: when NBO occupancies differ a great deal from 2.0 or 0.0, that’s the electron delocalization alarm going off. However, the beauty of NBO theory is that it helps one see that most molecules that we would expect to be very “Lewis friendly,” with wave functions adequately described by a set of localized MOs with integer occupancies, are in fact that simple! And for molecules that aren’t that simple, (a) it’s easy enough to switch into delocalized-MO mode and (b) strange occupancies point to election donation (1.7 instead of 2.0, say) or acceptance (0.3 instead of 0.0), which often aligns with our chemical intuition.

For the organic chemist, or even for the hobbyist who just wants to understand molecular orbital theory, my opinion is that NBO theory is a kinder, gentler theory. That doesn’t make it inferior to canonical MO theory in any way, shape, or form. On the contrary, in fact—the intuitive nature of NBO theory is its primary advantage.

Natural bond orbital theory needs its own Frank Lambert. Lambert is a known character to those of us who have taught introductory chemistry for a long time. The man made it his life’s mission to expunge the characterization of entropy as “disorder” from textbooks and teaching praxis and replace it with a more intuitive and broadly applicable description of entropy as “energy dispersal.” He runs an entire web domain devoted to the subject (secondlaw.oxy.edu, formerly secondlaw.com), has published numerous journal articles on the topic, and has ceaselessly advocated for it, for example by keeping track of descriptions of entropy in textbooks. Because of the sheer rarity of a single person moving the needle in such a dramatic way, Lambert is something of a legend among chemical educators. As the major advocates of natural bond orbital theory (Weinhold and Landis) are beginning to advance in years, I wonder if this area will gain its own knight in shining armor?

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