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My understanding is that the NBO methodology transforms the molecular orbital picture of a molecule into a collection of pairwise interactions (bond orbitals). This is obviously handy for didactic and comprehension purposes as it distils what might be a very complex and non-local MO picture into manageable lobes conforming to the introductory theories of chemical bonding (VB, orbital hybridisation) taught in high-school and early university courses.

Does natural bond orbital theory have utility outside of this role?

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  • $\begingroup$ The 2pz (2p0) state for hydrogen atom is a true stationary state and can remain forever. There is absolutely no constrain in quantum mechanics which states hydrogen atom must be symmetric. If QTAIM is not able to properly describe it, it is the shortcoming of quantum mechanics? $\endgroup$ – user17177 Jun 27 '15 at 17:25
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Yes, along with a family of related methods. I honestly don't fully understand the mechanics behind it, but the orbitals obtained with the NBO method can be used for a treatment called Natural Resonance Theory, which gives you an idea of what sort of Lewis-structure resonance components there are and in what weightings, as well as bond indices, and a measure of covalency.

There are three papers from the developers of the technique, covering theory, usage, and some more examples. (I'd probably start with the usage paper.)

Also, along with NBO, there are the Natural Atomic Orbitals which are often lumped in because they're also computed by the NBO program, and Natural Population Analysis which you can use the Natural Atomic Orbitals to do. These give you an idea of what sort of atomic orbital character is contributing to your molecular orbitals, and also atomic charges and net spins.

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The entire premise of NBO theory is to rotate canonical molecular orbitals into orbitals that have maximal chemical meaning, in the sense that is defined in the NBO papers. I am not aware of any purpose of NBOs and their corresponding natural charges beyond interpretation.

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(Fairness in reporting: I am a hard-core Quantum Theory of Atoms in Molecules partisan)

NBO is one of many attempts the apply rotations among molecular orbitals, each of which can spread over the entire molecule, (i.e. the wave function) so that they maximally-resemble localized atomic orbitals or "hybrid atomic orbitals". Then one may be able to talk about "pieces" of a overall state wave function, and draw connections to the historical descriptions of bonding.

But, the whole process of wave function localization/transformation is puzzling, because it leaves the observable--the electron density--just the way that it was, at least it ought to.

I believe that its motivation is good-intentioned. However, Schroedinger himself cautioned strongly against attempts to analyze the wave function directly. For example, since the wave function may be complex, what does one do with a localized wave function that has real and imaginary components? Why not just analyze the electron density (which is real and observable) directly?

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  • $\begingroup$ In reply to the partisan of QTAIM: QTAIM is a well-defined theory in the context of quantum physics. However, it does not meet essential axioms of chemistry (see below). So why one wishes to impose it to chemical interpretations? - Atomic (and molecular) volumes can be obtained in arbitrary ways in QTAIM. For example, the volume of hydrogen atom can range from nearly zero to infinite, depending on what we like to see. - There is no connection between chemical bond and QTAIM, as Bader define a new concept (bonded atoms) which is not chemical bond. So, it is of no worth for a chemist. - QTAIM de $\endgroup$ – user13404 Feb 14 '15 at 22:45
  • $\begingroup$ <con't> delocalization indices employ orbitals as wavefunction in contrast to its claim, electron density is the origin of world! QTAIM is absolutely inconsistent with excited states. Just analyze a hydrogen atom in 2p0 excited state. Three critical points appear, one of which is of rank two. What a funny chemistry is hidden behind! AND too many other flaws... $\endgroup$ – jonsca Feb 15 '15 at 0:47
  • $\begingroup$ Your wavefunction is wrong, not being spherically-symmetric. Garbage in, garbage out. $\endgroup$ – Eric Brown Feb 15 '15 at 0:51
  • $\begingroup$ What is a "chemical" bond? $\endgroup$ – Eric Brown Feb 15 '15 at 20:01
  • $\begingroup$ Atomic Volume is precisely defined in QTAIM. It's the area contained in the atomic basin, the union of all steepest ascent paths with their nuclear attractor $\endgroup$ – Eric Brown Feb 15 '15 at 20:03

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