# Can atoms delocalize in molecules?

Electrons can delocalize over multiple equally probable bonding structures. Can atoms delocalize over multiple equally probably bonding structures in certain cases?

It seems to me that any such effect would be most pronounced with very small atoms such as hydrogen.

Furthermore, I would expect such effects to be mostly to occur with hydrogen bonds and cation-pi interactions.

One possibility I am imagining sticking the ends of a bunch of linear molecules that end in OH groups or fluorine atoms together.

• I'm not exactly sure what you want. You can only talk about probability of bonding if you have sufficiently long timescale - there are quick reactions creating equilibria. – Mithoron Jul 5 '16 at 21:43
• Tautomerism in organic compounds? – EdmDroid Jul 6 '16 at 7:18

## 3 Answers

Can atoms delocalize over multiple equally probably bonding structures in certain cases?

If it happens at all, it exceedingly rare. Through my 10-years work in chemistry, I didn't once found a case where it may be relevant. However, what does and indeed affect chemistry is reversible rearrangements.

The simplest case is rotation of molecules around single bonds. Another one is nitrogen inversion. More complex cases also exist. Such things sometimes make interpretation of NMR quite difficult. NMR gives a peak for each non-equal nucleus in the molecule. When internal rearrangement is involved, it sometimes makes two atoms 'equal', i.e. exchanging places too fast for NMR to catch the difference and producing a single peak instead. This, however, is 'quasi-delocalisation', since there is no need in resorting to delocalisation to explain said phenomena.

Another quantum phenomena often observed is tunneling. It affects slightly effective reaction rates/barriers and vibrational spectra.

Anyway, de Broglie wave length for proton is thousand times smaller than for electrons, so quantum effects in nucleus movement usually overshadowed by quantum effects in electrons movement.

• The ring-whizzer mechanism in my book (Inorganic Chemistry, Miessler et al.) is a pretty cool example of a metal bonded monohapto to a cyclopentadienyl ligand, moving around it. (en.wikipedia.org/wiki/Fluxional_molecule) I wonder if that counts? – timaeus222 Jul 6 '16 at 2:56

Delocalization is a wave property. The less mass objects have, the more they behave like waves and the less like particles. Electrons are, by mass, 1837 times lighter than protons, so the wave character of an atomic nucleus is significantly less pronounced and usually of no consequence.

Take a look at three-center two-electron bonds (for example, in diborane) and three-center four-electron bonds (for example, in the biflouride anion $[F-H-F]^-$): This seems to relate to what you are talking about concerning the OH groups.

The wave character of nuclei and even bigger objects has been proven, though: see, for example, the experiments of Arndt et al. with $C_{60}$: http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v401/n6754/full/401680a0_fs.html&content_filetype=PDF

If what you suggest were commonplace then it would be difficult to decide what a molecule is as its structure may consist of innumerable forms. Thus x-ray crystallography would not produce a structure and nmr spectra would most likely be uninterpretable. As this is not generally the case there cannot be many (possibly any?) examples of these that do not involve H (or D) atoms.

One normally considers the ammonia inversion as H atoms tunnelling, but what about the rapid inversion ($10^{8}$ s$^{-1}$) of, for example the bowl shaped molecule corrannulene(C$_{20}$H$_{10}$ see below and web molecule-viewer.com for rotatable picture of 3D structure). Presumably corrannulene does not tunnel from one bowl shaped form to another as its mass is so great, but crosses the inversion barrier top due to thermal energy excitation. Similarly, rotation of alkyl groups in their rotational potential is thermally activated.

The important point is that there is always a competition between tunnelling and barrier crossing. All atoms can tunnel, light ones more easily than heavy ones but usually heavy atom tunnelling cannot compete with thermal barrier crossing and is not observed.

Other tunnelling examples are tautomers shown on the Wikipedia page and involve hydrogen. If tautomerism occurs in the gas phase then we should probably assume that its due to tunnelling of the H atom, but in solution it may be a different H atom that leaves and returns. Another example is the H bond, such as in the structure of DNA where the H atom can move between two other atoms (O..H..N and N..H..N) or a suggested by @Zubo .