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The quantitative
G.N.Lewis Model


  Vanishing lone pairs (LP) ? in QC and a flaw in VSEPR


I want to address the fact, that Lewis' concept of lone pair - such an important topic throughout molecular chemistry - did not manifest itself experimentally nor theoretically as expected. In fact, in regard to a tremendous effort to visualize the lone pair in NH3and amines, or the two lone pairs in H2O and derivatives, by density difference maps of X-ray crystallography, and by high precision ab initio computations, the results are disappointing, see Ethanol. The O-atom lone pairs should protrude


similarly to the C-H bonds on the -CH2- and -CH3 groups. Instead, we see just one red bulge, not much different from the single lone pair in |NH2CH3. Generally, lone pairs show up by a deformation of electron density nearer the nuclear cusps than expected, see e.g. the contour plot of p-Quinone, where two slight blue contour bulges mark the lone pairs at the O atoms, in contrast to the large "rabbit ears" of the Kimball projection.

You might also be aware that VSEPR "theory" has evolved by a remarkable change in argumentation over the years, taking account of this situation. At the beginning, the lone pairs were described as larger than the bonding pairs, because they are mainly



in the field of one nucleus only, therefore less compact, require more space than bonds between two nuclei and create higher repulsion (why?) LP-LP than BP-BP or LP-BP (BP bonding Pair). Now we have two arguments, almost contradictory: 1) larger LPs need more space and force Bps nearer together, and 2) LPs are much smaller, but compact and block part of the cores surface, hence less space for BPs. Actually (fall 2016), both arguments are used throughout the literature, revealing the status of a "theory" which deals in contradiction but has become a holy cow in high schools. The contradiction is home made! In my opinion, VSEPR has lost its educational value, after LPs have considerably deflated. F. Weinhold et al. have just written an interesting article about this issue.

If one does a reasonably accurate first principle computation of molecules with (formal) lone pairs, the density of the latter seems to be sheltering nearer to the nuclear cusp they are attached to. The mechanism by which they deploy their lone pair properties and why they seem to press bonddirections together is presently under discussion (see Weinhold). Fortunately, the compact lone pairs stay as alert as the inflated ones. They quickly harpoon an available proton, H+ + |NH3 -> H-NH3+ and engage in other nucleophilic reactions. And this is the main point: Lewis/Kimballs lone pairs are meant to represent this chemical experience and not, whether lone pairs are more voluminous than bonding pairs! The dashes and rabbit ear lone pairs are ready to catch an exposed nucleus.
Kimballs lone pairs are, of course, simplifications: E.g. the two lone pairs of O-atoms in water molecules or derivatives like R-OH, are not equivalent. This shows up already in the simplest quantumchemical approximation. One pair, the σ pair, is more stable and lies in the HOR plane, while the second is a π lone
pair perpendicular to that plane, occupying the HOMO of H2O. This can be modeled by the "extended" Kimball used for the "spherical" atoms, see O atom in formamide (turn the 3D image at the end around with mouse). Neither of these lone pairs gets expressed in the density surface, similar to ethanol, shown above.
Since 20 years it is on my agenda to harden the large lone pairs of the Kimball model, that are too soft. In Peregos Kimball.exe this weakness is revealed by systematic angle errors in the -5 to -10 range, e.g. the O-C=O angle in the carboxyl group which is always too small and shows H-bond formation with one of the O-lone pairs (Z conformation). The remedy is to assign different electron screening constants to lone and bonding pairs, see the figure at the end of Acetic acid. This density plot also demonstrates that the lone pairs of the O atom of the C=O group, which are in the plot plane, have almost vanished. Perhaps, the two slight bulges are the hideaways. For the OH group of the -COOH it is similar but even less visible. The density of the π lone pair is mainly off the projection plane.