Quantifying location and volume of "lone pairs" for VSEPR

Question

Of course molecular shape and the VSEPR model come up frequently.

As discussed previously in a valence bond picture like VSEPR, the lone pair electrons are closer to the atom than bonding pairs, and "fatter."

I can think of a few ways of quantifying this, but I'm trying to add more data when discussing molecular shape:

• Are there examples where the lone pair distance is estimated (e.g., for ozone or $\ce{NO2}$)? This could be compared to a typical bond length.
• Is there an example where the lone pair volume is quantified (e.g., through a polarizability volume, or an electron density isosurface)?

VSEPR is typically used to give qualitative valence bond understanding of shapes, but the lone pair effects are often confusing. So I'm wondering if data on volume / position can help clarify these effects for students.

Answer 1

There have been a few efforts to experimentally quantify the polarizability volume of lone pairs, including:

"Polarizability of Non-Bonding Electron Pairs" Australian Journal of Chemistry (1965) 18 (3) , pp.253-.

They estimate lone-pair polarizabilities from a series of molar refraction measurements (per lone pair).

The refractivity of a molecule can be regarded as the sum of the refractivities of the component bonds and of the unshared electron pairs.

Polarizabilities of Non-Bonding Electron Pairs in $Å^3$

$$ \begin{array}{ll|ll|ll} \hline {\text { Group V }} & & {\text { Group VI }} & & {\text { Group VII }} \\ \hline \mathrm{N} & 1.0 & \mathrm{O} & 0.5 & \mathrm{~F} & 0.2 \\ \mathrm{P} & 2.13 & \mathrm{S} & 1.5 & \mathrm{Cl} & 0.8 \\ \mathrm{As} & 3.3 & \mathrm{Se} & 2.2 & \mathrm{Br} & 1.2 \\ \mathrm{Sb} & 3.9 & \mathrm{Te} & 2.8 & \mathrm{I} & 1.8 \\ \mathrm{Bi} & 4.6 & & & & \\ \hline \end{array}$$

A related follow-up "Polarities and anisotropic electron polarisabilities of neutral ligands" J. Chem. Soc. A, (1969), 2735-2739 used dipole moment and molecular Kerr measurements in dioxane and benzene of a bunch of N, P, and As compounds. The polarizabilities of $\ce{N:}$ and $\ce{NO}$ compounds were remarkably similar, suggesting for N, P, and As, that the lone pair had similar polarizability volume to an oxygen atom.