The atomic partial charges zoo: A Guide for the perplexed

Atomic partial charges are among the most commonly used interpretive tools in quantum chemistry. Dozens of different ‘population analyses’ are in use, which are best seen as proxies (indirect gauges) rather than measurements of a “general ionicity”.

A taxonomy of partial charges can be constructed based on whether they are obtained from experimental data, from partitioning the electron density (into discrete or fuzzy domains), from partitioning valence orbitals, from fitting to molecular electrostatic properties, or by semiempirical adjustment of one of the above to better reproduce an observable.
Most partial charges do satisfy the weakened Cioslowski-Surjan observability criterion [1] that they smoothly converge to well-defined complete basis set limits. So does MBS-Mulliken (i.e., after projection onto a minimal basis set), but regular Mulliken does not.

For the GMTKN55 benchmark of nearly 2,500 main-group molecules that span a broad swathe of chemical space, some two dozen different charge distributions were evaluated near the 1-particle basis set limit. The correlation matrix between the different charge distributions exhibits blocking, broadly speaking, by charge distribution class. A principal component analysis on the entire dataset suggests that nearly all variation is accounted for by just two ‘principal components of ionicity’ [2]: one has all the distributions going in sync, while the second corresponds mainly to Bader QTAIM vs. all others. A weaker third component corresponds to electrostatic charge models in opposition to the others.
The single charge distribution that has the greatest statistical similarity to the first principal component is iterated Hirshfeld [3].

[1] J. Cioslowski and P. Surján, Theochem 255, 9 (1993)

[2] J. Meister and W. H. E. Schwarz, JACS 98, 8245 (1994)

[3] F. L. Hirshfeld, TCA 44, 129 (1977); P. Bultinck, C. Van Alsenoy, P. G. Ayers, and R. Carbo-Dorca, JCP 126, 144111 (2007)