Could an anisotropic molecular mechanics/dynamics potential account for sigma hole effects in the complexes of halogenated compounds?

Halogenated compounds are gaining an increasing importance in medicinal chemistry and materials science. Ab initio quantum chemistry (QC) has unraveled the existence of a "sigma hole" along the C-X (X = F, Cl, Br, I) bond, namely, a depletion of electronic density prolonging the bond, concomitant with a build-up on its sides, both of which are enhanced along the F < Cl < Br < I series. We have evaluated whether these features were intrinsically built-in in an anisotropic, polarizable molecular mechanics (APMM) procedure such as SIBFA (sum of interactions between fragments ab initio computed). For that purpose, we have computed the interaction energies of fluoro-, chloro-, and bromobenzene with two probes: a divalent cation, Mg(II), and water approaching X through either one H or its O atom. This was done by parallel QC energy-decomposition analyses (EDA) and SIBFA computations. With both probes, the leading QC contribution responsible for the existence of the sigma hole is the Coulomb contribution E(c). For all three halogenated compounds, and with both probes, the in- and out-of-plane angular features of E(c) were closely mirrored by the SIBFA electrostatic multipolar contribution (E(MTP)). Resorting to such a contribution thus dispenses with empirically-fitted "extra", off-centered partial atomic charges as in classical molecular mechanics/dynamics.