Point + Gaussian charge model for electrostatic interactions derived by machine learning

At short distances between atoms, point charges are a poor approximation of the electrostatic interaction. Due to overlapping electron clouds, charges are effectively shielded and the electrostatic interaction energy is modified. In molecular simulations, two main approaches have surfaced to deal with this. First, the Thole-screening [B. T. Thole, <i>Chem. Phys.</i>, 1981, <b>59</b>, 341-350], which introduces a mathematical modification of the Coulomb interaction at short range, and second, the use of Gaussian-distributed charges [C. M. Smith and G. G. Hall, <i>Theor. Chim. Acta</i> 1986, <b>69</b>, 63-69]. Here, we show that these approaches are practically equivalent, that is the screening functions are numerically very similar and their parameters related by a simple expression. A quantitative comparison between electrostatic interactions in alkali-halide ion pairs, computed using high level symmetry-adapted perturbation theory (SAPT), and in point charge models shows that the electrostatic interactions are not always weaker than those predicted by point charge approximations, highlighting that more complex atomic models may be needed. We then proceed to use machine learning with the Alexandria Chemistry Toolkit to train models for alkali-halides based on a positive core and a virtual site with a negative Gaussian-distributed charge and show that this model yields energies very close to SAPT.