Including charge penetration effects in molecular modeling

Electrostatic effects are often the dominant component of intermolecular interactions, but they are often modeled without accounting for charge penetration effects due to the finite extent of electronic orbitals. Here, we propose a new scheme to include charge penetration effects in electrostatic modeling, and we parametrize it and illustrate it by employing the electronically embedded combined quantum mechanical and molecular mechanical (QM/MM) method. It can also be extended to other molecular modeling approximations that include electrostatic effects. The method, which is based on introduction of a single parameter for each element, is simple in concept and implementation, modest in cost, and easily incorporated into existing codes. In the new scheme, the MM atomic charge density of an atom in a molecule is represented by a screened charge rather than by a point charge. The screened charge includes a point charge for the nucleus, core electrons, and inner valence electrons, and a smeared charge for the outer valence electron density, which is distributed in a Slater-type orbital representing the outer part of the atomic charge distribution such that the resulting pairwise interactions are still analytic central potentials. We optimize the exponential parameters of the Slater-type orbitals for 10 elements, in particular H, C, N, O, F, Si, P, S, Cl, and Br, to minimize the mean unsigned error (MUE) of the QM/MM electrostatic and induction energies with respect to the Hartree-Fock electrostatic energies and the sum of induction and induction-exchange energies calculated by symmetry-adapted perturbation theory (SAPT). The resulting optimized exponential parameters are very physical, which allows one to assign parameters to all nonmetal elements (except rare gases) with atomic number less than or equal to 35. For a test set of complexes, the improved description of MM charge densities reduces the error of electrostatic interactions between QM and MM regions in the QM/MM method from 8.1 to 2.8 kcal/mol and reduces the error of induction interactions from 1.9 to 1.4 kcal/mol.