S/G-1: an ab initio force-field blending frozen Hermite Gaussian densities and distributed multipoles. Proof of concept and first applications to metal cations.

We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.