Piece-wise Multipole-expansion Implicit Solvation for Arbitrarily Shaped Molecular Solutes

The multipole-expansion (MPE) model is an implicit solvation model used to efficiently incorporate solvent effects in quantum chemistry. Even within the recent direct approach, the multipole basis used in MPE to express the dielectric response still solves the electrostatic problem inefficiently or not at all for solutes larger than $\approx 10$ non-hydrogen atoms. In existing MPE parameterizations, the resulting systematic underestimation of the electrostatic solute-solvent interaction is presently compensated for by a systematic overestimation of non-electrostatic attractive interactions. Even though the MPE model can thus reproduce experimental free energies of solvation of small molecules remarkably well, the inherent error cancellation makes it hard to assign physical meaning to the individual free energy terms in the model, raising concerns about transferability. Here, we resolve this issue by solving the electrostatic problem piece-wise in 3D regions centered around all non-hydrogen nuclei of the solute, ensuring reliable convergence of the multipole series. The resulting method, which we call MPE-$n$c, thus allows for a much improved reproduction of the dielectric response of a medium to a solute. Employing a reduced non-electrostatic model with a single free parameter, in addition to the density isovalue defining the solvation cavity, MPE-$n$c yields free energies of solvation of neutral, anionic and cationic solutes in water in good agreement with experiment.