  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.
