solvent model (including $O(10^3)$ solvent molecules). However, such comparisons are misleading because implicit solvent models do not attempt to compute the energy of a particular configuration of solvent molecules but to compute the [*free energy*]{} of solvation, i.e., to average over all possible solvent configurations for a given configurations of solute molecules. Thus the chief benefit of an implicit solvent model is to reduce dramatically the number of degrees of freedom in the problem. In the generalized Born solvent models, the energy is written as the sum of two terms: a polar term which is usually called the “GB” term and a cavity term which is proportional to the solvent accessible surface area, the “SA” term.

The GB term involves long-range interactions and is the most costly to compute. We address the calculation of this term first. The basic expression is [@still90] $$\label{gpol}
G_\mathrm{pol} = -\frac12\frac1{4\pi\epsilon_0}
\biggl(1-\frac{\epsilon_0}{\epsilon_s}\biggr)
\sum_{i,j}q_iq_jf(r_{ij},\alpha_i,\alpha_j),$$ where $\epsilon_s$ is the permittivity of the solvent, $f(r_{ij},\alpha_i,\alpha_j)= [r_{ij}^2 +
\alpha_i\alpha_j\exp(-r_{ij}^2/(4\alpha_i\alpha_j))]^{-1/2}$, and the double sum runs over [*all*]{} pairs of atoms (including $i=j$ and $i\lessgtr j$). In eq. (\[gpol\]), $\alpha_i$ is the “generalized” Born radius of the $i$th atom, which is larger that the “bare” Born radius to account for the 