definition of the hard atom radius is $0.55 \rho_i$ for non-bonded atom pairs and $0.45 \rho_i$ for 1-4 atom pairs. We skip the check for 1-2 and 1-3 pairs and for those atoms with $\rho_i = 0$. This energy term can be implemented in essentially the same way as described above but with scope for additional speedups. The cutoff radius in the residue-residue distance check can be replaced by 0. An additional atom-residue distance check can be be used to avoid executing the inner atom loop if the outer atom is outside the sphere for the second residue. Finally, as soon as an overlap of hard spheres is detected the routine can immediately return an infinite result.

Implicit solvent models
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We now turn to the computation of the energy term for implicit solvent models. We focus here on the generalized Born solvent models [@still90] and we have considered various implementations [@qiu97; @hawkins95; @hawkins96; @tsui00; @tsui01; @onufriev04]. Evaluating the solvation energy for a system of molecules with such models is typically orders of magnitude slower than computing the energy of the molecules in vacuum. The computation time is frequently compared to the time to compute the energy with an explicit 