Efficiency and Accuracy of the Generalized Solvent Boundary Potential for Hybrid QM/MM Simulations: Implementation for Semiempirical Hamiltonians

We report the implementation of the generalized solvent boundary potential (GSBP) [Im, W.; Berneche, S.; Roux, B. J. Chem. Phys. 2001, 114, 2924] in the framework of semiempirical hybrid quantum mechanical/molecular mechanical (QM/MM) methods. Application of the GSBP is connected with a significant overhead that is dominated by numerical solutions of the Poisson-Boltzmann equation for continuous charge distributions. Three approaches are presented that accelerate computation of the values at the boundary of the simulation box and in the interior of the macromolecule and solvent. It is shown that these methods reduce the computational overhead of the GSBP significantly with only minimal loss of accuracy. The accuracy of the GSBP to represent long-range electrostatic interactions is assessed for an extensive set of its inherent parameters, and a set of optimal parameters is defined. On this basis, the overhead and the savings of the GSBP are quantified for model systems of different sizes in the range of 7000 to 40 000 atoms. We find that the savings compensate for the overhead in systems larger than 12 500 atoms. Beyond this system size, the GSBP reduces the computational cost significantly, by 70% and more for large systems (>25 000 atoms).