Combining the lattice-sum and reaction-field approaches for evaluating long-range electrostatic interactions in molecular simulations

Abstract

A new scheme, the lattice-sum-emulated reaction-field (LSERF) method, is presented that combines the lattice-sum (LS) and reaction-field (RF) approaches for evaluating electrostatic interactions in molecular simulations. More precisely, the LSERF scheme emulates a RF calculation (based on an atomic cutoff) via the LS machinery. This is achieved by changing the form of the electrostatic interactions in a standard LS calculation (Coulombic) to the form corresponding to RF electrostatics (Coulombic plus quadratic reaction-field correction term, truncated at the cutoff distance). It is shown (both analytically and numerically) that in the limit of infinite reciprocal-space accuracy, (i) the LSERF scheme with a finite reaction-field cutoff and a given reaction-field permittivity is identical to the RF scheme with the same parameters (and an atomic cutoff), and (ii) the LSERF scheme is identical to the LS scheme in the limit of an infinite reaction-field cutoff, irrespective of the reaction-field permittivity. This new scheme offers two key advantages: (i) from a conceptual point of view, it shows that there is a continuity between the RF and LS schemes and unifies them into a common framework; (ii) from a practical point of view, it allows us to perform RF calculations with arbitrarily large reaction-field cutoff distances for the same computational costs as a corresponding LS calculation. The optimal choice for the cutoff will be the one that achieves the best compromise between artifacts arising from the dielectric heterogeneity of the system (short cutoff) and its artificial periodicity (long cutoff). The implementation of the LSERF method is extremely easy, requiring only very limited modifications of any standard LS code. For practical applications to biomolecular systems, the use of the LSERF scheme with large reaction-field cutoff distances is expected to represent a significant improvement over the current RF simulations involving comparatively much shorter cutoffs.