Pairwise Alternatives to Ewald Summation for Calculating Long-Range Electrostatics in Ionic Liquids

Room temperature ionic liquid calculations require extensive sampling due to the large degree of localized structuring in the liquid phase relative to conventional solutions. Consequently, a large amount of computer time is required for the convergence of solvent properties, much of which is spent evaluating long-range electrostatics via Ewald summations. The damped Coulomb potential and cutoff-neutralized method of Wolf et al. (J. Chem. Phys. 1999, 110, 8254) provides the framework for an accurate, linear-scaling alternative to Ewald in the ionic liquid simulations. The method has been the subject of multiple modifications for improved accuracy, including the damped Coulombic potential of Zahn et al. (J. Phys. Chem. B 2002, 106, 10725), the damped shifted force method of Fennell and Gezelter (J. Chem. Phys. 2006, 124, 234104), and the shifted force gradient of Kale and Herzfeld (J. Chem. Theory Comput. 2011, 7, 3620). These pairwise electrostatic interaction alternatives along with the CHARMM shifted force potential and a new method proposed herein, the shifted force third derivative (SF3), have been examined on 59 unique ionic liquid combinations of 1-alkyl-3-methylimidazolium [RMIM] (R = M (methyl), E (ethyl), B (butyl), H (hexyl), and O (octyl)) and N-alkylpyridinium [RPyr] cations, along with Cl^–, PF₆^–, BF₄^–, NO₃^–, AlCl₄^–, Al₂Cl₇^–, and TfO^– anions. Monte Carlo simulations utilizing our custom OPLS-AA ionic liquid force field and employing the pairwise alternatives with multiple cutoff distances and electrostatic damping values are compared to the energetics from full Ewald sums.