A Modified Shifted Force Approach to the Wolf Summation

Abstract

The Wolf method for calculation of electrostatic interactions in molecular simulations is known to describe the energy well, whereas the forces have discontinuities. For a more reliable description of the forces this method can be extended with a shifted force approach. This leads to a good description of the forces and precise molecular dynamics simulation, but the description of the energy becomes poorer. In this study we propose a modification of a shifted force extension to describe the energy as well as the forces in better agreement to reference data as determined from the Ewald summation. We show that vapor−liquid phase equilibria (VLE) calculated with Monte Carlo simulations in the grand canonical ensemble and dynamic properties calculated with molecular dynamics simulations can be calculated reliably using this modification to describe the electrostatic interactions.

Reaction-field electrostatics in molecular dynamics simulations: development of a conservative scheme compatible with an atomic cutoff

“…The goal of this study is to assess the influence of the cutoff treatment on selected properties of pure liquids, as well as to eliminate the need for charge groups by introducing SH and SW schemes in combination with an AT truncation of the RFbased electrostatic interactions and LJ interactions, which are appropriate for low as well as high values of ε RF . This work follows analogous developments in the context of Wolf damping 119,120 and isotropic periodic sum 51 methods. The proposed RF(+LJ)/AT/SH and RF(+LJ)/AT/SW schemes have the following properties: (i) they bring the force but not the potential energy to zero at the cutoff; (ii) as a result, they lead to a modification of the interaction that is comparatively small; (iii) they permit rigorously conservative simulations; (iv) the energies can easily be corrected back to the unmodified form, either on the fly or in a post-processing step.…”

“…96,108,[111][112][113][114][115] The SW and SH approaches have also been applied to electrostatic interactions in complement to mean-field schemes, for example in the switched RF approach, 116 or in variants of the Wolf-damping method. 114,[117][118][119][120][121][122] In view of the small LJ forces at typical cutoff distances, the application of SH or SW schemes to the LJ interactions has been less frequently considered, 109,111,123 although it may still be useful if one wishes to enforce a strict energy conservation in simulations. Note that SH and SW schemes are irrelevant in the lattice-sum case, where the cutoff is only a numerical parameter and the level of noise is (nearly) exclusively controlled by the accuracy of the reciprocal-space evaluation.…”

Improving the accuracy of computing chemical potentials in CFCMC simulations

“…All molecules are modelled as rigid objects, and the intermolecular potential consists only of LJ and Coulombic interactions. A cut off radius of 14 Å is used for LJ interactions, and the DSF version of the Wolf method [66][67][68][69][70] is used for handling electrostatic interactions. R c and α were set to 14 Å and 0.12 Å −1 .…”

Improved cutoff functions for short-range potentials and the Wolf summation

“…where U (r) is a pair-potential or a related local function, T [U (r), a, n] the n'th order Taylor expansion of U (r) about r = a, and Θ(r) the Heaviside function. A shiftedpotential (SP) potential is obtained for n = 0, a shifted-force (SF) potential for n = 1 [9,10], and a shifted-curvature (SC) potential for n = 2. A disadvantage of the shifting procedure is that binding or cohesive energies decrease rather quickly with n at fixed r c .…”

“…Although simply cutting and shifting potentials is problematic for reasons discussed above as well as in Refs. [6,10,13], this original Wolf summation is taken as the reference for alternative cutting procedures investigated here below.…”