Unification of Ewald and shifted force methods to calculate Coulomb interactions in molecular simulations

Three new Ewald series are derived using a new strategy that does not start with a proposed charge spreading function. Of these, the Ewald series produced using shifted potential interactions for the Ewald real space series converges relatively slowly, while the corresponding expression using a shifted force (SF) interaction does not converge. A comparison is made between several approximations of the Ewald method and the SF route to include Coulomb interactions in molecular dynamics (MD) computer simulations. MD simulations of a model bulk molten salt and water were carried out. The recently derived α' variant of Ewald, by K. D. Hammonds and D. M. Heyes [J. Chem. Phys. 157, 074108 (2022)], has been developed analytically and found to be more accurate and computationally efficient than SF in part due to the smaller real space truncation distance that can be used. In addition, with α', the number of reciprocal lattice vectors required is reduced considerably compared with the standard Ewald implementations to give the same accuracy. The invention of the α' method shifts the computational balance back toward using an Ewald construction. The SF method shows greater errors in the Coulomb pressure and time dependent fluctuation properties compared to α'. It does not conserve the shadow Hamiltonian in a microcanonical MD simulation, whereas the α' method does, which facilitates long time stability and insignificant drift of properties over time. The speed of the Ewald computer code is improved by using a new lookup table method.