Calculating Coulomb interactions in molecular dynamics simulations: the Evjen method revisited

A new way is invented for computing Coulomb interactions in molecular dynamics simulations which works well for bulk phase and lamina systems. This direct summation (DS) or cell dipole approach is an extension of the `Evjen' method which was explored in the 1960s. The DS method is the Evjen method with a unit cell dipolar correction, and is cast entirely in real space and involves summing the original point charge $r^{-1}$ interactions which are truncated on a unit cell basis rather than spherically for the individual point charge interactions. The theory of the DS method is extended to encompass noncubic unit cells periodic in all three cartesian directions. For moderately sized systems the DS method performs with comparable accuracy and computational efficiency to that of the Ewald method, both of which are formally exact. The corresponding treatment is made for a lamina system where the charges are in 3D but the unit cells are only periodic in two of the three cartesian directions. The DS method has no adjustable parameters and is relatively straightforward to implement in existing computer codes which do not include Coulomb interactions, unlike Ewald.