It is the non-bonded interaction terms that are the most computationally demanding aspect of a force field calculation. There are N(N — 1)/2 interactions, where N is the number of atoms in the system. Bulk solution is represented most commonly by using a periodic boundary representation in which the unit cell is replicated infinitely in three dimensions. In
this case, the number of interactions for atoms in the primary cell becomes infinite and the standard pairwise electrostatic interaction term becomes a divergent sum. A reduction in the number of non-bonded interactions is thus required in order to make the computation tractable. Since the size of the van der Waals interaction between atoms decreases rapidly with distance it is possible to truncate the Lennard-Jones potential without introducing significant errors in the calculation. Unfortunately, the electrostatic interactions are longer ranged and truncating them can introduce significant errors into the calculation. Much effort has been expended over the years to develop effective cutoff methods that allow the electrostatic interaction to be truncated at some distance, typically below 15 A. However, all these methods suffer from problems arising due to cancellation of errors and it is now almost universally accepted that cutoffs should not be used unless a method is used which allows the “missing” energy to be calculated. One such method which is now commonly used in explicit solvent simulations is the Particle Mesh Ewald Method (PME) (8), which divides the electrostatic calculation into a direct space, pairwise evaluation, and a reciprocal space calculation. The direct space part of the calculation is conducted using a regular pairwise interaction within a cutoff, typically 8-10 Awhile the remainder of the “missing” electrostatic contribution from the infinitely replicated system is included by calculating the charge field on a grid and then using Fast Fourier Transforms to obtain the potential and force at each atom. This reduces the scaling of the calculation from N2 to N ln N while at the same time avoiding the approximations introduced by use of a cutoff.