New splitting formulations for lattice summations

Splitting formulations for the efficient evaluation of pairwise interactions of lattice summations were presented. The use of polynomial multiplication to the Gaussian core function to formulate desired mathematical or physical characteristics into a lattice summation methods was demonstrated. Second optimization statement was directed at minimizing the reciprocal space convergence rate to rapidly decaying Fourier transforms. Analysis suggested that the proposed approach requires modest adaptation to the Ewald formulation to enhance the performance of particle-mesh methods for large-scale systems.