We present a new formulation for the efficient evaluation of pairwise interactions for large nonperiodic or spatially periodic infinite lattices. Our optimally designed splitting formulation generalizes the Ewald method and its Gaussian core function. In particular, we show that a polynomial multiplication to the Gaussian core function can be used to formulate desired mathematical or physical characteristics into a lattice summation method. Two optimization statements are examined. The first incorporates a pairwise interaction splitting into the lattice sum, where the direct (real) and reciprocal space terms also isolate the near-field and far-field pairwise particle interactions, respectively. The second optimization defines a splitting with a rapidly convergent reciprocal space term that allows enhanced decay rates in the real-space term relative to the traditional Ewald method. These approaches require modest adaptation to the Ewald formulation and are expected to enhance performance of particle-mesh methods for large-scale systems. A motivation for future applications is large-scale biomolecular dynamics simulations using particle-mesh Ewald methods and multiple time step integration.