Molecular Dynamics simulations have become an interesting target for acceleration using Field-Programmable Gate Arrays (FPGA). Still to be attempted completely in FPGA hardware is the computation of the Coulombic interactions using the Smooth Particle Mesh Ewald (SPME) algorithm. In this work, we describe the design, the implementation, and the verification effort of an FPGA compute engine, named the Reciprocal Sum Compute Engine (RSCE), that calculates the reciprocal space contribution to the electrostatic energy and forces using the SPME algorithm. This is the first known attempt to fully capture the entire computation in dedicated FPGA hardware. We also investigate the fixed-point precision requirements, a strategy for parallelizing the RSCE and present an estimate of potential speedup.