The advent of systems biology requires the simulation of everlarger biomolecular systems, demanding a commensurate growth in computational power. This paper examines the use of the NVIDIA Tesla C870 graphics card programmed through the CUDA toolkit to accelerate the calculation of cutoff pair potentials, one of the most prevalent computations required by many different molecular modeling applications. We present algorithms to calculate electrostatic potential maps for cutoff pair potentials. Whereas a straightforward approach for decomposing atom data leads to low compute efficiency, a newer strategy enables fine-grained spatial decomposition of atom data that maps efficiently to the C870's memory system while increasing work-efficiency of atom data traversal by a factor of 5. The memory addressing flexibility exposed through CUDA's SPMD programming model is crucial in enabling this new strategy. An implementation of the new algorithm provides a greater than threefold performance improvement over our previously published implementation and runs 12 to 20 times faster than optimized CPU-only code. The lessons learned are generally applicable to algorithms accelerated by uniform grid spatial decomposition.