The advent of systems biology requires the simulation of ever- larger 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 electro- static potential maps for cutoff pair potentials. Whereas a straight- forward approach for decomposing atom data leads to low com- pute efcienc y, a newer strategy enables ne-grained spatial de- composition of atom data that maps efciently to the C870's mem- ory system while increasing work-efcienc y of atom data traver- sal by a factor of 5. The memory addressing e xibility exposed through CUDA's SPMD programming model is crucial in enabling this new strategy. An implementation of the new algorithm pro- vides 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 decom- position.