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General purpose graphical processing units (GPU's) offer high processingspeeds for certain classes of highly parallelizable computations, such asmatrix operations and Fourier transforms, that lie at the heart offirst-principles electronic structure calculations. Inclusion of exact-exchangeincreases the cost of density functional theory by orders of magnitude,motivating the use of GPU's. Porting the widely used electronic densityfunctional code VASP to run on a GPU results in a 5-20 fold performance boostof exact-exchange compared with a traditional CPU. We analyze performancebottlenecks and discuss classes of problems that will benefit from the GPU. Asan illustration of the capabilities of this implementation, we calculate thelattice stability {\alpha}- and {\beta}-rhombohedral boron structures utilizingexact-exchange. Our results confirm the energetic preference forsymmetry-breaking partial occupation of the {\beta}-rhombohedral structure atlow temperatures, but does not resolve the stability of {\alpha} relative to{\beta}.

VASP on a GPU: application to exact-exchange calculations of the stability of elemental boron