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