Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation

We demonstrate the use of graphical processing units (GPUs) to carry out complete self-consistent-field calculations for molecules with as many as 453 atoms (2131 basis functions). Speedups ranging from 28× to 650× are achieved as compared to a mature third-party quantum chemistry program (GAMESS) running on a traditional CPU. The computational organization used to construct the Coulomb and exchange operators is discussed. We also present results using three GPUs in parallel, combining coarse and fine-grained parallelism.