Acceleration of Electron Repulsion Integral Evaluation on Graphics Processing Units via Use of Recurrence Relations

Electron repulsion integral (ERI) calculation on graphical processing units (GPUs) can significantly accelerate quantum chemical calculations. Herein, the ab initio self-consistent-field (SCF) calculation is implemented on GPUs using recurrence relations, which is one of the fastest ERI evaluation algorithms currently available. A direct-SCF scheme to assemble the Fock matrix efficiently is presented, wherein ERIs are evaluated on-the-fly to avoid CPU-GPU data transfer, a well-known architectural bottleneck in GPU specific computation. Realized speedups on GPUs reach 10-100 times relative to traditional CPU nodes, with accuracies of better than 1 × 10(-7) for systems with more than 4000 basis functions.