Fast and Accurate GPU-Accelerated Computation of Two-Electron Four-Center Coulomb Repulsion Integrals.

Electron repulsion integrals are fundamental in ab initio quantum chemistry calculations, as their accurate evaluation is required for predicting molecular properties. We have developed GPU software for rapidly and accurately computing two-electron, four-center Coulomb repulsion integrals using Slater-type orbitals (STOs), with a runtime of approximately 0.06 s per integral for double-precision computations. The computations involve applying a simple transformation from classical electromagnetism to eliminate the Coulomb singularity in the integrals, and using numerical quadrature techniques. We implement our algorithms in a modern GPU-based computing environment, using CUDA intrinsic functions and high-performance computational strategies. We demonstrate the efficiency and accuracy of our code with several examples.