A Parallel Computation for McMurchie-Davidson Algorithm on the GPU

Abstract

The two-electron repulsion integral (ERI) is a fundamental component in quantum chemistry, involving the calculation of integrals over four basis functions. Quantum chemistry computations require O(M4) 4 ERI calculations for M basis functions, making ERI evaluations a significant bottleneck in these computations. In this paper, we propose an efficient GPU-based parallelization of the McMurchie-Davidson algorithm, which recursively computes ERI. Our method focuses on optimizing the computations by leveraging the shell parameter, which characterizes the shape of the basis functions. The results demonstrate that the shell-based optimization achieves a performance improvement of up to 15% compared to the nonoptimized approach.