The numerical evaluation of Slater integrals on graphics processing units

This article presents SlaterGPU, a graphics processing unit (GPU) accelerated library that uses OpenACC to numerically compute Slater-type orbital (STO) integrals. The electron repulsion integrals (ERI) are computed under the RI approximation using the Coulomb potential of the Slater basis function. To fully realize the performance capabilities of modern GPUs, the Slater integrals are evaluated in mixed-precision, resulting in speedups for the ERIs of over 80x. Parallelization on multiple GPUs allows for integral throughput of over 3 million integrals per second. This places STO integral throughput within reach of single-threaded, conventional Gaussian integration schemes. To test the quality of the integrals, the fluorine exchange reaction barrier in fluoromethane was computed using heat-bath configuration interaction (HBCI). In addition, the singlet-triplet gap of cyclobutadiene was examined using HBCI in a triple-zeta$$ \zeta $$, polarized basis set. These benchmarks demonstrate the library's ability to generate the full set of integrals necessary for configuration interaction with up to 6h$$ 6h $$ functions in the auxiliary basis.

Automated summary

This article introduces SlaterGPU, a GPU-accelerated library using OpenACC for numerically computing Slater-type orbital (STO) integrals. The electron repulsion integrals (ERI) are computed using the Coulomb potential of the Slater basis function under the RI approximation. By evaluating the Slater integrals in mixed-precision, the ERIs achieve speedups of over 80x, fully exploiting the performance capabilities of modern GPUs. Parallelization on multiple GPUs enables integral throughput of over 3 million integrals per second, making STO integral throughput comparable to single-threaded conventional Gaussian integration schemes. Benchmark tests on the fluorine exchange reaction barrier in fluoromethane and the singlet-triplet gap of cyclobutadiene demonstrate the library's ability to generate the necessary integrals for configuration interaction with up to 6h functions in the auxiliary basis.