Efficient GPU-Accelerated Bulk Evaluation of the Boys Function for Quantum Chemistry.

The Boys function is a mathematical integral function that is frequently evaluated in ab initio molecular orbital computations. The main contribution of this paper is to accelerate the bulk evaluation of the Boys function using GPUs. The proposed GPU implementation takes into account programming issues of the GPU architecture, including warp divergence and coalesced access to the global memory, etc. Additionally, the proposed GPU implementation selects the best numerical computational method among the three methods to achieve efficient computation while maintaining sufficient accuracy. Furthermore, to consider the actual molecular orbital computations, we implemented and evaluated two scenarios: single evaluation, which involves the direct evaluation of the Boys function, and incremental evaluation, which computes the Boys function incrementally. The execution time was evaluated for each scenario using an NVIDIA A100 Tensor Core GPU. As a result, the throughput of 8.81$\times $1$0^{9}$ and 5.73$\times$ 1$0^{10}$ evaluations per second was achieved for the single evaluation and incremental evaluation, respectively.