Designing quantum chemistry algorithms with just-in-time compilation

We introduce just-in-time (JIT) compilation to the integral kernels for Gaussian-type orbitals (GTOs) to enhance the efficiency of electron repulsion integral computations. For Coulomb and exchange (JK) matrices, JIT-based algorithms yield a 2x speedup for the small 6-31G* basis set over GPU4PySCF v1.4 on an NVIDIA A100-80G GPU. By incorporating a novel algorithm designed for orbitals with high angular momentum, the efficiency of JK evaluations with the large def2-TZVPP basis set is improved by up to 4x. The core CUDA implementation is compact, comprising only ~1,000 lines of code, including support for single-precision arithmetic. Furthermore, the single-precision implementation achieves a 3x speedup over the previous state-of-the-art.