Portable GPU Acceleration of snMECP+COSx via Algorithm–Architecture Codesign

Abstract

Efficient construction of Coulomb and exact-exchange matrices remains a major computational bottleneck in large-scale hybrid density functional theory (DFT) calculations. Here we present a portable GPU implementation of the multipole expansion of Coulomb potential, its seminumerical variant, and COSx, a revised COSX-type chain-of-spheres exact-exchange treatment implemented in the BDF quantum chemistry package, through an algorithm–architecture codesign strategy. The implementation establishes a unified heterogeneous CPU–GPU execution framework for energy and analytical nuclear-gradient evaluations while introducing method-specific optimizations for different computational kernels. For the fully numerical MECP Coulomb kernel, grid-centric accumulation, Morton (Z-order) spatial batching, and batch-level screening improve memory locality and reduce redundant memory traffic. For the snMECP Coulomb and COSx exact-exchange kernels, angular-momentum-aware on-the-fly contraction eliminates large intermediate integral storage and significantly increases arithmetic intensity. Benchmarks on diverse molecular systems and basis sets demonstrate speedups of up to 34.6× for the seminumerical Coulomb kernels and 11.3× for the COSx kernels relative to the corresponding optimized CPU implementations using the corresponding benchmark CPU allocations, while multi-GPU calculations achieve parallel efficiencies approaching 99% for the dominant seminumerical Coulomb workload. As a chemically realistic application, single-GPU B3LYP-D3(BJ)/6-31G(d,p) geometry optimizations of ZnPc dimers and trimers reproduce the reference electronic-structure and conformational-energy trends with CPU–GPU total-energy differences below 5 × 10–8Eh, while reducing the complete optimization wall time by 1.53×–1.80×. The portable HIP implementation supports both AMD and NVIDIA GPU platforms and establishes an efficient and scalable computational framework for large-scale hybrid DFT calculations within the BDF quantum chemistry package.