ABSTRACT In Quantum chemical computation, numerical schemes such as the Hartree–Fock (HF) and density functional theory (DFT) are widely used to solve the Schrödinger equation numerically, to realize experiment‐free prediction and analysis of key molecular properties such as structure and energy. Computing one‐electron integrals, such as kinetic energy integrals and nuclear attraction integrals, is essential in both HF and DFT to characterize the molecular electronic states. However, as molecules of practical interest grow in size and angular momentum, computing one‐electron orbitals becomes computationally expensive in most cases. Although computing kinetic energy integrals on CPUs is straightforward, bottlenecks in CPU‐GPU data transfer have often been overlooked. In this study, we propose an efficient method to compute both the kinetic‐energy and nuclear‐attractive integrals on GPUs. First, we explicitly and symbolically expand recurrence relations based on the Obara–Saika and McMurchie–Davidson methods to eliminate redundant operations, thus improving computational efficiency. Second, we implemented a hybrid method that selects the best/fastest of both methods depending on the integration task. Third, we achieved further speedups by using CUDA streams to parallelize the execution of multiple kernels and efficiently utilize multiprocessor resources on the GPU. Computational experiments using NVIDIA A100 GPUs and Intel Xeon Gold 6338 CPU on relevant molecules of interest demonstrated the superiority of our one‐electron integral GPU implementations, achieving a speedup of 20.2 times over PySCF, and a speedup of 132.6 times over GPU4PySCF.
ABSTRACT In Quantum chemical computation, numerical schemes such as the Hartree–Fock (HF) and density functional theory (DFT) are widely used to solve the Schrödinger equation numerically, to realize experiment‐free prediction and analysis of key molecular properties such as structure and energy. Computing one‐electron integrals, such as kinetic energy integrals and nuclear attraction integrals, is essential in both HF and DFT to characterize the molecular electronic states. However, as molecules of practical interest grow in size and angular momentum, computing one‐electron orbitals becomes computationally expensive in most cases. Although computing kinetic energy integrals on CPUs is straightforward, bottlenecks in CPU‐GPU data transfer have often been overlooked. In this study, we propose an efficient method to compute both the kinetic‐energy and nuclear‐attractive integrals on GPUs. First, we explicitly and symbolically expand recurrence relations based on the Obara–Saika and McMurchie–Davidson methods to eliminate redundant operations, thus improving computational efficiency. Second, we implemented a hybrid method that selects the best/fastest of both methods depending on the integration task. Third, we achieved further speedups by using CUDA streams to parallelize the execution of multiple kernels and efficiently utilize multiprocessor resources on the GPU. Computational experiments using NVIDIA A100 GPUs and Intel Xeon Gold 6338 CPU on relevant molecules of interest demonstrated the superiority of our one‐electron integral GPU implementations, achieving a speedup of 20.2 times over PySCF, and a speedup of 132.6 times over GPU4PySCF.
High Resolution Image Download MS PowerPoint Slide We introduce the first version of GPU4PySCF, a module that provides GPU acceleration of methods in PySCF . As a core functionality, this provides a GPU implementation of two-electron repulsion integrals (ERIs) for contracted basis sets comprising up to g functions using the Rys quadrature. As an illustration of how this can accelerate a quantum chemistry workflow, we describe how to use the ERIs efficiently in the integral-direct Hartree–Fock build and nuclear gradient construction. Benchmark calculations show a significant speedup of 2 orders of magnitude with respect to the multithreaded CPU Hartree–Fock code of PySCF and the performance comparable to other open-source GPU-accelerated quantum chemical packages, including GAMESS and QUICK, on a single NVIDIA A100 GPU.
Computational quantum chemistry aims to derive properties of a molecule, such as its energy, without the need for actual experimental work. This is done by taking the types and coordinates of atoms within the molecule as input. In this study, we accelerate the computation of the two-electron repulsion integrals that mainly dominate the computing time. Specifically, we focus on the McMurchie-Davidson algorithm, where the two-electron repulsion integrals are obtained through recurrence computation. The idea of the proposed GPU implementation is to expand the recurrence relations and efficiently compute them using multiple threads of the GPU. Our proposed method resulted in an acceleration of up to 3.5 times compared to GPU implementations using recursive functions, and up to 17 times compared to CPU implementations similar to those using the GPU.
GPU-accelerated quantum chemistry programs can dramatically reduce the time required for electronic structure calculations, yet most existing implementations either retrofit GPU kernels onto legacy CPU codebases or optimize individual kernels without addressing workflow-level integration overhead. We present GANSU (GPU Accelerated Numerical Simulation Utility), an open-source quantum chemistry framework written entirely in CUDA/C++ that integrates GPU-accelerated kernels for electron repulsion integrals, Fock matrix construction, and post-Hartree–Fock (post-HF) methods into a unified, GPU-resident execution pipeline. The key design principle is to eliminate host–device data transfers between computational stages by keeping all intermediate data, including density matrices, integral buffers, and Fock matrix replicas, on the GPU throughout the self-consistent field (SCF) iteration, combined with runtime-selectable integral strategies (stored ERI, resolution-of-the-identity, and Direct-SCF) that adapt to system size and available memory. On an NVIDIA H200 GPU, GANSU achieves end-to-end speedups of up to 52× over PySCF for SCF, 45× for MP2 on molecules with up to 470 basis functions, and 44× for FCI, while outperforming GPU4PySCF by up to 34× for FCI, across a range of molecular systems with up to 650 basis functions. The framework further provides analytical energy gradients and geometry optimization with nine algorithms, all operating within the same GPU-resident data flow. These results demonstrate that workflow-aware kernel integration, not just kernel-level optimization, is essential for realizing the full potential of GPU acceleration in scientific computing. GANSU is publicly available under the BSD-3-Clause license.
We present a GPU-accelerated software package for the evaluation of analytic two-electron energy and gradient contributions in Hartree-Fock (HF) and Density Functional theory (DFT) calculations. The implementation is provided as a Python library with a C++ backend, enabling straightforward integration into modern computational chemistry and drug-discovery workflows. The code supports single-point energy and nuclear gradient evaluations on both single- and multi-GPU systems, and employs MPI-based parallelization with dynamic load balancing in multi-node environments. We report comprehensive benchmarks demonstrating favorable scaling with respect to system size, as well as high throughput for batched evaluations relevant to molecular dynamics, geometry optimization, and large-scale virtual screening. Parallel execution of a single system was carried out on up to 24 A100 GPUs. The implementation builds on optimized GPU-enabled variants of the LibintX and GauXC libraries to efficiently compute density-fitted Coulomb, semi-numerical exchange, and exchange--correlation contributions.
Quantum chemistry offers the formal machinery to derive molecular and physical properties arising from (sub)atomic interactions. However, as molecules of practical interest are largely polyatomic, contemporary approximation schemes such as the Hartree–Fock scheme are computationally expensive due to the large number of electron repulsion integrals (ERIs). Central to the Hartree–Fock method is the efficient computation of ERIs over Gaussian functions (GTO-ERIs). Here, the well-known McMurchie–Davidson method (MD) offers an elegant formalism by incrementally extending Hermite Gaussian functions and auxiliary tabulated functions. Although the MD method offers a high degree of versatility to acceleration schemes through Graphics Processing Units (GPUs), the current GPU implementations limit the practical use of supported values of the azimuthal quantum number. In this paper, we propose a generalized framework capable of computing GTO-ERIs for arbitrary azimuthal quantum numbers, provided that the intermediate terms of the MD method can be stored. Our approach benefits from extending the MD recurrence relations through shells, batches, and triple-buffering of the shared memory, and ordering similar ERIs, thus enabling the effective parallelization and use of GPU resources. Furthermore, our approach proposes four GPU implementation schemes considering the suitable mappings between Gaussian basis and CUDA blocks and threads. Our computational experiments involving the GTO-ERI computations of molecules of interest on an NVIDIA A100 Tensor Core GPU (NVIDIA, Santa Clara, CA, USA) have revealed the merits of the proposed acceleration schemes in terms of computation time, including up to a 72× improvement over our previous GPU implementation and up to a 4500× speedup compared to a naive CPU implementation, highlighting the effectiveness of our method in accelerating ERI computations for both monatomic and polyatomic molecules. Our work has the potential to explore new parallelization schemes of distinct and complex computation paths involved in ERI computation.
We present a GPU-accelerated software package for the evaluation of analytic two-electron energy and gradient contributions in Hartree-Fock (HF) and Density Functional theory (DFT) calculations. The implementation is provided as a Python library with a C++ backend, enabling straightforward integration into modern computational chemistry and drug-discovery workflows. The code supports single-point energy and nuclear gradient evaluations on both single- and multi-GPU systems, and employs MPI-based parallelization with dynamic load balancing in multi-node environments. We report comprehensive benchmarks demonstrating favorable scaling with respect to system size, as well as high throughput for batched evaluations relevant to molecular dynamics, geometry optimization, and large-scale virtual screening. Parallel execution of a single system was carried out on up to 24 A100 GPUs. The implementation builds on optimized GPU-enabled variants of the LibintX and GauXC libraries to efficiently compute density-fitted Coulomb, semi-numerical exchange, and exchange--correlation contributions.