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arXiv:2507.09772 · The Journal of Chemical Physics

Designing quantum chemistry algorithms with just-in-time compilation

Xiaojie Wu, Qiming Sun, Yuanheng Wang

Published May 15, 2026• 2 citations
arXivHTMLPDF

Abstract

We introduce just-in-time (JIT) compilation to the integral kernels for Gaussian-type orbitals to enhance the efficiency of electron repulsion integral computations. For Coulomb and exchange (JK) matrices, JIT-based algorithms yield a 2× 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 4×. The core CUDA implementation is compact, comprising only ∼1000 lines of code, including support for single-precision arithmetic. Furthermore, the single-precision implementation achieves a 3× speedup over the previous state-of-the-art.

DOI
10.1063/5.0314659

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•Jan 1, 2011•6 citations
We introduce just-in-time (JIT) compilation to the integral kernels for Gaussian-type orbitals to enhance the efficiency of electron repulsion integral computations. For Coulomb and exchange (JK) matrices, JIT-based algorithms yield a 2× 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 4×. The core CUDA implementation is compact, comprising only ∼1000 lines of code, including support for single-precision arithmetic. Furthermore, the single-precision implementation achieves a 3× speedup over the previous state-of-the-art.
Modern videogames place increasing demands on the computational and graphical hardware, leading to novel architectures that have great potential in the context of high performance computing and molecular simulation. We demonstrate that Graphical Processing Units (GPUs) can be used very efficiently to calculate two-electron repulsion integrals over Gaussian basis functions [Formula: see text] the first step in most quantum chemistry calculations. A benchmark test performed for the evaluation of approximately 10(6) (ss|ss) integrals over contracted s-orbitals showed that a naïve algorithm implemented on the GPU achieves up to 130-fold speedup over a traditional CPU implementation on an AMD Opteron. Subsequent calculations of the Coulomb operator for a 256-atom DNA strand show that the GPU advantage is maintained for basis sets including higher angular momentum functions.
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.
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.
In this article, we present an effective approach to calculate quantum chemical two-electron integrals over basis sets consisting of Gaussian-type basis functions on graphical processing unit (GPU). Our framework generates several different variants called routes to the same integral problem with different integral algorithms (McMurchie-Davidson, Head-Gordon-Pople, and Rys) and precision. Each route is benchmarked on more GPU architectures, and with this data, a model is fitted to select the best available route for an integral task given a GPU architecture. Moreover, this approach supports the computation of high angular momentum orbitals up to g effectively on GPU, tested up to cc-pVQZ-sized basis sets. Rigorous analysis is shown regarding the effectiveness of our method. Molecule simulations with several basis sets are measured using NVIDIA GTX 1080 Ti, NVIDIA P100, and NVIDIA V100 cards.
The increasing availability of graphics processing units (GPUs) for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. However, the complexity of integral kernels for high angular momentum basis functions often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report the implementation of f function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH3) with complete active space self-consistent field are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules.
Abstract—Evaluation of electron repulsion integrals (ERIs) takes considerable time in modern quantum chemistry applications and also presents a certain difficulty to be efficiently computed on GPUs. Here, we describe a novel methodology for generating high-arithmetic-density kernels for ERI evaluation of d and higher angular momentum functions, as well as highlight challenges associated with the efficient use of GPUs for ERIs. Employing this approach allows to perform the ERI evaluations substantially faster than just using traditional CPU codes. Index Terms—GPUs; quantum chemistry; gaussian integrals; d-functions I.