Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor‐like polarizable continuum models
Fang Liu, David M. Sanchez, Heather J. Kulik, Todd J. Martı́nez
Abstract The conductor‐like polarizable continuum model (C‐PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C‐PCM solvation for Hartree‐Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU‐based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM‐related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C‐PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time‐dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)‐based implementation. In addition, our C‐PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed‐ups of up to 130× for restricted ESP‐based atomic charge evaluations, when compared to CPU‐based codes. We also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.
Abstract The conductor‐like polarizable continuum model (C‐PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C‐PCM solvation for Hartree‐Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU‐based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM‐related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C‐PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time‐dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)‐based implementation. In addition, our C‐PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed‐ups of up to 130× for restricted ESP‐based atomic charge evaluations, when compared to CPU‐based codes. We also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.
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.
Accurate and efficient gradients of molecular energy with respect to nuclear degrees of freedom are essential for geometry optimization and molecular dynamics, including simulations that go beyond the Born-Oppenheimer regime. A common approach involves deriving analytical formulas for new electronic structure methods, which is often conceptually difficult and requires tedious coding. Here, we implement analytical, semi-numerical, and automatic differentiation (AD)-based gradient pathways for semiempirical Hamiltonian models in the PYSEQM software package, leveraging both graphics processing unit (GPU) and central processing unit (CPU) architectures. We further extend these capabilities to excited states calculated using the configuration interaction singles and time-dependent Hartree-Fock ansätze. We benchmark wall time, peak memory usage, and accuracy across three molecular families of varying chemical complexity, including systems of up to a thousand atoms. For ground-state simulations, analytical and AD gradients achieve near-identical GPU runtimes, while semi-numerical gradients are slower on GPU but remain competitive on CPU. For excited states, both analytical and custom AD approaches using implicit differentiation show similar performance and low memory requirements, whereas gradients with full AD are memory-limited. AD gradients match analytical ones in accuracy across all tested systems, aided by a quaternion-based diatomic frame rotation for two-center quantities that ensures smooth energy surfaces. Overall, automatic differentiation emerges as a practical alternative to analytical gradients in semiempirical quantum chemistry, offering high accuracy while allowing seamless integration in AI-driven workflows and popular packages, such as PyTorch and JAX. Our results provide actionable guidance for selecting optimal gradient strategies in large-scale ground- and excited-state molecular dynamics simulations.
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.
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.
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.
ABSTRACT Applying quantum chemistry algorithms to large‐scale systems requires substantial computational resources scaling with the system size and the desired accuracy. To address this, ByteQC, a fully functional and efficient package for large‐scale quantum chemistry simulations, has been open sourced at https://github.com/bytedance/byteqc , leveraging recent advances in computational power and many‐body algorithms. Regarding computational power, several standard algorithms are efficiently implemented on modern GPUs, ranging from mean‐field calculations (Hartree‐Fock and density functional theory) to post‐Hartree‐Fock methods such as Møller‐Plesset perturbation theory and coupled cluster methods. For the algorithmic approach, we also employ a quantum embedding method, which significantly expands the tractable system size while preserving high accuracy at the gold‐standard level. All these features have been systematically benchmarked. For standalone algorithms, the benchmark results demonstrate up to a 60× speedup when compared to 100‐core CPUs. Additionally, the tractable system sizes have been significantly expanded: 1610 orbitals for coupled cluster with single and double excitations (1380 orbitals with perturbative triple excitations), 11,040 orbitals for Møller‐Plesset perturbation theory of second order, 37,120 orbitals for mean‐field calculations under open boundary conditions, and over 100,000 orbitals for periodic boundary conditions. For the advanced quantum embedding feature, two representative examples are demonstrated: the water cluster problem (2752 orbitals) and a water monomer adsorbed on a boron nitride surface (3929 orbitals), achieving the gold‐standard accuracy. With these efforts, ByteQC is expected to significantly advance research in quantum chemistry, particularly in large‐scale, high‐accuracy calculations.