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arXiv:2512.01055 · The Journal of Physical Chemistry A

Accelerating CCSD(T) on Graphical Processing Units (GPUs)

O. Jonathan Fajen, Joseph Kelly, Edward G. Hohenstein, Todd J. Martı́nez

Published Feb 26, 2026• 0 citations
arXivHTMLPDF

Abstract

Coupled cluster with singles, doubles, and perturbative triples (CCSD(T)) often provides ground state correlation energies within ″chemical accuracy", but it suffers from high computational cost and steep scaling with system size. We present a GPU-accelerated implementation of CCSD(T) in the TeraChem software package. The new implementation achieves state-of-the-art performance, enabling the calculation of the (T) correction for a system with 63 atoms and more than 1000 basis functions in a little under 8 h on a single node. Additionally, we demonstrate the utility of our optimized implementation for the rapid calculation of full CCSD(T)/CBS stacking energies for all ten unique DNA base pair stacked tetramers. We expect that the TeraChem CCSD(T) implementation will enable the rapid calculation of high-level data that was not previously accessible in a reasonable time frame.

DOI
10.1021/acs.jpca.5c08113

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•Jan 1, 2011•1 citation
Coupled cluster with singles, doubles, and perturbative triples (CCSD(T)) often provides ground state correlation energies within ″chemical accuracy", but it suffers from high computational cost and steep scaling with system size. We present a GPU-accelerated implementation of CCSD(T) in the TeraChem software package. The new implementation achieves state-of-the-art performance, enabling the calculation of the (T) correction for a system with 63 atoms and more than 1000 basis functions in a little under 8 h on a single node. Additionally, we demonstrate the utility of our optimized implementation for the rapid calculation of full CCSD(T)/CBS stacking energies for all ten unique DNA base pair stacked tetramers. We expect that the TeraChem CCSD(T) implementation will enable the rapid calculation of high-level data that was not previously accessible in a reasonable time frame.
It has been shown that coupled-cluster calculations with single-precision data are able to provide correlation energy with insignificant loss of accuracy. In this work, we employed consumer GPUs to accelerate open-shell spin-unrestricted CCSD and CCSD(T) calculations based on single-precision data. Some open-shell molecules are calculated to benchmark the acceleration performance of GPUs. In CCSD calculations, good acceleration performance on consumer GPUs is achieved for molecules when all the two-electron integrals can be saved in the host memory. On the other hand, I/O operations cost a lot of time for larger molecules and the performance of GPUs is not as significant. Good acceleration performance can usually be obtained in calculating the (T) correction employing GPUs since matrix contractions are always more costly than other operations. For systems with less than four hundred basis functions, our single-precision GPU code could provide an acceleration of 4-14 times for CCSD calculations and 12-20 times for (T) correction compared with double-precision CPU codes on the same hardware level.
An algorithm is presented for the coupled-cluster singles, doubles, and perturbative triples correction [CCSD(T)] method based on the density fitting or the resolution-of-the-identity (RI) approximation for performing calculations on heterogeneous computing platforms composed of multicore CPUs and graphics processing units (GPUs). The directive-based approach to GPU offloading offered by the OpenMP application programming interface has been employed to adapt the most compute-intensive terms in the RI-CCSD amplitude equations with computational costs scaling as O ( N O 2 N V 4 ), O ( N O 3 N V 3 ), and O ( N O 4 N V 2 ) (where N O and N V denote the numbers of correlated occupied and virtual orbitals, respectively) and the perturbative triples correction to execute on GPU architectures. The pertinent tensor contractions are performed using an accelerated math library such as cuBLAS or hipBLAS. Optimal strategies are discussed for splitting large data arrays into tiles to fit them into the relatively small memory space of the GPUs, while also minimizing the low-bandwidth CPU–GPU data transfers. The performance of the hybrid CPU–GPU RI-CCSD(T) code is demonstrated on pre-exascale supercomputers composed of heterogeneous nodes equipped with NVIDIA Tesla V100 and A100 GPUs and on the world’s first exascale supercomputer named “Frontier”, the nodes of which consist of AMD MI250X GPUs. Speedups within the range 4–8× relative to the recently reported CPU-only algorithm are obtained for the GPU-offloaded terms in the RI-CCSD amplitude equations. Applications to polycyclic aromatic hydrocarbons containing 16–66 carbon atoms demonstrate that the acceleration of the hybrid CPU–GPU code for the perturbative triples correction relative to the CPU-only code increases with the molecule size, attaining a speedup of 5.7× for the largest circumovalene molecule (C 66 H 20 ). The GPU-offloaded code enables the computation of the perturbative triples correction for the C 60 molecule using the cc-pVDZ/aug-cc-pVTZ-RI basis sets in 7 min on Frontier when using 12,288 AMD GPUs with a parallel efficiency of 83.1%.
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 A high‐performance implementation of the coupled‐cluster singles, doubles, and perturbative triples [CCSD(T)] is developed in the Massively Parallel Quantum Chemistry program. Novel features include: (1) reduced memory requirements via a density‐fitting (DF) CCSD implementation utilizing distributed lazy evaluation for tensors with more than two unoccupied indices and (2) the ability to utilize efficiently many‐core nodes (Intel Xeon Phi) and heterogeneous nodes with multiple NVIDIA GPUs on each node. All data that are greater than quadratic in the system size are distributed among processes. Excellent strong scaling is observed on distributed‐memory computers equipped with conventional CPUs, Intel Xeon Phi processors, and heterogeneous nodes with multiple NVIDIA GPUs Canonical CCSD(T) energies can be evaluated for systems containing 200 electrons and 1000 basis functions in a few days using a small size commodity cluster, with even larger computations possible on leadership‐class computing resources.
Heterogeneous nodes composed of a multicore CPU and at least one graphics processing unit (GPU) are increasingly common in high-performance scientific computing, and significant programming effort is currently being undertaken to port existing scientific algorithms to these unique architectures. We present implementations for two many-body quantum chemistry methods on heterogeneous nodes: the coupled-cluster with single and double excitations (CCSD) and time-dependent configuration interaction with single and double excitations (TD-CISD) methods. Both methods can be implemented on a computer as a series of dense matrix-matrix multiplications, operations that GPUs are particularly adept at performing. The GPU-accelerated CCSD algorithm is as much as 4.3 times faster than the corresponding CPU algorithm and 9.7 times faster than the algorithm in the Molpro package. The TD-CISD algorithm is accelerated by as much as a factor of 3.9 by GPUs. Enhanced performance is achieved by overlapping CPU and GPU computations.