Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Chemical Theory and Computation

Quantum Chemistry in Dataflow: Density-Fitting MP2

Bridgette Cooper, Stephen Girdlestone, Pavel Burovskiy, Georgi Nedeltchev Gaydadjiev, Vitali Averbukh, Peter J. Knowles, Wayne W. Luk

Published Oct 11, 2017• 11 citations
Publisher

Abstract

We demonstrate the use of dataflow technology in the computation of the correlation energy in molecules at the Møller-Plesset perturbation theory (MP2) level. Specifically, we benchmark density fitting (DF)-MP2 for as many as 168 atoms (in valinomycin) and show that speed-ups between 3 and 3.8 times can be achieved when compared to the MOLPRO package run on a single CPU. Acceleration is achieved by offloading the matrix multiplications steps in DF-MP2 to Dataflow Engines (DFEs). We project that the acceleration factor could be as much as 24 with the next generation of DFEs.

DOI
10.1021/acs.jctc.7b00649

Related papers

An Efficient RI-MP2 Algorithm for Distributed Many-GPU Architectures

Calum Snowdon, Giuseppe M. J. Barca

Second-order Møller-Plesset perturbation theory (MP2) using the Resolution of the Identity approximation (RI-MP2) is a widely used method for computing molecular energies beyond the Hartree-Fock mean-field approximation. However, its high computational cost and lack of efficient algorithms for modern supercomputing architectures limit its applicability to large molecules. In this paper, we present the first distributed-memory many-GPU RI-MP2 algorithm explicitly designed to utilize hundreds of GPU accelerators for every step of the computation. Our novel algorithm achieves near-peak performance on GPU-based supercomputers through the development of a distributed memory algorithm for forming RI-MP2 intermediate tensors with zero inter-node communication, except for a single O(N^2) asynchronous broadcast, and a distributed memory algorithm for the O(N^5) energy reduction step, capable of sustaining near-peak performance on clusters with several hundred GPUs. Comparative analysis shows our implementation outperforms state-of-the-art quantum chemistry software by over 3.5 times in speed while achieving an eightfold reduction in computational power consumption. Benchmarking on the Perlmutter supercomputer, our algorithm achieves 11.8 PFLOP/s (83% of peak performance) performing and the RI-MP2 energy calculation on a 314-water cluster with 7,850 primary and 30,144 auxiliary basis functions in 4 minutes on 180 nodes and 720 A100 GPUs. This performance represents a substantial improvement over traditional CPU-based methods, demonstrating significant time-to-solution and power consumption benefits of leveraging modern GPU-accelerated computing environments for quantum chemistry calculations.

Journal of Chemical Theory and Computation•Oct 18, 2024•7 citations

A GPU Implementation of the Second- and Third-Order Møller-Plesset Perturbation Theory

Satoki Tsuji, Yasuaki Ito, Nobuya Yokogawa +4 more

Post-Hartree-Fock methods are wavefunction-based quantum chemistry approaches that explicitly account for the electron correlation beyond the mean-field approximation, allowing accurate determination of electron orbitals and energies in a given system. However, their computational cost scales as the fourth power or higher with respect to the number of atoms, severely limiting their practical applications. This paper proposes an efficient GPU implementation of the Møller-Plesset method, a post-Hartree-Fock approach based on perturbation theory. We focus on the computation of second- and thirdorder perturbation energies (MP2 and MP3) for closed-shell systems, which incorporate electron correlation on top of the Hartree-Fock energy. To accelerate the extensive contraction operations arising in the Møller-Plesset method, our implementation employs a formulation that maximizes the use of highly optimized matrix multiplication routines. Furthermore, we effectively utilize computational capabilities of GPU architecture through a hierarchical reduction using warp-level primitives and shared memory, as well as contiguous coalesced access to matrix elements. Performance evaluation on an NVIDIA A100 GPU shows up to 255.5 and 71.1 times speedups for the MP2 correlation energy computation, compared with the widely used quantum chemistry software package PySCF and its GPU plugin GPU4PySCF, respectively. In the MP3 calculations, our DGEMM-based implementation achieves a maximum speedup of 96.2 times over PySCF.

International Symposium on Computing and Networking Workshops (CANDARW)•Nov 25, 2025•1 citation

Enabling large-scale correlated electronic structure calculations

Giuseppe M. J. Barca, Jorge Luis Galvez Vallejo, David Poole +4 more

Second-order Møller-Plesset perturbation theory using the Resolution-of-the-Identity approximation (RI-MP2) is a state-of-the-art approach to accurately estimate many-body electronic correlation effects. This is critical for predicting the physicochemical properties of complex molecular systems; however, the scale of these calculations is limited by their extremely high computational cost. In this paper, a novel many-GPU algorithm and implementation of a molecular-fragmentation-based RI-MP2 method are presented that enable correlated calculations on over 180,000 electrons and 45,000 atoms using up to the entire Summit supercomputer in 12 minutes. The implementation demonstrates remarkable speedups with respect to other current GPU and CPU codes, excellent strong scalability on Summit achieving 89.1% parallel efficiency on 4600 nodes, and shows nearly-ideal weak scaling up to 612 nodes. This work makes feasible ab initio correlated quantum chemistry calculations on significantly larger molecular scales than before on both large supercomputing systems and on commodity clusters, with a potential for major impact on progress in chemical, physical, biological and engineering sciences.

International Conference for High Performance Computing, Networking, Storage and Analysis (SC)•Oct 21, 2021•18 citations

Accelerating Density Fitting with Adaptive Precision and 8-Bit Integer on AI Accelerators

Hua Huang, Wenkai Shao, Jeff R. Hammond

The emergence of artificial intelligence (AI) accelerators like NVIDIA Tensor Cores offers new opportunities to speed up tensor-heavy scientific computations. However, applying them to quantum chemistry is challenging due to strict accuracy demands and irregular data patterns. We propose an adaptive precision algorithm to accelerate the density fitting (DF) method with Gaussian basis sets on AI accelerators using 8-bit integer (INT8) arithmetics. Implemented in the GPU-accelerated PySCF package, the algorithm is tested on more than 20 molecular systems with different NVIDIA GPUs. Compared to the standard FP64 code, our algorithm is up to 204% faster on an RTX 4090 gaming GPU and up to 364% faster on an RTX 6000 Ada workstation GPU without compromising the converged energy. This work demonstrates a practical approach to using AI hardware for reliable quantum chemistry simulations.

arXiv:2601.08077•The Journal of Physical Chemistry A•Apr 17, 2026•1 citation

Quartic scaling MP2 for solids: A highly parallelized algorithm in the plane wave basis

Tobias Schäfer, Benjamin Ramberger, Georg Kresse

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O(N4), with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

arXiv:1611.06797•The Journal of Chemical Physics•Mar 8, 2017•62 citations

Accurate Quantum Chemistry in Single Precision Arithmetic: Correlation Energy

Victor P. Vysotskiy, Lorenz S. Cederbaum

In the present work, we show the feasibility of using single precision in quantum chemistry, especially regarding the computation of electron correlation energy. On the example of the MP2 method, we clearly demonstrate that single precision arithmetic is sufficient for evaluating the molecular two-electron integrals by the use of the Cholesky decomposition method. The evaluation of integrals with single precision arithmetic introduces a negligible error into the computed MP2 correlation energy. In particular, the corresponding error in the MP2 correlation energy amounts to only 10(-7)Eh for the 113-atom taxol molecule in double-valence basis set (1099 basis functions). The practical relevance of our result is that 50% performance gain and 50% reduction in memory demands can be achieved by only minor changes in the existing codes. Our finding opens intriguing perspectives for doing accurate correlated quantum chemistry on specialized floating-point mathematical coprocessors.

Journal of Chemical Theory and Computation•Dec 23, 2010•22 citations
We demonstrate the use of dataflow technology in the computation of the correlation energy in molecules at the Møller-Plesset perturbation theory (MP2) level. Specifically, we benchmark density fitting (DF)-MP2 for as many as 168 atoms (in valinomycin) and show that speed-ups between 3 and 3.8 times can be achieved when compared to the MOLPRO package run on a single CPU. Acceleration is achieved by offloading the matrix multiplications steps in DF-MP2 to Dataflow Engines (DFEs). We project that the acceleration factor could be as much as 24 with the next generation of DFEs.
Second-order Møller-Plesset perturbation theory (MP2) using the Resolution of the Identity approximation (RI-MP2) is a widely used method for computing molecular energies beyond the Hartree-Fock mean-field approximation. However, its high computational cost and lack of efficient algorithms for modern supercomputing architectures limit its applicability to large molecules. In this paper, we present the first distributed-memory many-GPU RI-MP2 algorithm explicitly designed to utilize hundreds of GPU accelerators for every step of the computation. Our novel algorithm achieves near-peak performance on GPU-based supercomputers through the development of a distributed memory algorithm for forming RI-MP2 intermediate tensors with zero inter-node communication, except for a single O(N^2) asynchronous broadcast, and a distributed memory algorithm for the O(N^5) energy reduction step, capable of sustaining near-peak performance on clusters with several hundred GPUs. Comparative analysis shows our implementation outperforms state-of-the-art quantum chemistry software by over 3.5 times in speed while achieving an eightfold reduction in computational power consumption. Benchmarking on the Perlmutter supercomputer, our algorithm achieves 11.8 PFLOP/s (83% of peak performance) performing and the RI-MP2 energy calculation on a 314-water cluster with 7,850 primary and 30,144 auxiliary basis functions in 4 minutes on 180 nodes and 720 A100 GPUs. This performance represents a substantial improvement over traditional CPU-based methods, demonstrating significant time-to-solution and power consumption benefits of leveraging modern GPU-accelerated computing environments for quantum chemistry calculations.
Post-Hartree-Fock methods are wavefunction-based quantum chemistry approaches that explicitly account for the electron correlation beyond the mean-field approximation, allowing accurate determination of electron orbitals and energies in a given system. However, their computational cost scales as the fourth power or higher with respect to the number of atoms, severely limiting their practical applications. This paper proposes an efficient GPU implementation of the Møller-Plesset method, a post-Hartree-Fock approach based on perturbation theory. We focus on the computation of second- and thirdorder perturbation energies (MP2 and MP3) for closed-shell systems, which incorporate electron correlation on top of the Hartree-Fock energy. To accelerate the extensive contraction operations arising in the Møller-Plesset method, our implementation employs a formulation that maximizes the use of highly optimized matrix multiplication routines. Furthermore, we effectively utilize computational capabilities of GPU architecture through a hierarchical reduction using warp-level primitives and shared memory, as well as contiguous coalesced access to matrix elements. Performance evaluation on an NVIDIA A100 GPU shows up to 255.5 and 71.1 times speedups for the MP2 correlation energy computation, compared with the widely used quantum chemistry software package PySCF and its GPU plugin GPU4PySCF, respectively. In the MP3 calculations, our DGEMM-based implementation achieves a maximum speedup of 96.2 times over PySCF.
Second-order Møller-Plesset perturbation theory using the Resolution-of-the-Identity approximation (RI-MP2) is a state-of-the-art approach to accurately estimate many-body electronic correlation effects. This is critical for predicting the physicochemical properties of complex molecular systems; however, the scale of these calculations is limited by their extremely high computational cost. In this paper, a novel many-GPU algorithm and implementation of a molecular-fragmentation-based RI-MP2 method are presented that enable correlated calculations on over 180,000 electrons and 45,000 atoms using up to the entire Summit supercomputer in 12 minutes. The implementation demonstrates remarkable speedups with respect to other current GPU and CPU codes, excellent strong scalability on Summit achieving 89.1% parallel efficiency on 4600 nodes, and shows nearly-ideal weak scaling up to 612 nodes. This work makes feasible ab initio correlated quantum chemistry calculations on significantly larger molecular scales than before on both large supercomputing systems and on commodity clusters, with a potential for major impact on progress in chemical, physical, biological and engineering sciences.
The emergence of artificial intelligence (AI) accelerators like NVIDIA Tensor Cores offers new opportunities to speed up tensor-heavy scientific computations. However, applying them to quantum chemistry is challenging due to strict accuracy demands and irregular data patterns. We propose an adaptive precision algorithm to accelerate the density fitting (DF) method with Gaussian basis sets on AI accelerators using 8-bit integer (INT8) arithmetics. Implemented in the GPU-accelerated PySCF package, the algorithm is tested on more than 20 molecular systems with different NVIDIA GPUs. Compared to the standard FP64 code, our algorithm is up to 204% faster on an RTX 4090 gaming GPU and up to 364% faster on an RTX 6000 Ada workstation GPU without compromising the converged energy. This work demonstrates a practical approach to using AI hardware for reliable quantum chemistry simulations.
We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O(N4), with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.
In the present work, we show the feasibility of using single precision in quantum chemistry, especially regarding the computation of electron correlation energy. On the example of the MP2 method, we clearly demonstrate that single precision arithmetic is sufficient for evaluating the molecular two-electron integrals by the use of the Cholesky decomposition method. The evaluation of integrals with single precision arithmetic introduces a negligible error into the computed MP2 correlation energy. In particular, the corresponding error in the MP2 correlation energy amounts to only 10(-7)Eh for the 113-atom taxol molecule in double-valence basis set (1099 basis functions). The practical relevance of our result is that 50% performance gain and 50% reduction in memory demands can be achieved by only minor changes in the existing codes. Our finding opens intriguing perspectives for doing accurate correlated quantum chemistry on specialized floating-point mathematical coprocessors.