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Journal of Chemical Theory and Computation

GPU-Accelerated Graph-Based Semiempirical Quantum Chemistry

Maksim Kulichenko, Robert M. Stanton, Cheng-Han Li, Nicholas Lubbers, Sergei Tretiak, Michael E. Wall, Christian F. A. Negre, Joshua Finkelstein, Anders M. N. Niklasson

Published Oct 27, 2025• 1 citation
Publisher

Abstract

Graph-based electronic structure theory offers a scalable approach to study large, complex atomistic systems using distributed and hybrid computational platforms. We demonstrate the coupling of graph-based linear scaling electronic structure theory, as implemented in the Scalable Ecosystem, Driver, and Analyzer for Complex Chemistry Simulations (SEDACS), with semiempirical quantum chemistry methods as implemented in the PySEQM code, with Graphics Processing Unit (GPU) acceleration. This powerful combination enables efficient, scalable electronic structure calculations over many nodes, significantly reducing computational cost while naturally harnessing parallelism. Detailed analyses of parallelization efficiency, computational accuracy, and communication overheads are provided, highlighting an order-of-magnitude speedup for systems of up to 10,000 atoms.

DOI
10.1021/acs.jctc.5c00936

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Graph-based electronic structure theory offers a scalable approach to study large, complex atomistic systems using distributed and hybrid computational platforms. We demonstrate the coupling of graph-based linear scaling electronic structure theory, as implemented in the Scalable Ecosystem, Driver, and Analyzer for Complex Chemistry Simulations (SEDACS), with semiempirical quantum chemistry methods as implemented in the PySEQM code, with Graphics Processing Unit (GPU) acceleration. This powerful combination enables efficient, scalable electronic structure calculations over many nodes, significantly reducing computational cost while naturally harnessing parallelism. Detailed analyses of parallelization efficiency, computational accuracy, and communication overheads are provided, highlighting an order-of-magnitude speedup for systems of up to 10,000 atoms.
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Graphical Processing Units (GPUs) are highly parallel, programmable accelerators boasting high peak floating point performance. Over the last couple of years the use of GPUs for general purpose computing have revolutionized quantum chemistry. The computational bottleneck in an ab-initio quantum method is the calculation of a large number of twoelectron integrals. To date, a number of GPU accelerated two-electron integral implementations have been developed significantly improving the performance of a static quantum mechanical (QM) calculation. However, when performing an ab-initio QM gradient calculation, optimization, QM or Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) dynamics simulation the twoelectron integral derivatives arise as an additional bottleneck. Hybrid QM/MM methods particularly dynamics methods are commonly used to study large chemical/biological systems. These methods are a popular choice used for studying reaction mechanisms, conformational and configurational structures important in glycobiology. Usually a semiempirical QM method is used however, these have shown variable accuracy for the study of carbohydrate conformation and prevents an analytical investigation of electronic structure. The use of a higher level of theory, such as an ab initio method, is desirable however this comes at a much greater computational cost. Together with the bottlenecks above this cost results from the polarization of the QM region within an electrostatic embedding scheme, which requires the calculation of a large number of one-electron integral derivatives. Thus for QM/MM calculations the one-electron integral derivatives becomes a third bottleneck together with the two mentioned above. Recently, the above bottlenecks have become popular GPU acceleration targets. This thesis describes an extension of the GPU based Quantum Supercharger Library (QSL) to perform the above calculations/simulations. In contrast to GPU packages developed from the ground up, the QSL is a library of routines aimed at accelerating legacy codes, such as GAMESS-UK, GAMESS-US and NWChem, used in electronic structure calculations. Algorithms are presented for accelerating the one- and two-electron integral derivatives on a GPU. In addition to the derivatives, the one-electron integral calculation was ported to the GPU in order to remove a small additional cost arising for large QM/MM systems. Furthermore, the use of automatic code generation for generating GPU kernels was explored and compared to the original approach. Using the QSL library implemented in GAMESS-UK several benchmark calculations and simulations were performed. These were performed in double precision on a single GPU (Kepler K20) and compared to a single CPU using the 6-31G basis set. A speedup of up to 9.3X is achieved for an ab initio gradient calculation compared to the CPU running an optimized serial version of GAMESS-UK using the Schlegel method. For a single point QM/MM calculation of cellobiose in different sized water spheres (3267-24843 point charges) speedups of between 13X and 34X is achieved. QSL/GAMESS-UK coupled to the CHARMM molecular dynamics package was then used in order to perform accelerated molecular dynamics simulations. Benchmark QM and QM/MM molecular dynamics simulations were performed on cellobiose in vacuo and in a water sphere (45 QM atoms and 24843 point charges respectively). The QSL is able to perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics. Testing of the auto-generated version of the QSL showed better performance for lower angular momentum classes but reduced performance for higher angular momentum classes. The efficiency of the integral and derivative routines within the QSL library was tested on a computationally intense realistic glycobiological condensed phase free energy computation. Ab-initio pucker free energy surfaces/volumes of !-Ribofuranose and !-Glucopyranose in vacuum and in water were computed. These are the first converged Hartree-Fock/MM free energy simulations for these carbohydrates performed in solution. The value of the ab initio Free energy surfaces/volumes was demonstrated through an analysis of solvent polarization effects that are evident through a comparison of the vacuum and solution minimum free energy pathways. In particular the water structure around the pucker conformers, analysis of the primary alcohol distribution as well as analysis of the electronic structure of these conformers reveals that water significantly affects the free energy pathways, primary alcohol distribution and the barriers for inter-conversion between pucker conformers.
We introduce a parallel, GPU-accelerated implementation of the iterative qubit coupled cluster (iQCC) method that overcomes the exponential growth of the transformed Hamiltonian -- the principal bottleneck for classical emulation of quantum chemistry circuits. By distributing Hamiltonian terms across compute nodes via bit-wise partitioning and offloading Pauli contractions to GPUs, we achieve speedups exceeding two orders of magnitude over the serial CPU approach. Crucially, iQCC confines the variational evolution to a classically simulable operator subspace by selecting entanglers exclusively from the Direct Interaction Space, which guarantees non-vanishing energy gradients at every iteration and thereby naturally avoids the barren-plateau phenomenon that renders highly expressive quantum circuits untrainable. Leveraging these algorithmic and hardware advances, we simulate electronic-structure Hamiltonians for industrially relevant ruthenium catalysts in the 100--124 qubit regime, completing full ground-state calculations on NVIDIA GPUs in the ranges of 1.2 - 45 hrs and surpassing the accuracy of Density Matrix Renormalization Group. These results effectively de-quantize a significant portion of the NISQ roadmap: quantum advantage for chemistry is often assumed to emerge beyond ∼50{\sim}50∼50 qubits, yet our work demonstrates that this frontier lies significantly further -- potentially past 200 qubits -- reshaping expectations for where genuine quantum advantage may first appear.
The dynamic rearrangement of a molecule at finite temperature is not captured by a single static input geometry to a quantum chemical calculation. Multilevel workflows have established themselves as standard procedures to capture the dependence of the molecule’s configuration on computed properties. Each step within this workflow uses an electronic structure theory method that features the optimal computational time to accuracy ratio. For exploratory steps the computational expense of a method needs to be minimal as several thousand energy and nuclear gradient evaluations are needed. Semiempirical tight binding methods, such as GFN2-xTB are often used for such purposes. However, these methods usually lack the accuracy to rank conformers relative to each other within chemical accuracy (2 kcal/mol). Therefore, so-called “low-cost” DFT methods are commonly used for geometry optimizations and conformer ranking. The combination of (semi)empirical correction models with small basis sets leads to good accuracy at moderate computational cost. However, even these highly efficient methods reach the limits of feasibility for very large systems (> 200 atoms). This work proposes solutions to partially alleviate those restrictions and allow routine calculations of these system sizes outside of large high-performance computing facilities. The key to unlock those calculations is to combine tailored algorithmic developments with consumer-grade GPUs. A GPU-enabled linear algebra library is developed to accelerate further development and make the entry to GPU-accelerated software development easier. To demonstrate the ease of implementation, the addition of Mulliken-approximated exchange to GFN2-xTB will be shown. In most semiempirical methods, the general eigenvalue solver algorithm becomes the computational bottleneck, dominating the walltime with increasing system size. A density matrix purification algorithm is tailored to give up to six-fold acceleration of GFN2-xTB calculations using a mixed-precision approach. Lastly, 3c-methods are added to the GPU-accelerated TeraChem software package. In combination with the “mixed-precision” scheme for computing the electron repulsion integrals, this addition decreases the runtime of DFT calculations by up to an order of magnitude on mid-level consumer hardware. The overall goal of these projects is to make GPU-accelerated calculations in quantum chemistry more available. This achieve by exposing algorithmic developments that are performant on reasonably priced hardware and making GPU computing more accessible to non-experts.
Developed over the past decade, TeraChem is an electronic structure and ab initio molecular dynamics software package designed from the ground up to leverage graphics processing units (GPUs) to perform large-scale ground and excited state quantum chemistry calculations in the gas and the condensed phase. TeraChem's speed stems from the reformulation of conventional electronic structure theories in terms of a set of individually optimized high-performance electronic structure operations (e.g., Coulomb and exchange matrix builds, one- and two-particle density matrix builds) and rank-reduction techniques (e.g., tensor hypercontraction). Recent efforts have encapsulated these core operations and provided language-agnostic interfaces. This greatly increases the accessibility and flexibility of TeraChem as a platform to develop new electronic structure methods on GPUs and provides clear optimization targets for emerging parallel computing architectures.
We demonstrate the use of graphical processing units (GPUs) to carry out complete self-consistent-field calculations for molecules with as many as 453 atoms (2131 basis functions). Speedups ranging from 28× to 650× are achieved as compared to a mature third-party quantum chemistry program (GAMESS) running on a traditional CPU. The computational organization used to construct the Coulomb and exchange operators is discussed. We also present results using three GPUs in parallel, combining coarse and fine-grained parallelism.