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Journal of Chemical Information and Modeling

Quantum Mechanics/Molecular Mechanics Simulations on NVIDIA and AMD Graphics Processing Units

Madushanka Manathunga, Hasan Metin Aktulga, Andreas W. Götz, Kenneth M. Merz

Published Jan 31, 2023• 48 citations
Publisher

Abstract

quantum mechanics/molecular mechanics (QM/MM) implementation on AMD GPUs. This encompasses the entire Fock matrix build and force calculation in QUICK including one-electron integrals, two-electron repulsion integrals, exchange-correlation quadrature, and linear algebra operations. General performance improvements to the QUICK GPU code are also presented. Benchmarks carried out on NVIDIA V100 and AMD MI100 cards display similar performance on both hardware for standalone HF/DFT calculations with QUICK and QM/MM molecular dynamics simulations with QUICK/AMBER. Furthermore, with respect to the QUICK/AMBER release version 21, significant speedups are observed for QM/MM molecular dynamics simulations. This significantly increases the range of scientific problems that can be addressed with open-source QM/MM software on state-of-the-art computer hardware.

DOI
10.1021/acs.jcim.2c01505

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quantum mechanics/molecular mechanics (QM/MM) implementation on AMD GPUs. This encompasses the entire Fock matrix build and force calculation in QUICK including one-electron integrals, two-electron repulsion integrals, exchange-correlation quadrature, and linear algebra operations. General performance improvements to the QUICK GPU code are also presented. Benchmarks carried out on NVIDIA V100 and AMD MI100 cards display similar performance on both hardware for standalone HF/DFT calculations with QUICK and QM/MM molecular dynamics simulations with QUICK/AMBER. Furthermore, with respect to the QUICK/AMBER release version 21, significant speedups are observed for QM/MM molecular dynamics simulations. This significantly increases the range of scientific problems that can be addressed with open-source QM/MM software on state-of-the-art computer hardware.
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.
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.
This article describes an extension of the quantum supercharger library (QSL) to perform quantum mechanical (QM) gradient and optimization calculations as well as hybrid QM and molecular mechanical (QM/MM) molecular dynamics simulations. The integral derivatives are, after the two-electron integrals, the most computationally expensive part of the aforementioned calculations/simulations. Algorithms are presented for accelerating the one- and two-electron integral derivatives on a graphical processing unit (GPU). It is shown that a Hartree-Fock ab initio gradient calculation is up to 9.3X faster on a single GPU compared with a single central processing unit running an optimized serial version of GAMESS-UK, which uses the efficient Schlegel method for s- and l-orbitals. Benchmark QM and QM/MM molecular dynamics simulations are performed on cellobiose in vacuo and in a 39 Å water sphere (45 QM atoms and 24843 point charges, respectively) using the 6-31G basis set. The QSL can perform 9.7 ps/day of ab initio QM dynamics and 6.4 ps/day of QM/MM dynamics on a single GPU in full double precision. © 2015 Wiley Periodicals, Inc.
This dissertation is focused around enabling large-scale quantum chemistry calculations by developing novel algorithms on new heterogeneous hardware architectures. Section 2 contains a study on assessing the importance of many-body dispersion phenomena in molecular clusters and understanding the need to incorporate the phenomena into existing quantum chemistry methods to accurately capture long-range interactions. It is known that highly accurate quantum chemistry methods are computationally expensive; therefore, there is a need for new computer algorithms that will be able to vastly improve the time to solution and enable correlated quantum chemistry calculations on large molecular systems. Sections 3 and 4 focus on the development and implementation of various algorithms that enable quantum chemistry calculations on molecules of unprecedent sizes. Specifically, Section 3 describes a novel CUDA-based algorithm that enables GPU-acceleration of the main parts of the Self-Consistent Field (SCF) cycle, resulting in the fastest SCF code to date. Section 4 introduces a novel OpenMP-based implementation of the Fock build formation, which enables GPU-accelerated calculations on all existing GPU and CPU hardware. Section 5 expands upon the OpenMP work and describes a new GPU-accelerated library named LibERI for evaluating molecular integrals – often the main computational bottleneck in many quantum chemistry methods. LibERI is intended to serve as a library for fast quantum chemistry calculations that can be interfaced with any existing quantum chemistry software packages through the MolSSI Driver Interface (MDI). MDI is a standard interface between scientific computational codes. One of LibERI’s objectives is to seamlessly integrate with a Molecular Mechanics (MM) package using MDI to enable fast QM/MM calculations. This integration would allow for efficient GPU-accelerated treatment of large QM regions via LibERI. Lastly, Section 6 concludes this dissertation with a study that applies existing quantum chemistry methods to unravel the mechanism of a Pd-catalyzed carboacylation reaction involving the activation of ester C-O bonds.
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 modification of a general purpose code for quantum mechanical calculations of molecular properties (Q-Chem) to use a graphical processing unit (GPU) is reported. A 4.3x speedup of the resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) execution time is observed in single point energy calculations of linear alkanes. The code modification is accomplished using the compute unified basic linear algebra subprograms (CUBLAS) library for an NVIDIA Quadro FX 5600 graphics card. Furthermore, speedups of other matrix algebra based electronic structure calculations are anticipated as a result of using a similar approach.