This paper presents the first quantum chemistry calculations using a recently developed vectorized library for computing electron repulsion integrals. To lengthen the SIMD loop and thus improve SIMD utilization, the approach used in this paper is to batch together multiple integrals that can be computed using the same code path. The standard approach is to compute integrals one at a time, and thus a batching procedure had to be developed. This paper shows proof-of-concept and demonstrates the performance gains possible when the batched approach is used. Batching also enables certain optimizations when the integrals are used to compute the Fock matrix. We further describe several other optimizations that were needed to obtain up to a 270% speedup over the non-batching version of the code, making a compelling case for adopting the presented techniques in quantum chemistry software.
This paper presents the first quantum chemistry calculations using a recently developed vectorized library for computing electron repulsion integrals. To lengthen the SIMD loop and thus improve SIMD utilization, the approach used in this paper is to batch together multiple integrals that can be computed using the same code path. The standard approach is to compute integrals one at a time, and thus a batching procedure had to be developed. This paper shows proof-of-concept and demonstrates the performance gains possible when the batched approach is used. Batching also enables certain optimizations when the integrals are used to compute the Fock matrix. We further describe several other optimizations that were needed to obtain up to a 270% speedup over the non-batching version of the code, making a compelling case for adopting the presented techniques in quantum chemistry software.
This paper presents the first quantum chemistry calculations using a recently developed vectorized library for computing electron repulsion integrals. To lengthen the SIMD loop and thus improve SIMD utilization, the approach used in this paper is to batch together multiple integrals that can be computed using the same code path. The standard approach is to compute integrals one at a time, and thus a batching procedure had to be developed. This paper shows proof-of-concept and demonstrates the performance gains possible when the batched approach is used. Batching also enables certain optimizations when the integrals are used to compute the Fock matrix. We further describe several other optimizations that were needed to obtain up to a 270% speedup over the non-batching version of the code, making a compelling case for adopting the presented techniques in quantum chemistry software.
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.
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.
Abstract The impact which vector processing computers are having on ab initio quantum chemical calculations will be considered, giving special emphasis to the experiences of United Kingdom scientists. Recent work using the CRAY-1 computer at the S.E.R.C. Daresbury Laboratory will be described. The CRAY-1 computer is at the centre of a network providing large scale computational facilities for universities in the U.K. Experience of running and subsequent vectorisation of certain standard ab initio packages will be discussed. Integral evaluation, self-consistent-field and orbital transformation phases of quantum chemical studies will be considered together with both the many-body perturbation theory and configuration mixing approaches to the electron correlation problem in molecules. Not only are improvements to the traditional algorithms which are made possible by the use of vector processors discussed, but also new areas of research which such computers open up are outlined. Future developments are considered briefly.
Libcint is a library designed for the evaluation of analytical integrals for Gaussian type orbitals. It prioritizes simplicity, ease of use, and efficiency for the development of quantum chemistry programs. In the release of version 6.0, Libcint supports the computation of integrals for various operators, such as overlap, Coulomb, Gaunt, Breit, attenuated Coulomb, Slater-type geminals, and Yukawa potential, as well as arbitrary orders of derivatives for these operators. To enhance the usability of the library, Libcint provides a uniform function signature for all integral functions. A code generator is included to automate the implementation of new integrals. To achieve better performance on modern central processing unit architectures, the library employs explicit single instruction multiple data parallelization in the code implementation.
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.