GPU algorithms for density matrix methods on MOPAC: linear scaling electronic structure calculations for large molecular
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ORIGINAL PAPER
GPU algorithms for density matrix methods on MOPAC: linear scaling electronic structure calculations for large molecular systems Julio Daniel Carvalho Maia 1,2 & Lucidio dos Anjos Formiga Cabral 1 & Gerd Bruno Rocha 3 Received: 4 June 2020 / Accepted: 8 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Purification of the density matrix methods should be employed when dealing with complex chemical systems containing many atoms. The running times for these methods scale linearly with the number of atoms if we consider the sparsity from the density matrix. Since the efficiency expected from those methods is closely tied to the underlying parallel implementations of the linear algebra operations (e.g., P2 = P × P), we proposed a central processing unit (CPU) and graphics processing unit (GPU) parallel matrix-matrix multiplication in SVBR (symmetrical variable block row) format for energy calculations through the SP2 algorithm. This algorithm was inserted in MOPAC’s MOZYME method, using the original LMO Fock matrix assembly, and the atomic integral calculation implemented on it. Correctness and performance tests show that the implemented SP2 is accurate and fast, as the GPU is able to achieve speedups up to 40 times for a water cluster system with 42,312 orbitals running in one NVIDIA K40 GPU card compared to the single-threaded version. The GPU-accelerated SP2 algorithm using the MOZYME LMO framework enables the calculations of semiempirical wavefunction with stricter SCF criteria for localized charged molecular systems, as well as the single-point energies of molecules with more than 100.000 LMO orbitals in less than 1 h. Keywords Linear scaling algorithms . Density matrix methods . GPGPU programming . Sparse matrices . Semiempirical methods
Introduction One of the greatest challenges in molecular modeling is treating highly complex molecular systems, such as biomolecules, polymers, solutions, and materials, using quantum chemistry methods [1, 2]. The theoretical and computational This paper belongs to Topical Collection XX - Brazilian Symposium of Theoretical Chemistry (SBQT2019) Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00894-020-04571-6) contains supplementary material, which is available to authorized users. * Gerd Bruno Rocha [email protected] 1
Centro de Informática, Universidade Federal da Paraíba, João Pessoa, PB CEP: 58055-000, Brazil
2
Theoretical and Computational Biophysics Group - Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
3
Departamento de Química – CCEN, Universidade Federal da Paraíba, Caixa Postal: 5093, João Pessoa, PB CEP: 58051-970, Brazil
strategies employed usually need many-core, parallel computers, aligned with algorithms that scale both memory and CPU time linearly with the number of atoms from the system [3–6]. Nowadays, using modern computational architectures, it is possible to model large chemical systems, containing up to 1 million of a
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