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GPU algorithms for density matrix methods on MOPAC: linear scaling electronic structure calculations for large

Julio Daniel Carvalho Maia1,2, Lucidio Dos Anjos Formiga Cabral1, Gerd Bruno Rocha3

  • 1Centro de Informática, Universidade Federal da Paraíba, João Pessoa, PB, CEP: 58055-000, Brazil.

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|October 22, 2020
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Summary
This summary is machine-generated.

Density matrix purification methods are crucial for complex chemical systems. This study introduces a parallel CPU and GPU matrix multiplication algorithm (SP2) for faster electronic structure calculations, achieving up to 40x speedup.

Keywords:
Density matrix methodsGPGPU programmingLinear scaling algorithmsSemiempirical methodsSparse matrices

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Density matrix purification methods are essential for accurate electronic structure calculations in complex chemical systems.
  • The efficiency of these methods is often limited by the performance of underlying linear algebra operations, particularly matrix-matrix multiplication.
  • Existing methods struggle with large systems due to computational bottlenecks.

Purpose of the Study:

  • To develop and implement a parallel central processing unit (CPU) and graphics processing unit (GPU) matrix-matrix multiplication algorithm (SP2) for accelerating density matrix purification.
  • To integrate the SP2 algorithm into MOPAC's MOZYME method for enhanced semiempirical calculations.
  • To evaluate the accuracy and performance of the GPU-accelerated SP2 algorithm.

Main Methods:

  • Implementation of a parallel matrix-matrix multiplication algorithm (SP2) utilizing the symmetrical variable block row (SVBR) format.
  • Integration of the SP2 algorithm within MOPAC's MOZYME method, including LMO Fock matrix assembly and atomic integral calculations.
  • Leveraging the NVIDIA/CUDA platform for GPU acceleration and performance testing on a water cluster system.

Main Results:

  • The implemented SP2 algorithm demonstrates accuracy and significant speed improvements.
  • GPU acceleration achieved speedups of up to 40 times compared to single-threaded versions for a water cluster system (42,312 orbitals).
  • The GPU-accelerated SP2 enables faster calculations for semiempirical wavefunctions and single-point energies for large molecules (>100,000 orbitals).

Conclusions:

  • The parallel CPU and GPU SP2 algorithm offers a substantial acceleration for electronic structure calculations.
  • This advancement allows for more rigorous calculations (stricter SCF criteria) on localized charged molecular systems.
  • The developed method significantly reduces computation time for large molecular systems, making advanced calculations more accessible.