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Dynamic Precision for Electron Repulsion Integral Evaluation on Graphical Processing Units (GPUs).

Nathan Luehr1,2, Ivan S Ufimtsev1,2, Todd J Martínez1,2

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This study introduces a dynamic precision technique for quantum chemistry calculations on GPUs. It balances accuracy and performance by selectively using double precision for critical electron repulsion integrals.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Graphical Processing Units (GPUs) offer powerful computational capabilities.
  • GPUs have more hardware units for single precision than double precision.
  • Electronic structure theory (quantum chemistry) can benefit from GPU acceleration.

Purpose of the Study:

  • To develop a method for maximizing computational performance on GPUs for quantum chemistry.
  • To address the precision differences between single and double arithmetic in GPU hardware.
  • To enable efficient Hartree-Fock and density functional self-consistent field (SCF) calculations on GPUs.

Main Methods:

  • Implemented a dynamic precision technique for evaluating electron repulsion integrals (ERIs).
  • Electron repulsion integrals (ERIs) are selectively computed using double precision, while others use single precision.
  • Dynamically adjusted the precision cutoff during the self-consistent field (SCF) procedure.

Main Results:

  • Achieved controlled precision error by evaluating only the largest integrals in double precision.
  • Minimized the number of double precision integral evaluations for a desired accuracy.
  • Demonstrated the effectiveness of the dynamic precision scheme for molecules up to 2000 atoms.

Conclusions:

  • Dynamic precision offers an effective strategy for accelerating quantum chemistry computations on GPUs.
  • This method balances computational speed with the required accuracy for electronic structure calculations.
  • The technique is applicable to a wide range of molecular systems, from small to very large.