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Acceleration of Semiempirical Electronic Structure Theory Calculations on Consumer-Grade GPUs Using Mixed-Precision

Pit Steinbach1, Christoph Bannwarth1

  • 1Institute of Physical Chemistry, RWTH Aachen University, Melatener Str. 20, Aachen 52074, Germany.

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Summary

This study accelerates semiempirical electronic structure calculations using graphics processing units (GPUs) and a mixed-precision approach. The new method significantly speeds up density matrix construction for large molecules, enabling faster simulations.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Chemistry

Background:

  • Solving the Roothaan-Hall equations for the one-electron density matrix is a computational bottleneck in semiempirical electronic structure methods.
  • Directly solving for the density matrix without prior orbital calculation offers a potential solution.

Purpose of the Study:

  • To implement and optimize Niklasson's density matrix purification schemes on GPUs for enhanced computational efficiency.
  • To develop a mixed-precision (MP) scheme leveraging single-precision (FP32) performance on consumer-grade GPUs without compromising accuracy.

Main Methods:

  • Implementation of dense linear algebra for density matrix purification on GPUs.
  • Development of a tailored mixed-precision (MP) scheme for SCF calculations.
  • Benchmarking against LAPACK and cuSOLVER using the GFN2-xTB method for molecules with over 1000 basis functions.

Main Results:

  • The MP GPU implementation demonstrates superior speed compared to traditional diagonalization methods for large molecular systems.
  • Numerical precision of energies and gradients remains high, comparable to full double-precision (FP64) calculations.
  • Asynchronous GPU implementation allows parallel SCF calculations, accelerating conformational sampling via molecular dynamics.

Conclusions:

  • The developed GPU-accelerated MP scheme offers significant speedups for semiempirical calculations on commodity hardware.
  • This approach enhances the feasibility of large-scale simulations and advanced computational chemistry techniques.