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Efficient evaluation of three-center Coulomb integrals.

Gyula Samu1, Mihály Kállay1

  • 1MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary.

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This study identifies the most efficient algorithms for calculating three-center electron repulsion integrals (ERIs) using solid harmonic Gaussian functions. The simplified Obara-Saika scheme is generally most cost-effective, with specific alternatives for certain cases.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate calculation of electron repulsion integrals (ERIs) is crucial for quantum chemistry.
  • Evaluating three-center ERIs presents unique computational challenges compared to four-center ERIs.

Purpose of the Study:

  • To determine the most efficient computational pathways for evaluating three-center ERIs.
  • To adapt and analyze established four-center ERI techniques for three-center calculations.
  • To compare the performance of various algorithmic strategies.

Main Methods:

  • Adaptation of Obara-Saika, McMurchie-Davidson, Gill-Head-Gordon-Pople, and Rys quadrature schemes.
  • Analysis of algorithmic aspects including operation order, primitive loops, and prescreening.
  • Estimation of floating point operations (FLOPs) for algorithm comparison.
  • Implementation and practical performance evaluation of selected algorithms.

Main Results:

  • The simplified Obara-Saika scheme is identified as the most cost-effective for most three-center ERI calculations.
  • Modified Gill-Head-Gordon-Pople and Rys algorithms show advantages for specific shell triplets.
  • Performing solid harmonic transformation and horizontal recurrence at the primitive level is more efficient than at the contracted level.

Conclusions:

  • The simplified Obara-Saika scheme offers the best overall efficiency for three-center ERIs.
  • Specialized algorithms are recommended for particular computational scenarios.
  • Primitive-level operations enhance practical efficiency through improved prescreening and memory management.