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The three-dimensional representation of the electric field of a positive point charge requires tracing the electric field vectors, whose lengths decrease as the square of their distance from the charge and which point away from the charge at each point. This vector field is no doubt challenging to visualize. The visualization of electric fields becomes quickly intractable as the number of charges increases.
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Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F−
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Horizontal vectorization of electron repulsion integrals.

Benjamin P Pritchard1, Edmond Chow2

  • 1School of Computational Science and Engineering, Georgia Institute of Technology, 266 Ferst Drive, Atlanta, Georgia, 30332-0765.

Journal of Computational Chemistry
|September 14, 2016
PubMed
Summary
This summary is machine-generated.

We optimized the Obara-Saika algorithm for calculating electron repulsion integrals using vector intrinsics. This approach offers a 2-4 times speedup, particularly benefiting density fitting methods.

Keywords:
Obara-SaikaSIMDelectron repulsion integralshorizontal vectorizationtwo-electron integralsvectorization

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Algorithm optimization

Background:

  • Electron repulsion integrals (ERIs) are fundamental in quantum chemistry calculations.
  • Efficient computation of ERIs is crucial for large-scale electronic structure studies.
  • The Obara-Saika algorithm is a standard method for ERI calculation.

Purpose of the Study:

  • To present an efficient, vectorized implementation of the Obara-Saika algorithm.
  • To leverage Single Instruction, Multiple Data (SIMD) vector intrinsics for concurrent integral computation.
  • To analyze performance and identify bottlenecks in the vectorized algorithm.

Main Methods:

  • Implementation of the Obara-Saika algorithm using AVX (Advanced Vector Extensions) instructions.
  • Vectorization of primitive integral calculations for simultaneous processing.
  • Benchmarking against scalar implementations across various basis sets.

Main Results:

  • Achieved a 2-4 times speedup over scalar code using AVX instructions.
  • Demonstrated sensitivity of speedup to basis set contraction levels.
  • Identified optimal performance for specific integral quartets, enhancing suitability for density fitting.

Conclusions:

  • The vectorized Obara-Saika algorithm offers significant computational advantages.
  • This implementation is particularly well-suited for density fitting approximations.
  • Further analysis of performance bottlenecks can guide future optimizations.