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General recurrence-relation generation scheme for molecular integral evaluation.

Bin Gao1

  • 1Hylleraas Center for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø The Arctic University of Norway, Tromsø, Norway.

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|September 25, 2020
PubMed
Summary
This summary is machine-generated.

We present a novel computational chemistry method for evaluating molecular integrals using Gaussian type orbitals. This automated scheme enhances efficiency for calculating one- and two-electron integrals.

Keywords:
Gaussian type orbitalHermite Gaussiancode generationintegralrecurrence relation

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate evaluation of molecular integrals is crucial for computational chemistry.
  • Existing methods for calculating one- and two-electron integrals can be computationally intensive.
  • Developing efficient and automated schemes is essential for advancing computational chemistry.

Purpose of the Study:

  • To develop a new, automated scheme for evaluating molecular integrals using Gaussian type orbitals.
  • To improve the efficiency and flexibility of calculating one- and two-electron integrals.
  • To provide a generic programming approach for computational chemists.

Main Methods:

  • A two-step runtime evaluation scheme for molecular integrals.
  • A top-down procedure mapping recurrence relations to jagged arrays storing intermediate integrals in a "coarse-grained circular buffer".
  • A bottom-up procedure computing final integrals by backtracking array elements, with automated source code generation for different electron operators via a recurrence-relation compiler.

Main Results:

  • The developed scheme unifies the algorithm and source code for evaluating different one- and two-electron operators in the first step.
  • The second step enables automatic generation of specific source codes for electron operators.
  • The scheme allows users to introduce new electron operators and evaluate their integrals at runtime using just-in-time compilation.

Conclusions:

  • The proposed general recurrence-relation generation scheme offers a novel, generic, and automatic programming method for molecular integrals.
  • This approach significantly enhances the computational efficiency and user-friendliness of calculating essential integrals in computational chemistry.
  • The integration with just-in-time compilation allows for dynamic evaluation of integrals for new operators.