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Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods
Florian Weigend1, Marco Kattannek, Reinhart Ahlrichs
1Forschungszentrum Karlsruhe GmbH, Institut fur Nanotechnologie, P. O. Box 3640, D-76021 Karlsruhe, Germany. Florian.Weigend@int.fzk.de
The Journal of Chemical Physics
|May 2, 2009
Summary
We compared two computational methods for approximating two-electron integrals in electronic structure calculations. The resolution of the identity (RI) method is faster and accurate, while Cholesky decomposition (CD) is better for larger basis sets.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Molecular Electronic Structure
Background:
- Approximating two-electron integrals is crucial for computational efficiency in electronic structure calculations.
- Existing methods like Cholesky decomposition (CD) and resolution of the identity (RI) offer different trade-offs between speed and accuracy.
Purpose of the Study:
- To compare the efficiency and accuracy of Cholesky decomposition (CD) and resolution of the identity (RI) techniques for approximating two-electron integrals.
- To introduce and evaluate novel auxiliary basis sets for the Coulomb term within the RI framework.
Main Methods:
- Implementation and comparison of Cholesky decomposition (CD) for two-electron integrals.
- Application and testing of the resolution of the identity (RI) technique using preoptimized auxiliary/fitting basis sets.
- Development and validation of new auxiliary basis sets for approximating the Coulomb term in RI calculations.
Main Results:
- RI methods achieve insignificant errors, comparable to or better than CD treatments.
- RI procedures demonstrate superior computational speed compared to CD methods.
- New auxiliary basis sets for the Coulomb term enhance RI accuracy.
- CD methods show advantages for calculations involving extended basis sets.
Conclusions:
- Resolution of the identity (RI) methods offer a highly efficient and accurate approach for approximating two-electron integrals in molecular electronic structure.
- Cholesky decomposition (CD) remains a valuable alternative for specific cases, particularly with extended basis sets.
- The developed auxiliary basis sets further improve the performance of RI techniques.
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