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Contracted auxiliary Gaussian basis integral and derivative evaluation.
Timothy J Giese1, Darrin M York
1Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA.
The Journal of Chemical Physics
|February 20, 2008
Summary
This study presents a faster method for calculating two-center Coulomb and overlap integrals using contracted auxiliary solid harmonic Gaussian functions. The new approach simplifies calculations and proves superior to Cartesian Gaussian-based methods.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Theoretical Chemistry
Background:
- Accurate calculation of molecular integrals is crucial for quantum chemistry.
- Existing methods for evaluating two-center integrals can be computationally intensive.
Purpose of the Study:
- To develop a computationally efficient method for evaluating two-center Coulomb and overlap integrals.
- To simplify the calculation of integrals and their derivatives for contracted Gaussian functions.
Main Methods:
- Derivation of integral expressions using Hobson's theorem and spherical tensor gradient operator rules.
- Application of primitive normalization constants to simplify contracted function calculations.
- Development of derivative expressions that avoid chain rules.
Main Results:
- A simplified method for calculating contracted functions for Gaussian multipole expansions.
- Derivative calculations expressed as linear combinations of auxiliary integrals.
- Demonstrated superiority over Cartesian Gaussian-based methods for integral and derivative evaluation.
Conclusions:
- The proposed method offers significant computational advantages for evaluating integrals and derivatives.
- This approach simplifies complex calculations in quantum chemistry.
- The method is effective for both primitive and contracted Gaussian functions.
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