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Updated: Jul 23, 2025
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Published on: May 27, 2020
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Analytical quadrature method using recurrence formulas for two-electron integrals of frequency-dependent Breit
Nobuki Inoue1, Takahito Nakajima1
1RIKEN Center for Computational Science, Kobe, Hyogo, Japan.
Journal of Computational Chemistry
|July 11, 2023
Summary
This study introduces a recursive method for calculating two-electron integrals involving frequency-dependent Breit interactions in electronic structure calculations. The findings validate recurrence relations and introduce a new function for computational chemistry.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Theoretical Chemistry
Background:
- Calculating two-electron integrals is crucial for electronic structure calculations.
- Frequency-dependent Breit interactions are important for relativistic effects.
- Existing methods may have limitations in efficiency or scope.
Purpose of the Study:
- To develop an efficient recursive scheme for calculating two-electron integrals of frequency-dependent Breit interactions.
- To derive explicit expressions for the generalized molecular incomplete gamma function for specific potentials.
- To provide a computational implementation for the derived functions.
Main Methods:
- A recursive scheme based on previously validated vertical recurrence relations.
- Derivation of explicit expressions for generalized molecular incomplete gamma functions.
- Development of asymptotic formulas for these functions.
- Implementation of a computational method for the generalized molecular incomplete gamma function.
Main Results:
- Validation of both vertical and horizontal recurrence relations for the integrals.
- Derivation of explicit expressions and asymptotic formulas for generalized molecular incomplete gamma functions.
- Numerical calculations showing significant energy dependence of these functions.
Conclusions:
- The proposed recursive scheme is effective for calculating two-electron integrals of frequency-dependent Breit interactions.
- The derived generalized molecular incomplete gamma functions and their implementations are valuable tools for electronic structure calculations.
- The energy dependence of these functions highlights the importance of frequency-dependent treatments.
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