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Upper Bounds on Gaussian Geminal Integrals
Jong-Won Song1, Peter M W Gill2
1Department of Chemistry Education, Daegu University, Daegudae-ro 201, Gyeongsan-si, Gyeongsangbuk-do 38453, Republic of Korea.
Journal of Chemical Theory and Computation
|July 21, 2026
Summary
Researchers developed new upper bounds for Gaussian geminal integrals in quantum chemistry. These bounds efficiently screen out negligible contributions, significantly reducing computational cost in molecular calculations.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Theoretical Chemistry
Background:
- Gaussian geminal (GG) integrals are crucial for accurate molecular electronic structure calculations.
- Efficient computation of these integrals is essential for large molecular systems.
Purpose of the Study:
- To derive tight upper bounds for integrals involving contracted Gaussian basis functions and the GG operator.
- To develop a method for efficiently screening negligible GG integrals.
Main Methods:
- Derivation of a matrix recurrence relation for normalized primitive GG integrals.
- Application of the Triangle Inequality to create a recurrence relation for rigorous upper bounds on GG integrals.
- Testing the bounds on over 32 million quartets for the n-decane molecule using the pc-1 basis set.
Main Results:
- Successfully derived tight upper bounds for GG integrals.
- Demonstrated that the bounds effectively screen out almost all quartets yielding negligible integrals.
- The method significantly reduces the number of integrals to be computed.
Conclusions:
- The developed upper bounds provide an efficient way to screen GG integrals.
- This method has the potential to accelerate quantum chemistry calculations, especially for large molecules.
- The approach is validated by its successful application to a large molecular system.
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