Modification of Rys quadratures for two- and three-center electron repulsion integrals calculation

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Gaussian-type orbitals (GTOs) are fundamental to quantum chemical calculations.
• Efficient computation of various integrals is crucial for advancing quantum chemistry.
• Existing methods may present computational bottlenecks.

Purpose of the Study:

• To develop and implement efficient methods for calculating nuclear attraction and electron repulsion integrals.
• To leverage Rys quadratures for enhanced computational performance.
• To compare the efficiency of the new methods against established libraries like LIBINT.

Main Methods:

• Implementation of nuclear attraction and two- and three-center electron repulsion integral calculations.
• Application of Rys quadratures for integral computation.
• Utilized modified Rys quadratures with fewer roots for specific electron repulsion integrals.

Main Results:

• Achieved a 1.6-fold speed-up for certain electron repulsion integral calculations using modified Rys quadratures.
• Nuclear attraction integral calculations demonstrated an 8-10 times speed increase compared to LIBINT for electrostatic potential tasks.
• Three-center electron repulsion integral calculations were 2-4 times faster than LIBINT.

Conclusions:

• The implemented Rys quadrature methods offer significant computational speed-ups for key quantum chemical integrals.
• Modified Rys quadratures provide a viable approach for accelerating specific integral calculations.
• These advancements contribute to more efficient quantum chemical simulations.