Efficient evaluation of three-center Coulomb integrals

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of electron repulsion integrals (ERIs) is crucial for quantum chemistry.
• Evaluating three-center ERIs presents unique computational challenges compared to four-center ERIs.

Purpose of the Study:

• To determine the most efficient computational pathways for evaluating three-center ERIs.
• To adapt and analyze established four-center ERI techniques for three-center calculations.
• To compare the performance of various algorithmic strategies.

Main Methods:

• Adaptation of Obara-Saika, McMurchie-Davidson, Gill-Head-Gordon-Pople, and Rys quadrature schemes.
• Analysis of algorithmic aspects including operation order, primitive loops, and prescreening.
• Estimation of floating point operations (FLOPs) for algorithm comparison.
• Implementation and practical performance evaluation of selected algorithms.

Main Results:

• The simplified Obara-Saika scheme is identified as the most cost-effective for most three-center ERI calculations.
• Modified Gill-Head-Gordon-Pople and Rys algorithms show advantages for specific shell triplets.
• Performing solid harmonic transformation and horizontal recurrence at the primitive level is more efficient than at the contracted level.

Conclusions:

• The simplified Obara-Saika scheme offers the best overall efficiency for three-center ERIs.
• Specialized algorithms are recommended for particular computational scenarios.
• Primitive-level operations enhance practical efficiency through improved prescreening and memory management.