A rigorous and optimized strategy for the evaluation of the Boys function kernel in molecular electronic structure theory.

Abstract

This work is focused on the efficient evaluation of the Boys function located at the heart of Coulomb and exchange type electron integrals. Different evaluation strategies for individual orders and arguments of the Boys function are used to achieve a minimal number of floating-point operations. Based on previous work of other groups, two similar algorithms are derived that are compared based on both accuracy and efficiency: The first algorithm combines the work of Gill et al. (Int. J. Quantum Chem. 1991, 40, 745) and Kazuhiro Ishida (Int. J. Quantum Chem. 1996, 59, 209 and following work), amplifying the benefits of the two strategies. © 2015 Wiley Periodicals, Inc.