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Mathematical and Computational Science Issues in High Precision HyIleraas-Configuration Interaction Variational Calculations: I. Three-Electron Integrals

Published

Author(s)

James S. Sims, Stanley A. Hagstrom

Abstract

The most difficult integral arising in Hylleraas-Configuration Interaction (Hy-CI) calculations, the three-electron triangle integral, is discussed. We focus on recursive techniques at both the double precision and quadruple precision level of accuracy while trying to minimize the use of higher precision arithmetic. Also, we investigate the use of series acceleration to overcome problems of slow convergence of certain integrals defined by infinite series. We find that a direct + tail Levin $u$-transformation convergence acceleration overcomes problems that arise when using other convergence acceleration techniques, and is the best method for overcoming the slow convergence of the triangle integral. The question of calibrating an acceleration method is also discussed, as well as ways to improve our work.
Citation
Journal of Physics B-Atomic Molecular and Optical Physics
Volume
37
Issue
No. 7

Keywords

atomic, configuration interaction, convergence acceleration, Hy-CI, Hylleraas, integrals, Lein u, Remiddi, three-electron

Citation

Sims, J. and Hagstrom, S. (2004), Mathematical and Computational Science Issues in High Precision HyIleraas-Configuration Interaction Variational Calculations: I. Three-Electron Integrals, Journal of Physics B-Atomic Molecular and Optical Physics, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150877 (Accessed March 1, 2024)
Created April 1, 2004, Updated February 17, 2017