Convergence accelerator approach for the high-precision evaluation of three-electron correlated integrals

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Abstract
The standard series expansion that has long been employed to evaluate one-center correlated three-electron integrals is converted into a different form. The alternative expression obtained allows convergence accelerator techniques to be directly applied in a very effective manner. The resulting expansion is found to be numerically stable, in contrast to the series obtained when convergence accelerator techniques are applied to the standard expansion. Using this approach, the increase in computational speed is found to be very significant for the most slowly converging integrals. Some representative values are presented for a number of three-electron correlated integrals calculated using the method suggested herein.