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An improved algorithm to evaluate the nonrelativistic three-electronHylleraas-Configuration Interaction (Hy-CI) kinetic energy integrals overSlater orbitals and the Hamiltonian in Hylleraas coordinates is shown. Theresulting analytical expressions are general for all quantum numbers of theorbitals. From there, the restriction of employing orbitals with quantumnumbers $l \le 2$ of the above algorithm presented in paper I of this serieshas been removed. With the new algorithm it is possible, in the directintegration method described in this series, to carry out Hy-CI atomicstructure calculations including $f$-, $g$-, $\ldots$ , $l$ and higherangular-momentum Slater orbitals and to determine $F$, $G$, $\ldots$ , $L$ andstates of higher order symmetry.

journal of mathematical chemistry

Evaluation of Hylleraas-CI atomic integrals by integration over the  coordinates of one electron. IV. An improved algorithm for three-electron  kinetic energy integrals