Mathematical and computational science issues in high precision Hylleraas–configuration interaction variational calculations: II. Kinetic energy and electron–nucleus interaction integrals

Three-electron kinetic energy and electron–nucleus interaction integrals arising in Hylleraas–configuration interaction (Hy–CI) calculations are discussed. We show that the electron–nucleus interaction operators introduce no new integral complications and that the kinetic energy operators lead to integrals which have much in common with electron interaction integrals treated in the first paper of this series. We discuss the efficient evaluation of the kinetic energy integrals and give selected values of the integrals to 30 digit accuracy. The one new W auxiliary function which arises in treating the kinetic energy operator is discussed in appendix B. We also give a few details on accurate evaluations of the Condon and Shortley cs which arise in Hy–CI calculations in appendix A.