Exponentially correlated Hylleraas‐configuration interaction nonrelativistic energy of the 1S ground state of the helium atom

A generalization of the Hylleraas‐configuration interaction method (Hy‐CI) first proposed in a previous study, the exponentially correlated Hylleraas‐configuration interaction method (E‐Hy‐CI) in which the single rij of an Hy‐CI wave function is generalized to a form of the generic type rijνije−ωijrij, is explored. This type of correlation, suggested by Hirshfelder in 1960, has the right behavior in the vicinity of both the rij cusp as rij goes to 0 and as rij goes to infinity; this work explores whether wave functions containing both linear and exponential rij factors converge more rapidly than either one alone. The method of calculation of the two‐electron E‐Hy‐CI kinetic energy and electron repulsion integrals in a stable and efficient way using recursion relations is discussed, and the relevant formulas are given. The convergence of the E‐Hy‐CI wave function expansion is compared with that of the Hy‐CI wave function without exponential correlation factors, demonstrating both convergence acceleration and an improvement in the accuracy for the same basis. This makes the application of the E‐Hy‐CI method to systems with N > 4, for which this formalism with at most a single rijνije−ωijrij factor per term leads to solvable integrals, very promising. E‐Hy‐CI method variational calculations with up to 10,080 expansion terms are reported for the ground 1S state of the neutral helium atom, with a resultant nonrelativistic energy of −2.9037 2437 7034 1195 9831 1084 hartree for the best expansion. The exponentially correlated Hylleraas‐configuration interaction wave function (E‐HyCI) is a generalization of the Hylleraas‐configuration interaction (Hy‐CI) in which the single rij of an Hy‐CI wave function is generalized to the generic type rijνije−ωijri. This type of correlation has the right behavior both in the vicinity of the rij cusp and as rij goes to infinity; this work explores whether wave functions containing both linear and exponential rijfactors converge more rapidly than either one alone. E‐Hy‐CI variational calculations with up to 10 ,080 configurations lead to a nonrelativistic energy of −2.9037 2437 7034 1195 9831 1084 hartree for the 1S ground state of the helium atom.