Atomic Hartree–Fock limit calculations using Lambda functions

Nonrelativistic Hartree–Fock limit calculations are performed for the group 18 atoms using Lambda functions, which are Laguerre-type basis functions (LTFs). Since Lambda functions form a complete orthonormal set for bound states, the total energy approaches the Hartree–Fock limit monotonically upon increasing the number of expansion terms, as determined by the maximum number ( N ) of the principal quantum number ( n ) in a set. The convergence behavior of the total energy in relation to the number of expansion terms is investigated. For Rn, N  = 116 is required to satisfy the convergence criterion ∣ Δ E / E ∣ < 10 − 15 . Here E is the total energy and Δ E is ( E ( N −1) − E ( N )). Total energies are obtained with 30 significant digits for He, with 14 digits for Ne, Ar, Kr, Xe, and Rn, and with 13 digits for Og. This approach gives −2.86167999561223887877554374002 au as the Hartree–Fock energy of He.