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 $|\Delta E/E|<{10}^{-15}$. Here E is the total energy and ΔE 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. (paper)