Ground-state energy of H−: a critical test of triple basis sets

Abstract

We report an improved variational upper bound for the ground state energy of H− using Hylleraas-like wave functions in the form of a triple basis set having three distinct distance scales. The extended precision DQFUN of Bailey, allowing for 70 decimal digit arithmetic, is implemented to retain sufficient precision. Our result exceeds the previous record [A. M. Frolov, Euro. J. Phys. D 69, 132 (2015)], indicating that the Hylleraas triple basis set exhibits comparable convergence to the widely used pseudorandom all-exponential basis sets, but the numerical stability against roundoff error is much better. It is argued that the three distance scales have a clear physical interpretation. The new variational bound for infinite nuclear mass is –0.527 751 016 544 377 196 590 814 478 a.u. New variational bounds are also presented for the finite mass cases of the hydrogen, deuterium, and tritium negative ions H−, D−, and T−.