Highly accurate evaluation of the singular properties for the positronium and hydrogen negative ions

A large number of regular and some singular bound state properties of the ground 1(1)S(L= 0)-states of the positronium Ps(-) and hydrogen infinity H(-)negative ions are determined to a very high numerical accuracy. The highly accurate variational wavefunctions are constructed with the use of exponential basis functions written in the three-body perimetric coordinates. In particular, the total energy of the ground state of the Ps- ion determined in our calculations is E = -0.262 005 070 232 980 107 770 3745 au, while the analogous ground state energy for the infinity H- ion is E = -0.527 751 016 544 377 196 589 733 au. These values are the best-to-date variational energies obtained for these systems.