Optimization of nonlinear parameters in trial wave functions with a very large number of terms

A procedure is proposed to construct highly accurate variational wave functions with large and very large numbers of basis functions. The procedure has a number of advantages in actual computations on parallel computer clusters. In particular, by using this procedure we have determined very accurate numerical values of the ground-state energies in the positronium ion Ps(-) (or e(-)e(+)e(-)) (E=-0.262 005 070 232 980 107 770 375 a.u.) and hydrogen ion H-infinity(-) (E=-0.527 751 016 544 377 196 589 759 a.u.) The variational energies of the negative hydrogenlike ions (or H--like ions) with the finite nuclear masses (T-, D-, H-1(-), and Mu(-)) are also presented. These energies are the best variational ground-state energies ever obtained for these ions.