Coulomb three-body bound-state problem: Variational calculations of nonrelativistic energies - art. no. 064503

It is known that variational methods are the most powerful tool for studyin g the Coulomb three-body bound-state problem. However, they often suffer fr om loss of stability when the number of basis functions increases. This pro blem can be cured by applying the multiprecision package designed by D. H. Bailey. We consider variational basis functions of the type exp(-alpha(n)r( 1)-beta(n)r(2)-gamma(n)r(12)) with complex exponents. The method yields the best available energies for the ground states of the helium atom and the p ositive hydrogen molecular ion as well as many other known atomic and molec ular systems.