Accuracy of the optimal subset approximation

The accuracy of the optimal subset approximation, which reduces the number of coupled equations in the hyperspherical harmonic method, is checked theoretically and numerically. The critical parameter that determines the error of the method is shown to be proportional to the product of potential matrix elements connecting the K=0 state to states with K>0, and the matrix elements between K>0 states. In particular this means that the accuracy is largely independent of the degree of excitation of the system. The numerical precision of the optimal subset method in calculating energies and expectation values of Coulomb-bound three-body systems is checked by comparison of optimal subset results with exact results for fixed maximum global angular momentum Kmax. Errors range from less than one percent for the helium atom ground state energy to 100 percent or more for certain positronium ion expectation values. This precision is consistent with the theoretically determined error parameters.