2 ELECTRONS IN AN EXTERNAL OSCILLATOR POTENTIAL - MULTIPLET SPLITTINGS FROM EXACT-SOLUTIONS AND ONE-PARTICLE APPROXIMATIONS

We use the two-electron oscillator (with Coulomb interaction between t he electrons) as a test system for the calculation of singlet-tripler splittings of excited states. Apart from exact solutions, we obtain va lues from simple and weighted (Ziegler, Rauk and Baerends (ZRB) and vo n Barth) total energy differences. We also calculated differences of K ohn-Sham (KS) eigenvalues (both exact and LDA values) and included cor rections to these values proposed by Petersilka, Gossman and Gross (PG G) and by Gorling (G). It turns out that ZRB, PGG and G are virtually equivalent for low-energy excitations, whereas for higher excitations, PGG and G underestimate the necessary correction to the Kohn-Sham ene rgy differences considerably. ZRB, on the other hand, is reasonable fo r a wide range of excitation energies and much better than simple tota l energy differences. The best results are obtained from a new ad hoc formula using non-integer occupation numbers in a way different from G unnarson and Lundqvist.