HYLLERAAS WAVE-FUNCTIONS REVISITED

Optimality of the combination of N terms used in the Hylleraas N-term wave function is examined for several two-electron atoms. It is pointed out that the N-term wave function given in the literature is not always the best N-term function for a fixed N. For example, the known Hylleraas six-term function PSI(6) = exp(-zeta-s) (1 + c1u + c2t2 + c3s + c4s2 + c5u2) yields the energy of -2.903 329 354 a.u. for the helium atom, whereas a new six-term function PSI(6,opt) = exp(-zeta-s) (1 + c1u + c2t2 + c3u2 + c4s2u + c5s3u) gives a much lower energy of -2.903 452 763 a.u. It is also shown that the best combination of N terms depends largely on the nuclear charge.