for the Helium Sequence Wai-Kee Li The Chinese University of Hong Kong. Shatin, N.T.. Hong Kong The variational treatment of the helium atom and heliumlike ions is a standard topicin quantum chemistry texts. The results of the one-parameter trial functions are, of course, well known. They are included below so that they may be compared with the results of the less familiar two-parameter functions. It is noted that atomic units are employed throughout the following discussion. The Hamiltonian for the helium sequence is written as
ing two-parameter trial function more than a half century
The energy expression for this function is as follows:
a
The one-parameter trial function has the form = e-""l+rx'
where a is the effective nuclear charge. When a = Z this function assumes its minimum energy
(2)
where
- (5/16),
Thus the ionization potential (IF)for the helium sequence is
d2
64a3P3 = ----
( a + LV6
and X=-
B a
The comparison of this result with the experimental values for Z = 1to Z = 10 species are given in the third, fourth, and fifth columns of the table. Considering the crudeness of the trial function (eq 2), the agreement is quite good. The difference between the calculated and experimental values is almost independent of Z, this is particularly so for the first few members of the series. However, this approximation fails to yield a stable hydride ion, H-: its IP is calculated to be nerative. 'I'hr tnul iunction irg 2) assumes that the effecti\,enucle;ir (.har~est'or both rlwlronsare identi
