Variational calculations on the helium isoelectronic sequence

We have performed variational calculations on the helium isoelectronic sequence for values of the nuclear charge $Z$ ranging from 1 to 10. The basis used is a modification of that employed by Frankowski and Pekeris in 1966, whose calculation has not been superseded before now. Using 230-term wave functions, we obtain for $Z=2\mathrm{}$ through 10 variational energies accurate to better than a few parts in ${10}^{13}$. Our results illustrate the importance of using basis functions which have the same analytic structure as the exact wave function being approximated.