This result was originally derived by Hirao et al.. We will call the approximation in Eq. ( ) a GSTM because it requires two SCF calculations to obtain BE i , one with q = 0 and another with q = 2/3. However, q = 0 corresponds to a standard integer-occupancy SCF calculation, which is often a prerequisite for performing fractional-occupancy SCF calculations. In that case, this particular GSTM does not incur additional overhead as compared to the STMs described in Section II B. The method of Eq. ( ) is listed in Table I under the nomenclature F[0; n] with n = 3. The n = 4 result, F[0; 4], is also shown for comparison, however that approach incurs cubic rather than quartic error in E(q), despite also requiring two SCF calculations.