It is demonstrated that for BH the sum of the pair correlation energies depends on the choice of SCF orbitals. The pair correlation energy is defined as the energy improvement in a variational calculation using excitations of only one pair of orbitals. The sum of all pair energies approximates the total correlation energy. The sum of all pair energies is shown to vary with a tunitary transformation among the SCF orbitals. Results are reported for the canonical SCF, Ruedenberg localized SCF, and pair energy optimized SCF orbitals.