The total ener=g of Ne2 has been calculated in two realizations of the XCY model. Both the full non-muffii-tin correction to the 31s Xa result and a high-precision LCAO Xcc give overbindin,, 0 cor&ming an earlier. less-inclusive result. Local density treatments of exchange and correlation in many-electron systems had their origins in efforts to simplify the Hartree-Fock model for application to solids and, subsequently, large molecules. The discovery [I], some years ago, that the simple Xa! model? yielded crystalline binding energies for the rare gas crystals which were at least qualitatively acceptable was therefore somewhat surprising and controversial. Some misgivings were expressed about the possible introduction of spurious effects because of the use of the auffii-tin (MT) approximation (in the multiple-scattering Xa, or MS X@, scheme). Exploration of this particular difficulty began with a MT calculation on Ne, which showed no binding [3] _ mere followed a calcilation 143 of what were expected to be the dominant contributions to rhe lowest order non-muffin-tin (NMT) correction, namely those terms linear in the hWT charge &(& = p -p, where pis the MT charge; see ref-[43)_ The result was a somewhat overbound molecule, as compared with experiment. Overbinding has also been found in the MT treatment of crystalline Ne [S] , so the two results seemed consistent. However, Danese [6] has recently reported the calculation of lowest-order NMT corrections including all contributions. The effect of including the previously omitted corrections (those second-order in &) was to * Work supported in part by National Science Foundation and American Gas _Assotiation.