The center-of-mass (c.m.) correction, due to the violation of the translational invariance, is always included in calculations, but its practical implementations differ from functional to functional [57,8]. For some functionals the treatment is fully variational; for some others the c.m. term is computed following the HFB procedure; for some functionals a simple one-body approximation is used. These apparently technical differences do matter as the actual form of the c.m. correction has a significant impact on the surface properties [57].
A good example nicely illustrating the above point has recently been discussed in Ref. [51]: for the two functionals, SLy4 and SLy6, which were fitted with precisely the same strategy but differ in their treatment of c.m. correction, the surface energy coefficient differs by as much as 0.7 MeV. While the two-body (albeit perturbative) treatment of the c.m. correction does not reduce the overall rms error of the fit to nuclear masses [20], it certainly has a significant impact on binding energies of highly deformed configurations (such as fission isomers), fission barriers, and fission trajectories.