  We derive a zero-range pseudopotential that includes all possible terms up to
sixth order in derivatives. Within the Hartree-Fock approximation, it gives the
average energy that corresponds to a quasi-local nuclear Energy Density
Functional (EDF) built of derivatives of the one-body density matrix up to
sixth order. The direct reference of the EDF to the pseudopotential acts as a
constraint that divides the number of independent coupling constants of the EDF
by two. This allows, e.g., for expressing the isovector part of the functional
in terms of the isoscalar part, or vice versa. We also derive the analogous set
of constraints for the coupling constants of the EDF that is restricted by
spherical, space-inversion, and time-reversal symmetries.
