  We apply the density matrix expansion (DME) at Hartree-Fock level with
long-range chiral effective field theory interactions defined in coordinate
space up to next-to-next-to-leading order. We consider chiral potentials both
with and without explicit Delta isobars. The challenging algebra associated
with applying the DME to three-nucleon forces is tamed using a new organization
scheme, which will also facilitate generalizations. We include local regulators
on the interactions to mitigate the effects of singular potentials on the DME
couplings and simplify the optimization of generalized Skyrme-like functionals.
