  We extend a recent calculation of the nuclear energy density functional in
the framework of chiral perturbation theory by computing the isovector surface
and spin-orbit terms: $(\vec \nabla \rho_p- \vec \nabla \rho_n)^2 G_d(\rho)+
(\vec \nabla \rho_p- \vec \nabla \rho_n)\cdot(\vec J_p-\vec J_n)
G_{so(\rho)+(\vec J_p-\vec J_n)^2 G_J(\rho)$ pertaining to different proton and
neutron densities. Our calculation treats systematically the effects from
$1\pi$-exchange, iterated $1\pi$-exchange, and irreducible $2\pi$-exchange with
intermediate $\Delta$-isobar excitations, including Pauli-blocking corrections
up to three-loop order. Using an improved density-matrix expansion, we obtain
results for the strength functions $G_d(\rho)$, $G_{so}(\rho)$ and $G_J(\rho)$
which are considerably larger than those of phenomenological Skyrme forces.
These (parameter-free) predictions for the strength of the isovector surface
and spin-orbit terms as provided by the long-range pion-exchange dynamics in
the nuclear medium should be examined in nuclear structure calculations at
large neutron excess.
