  We derive and motivate a Laplacian-level, orbital-free
meta-generalized-gradient approximation (LL-MGGA) for the exchange-correlation
energy, targeting accurate ground-state properties of $sp$ and $sd$ metallic
condensed matter, in which the density functional for the exchange-correlation
energy is only weakly nonlocal due to perfect long-range screening. Our model
for the orbital-free kinetic energy density restores the fourth-order gradient
expansion for exchange to the r$^2$SCAN meta-GGA [Furness et al., J. Phys.
Chem. Lett. 11, 8208 (2020)], yielding a LL-MGGA we call OFR2. OFR2 matches the
accuracy of SCAN for prediction of common lattice constants and improves the
equilibrium properties of alkali metals, transition metals, and intermetallics
that were degraded relative to the PBE GGA values by both SCAN and r$^2$SCAN.
We compare OFR2 to the r$^2$SCAN-L LL-MGGA [D. Mejia-Rodriguez and S.B.
Trickey, Phys. Rev. B 102, 121109 (2020)] and show that OFR2 tends to
outperform r$^2$SCAN-L for the equilibrium properties of solids, but
r$^2$SCAN-L much better describes the atomization energies of molecules than
OFR2 does. For best accuracy in molecules and non-metallic condensed matter, we
continue to recommend SCAN and r$^2$SCAN. Numerical performance is discussed in
detail, and our work provides an outlook to machine learning.
