  The double perovskite Ba$_{2}$NaOsO$_{6}$ (BNOO), an exotic example of a very
high oxidation state (heptavalent) osmium $d^1$ compound and also uncommon by
being a ferromagnetic Mott insulator without Jahn-Teller (JT) distortion, is
modeled using the density functional theory (DFT) hybrid functional based exact
exchange for correlated electrons (oeeHyb) method and including spin-orbit
coupling (SOC). The experimentally observed narrow gap ferromagnetic insulating
ground state is obtained, with easy axis along [110] in accord with experiment,
providing support that this approach provides a realistic method for studying
this system. The predicted spin density for [110] spin orientation is nearly
cubic (unlike for other directions), providing an explanation for the absence
of JT distortion. An orbital moment of -0.4$\mu_B$ strongly compensates the
+0.5$\mu_B$ spin moment on Os, leaving a strongly compensated moment more in
line with experiment. Remarkably, the net moment lies primarily on the oxygen
ions. An insulator-metal transition by rotating the magnetization direction
with an external field under moderate pressure is predicted as one consequence
of strong SOC, and metallization under moderate pressure is predicted.
Comparison is made with the isostructural, isovalent insulator Ba$_2$LiOsO$_6$
which however orders antiferromagnetically.
