  A range of honeycomb Co oxide compounds has been proposed and investigated in
the search for a topological Kitaev spin liquid. Analyzing the quantum
chemistry of interacting magnetic moments in Na$_3$Co$_2$SbO$_6$, a
representative $LS$-coupled $t_{2g}^5e_g^2$ magnet, we find that the Kitaev and
off-diagonal $\Gamma$ interactions are sizable and antiferromagnetic but still
weaker than the Heisenberg contribution. Except $\Gamma$', all nearest-neighbor
couplings are mainly determined by Coulomb exchange, different from current
representations of anisotropic interaction terms. This highlights the
limitations of existing anisotropic models and the need for systematic
wave-function quantum chemical studies to clarify exchange mechanisms in
Kitaev-Heisenberg systems.
