  Iridate oxides on a honeycomb lattice are considered promising candidates for
realization of quantum spin liquid states. We investigate the magnetic
couplings in a structural model for a honeycomb iridate K$_2$IrO$_3$, with
$C_3$ point group symmetry at the Ir sites, which is an end member of the
recently synthesized iridate family K$_x$Ir$_y$O$_2$. Using \textit{ab-initio}
quantum chemical methods, we elucidate the subtle relationship between the real
space symmetry and magnetic anisotropy and show that the higher point group
symmetry leads to high frustration with strong magnetic anisotropy driven by
the unusually large off-diagonal exchange couplings ($\Gamma$'s) as opposed to
other spin-liquid candidates considered so far. Consequently, large quantum
fluctuations imply lack of magnetic ordering consistent with the experiments.
Exact diagonalization calculations for the fully anisotropic $K$-$J$-$\Gamma$
Hamiltonian reveal the importance of the off-diagonal anisotropic exchange
couplings in stabilizing a spin liquid state and highlight an alternative route
to stabilize spin liquid states for ferromagnetic $K$.
