  The pyrochlore iridate In$_2$Ir$_2$O$_7$ is a strong $J_{\mathrm{eff}} = 1/2$
Mott insulator with frustrated magnetism. Despite the large trigonal crystal
field, a small admixture of $J_{\mathrm{eff}} = 3/2$ component in the
$J_{\mathrm{eff}} = 1/2$ bands and a small splitting of $J_{\mathrm{eff}} =
3/2$ bands are observed as compared with other pyrochlore iridates
A$_2$Ir$_2$O$_7$ (A: trivalent cation). We argue that the reduced inter-site
hopping between the $J_{\mathrm{eff}} = 1/2$ and the $J_{\mathrm{eff}} = 3/2$
manifold plays a predominant role in the distinct behavior of In$_2$Ir$_2$O$_7$
compared with other A$_2$Ir$_2$O$_7$. The effect of the intersite hopping
should not be dismissed in the local physics of spin-orbital-entangled
$J_{\mathrm{eff}} = 1/2$ Mott insulators.
