The spin–orbit splitting (E[Formula: see text]) of valence band maximum at the [Formula: see text] point is significantly smaller in 2D planner honeycomb structures of graphene, silicene, germanene and BN than that in the corresponding 3D bulk counterparts. For 2D planner honeycomb structure of SiC, it is almost same as that for 3D bulk cubic SiC. The bandgap which opens at the K and K[Formula: see text] points due to spin–orbit coupling (SOC) is very small in flat honeycomb structures of graphene and silicene, while in germanene it is about 2 meV. The buckling in these structures of graphene, silicene and germanene increases the bandgap opened at the K and K[Formula: see text] points due to SOC quadratically, while the E[Formula: see text] of valence band maximum at the [Formula: see text] point decreases quadratically with an increase in the magnitude of buckling.