  Understanding the origin of splitting of valance band is important since it
governs the unique spin and valley physics in few-layer MoS2. With first
principle methods, we explore the effects of spin-orbit coupling and layer's
coupling on few-layer MoS2. It is found that intra-layer spin-orbit coupling
has a major contribution to the splitting of valance band at K. In double-layer
MoS2, the layer's coupling results in the widening of energy gap of splitted
states induced by intra-layer spin-orbit coupling. The valance band splitting
of bulk MoS_2 in K can follow this model. We also find the effect of
inter-layer spin-orbit coupling in triple-layer MoS2. In addition, the
inter-layer spin-orbit coupling is found to become to be stronger under the
pressure and results in the decrease of main energy gap in the splitting
valance bands at K.
