  In this work, we employ the LDA, GGA and GGA with four vdW corrections to
study crystal and electronic structures of bilayer transition metal
dichalcogenides (TMDs) with different twist angles. We find the GGA interlayer
distance of bilayer MoS2 has good agreement with experimental value while vdW
correction method still needs to be further improved. Our results indicate the
GGA interlayer distances of bilayer XS2 (X= Mo, Cr) with twist angles are
smaller than that of normal bilayer, which is the opposite in the LDA case. The
GGA results show that reduced bandgap is due to the reduction of interlayer
distance and, flat valley and conductivity bands appear owing to twist angle.
Our study not only supports valuable information for application possibility of
twisted two-dimensional (2D) materials but also stimulates more related
research.
