Energy bands and density of states (DOS) of mixed molybdenum dichalcogenides like MoS 2 , MoSeS, MoSe 2 , MoTe 2 , MoTeS, and MoTe 0.5 S 1.5 are reported for the first time using the Tran–Blaha modified Becke–Johnson potential within full potential-linearised augmented plane wave technique. From the partial DOS, a strong hybridisation between the Mo- d and chalcogen- p states is observed below the Fermi energy E F . In addition, the dielectric constants, absorption coefficients, and refractivity spectra of these compounds have also been deduced. The integrated absorption coefficients derived from the frequency-dependent absorption spectra within the energy range of 0–4.5 eV show a possibility of using molybdenum dichalcogenides, particularly MoTe 0.5 S 1.5 , in solar cell applications. Birefringence and degree of anisotropy are also discussed using the data on refractivity and imaginary components of the dielectric constant.