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The present work deals with electronic band structure and derived optical spectra of MgxZn1−xO in the hypothetical rocksalt structure. The computations are performed using full-potential linearised augmented plane wave method. The exchange–correlation potential is described using the Wu-Cohen and Tran-Blaha modified Becke–Johnson generalised gradient approximation (TB-mBJ-GGA). The calculated lattice parameter deviates by less than 1% from experiment showing a net improvement when compared with previous calculations. Moreover, its variation with respect to x does not violate Vegard's law. The TB-mBJ-GGA approach improves the magnitude of the fundamental band gap with respect to experiment. The rocksalt MgxZn1−xO is found to be an indirect gap semiconductor for x = 0, 0.25, 0.50 and 0.75 and a direct gap semiconductor for x = 1. The nature of the gap for rocksalt MgxZn1−xO is still in controversy and further investigations are required in this respect. The optical spectra of MgxZn1−xO are analysed and discussed. Our findings yield values of 1.55 and 1.25 for the static refractive index and 2.4 and 1.55 for the static dielectric constant for rocksalt ZnO and rocksalt MgO, respectively. [ABSTRACT FROM AUTHOR]