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We explore the direct to indirect band gap transitions in MX$_2$ (M= Mo/W, X=S/Se) transition metal dichalcogenides heterobilayers for different systemcompositions, strains, and twist angles based on first principles densityfunctional theory calculations within the G$_0$W$_0$ approximation. Theobtained band gaps that typically range between 1.4$-$2.0 eV aredirect/indirect for different/same chalcogen atom systems and can often beinduced through expansive/compressive biaxial strains of a few percent. Adirect to indirect gap transition is verified for heterobilayers uponapplication of a finite 16$^{\circ}$ twist that weakens interlayer coupling.The large inter-layer exciton binding energies of the order of $\sim$~250~meVestimated by solving the Bethe-Salpeter equation suggest these systems areamenable to be studied through infrared and Raman spectroscopy.

Tuning electronic properties in transition metal dichalcogenides MX$_2$ (M= Mo/W, X= S/Se) heterobilayers with strain and twist angle