  When considering transition-metal dichalcogenides (TMDCs) in van der Waals
(vdW) heterostructures for periodic ab-initio calculations, usually, lattice
mismatch is present, and the TMDC needs to be strained. In this study we
provide a systematic assessment of biaxial strain effects on the orbital,
spin-orbit, and optical properties of the monolayer TMDCs using ab-initio
calculations. We complement our analysis with a minimal tight-binding
Hamiltonian that captures the low-energy bands of the TMDCs around K and K'
valleys. We find characteristic trends of the orbital and spin-orbit parameters
as a function of the biaxial strain. Specifically, the orbital gap decreases
linearly, while the valence (conduction) band spin splitting increases
(decreases) nonlinearly in magnitude when the lattice constant increases.
Furthermore, employing the Bethe-Salpeter equation and the extracted
parameters, we show the evolution of several exciton peaks, with biaxial
strain, on different dielectric surroundings, which are particularly useful for
interpreting experiments studying strain-tunable optical spectra of TMDCs.
