The deformation potentials D₁ ¹, D₃ ³, D₁ ⁵, and D₃ ⁵, which represent the effects of strain on the E₁ electronic interband transitions, have been calculated for Ge, GaAs, InP, ZnSe, and ZnTe using the full-potential linear muffin-tin orbital method within the local-density approximation. These deformation potentials exhibit no strong variations between L and Γ throughout the Brillouin zone. It is therefore legitimate to use an average to interpret strain-optical experiments. The values of these deformation potentials are approximately the same for all calculated materials. The agreement with experimental data is good for Ge, GaAs, and InP. For ZnSe and ZnTe the agreement with the few extant experimental data is poorer: The magnitude of the calculated deformation potentials is smaller than found experimentally. This may reflect a breakdown of the conventional theory of strain optical constants based on one-electron interband transitions. The corresponding deformation potentials, D_1,0 ⁵ and D_3,0 ⁵, representing the effects of optical phonons at the center of the Brillouin zone on the E₁ transitions are also presented.