A systematic density functional theory (DFT) study of strain effects on the electronic band structure of the group-III nitrides (AlN, GaN and InN) is presented. To overcome the deficiencies of the local-density and generalized gradient approximations (LDA and GGA) the Heyd-Scuseria-Ernzerhof hybrid functional (HSE) is used. Cross-checks for GaN demonstrate good agreement between HSE and exact-exchange based G0W0 calculations. We observe a pronounced nonlinear dependence of band-energy differences on strain. For realistic strain conditions in the linear regime around the experimental equilibrium volume a consistent and complete set of deformation potentials is derived.PACS numbers: 71.20. Nr, 71.70.Fk, 85.60.Bt The group-III nitride compounds and their alloys have recently received considerable attention as a versatile materials class. AlN, GaN and InN all crystallize in the wurtzite structure, but have vastly different band gaps ranging from 6.0 eV for AlN down to 0.7 eV for InN. For light emitting diodes (LEDs) 1 and laser diodes (LDs) 2,3 the group-III-nitrides are currently the only commercially available materials class for the green to the deep ultraviolet part of the spectrum, and future applications as chemical sensors, 4 in quantum cryptography 5 or in photocatalysis 6 are being explored. Applications in solid state lighting, however, are currently limited by loss mechanisms 7,8 and a deeper understanding of the fundamental materials properties is required. One crucial factor is the effect of strain.Due to the large differences in lattice parameters and thermal expansion coefficients between the substrate and the nitride overlayers, and between nitride layers with different alloy compositions, strain is always present in group-III-nitride based devices. Strain influences the optical properties, 9-11 in particular the energy of optical transitions, and for nonpolar or semipolar devices the polarization of the emitted light. 12 The effects of strain are characterized by the change of a transition energy (energy difference) upon application of strain, and the linear coefficient is defined as deformation potential. Together with the Luttinger (band) parameters, the deformation potentials constitute essential input for device modeling. 13 The experimental determination of deformation potentials is quite difficult, and aggravated by the fact that not all strain components can be determined accurately or without further approximations and that the deformation potentials cannot be isolated from each other, because uniaxial and biaxial strain cannot be applied separately. As a result the experimental data for GaN are scattered over a very large range. 10,11,14-17 For AlN and InN no experimental data are available, except for the hydrostatic deformation potential of the band gap in InN. 18 Previous theoretical studies have also produced widely differing values, resulting in a large uncertainty range. [19][20][21] The error bars can, in part, be attributed to the band-gap problem of density functional theory (DF...