Accurate experimental values for the vibrational ground tone or fundamental vibrational energy splitting of H 2 , HD, and D 2 are presented. Absolute accuracies of 2 × 10 −4 cm −1 are obtained from Doppler-free laser spectroscopy applied in a collisionless environment. The vibrational splitting frequencies are derived from the combination difference between separate electronic excitations from the X 1 Σ + g , v = 0, J and v = 1, J vibrational states to a common EF 1 Σ + g , v = 0, J state. The present work on rotational quantum states J = 1, 2 extends the results reported by Dickenson et al. on J = 0 [Phys. Rev. Lett. 110 (2013) 193601]. The experimental procedures leading to this high accuracy are discussed in detail. A comparison is made with full ab initio calculations encompassing Born-Oppenheimer energies, adiabatic and non-adiabatic corrections, as well as relativistic corrections and QED-contributions. The present agreement between the experimental results and the calculations provides a stringent test on the application of quantum electrodynamics in molecules. Furthermore, the combined experimental-theoretical uncertainty can be interpreted to provide bounds to new interactions beyond the Standard Model of Physics or fifth forces between hadrons.