A six-dimensional ab initio potential energy surface (PES) for H2-N2O which explicitly includes the symmetric and asymmetric vibrational coordinates Q1 and Q3 of N2O is calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triple level using an augmented correlation-consistent polarized-valence quadruple-zeta basis set together with midpoint bond functions. Four-dimensional intermolecular PESs are then obtained by fitting the vibrationally averaged interactions energies for υ3(N2O) = 0 and 1 to the Morse∕long-range analytical form. In the fits, fixing the long-range parameters at theoretical values smoothes over the numerical noise in the ab initio points in the long-range region of the potential. Using the adiabatic hindered-rotor approximation, two-dimensional PESs for hydrogen-N2O complexes with different isotopomers of hydrogen are generated by averaging the 4D PES over the rotation of the hydrogen molecule within the complex. The band-origin shifts for the hydrogen-N2O dimers calculated using both the 4D PESs and the angle-averaged 2D PESs are all in good agreement with each other and with the available experimental observations. The predicted infrared transition frequencies for para-H2-N2O and ortho-D2-N2O are also consistent with the observed spectra.