The second-order Moller-Plesset ab initio electronic structure method is used to compute points on the potential energy surface of glycine. Some 50 000 points are computed, covering the spectroscopically relevant regions, in the vicinity of the equilibrium structures of the three lowest-lying conformers of glycine. The vibrational states and spectroscopy are computed directly from the potential surface points using the correlation corrected vibrational self-consistent field (CC-VSCF) method, and the results are compared with experiment. Anharmonic effects and couplings between different vibrational modes that are included in the treatment are essential for satisfactory accuracy. The following are found: (1) The spectroscopic predictions from the ab initio potential are in very good accord with matrix experiments. (2) Theory agrees even more closely with spectroscopic data for glycine in He droplets, where environmental effects are much weaker than in the matrix. This suggests that errors in the ab initio potential are smaller than rare-gas matrix effects. (3) The accuracy of the ab initio potential is. by this spectroscopic test, much superior to that of OPLS-AA, a state-of-the-cut empirical potential. The relative failure of the empirical potential is due to its inability to describe: details of the hydrogen-bonded interactions, and is most critical in one of the glycine conformers where such interactions play an especially important role.