A systematic perturbation theory has been developed to analyze the terms contributing to the H-3 potential energy surface. Group theory is used to find the irreducible representations of the Hamiltonian matrix elements which then are decoupled to their simplest level. In the case of diatomic molecules, this approach leads naturally to the Generalized Heitler-London (GHL) theory derived previously [K. T. Tang and J. P. Toennies, J. Chem. Phys. 95, 5918 (1991)]. Many previous semi-empirical potential surfaces for the H-3 triatomic system including the well known LEPS surface are examined in the light of the present results. In particular, the Cashion-Herschbach (or diatomics-in-molecules without overlap) surface is shown to encompass far more information than previously recognized. The new theory now contains all the terms needed for an exact perturbation calculation of the potential energy surface.