A systematic perturbation theory has been developed to analyze the terms co
ntributing to the H-3 potential energy surface. Group theory is used to fin
d the irreducible representations of the Hamiltonian matrix elements which
then are decoupled to their simplest level. In the case of diatomic molecul
es, this approach leads naturally to the Generalized Heitler-London (GHL) t
heory 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 dia
tomics-in-molecules without overlap) surface is shown to encompass far more
information than previously recognized. The new theory now contains all th
e terms needed for an exact perturbation calculation of the potential energ
y surface. (C) 1999 American Institute of Physics. [S0021-9606(99)30832-1].