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A method for the analytical representation of ab initio energy surface results is described. For a three-atom surface, the potential function is written as a sum of atomic, two-body, and three-body terms. This allows an easy fitting of the whole surface, including the dissociated and united atom limits. The theory is applied to an H3 surface of limited accuracy calculated for these purposes. Comparisons are made, where possible, with more accurate calculations. Extensions to surfaces involving four or more atoms are also discussed.