The potential energy of a diatomic molecule as a function of the difference (r – r_e), where r is the variable interatomic distance and r_e is the equilibrium interatomic distance. The Morse potential U(r – r_e) is given by

where D_e is the dissociation energy at the minimum of the curve (i.e. when r = r_e) and β‎ is a constant. In 1929 the Morse potential was used by the US physicist Philip M. Morse (1903–85) in solving the Schrödinger equation. The Morse potential is a reasonably good representation of a potential-energy function except that as r approaches 0, U does not approach infinity as it should for a true potential energy function. Modifications of the Morse potential have been suggested to improve on this aspect.