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Much of the impetus for the study of the nonlinear optical properties of molecules comes from the search for materials with nonlinear properties suitable for the construction of practical devices for optical harmonic generation and signal processing. While organic crystals and polymers are envisioned for applications, studies of isolated atoms and small molecules play an important role in refining the fundamental understandingof the nonlinear optical properties of materials and in developing methods for accurately predicting these properties. The nonlinear response of a molecule to applied electric fields is described in terms of the hyperpolarizabilities of the molecule. So far, the most systematic measurements and rigorous calculations of the hyper-polarizabilities have been done for atoms and small molecules. Gas-phase measurements of the hyperpo-larizabilities have the special advantage of being directly …