Empirical study of cubic and quartic vibrational force constants for diatomic molecules shows them to be approximately exponential functions of internuclear distance. A family of curves is obtained, determined by the location of the bonded atoms in rows of the periodic table. Displacements between successive curves correspond closely to those in Badger's rule for quadratic force constants (for which the parameters are redetermined to accord with all data now available). Constants for excited electronic and ionic states appear on practically the same curves as those for the ground states. Predictions based on the diatomic correlations agree with the available cubic constants for bond stretching in polyatomic molecules, regardless of the type of bonding involved. Implications of these regularities are discussed. (auth)

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