It is shown that first-order changes in the normal modes of vibration of a polyatomic molecule do not alter the normal frequencies except in second or higher order. This fact provides a convenient method of obtaining the best fit between the observed and calculated frequencies by adjusting the potential constants and also of ascertaining the relative importance of each constant in its effect on the spectrum. It further emphasizes, however, the well-known difficulties in obtaining reliable potential functions and shows that very considerable errors may occur in the determination of the potential and of the normal modes.
DAVID M. DENNISON, "Note on the Determination of the Potential Functions of Polyatomic Molecules," J. Opt. Soc. Am. 50, 1267-1268 (1960)