UPPER AND LOWER BOUNDS OF QUARTIC CENTRIFUGAL-DISTORTION CONSTANTS

Expressions are obtained for the maximum and minimum possible values of the equilibrium centrifugal distortion constants ταβγδ for a molecule with given structure and vibrational frequencies. The method of calculation, based on Lagrangian multipliers, is also applied to the empirical centrifugal constants (such as DJ, DJK, DK, or ΔJ, ΔJK, ΔK, δJ, δK) employed in fitting the rotational structure of spectra. These formulas make it possible to test whether a set of observed centrifugal constants is consistent with the rotational constants and vibrational frequencies. When inconsistencies arise, they are probably due to zero-point vibrational effects. By means of a second method employing inequalities, simpler formulas are derived for wider bounds. These are useful in calculating approximate values of the constants, as a preliminary to deciding which terms to include in the rotational Hamiltonian of any particular molecule. © 1979.