Harmonically coupled, anharmonic oscillator model for the bending modesof acetylene

The harmonically coupled anharmonic oscillator model developed by Child and co-workers is extended to treat the coupling of two doubly degenerate “local benders” as may be expected in acetylene. This effective Hamiltonian is transformed to the normal mode representation and a set of “x-K ” relations derived that relate the anharmonic and Darling-Dennison-type resonance terms to the diagonal local bending anharmonic constant. It is found that these relations agree very poorly with the experimental constants determined by Pliva in a fit to the acetylene spectrum. This failure is attributed to a remarkable cancellation of cubic and quartic contributions to the constants.