The two-dimensional anharmonic oscillator: Vibration-rotation constants of fulminic acid,HCNO

The lowest-wavenumber vibration of HCNO and DCNO, ν₅, is known to involve a largeamplitude low-frequency anharmonic bending of the CH bond against the CNO frame. In this paper the anomalous vibrational dependence of the observed rotational constants B(v₅, l₅), and of the observed l-doubling interactions, is interpreted according to a simple effective vibration-rotation Hamiltonian in which the appropriate vibrational operators are averaged in an anharmonic potential surface over the normal coordinates (Q_5x, Q_5y). All of the data on both isotopes are interpreted according to a single potential surface having a minimum energy at a slightly bent configuration of the HCN angle (～170°) with a maximum at the linear configuration about 2 cm^?1 higher. The other coefficients in the Hamiltonian are also interpreted in terms of the structure and the harmonic and anharmonic force fields; the substitution structure at the “hypothetical linear configuration” determined in this way gives a CH bond length of 1.060 Å, in contrast to the value 1.027 Å determined from the ground-state rotational constants.We also discuss the difficulties in rationalizing our effective Hamiltonian in terms of more fundamental theory, as well as the success and limitations of its use in practice.