Vibration-rotation interactions between overtone and combination levels of asymmetric-top molecules: Application to the infrared spectroscopy of formaldehyde and ketene

Abstract

The conventional vibration-rotation Hamiltonian for an asymmetric-top molecule is rewritten by expanding the elements of the inverse inertial tensor about the equilibrium molecular geometry. The approach allows the identification of terms in the Hamiltonian that couple states differing by two, three, or four vibrational quanta and hence the calculation of dimensioned Coriolis xi coupling coefficients for interacting fundamental, overtone, and combination levels. The matrix elements that result from the application of the expanded Hamiltonian depend upon the harmonic vibrational wave numbers, equilibrium moments of inertia, Coriolis zeta parameters, and the derivatives of the elements of the inertial tensor matrix with respect to each of the normal coordinates. The Coriolis coupling coefficients may be calculated through evaluation of the summations that result from the appropriate terms. The validity of the approach is demonstrated through the calculation of coupling coefficients for interacting levels in formaldehyde and ketene. The uncertainty in the calculated values of the coupling coefficients is typically better than +/-6%, although the values calculated for interactions that involve low-frequency vibrational modes are less reliable. Comparisons are made between the calculated values and experimental results.