Third-order derivatives of the dipole moment function for the ozone molecule

Abstract

The third-order contributions to the dipole moment function of ozone has been evaluated from available experimental values of the transition moment parameters for the second overtone and ternary combination vibration–rotation bands. The calculations are based on the formalism of effective dipole moment operators. The purely vibrational part of the transformed transition moment operators for three-quanta bands is presented in the form suitable for an iterative programming. It allows one to determine the values and to make the optimal choice of signs of the third derivatives of the dipole moment function using the transition moment parameters deduced from experimental spectra. The estimation of the errors have been done by an error propagation of uncertainties in anharmonicity parameters of the potential function and previously determined first- and secondorder dipole moment derivatives.