Semiclassical Calculation of the g-Factors for l-States of the Bending Vibration of a Linear Molecule

摘要

The semiclassical model, proposed earlier (Rebane, T.K., Opt. Spektrosk., 1995, vol. 78, no. 6, pp.911–916) to describe excited l-states of the bending vibration of linear molecules and to calculate their vibrational and rotational g-factors, is refined by taking into account the elongation of bond lengths and the change in the vibrational frequency with increasing the quantum number l. The l-dependences of geometrical parameters and the frequencies of a doubly degenerate, circularly polarized bending vibration of the HCN molecule are calculated from the solution of the problem of dynamic equilibrium of the elastic and centrifugal forces acting on atoms. The H–C and CN bonds are found to become elongated by 6.5 and 1%, respectively, as l varies from 1 to 20. The l-dependences of the vibrational and rotational g-factors of the HCN molecule are computed. Therefined dynamical approach, as compared to the model of fixed bond lengths, leads to a stronger l-dependence of the vibrational g-factor and to a weaker l-dependence of the rotational g-factor of the molecule.