Hindered and modulated rotational states and spectra of adsorbed diatomic molecules

Both vertical and horizontal adsorption configurations of a diatomic molecule were modeled as the rigid rotor with which the spatial motion was confined by a finite conical well. In addition to the polar hindering potential, a sinusoidal azimuthal modulation, which bears the local symmetry of the adsorption site, was incorporated. Eigenfunctions for different models were expressed analytically in terms of the hypergeometric functions, and eigenvalues were solved numerically. We found that the rotational energy levels exhibit oscillatory behavior when plotted as functions of the hindrance angle. This particular phenomenon was interpreted as the occurrence of resonance transmission of the rotor wave function at certain hindrance condition. We also found that the rotational levels were grouped into bands when the azimuthal modulation strength was increased. The solutions were used to calculate the rotational-state distribution of desorbed molecules, and agreement with the previous experiment was obtained.