Finite-conical-well model for vertically adsorbed diatomic molecules

We present studies of the rotational spectra of a diatomic molecule adsorbed vertically on a solid surface. The hindrance configuration was modeled as a rigid rotor whose spatial motion was confined by a finite conical well. The eigenfunctions can be expressed analytically in terms of the hypergeometric functions, and eigenvalues were solved numerically. We found that the rotational energy levels and the confinement probabilities exhibit oscillatory behaviors when plotted as functions of the hindrance angle. The solutions were used to calculate the rotational-state distribution of the suddenly unhindered rotors and general features which agree with the previous experimental findings were obtained.