Second-Order Perturbation Calculation of the Hindered Rotator Model for Adsorbed Hydrogen

A refinement of the previously reported models for adsorbed hydrogen is presented, based on the assumption that each hydrogen atom interacts with the adsorbent by a van der Waals force of the Lennard-Jones type. The calculation is accomplished by using the previous model based on a parabolic potential well interaction, for which exact wave functions are obtained, as the zeroth-order approximation and then carrying out a second-order perturbation calculation to obtain accurate results for the Lennard-Jones type interaction. The results lead to the conclusion that agreement with data on ortho-para hydrogen separation coefficients can be obtained only by assuming a magnitude for the rotational barrier which is inconsistent with data on adsorption energies. To eliminate this discrepancy a perturbing term involving a hindrance to rotation in the plane parallel to the surface is introduced and a second-order perturbation analysis shows that such a term can lead to agreement with both separation coefficient and adsorption energy data.