partition functions - between vibration and translation

 	Dear CCL'ers,
 	4 days ago, I have posted some questions associated with
 calculating partition functions. I need in some information more,
 concerning the following, may be, more general problem.
 	Suppose, we have some weak interaction, e.g., physisorption, with
 the depth of the potential well about 2 - 3 kcal/mol, or even less.
 To calculate properly the vibrational partition function (for the motion
 of the adsorbed molecule, as a whole, against the surface) one has to keep
 in mind that:
 	(1) traditional harmonic approximation may give a noticeable
 	(2) just that I would like to discuss: since the dissociation
 limit is low-lying, then, probably, there could be some NON-NEGLIGIBLE
 contribution to the partition function from the states which lye ABOVE the
 dissociation limit. The latter could be treated in the manner similar to
 that for estimating the translational partition function.
 However, it is not so easy to do it analytically, without
 introducing approximations. The problems of this kind (even the
 simplest ones, e.g., rectangular potential well with finite-height walls)
 are known not to have closed solutions. Probably, such problems can be
 treated approximately, by, e.g., Wentzel-Kramers-Brillouin method.
 	Speaking on the NON-NEGLIGIBILITY of the contribution from the
 states lying above the dissociation limit, I mean also that, if the latter
 tends to zero (no interaction), or if the temperature tends to infinity,
 our partition function should tend to the translational one which is
 usually HUGE with respect to any vibrational partition function
 (corresponding to the strong interaction) Thus, one
 needs to fill the gap between these two limiting cases by anything.
 	There is an obvious similarity between that was discussed above,
 and hindered rotation. In the latter case, we have a contribution to the
 partition function form the vibrations (states below the rotational
 barrier) and more-or-less free rotations (above the barrier). At T ->inf,
 one can neglect the former; at T -> 0 - the latter. What to do for the
 moderate temperatures?
 I beleive, such problems arose (and, probably, were solved) in the past.
 	I am grateful in advance to anybody for any discussion and
 	Dr. Alexei Arbouznikov
         Ecole Nationale Superieure de Chimie,
 	Laboratoire de Materiaux Catalytiques et Catalyse en
 	Chimie Organique, UMR 5618 CNRS-ENSCM - Prof. F.Fajula,
         8, rue de l'Ecole Normale
         34296 Montpellier, Cedex 5
         Telephone: (33) 4-67-14-72-68
         Fax:   (33) 4-67-14-43-49
         E-mail: alexei #*at*#