*From*: Arbouznikov Alexei <alexei #*at*# palladium.enscm.fr>*Subject*: partition functions - between vibration and translation*Date*: Tue, 8 Sep 1998 11:35:54 +0200 (MDT)

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 error; (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 references. Alexei ======================================================================== 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 FRANCE Telephone: (33) 4-67-14-72-68 Fax: (33) 4-67-14-43-49 E-mail: alexei #*at*# palladium.enscm.fr