From chemistry-request@www.ccl.net Tue Sep 8 05:42:00 1998
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Date: Tue, 8 Sep 1998 11:35:54 +0200 (MDT)
From: Arbouznikov Alexei
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Reply-To: Arbouznikov Alexei
To: CHEMISTRY@www.ccl.net
Subject: partition functions - between vibration and translation
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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@palladium.enscm.fr