Subject: distribution of rotameric species

From: Kay Kreidler <[email-masked]>
Date: Thu, 6 Jul 95 20:39:34 MESZ

Dear netters!

Almost one and a half year ago I asked a question concerning the
rotational barrier of molecules. For better reference and comprehension, I
will repeat my original question:

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I have a question about the thermal energy, concerning rotational
barriers. How can you calculate this energy in dependence of the absolute
temperature? Some people told me it must be E = 3/2 * RT for a non-linear
molecule, but this doesn't fit to experimental data (Ethane has a
rotational barrier of approx. 3 kcal/mol and 3/2 * RT would be only 0.89
kcal/mol for T=298K). Any suggestions?
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I received a number of interesting answers and posted them to this mailing
list. Although I still was not very happy with the result of this, because
it did not make things clear. Today I found something in a textbook about
physical chemistry (W.J. Moore and D. Hummel, "Physikalische Chemie",
Walter de Gruyter Berlin, New York, 1983).

They wrote, that in some molecules like ethene or ethane, internal degrees
of freedom cannot be divided in vibrations and rotations. In the case of
ethane, a degree of freedom for the vibrations gets lost, therefor you
have an additional one for the internal rotation around the C-C single bond.

When the barrier of rotation exceeds RT (= approx. 2.5 kJ/mol = 0.59
kcal/mol) it must be treated as a hindered rotation. For this case there
is no easy formula available for the "Zustandssumme" (sum of states in
English ?). You can calculate the amount of the rotational barrier from 
U = 0.5 * U(max) * (1 - cos(gamma*phi)) with phi being the rotational angle,
gamma a structural factor depending on the symmetry ("Zaehligkeit") of the
rotational axis. U(max) has to be calculated with quantum mechanical
methods for each case or sometimes can be obtained by microwave
spectroscopy, where the rotational transitions are split due to this
internal rotation. For further investigations the authors recommend two
historical papers:

E.B. Wilson, Science 162 (1968) p.59 and
R.M. Pitzer, J. Chem. Phys. 39 (1963) p.1995

My problem is, that now I know that there is no easy way of calculating this
barrier of rotation but once one has done it (with quantum mechanical 
calculations) one still has no knowledge, if the rotation can proceed in
dependence of the temperature.

Comments on my explanations are highly welcomed. When I find more about 
this topic, I will let you know.

Sincerely

Kay Kreidler

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Kay Kreidler
Institut fuer Anorganische Chemie und Strukturchemie I
Heinrich-Heine-Universitaet Duesseldorf
Universitaetsstr. 1
40225 Duesseldorf - Deutschland
e-mail: [email-masked]
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