Subject: Rotation rates: confirmation &/or comments

From: <[email-masked]>
Date: Mon, 17 Jul 1995 08:03:29 +0200 (MEST)

Dear Colleagues;

     For some work in which I find myself currently engaged, I am interested in
estimating the rate of rotation about the C-C. bond of n-alkyl radicals of the
type

                                   H H
                                   | |
                                 R-C-C.
                                   | |
                                   H H

According to Krusic et al. [Electron spin resonance studies of coformations and
hindered internal rotation in transient free radicals, J. Phys. Chem. 75: 3438-
3453 (1971)], n-alkyl radicals of the type RCH2-CH2. have C-C. rotational bar-
riers of ca. 3.1 kcal/mol.  If the corresponding value of the Arrhenius pre-
exponential factor A is 10^12.5 [Chen et al., Conformations and rotation bar-
riers in allylcarbinyl radicals by electron spin, JACS 95: 7036-7043 (1973)],
then is it proper to estimate the rat of rotation using the equation

                   k(rot) = A exp (-Ea/RT)

where A = 10^12.5 and Ea = 3.1 kcal/mol?  When I make the approriate substitu-
tions and assume that T = 37oC, I get k(rot) = 2 x 10^10/sec, i.e., the C-C.
bond  makes 2 x 10^10 360o rotations per second.  Does this make sense?  Any
confirmations, comments, or criticisms are most welcome.

       A related question: if we assume that the above value of k(rot) was cal-
culated correctly, then k(rot) = 2 x 10^10/sec would represent an _average_
value for the rotation rate constant.  However, I would expect that under "real"
conditions there would be a distribution of rotation rates for a large ensemble
of molecules all at the same "average" temperature (e.g., 37oC), i.e., some
would be rotating faster andother rotating slower.  From the above information
is there a way of calculating the distribution of  k(rot) values for a large
ensemble of molecules?

     Again, all comments, criticisms, and advice are enthusiastically encour-
aged.  Of course, relevant literature references are always welcome.

     Thanks in advance to all responders.

Sincerely,

(Dr.) S. Shapiro
Inst. f. orale Mikrobiol. u. allg. Immunol.
Zent. f. Zahn-, Mund- u. Kieferheilkd. der Univ. ZH
Plattenstr. 11
Postfach
CH-8028 Zuerich 7
Switzerland

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