Subject: CCL: summary conformers and rate(at)trentu.cA

From: Errol Lewars <elewars(at)trentu.cA>
Date: Mon, 12 Jul 2004 12:48:46 -0400

2004 July 12

Here is the summary of the answers I got to the question below. Thanks 
very much to all who responded (I hope I haven't omitted anyone).
Those interested in cases like s-cis-butadiene/s-trans-butadiene + a 
dienophile might wish to note #4 below,  and E. Goldstein, B. Beno, and 
K. N. Houk, JACS, 1996, 118, 6036.
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QUESTION

2004 July 8

The rate of formation of products Pa and Pb from quickly interconverting
conformers Ca and Cb is treated with the the Curtin/Hammett and
Winstein-Holness equations (the Curtin-Hammett principle, in particular,
is well-known): J. I Seeman, Chem Rev, 1983, 83, 83; E. L. Eliel, "From
Cologne to Chapel Hill", ACS, 1990, pp. 31-33.

Question: has anyone a reference to a discussion of the case of rapidly
interconverting conformers Ca and Cb, where Ca, although the minor
conformer, is the only one that can react with X to form a product CaX,
through transition state Ta; intuition aside, has someone explicitly
addressed whether the _experimental_ activation E is measuring the Ta-Ca
energy difference, or the Ta-Cb difference?

Thanks.

EL
-----------

#1
Per-Ola Norrby

    Provided that the interconversion is fast relative to the final 
reaction, the free energy of activation should be relative to the 
ensemble energy (which is slightly lower than the lowest of Ca and Cb).  
The apparent activation energy is taken from an expression where you 
consider the total concentration of reactant.  The sole effect of the 
pre-equilibrium is to make the effective concentration lower, with a 
concominant lowering of the rate which corresponds exactly to the free 
energy difference between the reacting conformer and the free energy of 
the ensemble.  You can get the latter by assuming a virtual species 
corresponding to the total concentration of the reagent, and use the 
standard Boltzmann expression.

    The above wasn't perfectly clear (I haven't digested my coffee yet), 
but it should be correct.  The math is available in the Ph.D. Thesis of 
Torben Rasmussen (Copenhagen 2001), and he took much of it from H 
Maskil, "The Physical Basis of Organic Chemistry", Oxford 1985.

    /Per-Ola
-- 
Per-Ola Norrby, Assoc. Professor, http://organisk.kemi.dtu.dk/PON/
Technical University of Denmark, Department of Chemistry
Building 201, Kemitorvet, DK-2800 Kgs. Lyngby, Denmark
Email: pon(at)kemi.dtu.dk  tel +45-45252123,  fax +45-45933968
==========
#2
Andreas Klamt

Errol,

sorry for replying with a theoretical aspect:
Do you really expect a unique answer? The answer will depend on the 
question, whether the exchange rate between Ca and Cb is larger or 
smaller than the reaction rate. In the first case you will observe Ta-Ca 
as activation energy, in the seond case Ca-Cb!!! because this step 
becomes rate determining. I am not sure whether you ever will observe 
Ta-Cb as activation energy.

Andreas

klamt(at)cosmologic.de
=================
#3
Philip Hultin

We have been dealing with a similar question, and have had some arguments
with referees on this question.

I don't know of any experimental demonstrations, but Seeman's paper does
make the point very clearly that populations DO matter, at least in what he
calls the "Case II Kinetics" scenario.  The total rate is a
population-weighted sum of the two individual rates, which implies that the
individual activation barriers play a population-weighted role in the
"apparent" activation barrier you would measure experimentally.

Please, let me know of any comments you receive on this question.

Dr. Philip G. Hultin
Associate Professor of Chemistry
University of Manitoba
Winnipeg, MB, Canada R3T 2N2
(vox) 204-474-9814
(fax) 204-474-7608
mailto:hultin(at)cc.umanitoba.ca
http://www.umanitoba.ca/chemistry/

=================
#4
Jose Ignacio Garcia-Laureiro

Dear Prof. Lewars,

Indeed, there is a very common situation in which that happens, namely the
s-cis/s-trans conformational equilibrium of open-chain dienes in 
Diels-Alder
reactions. For instance, only the s-cis conformer (BDc) of butadiene is 
able to react,
whereas the s-trans (BDt), the major conformer, is inactive towards the 
cycloaddition.
In these conditions, the experimental activation barrier is measuring 
the TS-BDt
energy difference, and this is because the same reasons operating in the 
Curtin-Hammett
equation: the preequilibrium constant s-cis/s-trans appears in the 
kinetic equation
as a multiplicative term, so that the apparent rate constant is in fact 
the product
between the kcis (representing the TS-BDc activation barrier), and K 
(the conformational
equilibrium constant, representing the s-trans - s-cis energy difference).
I hope this can help you.
Best regards.

Josi I. Garcma

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Dr. Jose Ignacio Garcia-Laureiro, Investigador Cientmfico del CSIC
Depto. Quimica Organica. Instituto de Ciencia de Materiales de Aragon
Facultad de Ciencias (edificio D). Universidad de Zaragoza-CSIC
c/ Pedro Cerbuna, 12. E-50009 Zaragoza (Spain)
Phone: +34 976762271       e-mail: jig(at)unizar.es
Fax:     +34 976762077
http://wzar.unizar.es/acad/fac/cie/quiorg/catalisis/index.htm
==============