The Diels-Alder Reaction

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The Diels-Alder Reaction

• Explorations in Computational Chemistry
• By Igor Gorodezky and Ryan Spielvogel
• Fall 2000

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Introduction
The Diels-Alder reaction is a method of producing
cyclical organic compounds (a cycloaddition
reaction), and is named for Otto Diels and Kurt
Alder who in 1950 received the Nobel Prize for
their experiments. It is a pericyclic reaction,
meaning it goes on in one step with a cyclic flow
of electrons, and involves the addition of a
diene molecule to a dienophile (literally, diene
loving molecule). The reaction is
stereoselective, meaning it is possible to create
different geometric configurations of the product
depending on the conditions, and is frequently
used to create molecules of theoretical interest
that do not occur in nature. In this project, I
studied how properties of the dienophile affect
the rate of reaction, as well as studying
transition states, kinetic and thermodynamic
reaction pathways, and stereoselectivity in one
example of Diels-Alder.
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Scientific Background I
As mentioned, the Diels-Alder reaction involves a
diene molecule that reacts with a dieneophile in
a cycloaddition reaction. Good dienophiles have
attached to them very electronegative groups that
help withdraw electrons, such as nitrile, ester,
or carbonyl groups. The accepted reaction
mechanism involves the reactants approaching each
other on parallel planes, with new bonds forming
as a result of the overlap of p-electrons clouds
(with the dienophile withdrawing electrons).
Frontier Molecular Orbital theory (FMO) is used
to explain the mechanism. Accordingly, the
reaction depends on the interaction between the
dienes highest occupied molecular orbital (HOMO)
and the dienophiles lowest unoccupied molecular
orbital (LUMO). The reaction goes on more readily
when the energy difference between the two
orbitals is small, and electrons are readily
traded. In addition, minimal electrostatic
repulsion between the products should accelerate
the reaction.
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Scientific Background I, cont
These will be tested in the first part of the
project, where properties of the diene 1,3-butene
and various dienphiles will be examined.
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Scientific Background II
The second part involved a reaction between
cyclopentadiene (diene) and acrylonitrile
(dienophile). As mentioned, experimental
conditions can affect the geometry of Diels-Alder
products, as frequently happens with many
chemical reactions. This depends on two
theoretical reactions paths kinetic and
thermodynamic. While both types of reaction are
exothermic, the thermodynamic pathway achieves a
lower energy and hence more stable product, but
requires more energy to initiate the reaction.
It is evident how conditions such as temperature
can affect the reaction.
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Scientific Background II, cont
In the project, transition structures for exo and
endo geometries of the product were calculated in
an attempt to determine which geometry
represented which reaction type. This is possible
since transition states represent highest energy
structure attained during the reaction.
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Computational Approach
The calculations for both parts were done using
the MacSpartan program, and were all performed on
the AM1 level of calculations (unless otherwise
specified), sacrificing some accuracy for a
shorter calculation time. For part one, diene
and dienophile geometries were optimized, and
HOMO and LUMO energies, respectively, were
calculated at the ab initio 3-21G level.
Electrostatic potential for all molecules was
also calculated, at the AM1 level. The data was
plotted and fitted using Graphical Analysis for
Windows. In order to improve the initial guess
at a transition state during the second part of
the project, a frequency calculation on the AM1
level was run on the two candidates, and then a
transition structure optimization was performed,
again on the AM1 level, with the restart
option, and with the number of cycles increased
to 700. Then, another frequency calculation was
performed, yielding one imaginary vibration that
represented the molecules separation into the
reactants. This was performed seemingly
backwards because it is much easier to find a
correct geometry for one molecule separating into
two than to fit two molecules together. All data
is still applicable. The geometry was initially
optimized using AM1.
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Data and Results
Diene HOMO value - 0.0247
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Diene
Electrostatic Potential
HOMO
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LUMOs
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LUMOs, cont
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Electrostatic Potential Maps
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Electrostatic Potential Maps, cont
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Transition States for endo/exo Products of
Diels-Alder Reaction
Endo product - ?H formation 58.973167
kcal/mol Transition structure - Imaginary
vibration frequency - frequency 3.76 of type A
(frequency rather low compared to real
vibrations) ?H formation 81.925495 kcal/mol
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Transition States for endo/exo Products of
Diels-Alder Reaction
Exo product - ?H formation 58.535988
kcal/mol Transition structure - Imaginary
vibration frequency - frequency 866.43 of type A
(frequency considerably higher than all real
vibrations) ?H formation 110.785824 kcal/mol
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Conclusions - Part I
Using information gathered in the first part of
the experiment, we can deduce there is indeed a
relationship between LUMO energy and reaction
rate for Diels-Alder reactions. This relationship
states that the reaction rate will increase as
LUMO energy decreases, meaning the HOMO/LUMO
energy difference will be smaller and electron
transfer will be easily facilitated. This is in
accordance with FMO theory. Also, reaction rate
seems to increase as the dienophiles
electrostatic potential increases. In the
electrostatic potential map of the diene, the
region that, according to the accepted mechanism,
is brought near the dienophile has distinct
electronegative regions. Consequentially, very
high reaction rates are associated with a very
electropositive face on the dienophile, such as
seen on tetracyanoethylene. It is more difficult
to tell the magnitude of the electrostatic
potential on the isomers. There, it is probable
that geometry, and not simply the magnitude of
the electrostatic potential, affects reaction
rate. One can also draw the same conclusion
about the LUMO. LUMO energy seems to decrease as
electron withdrawing groups are added, though it
is difficult to derive LUMO magnitude from visual
representations.
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Conclusions - Part II
For the second part of the experiment, dealing
with a specific Diels-Alder reaction, it is now
possible to determine which product geometry is
the result of the kinetic reaction pathway and
which is the result of the thermodynamic reaction
pathway. Since the end products energies of
formation are almost exactly the same, we know
geometry does not dictate the stability of the
end product. Because the exo form of the
transition structure has a much higher energy
than the endo form, we know the energy barrier
for the reaction that achieves the exo form is
higher than that which achieves the endo form.
It should be noted, however, that both forms of
the product have about the same energy, meaning
the reaction coordinate diagram should look like
this
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Reaction Coordinate Diagram
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Conclusions - Part II, cont
This means that the exo reaction could be labeled
as the thermodynamic pathway, but the end product
is no more stable than the one for the kinetic
pathway. It is evident, then, that the endo form
of the product will be in much greater abundance
than the exo form, because the exo form is just
as stable but has a much greater energy barrier.
In this case, temperature can increase the
amount of the exo product, but over time, the
concentration of the endo product should remain
larger than that of the exo product.
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References
Experiment adapted in large part from A
Laboratpry Book of Computational Organic
Chemistry, by W.J. Hehre, A.J. Shusterman, W.W.
Huang, 1996 by Wavefunction Inc. Gotwals,
Robert R. Personal Conversations. Computational
Chemistry Seminar, fall 2000. Tips about
transition state calculations from Transition
States for Diels-Alder Reactions, by Eilers,
James E., Southern Illinois University -
Edwardsville http//www.siue.edu/CHEMISTRY/eile
rs/projects/project_8.html Louden, G. Marc,
Organic Chemistry. The Benjamin/Cummings
Publishing Co. Reading, Ma. 2nd ed,
1988 Carroll, Felix A. Perspectives on
Structure and Mechanism in Organic Chemistry.
Brook/Cole Publishing CO. New York. 1998