Transcript The Diels-Alder Reaction

The Diels-Alder
Reaction
Explorations in Computational
Chemistry
By Igor Gorodezky and Ryan Spielvogel
Fall 2000
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.
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 π-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 diene’s highest
occupied molecular orbital (HOMO) and the dienophile’s 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.
Scientific Background I,
con’t
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.
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.
Scientific Background II,
con’t
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.
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.
Data and Results
dienophile
log(rxn rate) LUMO energy electrostatic
potential
acrylonit rile
0
0.0434
41.0731
cis-1,2-dicyanoethyl ene
1.892
0.0341
57.2961
trans-1,2-dicyanoethyl ene
1.944
0.035
59.5593
1,1-dicyanoethyl ene
4.643
0.0447
55.3869
tricyanoethyl ene
5.663
0.0363
71.3403
tetracyanoethyl ene
7.613
0.0296
42.8917
Diene HOMO value - 0.0247
Diene
Electrostatic
Potential
HOMO
LUMOs
acrylonitrile
trans-1,2-dicyanoethy lene
cis-1,2-dicyanoethy lene
LUMOs, con’t
1,1-dicyanoethy lene
tricyanoe thylen e
tetracyanoethylene
Electrostatic Potential
Maps
acrylonitrile
trans-1,2-dicyanoethy lene
cis-1,2-dicyanoethy lene
Electrostatic Potential
Maps, con’t
1,1-dicyanoethy lene
tricyanoe thylen e
tetracyanoethylene
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
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
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 dienophile’s 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.
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 –
Reaction Coordinate
Diagram
Conclusions - Part II, con’t
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.
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/eilers/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