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 Diene HOMO value

Diene HOMO Electrostatic Potential

LUMOs

LUMOs, con’t

Electrostatic Potential Maps

Electrostatic Potential Maps, con’t

Transition States for endo/exo Products of Diels-Alder Reaction Endo product - ∆H formation = kcal/mol Transition structure - Imaginary vibration frequency - frequency 3.76 of type A (frequency rather low compared to real vibrations) ∆H formation = kcal/mol

Transition States for endo/exo Products of Diels-Alder Reaction Exo product - ∆H formation = kcal/mol Transition structure - Imaginary vibration frequency - frequency of type A (frequency considerably higher than all real vibrations) ∆H formation = 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 Tips about transition state calculations from: “Transition States for Diels-Alder Reactions”, by Eilers, James E., Southern Illinois University - Edwardsville 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