In the Laboratory
Integration of Computational and Preparative Techniques W To Demonstrate Physical Organic Concepts in Synthetic Organic Chemistry: An Example Using Diels–Alder Reactions David R. J. Palmer Department of Chemistry, University of Saskatchewan, 110 Science Place, Saskatoon, SK Canada, S7N 5C9;
[email protected] Intermediate-level organic chemistry introduces students to new concepts in reactivity that go beyond their knowledge of structure, bonding, and reactivity as described at the introductory level. Good examples of such concepts are the relative energies of molecules, orbital overlap as a means of predicting reactions, reactions under kinetic or thermodynamic control, and the Hammond postulate. Students may encounter a conceptual barrier between these concepts and those of preparative chemistry, which can be exacerbated when laboratory experiments do not integrate the concepts. The incorporation of computational experiments into laboratory experiments provides an excellent means of demonstrating many of the concepts above, through molecular orbital calculations or even kinetic simulations. The integrated experiment can help a student see how these ideas affect reactions in the “wet” laboratory. O
O
+
O
+ O
rxn 1
rxn 2
O
O
O O
O
O
O
endo-2
endo-1 O
O
O O
O O
O exo-1
exo-2
Figure 1. The reaction of maleic anhydride with cyclopentadiene (reaction 1) and with furan (reaction 2), showing the associated endo-and exo-forms of each product.
www.JCE.DivCHED.org
•
The Diels–Alder reaction (1, 2) is perhaps the clearest example of the how the integration of these abstract concepts is necessary to understand the result of a preparative reaction. There are many well-established Diels–Alder reaction experiments published in textbooks (3) and in this Journal (4–6), including an “easy puzzle” consisting of determining whether the endo- or exo-products have resulted from two Diels–Alder reactions (5), and a demonstration of kinetic and thermodynamic control of a reaction that typically yields a mixture of products (6). However these experiments stop short of exploring the origins of how two similar reactions might occur under similar conditions, yet one yields the kinetic product and one the thermodynamic product. Herein is described the extension of the “easy puzzle” to incorporate computational techniques and more advanced concepts in reactivity as a means of providing an integrated laboratory experience. The experiment requires both traditional chemistry laboratory facilities and a computer laboratory. The experiment can be run over several lab periods, or the computational aspects can be assigned as work outside of lab if desired. We have used Spartan ’02 for Windows (1991–2002 Wavefunction, Inc.) for this experiment, but other comparable programs could be substituted. The preparative experiment was chosen specifically to be simple for students to perform; this experiment is intended to demonstrate concepts, rather than teach new laboratory techniques. The experiments, the computational methods, and the analysis of the results can be varied to suit the level of the students and the intent of the course. This experiment compares the suprafacial [4 + 2] cycloaddition of maleic anhydride with cyclopentadiene and with furan (Figure 1). The substitution of oxygen for the methylene group in cyclopentadiene results in a slower reaction and in the isolation of the exo-adduct (the thermodynamic product) rather than the endo-adduct (the kinetic product). The course of lectures I offer provides students with a series of concepts that must be integrated to appreciate the differences in the two reactions. Briefly these concepts include: • the endo-adduct is the kinetic product owing to the favorable secondary orbital overlap of the endo-transition state; • the Diels–Alder reaction usually results in the isolation of the kinetic product, in part owing to the highly exergonic nature of the reaction, that is, the retroDiels–Alder reaction is usually unimportant; • the Hammond postulate predicts that a comparable but more energetically neutral (i.e., less downhill) re-
Vol. 81 No. 11 November 2004
•
Journal of Chemical Education
1633
In the Laboratory action has a later transition state, with an energy closer to that of the products, than does a highly exergonic reaction; and • furan can be considered an aromatic compound (having an uninterrupted cyclic π-system containing six electrons), in contrast with cyclopentadiene.1
Students may question whether these concepts are related and whether they have an effect on what is observed in the lab. The goal of this experiment is to connect these ideas explicitly. The Experiment The experiment was delivered to students in the form of a manuscript from which the results and discussion had been removed (available in the Supplemental MaterialW). The intent is to give students a taste of repeating an experiment from the literature. The handout was composed of a brief introduction and a description of the molecular modeling and chemical synthesis. The synthetic procedure is adapted from ref 5.
Molecular Modeling All calculations were performed using the program Spartan ’02 for Windows, from Wavefunction. Cyclopentadiene, furan, and maleic anhydride were each built and their equilibrium geometry calculated using Hartree-Fock 3-21G* calculations. For each diene, a surface corresponding to the HOMO was generated. For maleic anhydride, a surface corresponding to the LUMO was generated. By visual observation of the overlap of the reactant HOMO and LUMO, a prediction of the kinetic product of each reaction could be made based on qualitative frontier molecular orbital theory. The ground-state energy of each reactant was recorded.
Table 1. Calculated Energies for the Reaction of Cyclopentadiene and Maleic Anhydride Reaction Component
3-21G* Energy/ Hartreesa
Normalized Energy/ (kJ mol᎑1)
Reactants
᎑566.8205
162.7
Endo-transition state
᎑566.7945
231.1
Endo-product (1)
᎑566.8803
5.798
Exo-product (1)
᎑566.8825
0
a
One Hartree is equal to 2625.5 kJ/mol.
Table 2. Calculated Energies for the Reaction of Furan and Maleic Anhydride Reaction Component
3-21G* Energy/ Hartreesa
Reactants
᎑602.4536
Endo-transition state
᎑602.4179
Endo-product (2)
᎑602.4840
Exo-product (2)
᎑602.4887
a
Normalized Energy/ (kJ mol᎑1) 92.40 186.1 12.61 0
One Hartree is equal to 2625.5 kJ/mol.
1634
Journal of Chemical Education
•
The equilibrium ground-state energies of the endo- and exo-forms of 1 and 2 were then calculated as described above for the reactants. This allowed prediction of the thermodynamic product of each reaction. Considering the energies of the reactants and product for each reaction, a qualitative prediction of the relative positions along the reaction coordinate of the transition states could be made based on the Hammond postulate. The transition-state energy of the kinetic product was calculated for reactions 1 and 2. Starting with the product structure, the “Reaction” (blue curved arrow) module was used to draw arrows representing the retro-Diels–Alder reaction. The energy was then calculated by optimizing the transition state geometry using ab initio calculations at the 3-21G* level. With the energies of the reactants, transition state, and products for the formation of endo-1 and endo-2, it was possible to estimate the relative rates of these two reactions in the forward, (k1兾k2)f, and the reverse directions, (k1兾k2)r. This requires the assumption that the entropy of activation (∆S ‡) of these processes is approximately equal. Thus
∆H ‡1 − ∆H ‡2 ≈ ∆G ‡1 − ∆G ‡2 = ∆∆G ‡ and k =
−∆G ‡ kB T exp h RT
Therefore k1 −∆∆G ‡ = exp k2 RT The reversibility of these two reactions was taken into account when rationalizing the stereochemistry of the isolated products of reactions 1 and 2. Hazards Maleic anhydride and the Diels–Alder adducts are intense skin irritants. Ethyl acetate and diethyl ether are volatile flammable solvents that should be handled in the fume hood. Discussion When performed as described, the experiment results in the isolation of endo-1 and exo-2. The calculations result in the values shown in Tables 1 and 2. The aromaticity of furan lowers the energy of the reactants, but not the products, of reaction 2, resulting in a more thermoneutral process. The Hammond postulate predicts a later transition state, with a lower rate in the forward direction and a higher rate in the reverse direction. Using the calculated data, the relative rate of the forward reactions (k1兾k2)f ≈ exp(᎑∆∆G ‡兾RT ) = exp [(25,276 J mol᎑1)兾(298 K × 8.314 J K᎑1 mol᎑1)] = 2.70 × 104. Cyclopentadiene is estimated to react with maleic anhydride about 27,000 times faster than does furan. The ratio of rate constants for the retro-Diels–Alder reactions of the endo-products, (k1兾k2)r ≈ 8 × 10᎑10; an eighty billionfold difference. Thus the reaction of furan with maleic anhydride, although still exothermic, is much more likely to equilibrate, resulting in the thermodynamic product.
Vol. 81 No. 11 November 2004
•
www.JCE.DivCHED.org
In the Laboratory
Students are required to write a report in which they describe their results and discuss their conclusions. It has been my experience that every student at the intermediate level can appreciate most of the concepts of this experiment after discussing the ideas with their instructor or the teaching assistant. Students must grasp the idea that a kinetic product can be isolated under irreversible conditions, but not under conditions in which the product readily reverts to starting materials. Calculating the relative rates serves as a good reminder of the implications of the exponential relationship between rate and energy: 25 kJ兾mol (or 6 kcal兾mol) may not sound like much, but 27,000 times slower sends a different message. The better students will pursue the idea that the Hammond postulate is at work and observe the differences in the transition state structures for the two reactions. Spartan predicts a more reactant-like transition state for the reaction of cyclopentadiene: the maleic anhydride moiety of the activated complex has deviated from planarity to a lesser extent and the forming “bonds” between the two reactants are longer. It is important for students to realize that computational results should not be accepted without question; “calculated” energies are really estimates based on a method rife with approximations. Indeed, for many Diels–Alder reactions, including that of furan and maleic anhydride, the exo-product is predicted to be the kinetic product, even using the 6-31G* basis set.2 Nevertheless, the marriage of preparative and computational aspects described broadens the students’ laboratory experience. W
Supplemental Material
The handout for the students and notes for the instructor are available in this issue of JCE Online. Acknowledgments The author thanks H. Martin Gillis and Christopher P. Phenix for their assistance in the development and delivery of this laboratory experiment. Laboratory development funding was provided by the Department of Chemistry, University of Saskatchewan.
www.JCE.DivCHED.org
•
Notes 1. In my laboratory program, this experiment is preceded by a computational experiment exploring the concept of aromaticity. The experiment is similar to a published example (7). In this experiment students calculate the successive heats of hydrogenation of benzene, cyclohexadiene, and cyclohexene, to arrive at a resonance energy that distinguishes benzene from 1,3,5-cyclohexatriene. This exercise is repeated for thiophene, furan, and cyclopentadiene, clearly demonstrating that the two heterocycles are stabilized by resonance to an extent that cyclopentadiene is not, and also that electronegativity has an apparent effect on orbital overlap and the associated stabilization. The concept that furan is aromatic, and cyclopentadiene is not, has therefore been dealt with on the blackboard and in the lab before the Diels–Alder experiment. 2. The calculation of the exo-transition states for the two reactions can be included in this experiment, rather than the qualitative methods described here. The results suggest that the transition states forming endo-2 and exo-2 are very close in energy, with the exo-adduct slightly favored. A discussion of the limitations of the computational methods would be appropriate, so that students do not conclude that the exo-adduct is the kinetic product in this case.
Literature Cited 1. Hoffman, R.; Woodward, R. B. J. Amer. Chem. Soc. 1965, 87, 4388. 2. Lee, M. W.; Herndon, W. C. J. Org. Chem. 1978, 43, 518. 3. For example, Williamson, K. L. Macroscale and Microscale Organic Experiments, 3rd ed.; Houghton Mifflin Company: Boston, MA, 1999; pp 572. Wilcox, C. F., Jr. Experimental Organic Chemistry: Theory and Practice; Macmillan Publishing: New York, 1984; p 390. 4. Jarret, R. M.; New, J.; Hurley, R.; Gillooly, L. J. Chem. Educ. 2001, 78, 1262. 5. Pickering, M. J. Chem. Educ. 1990, 67, 524. 6. Cooley, J. H.; Williams, R. V. J. Chem. Educ. 1997, 74, 582. 7. Hehre, W. J.; Shusterman, A. J.; Huang, W. W. A Laboratory Book of Computational Chemistry; Wavefunction Inc: Irvine, CA, 1998; pp 10–16.
Vol. 81 No. 11 November 2004
•
Journal of Chemical Education
1635
