Abstract
Molecular modeling of chemical reactions using Spartan programs has proven to be a useful exercise yielding both thermodynamic and kinetic information about Diels-Alder electrocyclic systems comparable to experiment. The program suite is user friendly for both undergraduate and graduate students not familiar with the details of the computational methods. Equilibrium constants based on the PM3 model, and activation energies based on the B3LYP model, not only compare favorably with experiment but also suggest trends that illustrate known mechanistic principles. The effect of acid catalysis is also accurately reflected.
Our research has shown the usefulness of Spartan programs in modeling chemical reactions which can be incorporated in undergraduate and graduate studies. We chose to examine the adequacy of the currently available suite of programs to predict H, S, and Ea for a related set of concerted reactions containing both known and unreported parameters. In this manner one validates the level of theory and suggests future experimental tests. A different approach using molecular modeling for first year college students was performed by Ealy1, whose work showed that students exposed to molecular modeling classes did better in their final exams than students not exposed to the same experience.
Several works have been published on molecular modeling in education. Ringen et al.2 found that a molecular modeling exercise proved useful in illustrating the three dimensional difference between pairs of enantiomers. It helped also to visualize the concepts of torsion angle and conformational analysis. Casanova3 reviewed both the historical development of computer-based molecular modeling in structural chemical education, as well as the current direction of introducing higher levels of computational chemistry into the curriculum.
A software development in the study of molecular structure in undergraduate courses has been described by Yano et al.4 Their software designs the molecular structure for display and derives the dipole moment of the molecules. Hermann5 has discussed the details of introducing an introductory course in molecular modeling. The purpose of this course is to allow students from various academic backgrounds to familiarize themselves with computational chemistry, and to explain different concepts such as ionic and molecular interactions in a simplified way through methods of molecular simulations. In addition to the traditional modes of evaluation of a final exam and a synopsis of an assigned article, half of the grade is decided on the basis of practical work with the computer.
In our work with Spartan Pro we modeled a concerted Diels-Alder reaction (Scheme 1) and showed that the semi-empirical AM1 and PM3 levels of theory are competent to predict thermodynamic quantities of interest. We found this by comparing experimental values of various reaction enthalpies and percent yields with the corresponding computed quantities using several computational methods. It was found in general that these semi-empirical methods gave the most accurate and efficient results. In addition, it was reported by Houk and Evanseck7 that for a model Diels-Alder reaction, the B3LYP version of the density functional method was the most accurate in modeling transition state energies. When we tried this theoretical option in the Spartan-04 program, we found8 that B3LYP also gives accurate activation energies for our systems. In addition, we investigated the exo/endo selectivity of Diels-Alder reactions of the four five-membered heterocyclic rings with acrolein using B3LYP/6-31G*, and found results as expected due to secondary orbital overlap in all four cases (Scheme 2). The extra orbital interaction occurs only in the endo transition state, thereby leading to lower activation energies. Our results give confidence that these modeling programs are generally successful in both research and education.
For our thermodynamic6 study of the Diels-Alder reactions of 3,4-disubstituted five-membered heterocyclic aromatic rings with acrolein, we found that EHOMO and ELUMO of the dienes correlate linearly with p and m of Hammett equation. Electron donating groups raise the energy of the HOMO/LUMO and electron withdrawing groups stabilize their energy. We found also that the exothermicity of these reactions is sensitive to the nature of the substituent on the diene. The more electron donating the substituent is, the larger the exothermicity. The equilibrium constant is also sensitive to the electron donating and withdrawing power of the diene substituent. The more electron donating the substituent, the larger the equilibrium constant. (Ke are calculated from G0 in the usual way, G0 = -RTlnKe, and G0 is calculated from the H0 and S0 values provided by the Spartan output.) In addition we used the modeling program to reproduce the reactivity of various Diels-Alder reactions and compared the values of the computed equilibrium constants to references in the literature. The program predicted in three cases favorable equilibrium constants and one unfavorable equilibrium constant as found experimentally for these reactions.
Tables 1a-c contrast experimental and computed equilibrium constants, enthalpies and activation energies. Table 1c shows that the PM3 model that succeeds in reproducing thermodynamic parameters is not adequate for kinetic modeling, and that B3LYP is more successful here.
Table 2 shows computed equilibrium constant values of the Diels-Alder reactions, which predict that phosphole derivatives and one furan derivative are reactive dienes while the others have unfavorable equilibrium constants. A typical plot of the equilibrium constant vs is given in Figure 1 demonstrates the electron withdrawing and donating effects.
Table 1a: Computed equilibrium constants (PM3) and experimental yields for known reactions
Reaction Experimental yield Equilibrium constant
3,4-Dimethyl-1-phenyl-1H-phosphole and phenylethynyl-phosphonic acid diethyl ester8d 90% 102
Thiophene and maleic anhydride8a 0% 10-6
Pyrrole and 1,2,3,4,5,6-hexafluoro-bicyclo[2.2.0]hexa-2,5-diene8c >50% 104
Furan and maleic anhydride8b >50% 100
Table 1b: Experimental and calculated values of reaction enthalpy of Diels-Alder reactions using the PM3 level model.
Reaction (Table 2) Reaction enthalpy (computed) (kcal/mole) Reaction enthalpy
(experimental) (kcal/mole)
Ethylene and butadiene cycloaddition8g -52.5 -36.3
Dimerization of cyclopentadiene8h -19.3 -17+/- 1
Cycloaddition reaction of cyclopentadiene and acrolein8h -22 -19.3+/- 1.9
2-Methylfuran and maleic anhydride8f -14.69 -13.95
Tetracyanoethylene and isoprene8i -37.9 -43.8 +/- 2.8
2-Methoxyfuran and dimethylacelylene-dicarboxylate8j 25.3 26.3
Table 1c: Experimental and calculated values of the activation energy of the Diels-
Alder reactions using semi-empirical and density functional methods.
Reaction Method Activation energy (computed) (kcal/mol) Activation energy (experimental) (kcal/mol)
Endo dimerization of cyclopentadiene8k PM3 37.8 16
B3LYP 21.7
Endo cycloaddition of cyclohexadiene and methyl vinyl ketone8l PM3 31 18.4 +/- 1.4
B3LYP 22.3
Endo cycloaddition of cyclopentadiene and acrolein8k PM3 32 15
B3LYP 17.46
Endocycloaddition of cyclopentadiene and methyl vinyl ketone8l PM3 29.9 12.8 +/- 0.7
B3LYP 18.6
Table 2: Log Ke values of endo reaction between 3,4 disubstituted furan, thiophene, pyrrole and phosphole with acrolein showing the substituent effect.
Substituent -CN -C(O)OCH3 -H CH3O- (CH3)2N- System
Log Ke 2.64 2.99 3.60 2.80 3.50 Phosphole
Log Ke -10.0 -9.55 -6.83 -4.65 -5.64 Pyrrole
Log Ke -2.53 -4.59 -3.00 1.45 -1.60 Furan
Log Ke -9.92 -9.83 -8.52 -7.26 -7.78 Thiophene
Figure 1: A plot of the equilibrium constant of the Diels-Alder reaction of 3, 4- disubstituted five membered heterocyclic aromatic rings with acrolein vs p of Hammett equation.
In our kinetic studies, all calculations were done at the B3LYP/6-31G* level of treatment. Energy profiles were generated for retro-Diels-Alder reactions after optimizing the geometry and minimizing the energy. The activation energies were calculated from spreadsheets of the corresponding reaction energy profiles, an example of which is shown in Figure 2, from the difference between the transition state energy and the minimum energies of the starting materials.
As a modeling exercise we chose the acid catalyzed Diels-Alder reactions of the four heterocyclic rings (furan, thiophene, pyrrole and phosphole) with acrolein as dienophile, using only catalytic amounts of the acid to ensure the sole protonation of the acrolein oxygen, which is more basic than the heteroatom on the ring. A literature search for similar studies on these specific reactions gave no results, though in one case furan was used as a diene with a different dienophile.6b
Figure 2: Representative energy profile for a retro-Diels-Alder reaction, between thiophene and ethylene. The activation energy is computed between the barrier height and the separated molecules.
Scheme 3 illustrates the reacting systems whose activation energies we characterized.
Acid catalyzed Diels-Alder reactions are well known in current9-15 and
early16-17 literature. Various systems of Diels-Alder reactions under acid catalysis show there is endo product selectivity enhancement upon Lewis acid catalysis of the reaction.18 This has been rationalized by the finding that the p-orbital coefficient on the carbonyl carbon of acrolein becomes larger upon Lewis acid binding to the oxygen in the case of acrolein.
Upon protonation of this oxygen there is a dramatic stabilization of its LUMO, which becomes closer in energy to the HOMO of the heterocycle (Scheme 4).
This stabilization can be explained by the fact that acrolein becomes more electron deficient upon protonation, which in turn explains the lower activation energy for the catalyzed reactions, because it was found the activation energies correlate with EHOMO(diene) ELUMO(dienophile).19 The smaller the difference between EHOMO and ELUMO the smaller the activation barrier to this reaction. Table 3 shows computed values of activation energies of catalyzed and uncatalyzed Diels-Alder reactions of furan, thiophene, pyrrole and phosphole. In all four reactions there is a decrease in activation energy.
Table 3: Computed activation energies of exo and endo catalyzed and non-catalyzed Diels Alder reactions of pyrrole, phosphole, furan, and thiophene with acrolein.
Reaction Activation energy (non catalyzed) (kcal/mol) Endo Activation energy (non catalyzed) (kcal/mol)
Exo Activation energy (catalyzed) (kcal/mol)
Endo Activation energy
(catalyzed) (kcal/mol)
Exo
Pyrrole and acrolein 34.4 36.5 23.3 21.7
Phosphole and acrolein 21 23.7 12.4 18.6
Furan and acrolein 21.9 23.5 9.3 14.2
Thiophene and acrolein 29.5 31.7 22 20.2
The catalyzed reaction of pyrrole lowers the activation barrier by about 10 kcal/mol, which is comparable to the activation energy of the uncatalyzed reactions of furan and phosphole. As a result, the reactions of pyrrole and thiophene which were found to be unfavorable become more favorable upon acid catalysis, such that they are expected to proceed favorably under these conditions. Likewise the uncatalyzed reactions of furan and phosphole, which were shown earlier6 to be favorable, become even more favorable upon acid catalysis. The apparent lack of selectivity of the endo isomer for pyrrole and thiophene may be related to their more aromatic character, causing delocalization of the p-orbital participating in secondary orbital overlap. Overall we see that these results are in accord with the literature about acid catalysis of Diels-Alder reactions. This in turn puts confidence in using this modeling program to describe the reactivity of at least concerted Diels-Alder reactions.7
In summary, our work shows that we can obtain reliable thermodynamic and kinetic information about chemical reactivity and get information about reactions that have not yet been performed experimentally. Teachers can use these Spartan programs in the lecture hall as a supplementary tool to provide a visual description of factors which govern both chemical structure and reactivity
Acknowledgment
The Department of Chemistry at YSU is gratefully acknowledged for financial support and for providing computer facilities.
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