The [1,5]-H migration in cyclopentadiene seems like it should be a very ordinary reaction. A molecular dynamics study by Carpenter at first glance appears to confirm this notion.¹ Trajectories studies show that the ratio of endo:exo migration is very close to 1:1, suggesting, as expected, statistical behavior. However, inspection of the time dependence of the endo to exo migration shows oscillatory behavior. This oscillation corresponds to the B₁ vibration that effectively flips the methylene group through the ring plane and interchanges the exo and endo hydrogens. The hydrogen preferentially migrates from the endo position, with the ring bent by typically 10°, a point far from the computed [1,5]-H migration transition state (which is planar).

Differential damping this B₁ vibration should then lead to variable endo:exo ratios, and Carpenter suggests that performing this reaction in the gas phase and in solution with different solvent viscosities should exhibit such a variable ratio. The experiment awaits an experimenter!

Once again the take-home message is that dynamics matter, even in seemingly simple and well-understood processes. Reactions can take place far from the nominal transition state and the consequences can be significant.

References

(1) Goldman, L. M.; Glowacki, D. R.; Carpenter, B. K., "Nonstatistical Dynamics in Unlikely Places: [1,5] Hydrogen Migration in Chemically Activated Cyclopentadiene," J. Am. Chem. Soc. 2011, 133, 5312-5318, DOI: 10.1021/ja1095717

One of the great challenges to computational chemistry and computational biochemistry is rational design of enzymes. Baker and Houk have been pursuing this goal and in their recent paper they report progress towards an enzyme designed to catalyze a Diels-Alder reaction.¹

They envisaged an enzyme that could catalyze the Diels-Alder of 1 with 2 by having a suitable hydrogen bond acceptor of the carbamide proton of 1 (such as the carbonyl oxygen of glutamine or asparagine) along with a suitable donor to the oxygen of 2 (such as the hydroxyl of tyrosine, serine or threonine) – as shown below. Along with positioning the diene and dienophile near each other and properly orienting them for reaction, the activation barrier should be lowered by narrowing the HOMO-LUMO gap.

A series of transition states for the Diels-Alder reaction of 1 with 2 along with the hydrogen-bonded amino acids were optimized B3LYP/6-31+G(d,p) and used as constraints within the RosettaMatch code for locating a protein scaffold that could accommodate this TS structure. This resulted in 84 protein designs, each of which were synthesized and screened for activity in catalyzing the Diels-Alder reaction. Of these potential enzymes, 50 were soluble and of these 50, only 2 showed any activity. These two were selectively mutated to try to improve activity, and some improvement was obtained.

Of particular note is that mutation that removed one or both of the residues designed to hydrogen bond to the substrates resulted in complete loss of activity.

In principle 8 different steriosomeric products are possible in the reaction of 1 with 2. In solution in the absence of enzyme, four products are observed, with the major product (47%) the 3R,4S endo prodcut 3. The designed enzymes were constructed to make this product, and in fact it is the only observed stereoisomer formed in the reaction in the presence of enzyme. Furthermore, the designed enzymes are quite selective; for example, changing a single N-methyl group to N-ethyl on 2 reduced the rate by a factor of 2 and larger substituents resulted in a greater rate suppression.

Turnover rate is high and suggests that these enzymes might have real application in chemical synthesis. The disappointing aspect of the study was the poor ratio of predicted enzymes (84) to ones that actually had activity (2).

References

(1) Siegel, J. B.; Zanghellini, A.; Lovick, H. M.; Kiss, G.; Lambert, A. R.; St.Clair, J. L.; Gallaher, J. L.; Hilvert, D.; Gelb, M. H.; Stoddard, B. L.; Houk, K. N.; Michael, F. E.; Baker, D., "Computational Design of an Enzyme Catalyst for a Stereoselective Bimolecular Diels-Alder Reaction," Science, 2010, 329, 309-313, DOI: 10.1126/science.1190239

I missed this short communication last year, (thanks to the computational chemistry list CCL for bringing this to our attention!) but it is worth commenting on even a year later as this topic is one that frequently confuses users.

Ho, Klamt, and Coote¹ note that popular quantum chemistry codes, including the Gaussian series, present the output of continuum solvent models in a way that can be misleading. What is called the free energy is in fact the sum of the electronic energy in solution and the free energy associated with non-electrostatic contributions. What is missing are corrections to the solute to give its free energy. What is assumed (oftentimes without fully recognizing this assumption) is that the thermal corrections for the solute in the gas and solution phase will cancel – but this does not have to be. Let the QM code user (and reader of the literature) beware!

References

(1) Ho, J.; Klamt, A.; Coote, M. L., "Comment on the Correct Use of Continuum Solvent Models," J. Phys. Chem. A 2010, 114, 13442-13444, DOI: 10.1021/jp107136j

Suppose a compound could exist in one of two ways: (a) a symmetrical structure like the bromonium cation A or (b) equilibrating structures that on a time-average basis appear symmetrical, like B. How would one differentiate between these two possibilities?

Saunders developed a method whereby the species is isotopically labeled and then examined by NMR.^1-3 For case B, isotopic labeling will desymmetrize the two structures and so the chemical shifts of what were equivalent nuclei will become (often quite) different. But the isotopic labeling of A, while breaking the symmetry, does so to a much lesser extent, and the chemical shit difference of the (former) equivalent nuclei will be similar.

Singelton has employed this concept using both experiment and theory for two interesting cases.⁴ For the bromonium cation 1, Ohta⁵ discovered that the ¹³C NMR chemical shifts differed by 3.61 ppm with the deuterium labels. This led Ohta to conclude that the bomonium cation is really two equilibrating structures. It should be noted that the DFT optimized structure has C_2v symmetry (a single symmetric structure). Singleton applied a number of theoretical methods, the most interesting being an MD simulation of the cation. A large number of trajectories were computed and then the NMR shifts were computed at each point along each trajectory to provide a time-averaged difference in the chemical shifts of 4.8 ppm. Thus 2 can express a desymmetrization even though the unlabled structure is symmetric. This desymmetrization is due to coupling of vibrational modes involving the isotopes.

The second example is phthalate 2. Perrin observed a large ¹⁸O chemical shift difference upon isotopic labeling of one of the oxygen atoms, suggesting equilibrating structures.⁶ An MD study of such a system would take an estimated 1500 processor-years. Instead, by increasing the mass of the label to ²⁴O, the trajectories could be computed in a more reasonable time, and this would result in an isotope effect that is 4 times too large. The oxygen chemical shifts of more the 2.5 million trajectory points were computed for the two labeling cases, and each again showed a large chemical shift difference even though the underlying structure is symmetrical.

Thus, isotopic labeling can desymmetrize a symmetrical potential energy surface.

References

(1) Saunders, M.; Kates, M. R., "Isotopic perturbation of resonance. Carbon-13 nuclear magnetic resonance spectra of deuterated cyclohexenyl and cyclopentenyl cations," J. Am. Chem. Soc., 1977, 99, 8071-8072, DOI: 10.1021/ja00466a061

(2) Saunders, M.; Telkowski, L.; Kates, M. R., "Isotopic perturbation of degeneracy. Carbon-13 nuclear magnetic resonance spectra of dimethylcyclopentyl and dimethylnorbornyl cations," J. Am. Chem. Soc., 1977, 99, 8070-8071, DOI: 10.1021/ja00466a060

(3) Saunders, M.; Kates, M. R.; Wiberg, K. B.; Pratt, W., "Isotopic perturbation of resonance. Carbon-13 nuclear magnetic resonance of 2-deuterio-2-bicyclo[2.1.1]hexyl cation," J. Am. Chem. Soc., 1977, 99, 8072-8073, DOI: 10.1021/ja00466a062

(4) Bogle, X. S.; Singleton, D. A., "Isotope-Induced Desymmetrization Can Mimic
Isotopic Perturbation of Equilibria. On the Symmetry of Bromonium Ions and Hydrogen Bonds," J. Am. Chem. Soc., 2011, 133, 17172-17175, DOI: 10.1021/ja2084288

(5) Ohta, B. K.; Hough, R. E.; Schubert, J. W., "Evidence for β-Chlorocarbenium and β-Bromocarbenium Ions," Organic Letters, 2007, 9, 2317-2320, DOI: 10.1021/ol070673n

(6) Perrin, C. L., "Symmetry of hydrogen bonds in solution," Pure Appl. Chem., 2009, 81, 571-583, DOI: 10.1351/PAC-CON-08-08-14.