Schreiner has written a very nice review of the role of tunneling in organic chemistry.¹ This includes tunneling in the conformations of carboxylic acids and in hydrogen abstractions. But the major emphasis is on his own group’s contributions regarding tunneling on a variety of hydroxycarbenes (see these posts: cyclopropylhydroxycarbene, methylhydroxycarbene, phenylhydroxycarbene, dihydroxycarbene, and hydroxymethylene). This led to the development of a third means for controlling reactions: not just kinetic and thermodynamic control, but tunneling control as well.

Recommended reading for anyone interested in learning how quantum mechanical tunneling can have very real-world chemical consequences.

References

(1) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunnelling control of chemical reactions – the organic chemist’s perspective," Org. Biomol. Chem., 2012, 10, 3781-3790, DOI: 10.1039/C2OB07170C.

Here are a couple of articles describing computational approaches to catalytic enantioselective reactions using variations upon the classic proline-catalyzed aldol reaction of List and Barbas¹ that started the whole parade. I have discussed the major computational papers on that system in my book (Chapter 5.3).

Yang and Wong² investigated the proline-catalyzed nitro-Michael reaction, looking at four examples, two with aldehydes and two with ketones (Reactions 1-4).

These four reactions were examined atMP2/311+G**//M06-2x/6-31G**, and PCM was also applied. The key element of this study is that they examined two different types of transition states: (a) based on the Houk-List model involving a hydrogen bond and (b) an electrostatic based model with no hydrogen bond. These are sketched in Scheme 1. For each of the reactions 1-4 there are 8 located transition states differing in the orientation of the attack on to the syn or anti enamine.

Scheme 1. TS models

The two lowest energy TS are shown in Figure 1. TS1-β1-RS is the lowest TS and it leads to the major enantiomer. The second lowest TS, TS1-β3-SR, lies 2.9 kJ mol^-1 above the other TS, and it leads to the minor enantiomer. This lowest TS is of the Houk-List type (Model A) while the other TS is of the Model B type. The enthalpies of activation suggest an ee of 54%, in reasonable
agreement with experiment.

TS1-β1-RS

TS1-β1-RS

Figure 1. M06-2x/6-31G** optimized geometries of TS1-β1-RS and TS1-β1-RS.

The computations of the other three reactions are equally good in terms of agreement with experiment, and importantly the computations indicate the reversal of stereoselection between the aldehydes and the ketones. These computations clearly implicate both the Houk-List and the non-hydrogen bonding TSs in the catalyzed Michael additions.

Houk in collaboration with Scheffler and Mahrwald investigate the use of histidine as a catalyst for the asymmetricaldol reaction.³ Examples of the histidine-catalyzed aldol are shown in Reactions 5-7.

	Reaction 5
	Reaction 6
	Reaction 7

The interesting twist here is whether the imidazole can also be involved in hydrogen bonding to the acceptor carbonyl group, serving the purpose of the carboxylic acid group in the Houk-List TS when proline is the catalyst (Model A). The transition states for these and a few other reactions were computed at M06-2x/6-31+G(d,p) including with the SMD continuum solvent model for water. The two lowest energy TSs for the reaction of isobutyraldehde and formaldehyde are shown in Figure 2; TS1 has the carboxylic acid group as the hydrogen donor while the imidazole is the donor in TS2. Of note is that these two TS are isoenergetic, indicating that both modes of stabilization are at play with histidine as the catalyst.

TS1

TS2

Figure 2. M06-2x/6-31+G(d,p) geometries of the two lowest energy TSs for the reaction of isobutyraldehde and formaldehyde catalyzed by histidine.

The possible TSs for Reactions 5-7 were also located. For example, with Reaction 5, the lowest energy TS involves the imidazole as the hydrogen donor and it leads to the major product. The lowest energy TS that leads to the minor product involves the carboxylic acid as the donor. The computed ee’s for Reactions 5-7 are in very good, if not excellent, agreement with the experimental values. The study should spur further activity in which one might tune the stereoselectivity by using catalysts with multiple binding opportunities.

References

(1) List, B.; Lerner, R. A.; Barbas, C. F., III; "Proline-Catalyzed Direct Asymmetric Aldol Reactions," J. Am. Chem. Soc., 2000, 122, 2395-2396, DOI: 10.1021/ja994280y.

(2) Yang, H.; Wong, M. W. "(S)-Proline-catalyzed nitro-Michael reactions: towards a better understanding of the catalytic mechanism and enantioselectivity," Org. Biomol. Chem.,
2012, 10, 3229-3235, DOI: 10.1039/C2OB06993H

(3) Lam, Y.-h.; Houk, K. N.; Scheffler, U.; Mahrwald, R. "Stereoselectivities of Histidine-Catalyzed Asymmetric Aldol Additions and Contrasts with Proline Catalysis: A Quantum Mechanical Analysis," J. Am. Chem. Soc. 2012, 134, 6286-6295, DOI: 10.1021/ja2118392

Once again the Singleton group reports experiments and computations that require serious reconsideration of our notions of reaction mechanisms.¹ In this paper they examine the reaction of dichloroketene with labeled cis-2-butene. With ¹³C at the 2 position of 2-butene, two products are observed, 1 and 1’, in a ratio of 1’:1 = 0.993 ± 0.001. This is the opposite what one might have imagined based on the carbonyl carbon acting as an electrophile.

The first interesting item is that B3LYP/6-31+G** fails to predict the proper structure of the transition state. It predicts an asymmetric structure 2, shown in Figure 1, while MPW1k/6-31+G**, M06, and MP2 predict a C_s transition structure 3. The C_s TS is confirmed by a grid search of M06-2x geometries with CCSD(T)/6-311++G88/PCM(CH₂Cl₂) energies.

2

3

Figure 1. Optimized TSs 2 (B3LYP/6-31+G**) and 3 (MPW1K/6-31+G**).

The PES using proper computational methods is bifurcating past TS 3, falling downhill to product 1 or 1’. Lying on the C_s plane is a second transition state that interconverts 1 and 1’. On such a surface, conventional transition state theory would predict equal amounts of 1 and 1’, i.e. no isotope effect! So they must resort to a trajectory study – which would be impossibly long if not for the trick of making the labeled carbon super-heavy – like ²⁸C,⁴⁴C, ⁷⁶C and ¹⁴⁰C and then extrapolating back to just ordinary ¹³C. These trajectories indicate a ratio of 1’:1 of 0.990 in excellent agreement with the experimental value of 0.993.

Interestingly, most trajectories recross the TS, usually by reaching into the region near the second TS. However, the recrossing decreases with increasing isotopic mass, and this leads to the isotope effect. It turns out the vibrational mode 3 breaks the C_s symmetry; movement in one direction along mode 3 has no mass dependence but in the opposite direction, increased mass leads to decreased recrossing – or put in another way, in this direction, increased mass leads more often to product.

But one can understand this reaction from a statistical point of view as well. If one looks at the free energy surface, there is a variational TS near 3, but then there is a second set of variational transition states (one leading to 1 and one to 1’) which are associated with the formation of the second C-C bond. In a sense there is an intermediate past 3 that leads to two entropic barriers, one on a path to 1 and one on the path to 1’. RRKM using this model gives a ratio of 0.992 – again in agreement with experiment! It is as Singleton notes “perplexing”; how do you reconcile the statistical view with the dynamical (trajectory) view? Singleton has no full explanation.

Lastly, they point out that a similar situation occurs in the organocatalyzed Diels-Alder reaction of MacMillan shown below.² (This reaction is also discussed in a previous post.) Now Singleton finds that the “substituent effects, selectivity, solvent effects, isotope effects and activation parameters” are all dictated by a second variational TS far removed from the conventional electronic TS.

References

(1) Gonzalez-James, O. M.; Kwan, E. E.; Singleton, D. A., "Entropic Intermediates and Hidden Rate-Limiting Steps in Seemingly Concerted Cycloadditions. Observation, Prediction, and Origin of an Isotope Effect on Recrossing," J. Am. Chem. Soc. 2012, 134, 1914-1917, DOI: 10.1021/ja208779k

(2) Ahrendt, K. A.; Borths, C. J.; MacMillan, D. W. C., "New Strategies for Organic Catalysis: The First Highly Enantioselective Organocatalytic Diels-Alder Reaction," J. Am. Chem. Soc. 2000, 122, 4243-4244, DOI: 10.1021/ja000092s.

InChIs

2-butene: InChI=1/C4H8/c1-3-4-2/h3-4H,1-2H3/b4-3-
InChIKey=IAQRGUVFOMOMEM-ARJAWSKDBO

Dichloroketene: InChI=1/C2Cl2O/c3-2(4)1-5
InChIKey=TVWWMKZMZALOFP-UHFFFAOYAY

1 (no isotope): InChI=1/C6H8Cl2O/c1-3-4(2)6(7,8)5(3)9/h3-4H,1-2H3/t3-,4+/m0/s1
InChIKey=BAEYWHUXGUIZSP-IUYQGCFVBH

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

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.

How should one add diffuse functions to the basis set? Diffuse functions are known to be critical in describing the electron distribution of anions (as discussed in my book), but they are also quite important in describing weak interactions, like hydrogen bonds, and can be critical in evaluating activation barriers and other properties.

The Truhlar group has been active in benchmarking the need of basis functions and their recent review¹ summarizes their work. In particular, they recommend that for DFT computations a minimally augmented basis set is appropriate for examining barrier heights and weakly bound systems. A minimally augmented basis set would have s and p diffuse functions on heavy atoms for the Pople split-valence basis sets and the Dunning cc-pVxZ basis sets.

For wavefunction based computations, they recommend the use of the “jun-“ basis sets. The “jun” basis set is one of the so-called calendar basis set derived from the aug-cc-pVxZ, which includes diffuse functions of all types. So, for C in the aug-cc-pVTZ basis set, there are diffuse s, p, d, and f functions. The “jun-“ basis set omits the diffuse f functions along with all diffuse functions on H.

The great advantage of these trimmed basis sets is that they are smaller than the fully augmented sets, leading to faster computations. And since trimming off some diffuse functions leads to little loss in accuracy, one should seriously consider using these types of basis sets. As Truhlar notes, these trimmed basis sets might allow one to use a partially augmented but larger zeta basis set at the same cost of the smaller zeta basis that is fully augmented.

References

(1) Papajak, E.; Zheng, J.; Xu, X.; Leverentz, H. R.; Truhlar, D. G., "Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions," J. Chem. Theory Comput., 2011,
7, 3027-3034, DOI: 10.1021/ct200106a

For those of you interested in learning about dispersion corrections for density functional theory, I recommend Grimme’s latest review article.¹ He discusses four different approaches to dealing with dispersion: (a) vdW-DF methods whereby a non-local dispersion term is included explicitly in the functional, (b) parameterized functional which account for some dispersion (like the M06-2x functional), (c) semiclassical corrections, labeled typically as DFT-D, which add an atom-pair term that typically has an r^-6 form, and (d) one-electron corrections.

The heart of the review is the comparison of the effect of including dispersion on thermochemistry. Grimme nicely points out that reaction energies and activation barriers typically are predicted with errors of 6-8 kcal mol^-1 with conventional DFT, and these errors are reduced by up to 1.5 kcal mol^-1 with the inclusion fo the “-D3” correction. Even double hybrid methods, whose mean errors are much smaller (about 3 kcal mol^-1), can be improved by over 0.5 kcal mol^-1 with the inclusion of the “-D3” correction. The same is also true for conformational energies.

Since the added expense of including the “-D3” correction is small, there is really no good reason for not including it routinely in all types of computations.

(As an aside, the article cited here is available for free through the end of this year. This new journal WIREs Computational Molecular Science has many review articles that will be of interest to readers of this blog.)

References

(1) Grimme, S., "Density functional theory with London dispersion corrections," WIREs Comput. Mol. Sci., 2011, 1, 211-228, DOI: 10.1002/wcms.30

In a follow-up to their experimental study that found that cyclobutenone is an excellent dienophile (and which I blogged about here), Danishefsky teams up with Houk and provides an insight into the reactivity.¹ In the Diels-Alder reaction of cyclopentadiene with 2-cyclohexenone, 2-cyclopentenone and cyclobutenone, the product yield increases in the order 36%, 50% and 77%. M06-2x activation enthalpies decrease in this series 15.0, 13.3 and 10.5 kcal mol^-1.

While these activation energies do not correlate with reaction energies, the activation energies do correlate nicely with the distortion energy. (Distortion energy is the energy required to distort reactants to their geometries in the transition state, but without their interaction.) Houk and Danishefsky argue that it is much easier to distort cyclobutenone to its geometry in the TS (and this distortion is primarily moving the alkenyl hydrogens out of plane, away from the incoming diene) than for the larger rings. This is due to (a) the larger s-character of the C-H bond in the smaller ring and (b) the C-C-C angle in the smaller ring is closer to the angle in the pyramidalized TS structure.

References

(1) Paton, R. S.; Kim, S.; Ross, A. G.; Danishefsky, S. J.; Houk, K. N., "Experimental Diels–Alder Reactivities of Cycloalkenones and Cyclic Dienes Explained through Transition-State Distortion Energies," Angew. Chem. Int. Ed., 2011, 44, 10366–10368, DOI: 10.1002/anie.201103998

Compounds with long C-C bonds have typically been designed by placing large, sterically bulky groups attached to the two carbons. Not only does this lead to a longer bond (like the 1.67 Å C-C bond in 1) but these bulky groups also weaken the bond. This leads to molecules that tend to be difficult to isolate.

1 R = t-But

Schreiner has taken an alternative approach: design a sterically crowded molecules that is stabilized by dispersive forces between the large groups!¹ The dimer formed from diamantane 2 was prepared and isolated. The C-C distance is quite long: 1.647 Å. The compound is stable up to at least 300 ° C.

2

Computations of 2 were performed with a variety of density functional, all of which predict a long C-C bond. The bond dissociation energy of 2 is predicted to be 43.9 kcal mol^-1 at B3LYP/6-31G(d,p), a value consistent with the long CC bond. However, B3LYP does not account for dispersion. The H^…H distances between the two diamantyl groups range from 1.94 – 2.28 Å, suggesting that there could be appreciable dispersion stabilization. In fact, computing the BDE with B3LYP+D (Grimme’s dispersion correction) or B97D or M06-2x (all of which account for dispersion to some extent), predicts a much stronger bond, with the BDE ranging from 65-71 kcal mol^-1! Here is a stable molecule with a stroing, yet long C-C bond – where a good deal of the strength results not form the interaction between the two atoms of the formal bond, but rather from the energy associated form interactions across the entire molecule. This is a true delocalization effect!

Figure 1. B3LYP-D/6-31G(d,p) optimized structure of 2.

References

(1) Schreiner, P. R.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Schlecht, S.; Dahl, J. E. P.; Carlson, R. M. K.; Fokin, A. A., "Overcoming lability of extremely long alkane carbon-carbon bonds through dispersion forces," Nature, 2011, 477, 308-311, DOI: 10.1038/nature10367.

InChIs

1: InChI=1/C86H126/c1-73(2,3)55-37-56(74(4,5)6)44-67(43-55)85(68-45-57(75(7,8)9)38-58(46-68)76(10,11)12
,69-47-59(77(13,14)15)39-60(48-69)78(16,17)18)86(70-49-61(79(19,20)21)40-62(50-70)80(22,23)24,71-51
-63(81(25,26)27)41-64(52-71)82(28,29)30)72-53-65(83(31,32)33)42-66(54-72)84(34,35)36/h37-54H,1-36H3
InChIKey=SFCRGHMFOGXDMZ-UHFFFAOYAS

2: InChI=1/C28H38/c1-13-7-23-19-3-15-4-20(17(1)19)24(8-13)27(23,11-15)28-12-16-5-21-18-2-14(9-25(21)28)
10-26(28)22(18)6-16/h13-26H,1-12H2
InChIKey=MMYAZLNWLGPULP-UHFFFAOYAU

We have all learned about aromatic substitution as proceeding via the following mechanism

(Worse yet – many of us have taught this for years!) Well, Galabov, Zou, Schaefer and Schleyer pour a whole lot of cold water on this notion in their recent Angewandte article.¹ Modeling the reaction of benzene with Br₂ and using B3LYP/6-311+G(2d,2p) for both the gas phase and PCM simulating a CCl₄ solvent, attempts to locate this standard intermediate led instead to a concerted substitution transition state TS1 (see Figure 1).

TS1

Figure 1. PCM/B3LYP/6-311+G(2d,2p) optimized transitin state along the concerted pathway

However, this is not the lowest energy pathway for substitution. Rather and addition-elimination pathway is kinetically preferred. In the first step Br₂ adds in either a 1,2 or 1,4 fashion to form an intermediate. The lower energy path is the 1,4 addition, leading to P3. This intermediate then undergoes a syn,anti-isomerization to give P5. The last step is the elimination of HBr from P5 to give the product, bromobenzene. This mechanism is shown in Scheme 2 and the critical points are shown in Figure 3.

Scheme 1

TS3	P3
TS6	P5
TS9

Figure 2. PCM/B3LYP/6-311+G(2d,2p) optimized critical points along the addition-elimination pathway

The barrier for the concerted substitution process through TS1 is 41.8 kcal mol^-1 (in CCl₄) while the highest barrier for the addition-elimination process is through TS3 of 39.4 kcal mol^-1.

Now a bit of saving grace is that in polar solvents, acidic solvents and/or with Lewis acid catalysts, the intermediate of the standard textbook mechanism may be competitive.

Textbook authors – please be aware!

References

(1) Kong, J.; Galabov, B.; Koleva, G.; Zou, J.-J.; Schaefer, H. F.; Schleyer, P. v. R., "The Inherent Competition between Addition and Substitution Reactions of Br₂ with Benzene and Arenes," Angew. Chem. Int. Ed. 2011, 50, 6809-6813, DOI: 10.1002/anie.201101852