The importance of dispersion in determining molecular structure, even the structure of a single medium-sized molecule, is now well recognized. This means that quantum methods that do not account for dispersion might give very poor structures.

Grimme¹ takes an interesting new twist towards assessing the geometries produced by computational methods by evaluating the structures based on their rotational constants B₀ obtained from microwave experiments. He uses nine different molecules in his test set, shown in Scheme 1. This yields 25 different rotational constants (only one rotational constant is available from the experiment on triethylamine). He evaluates a number of different computational methods, particularly DFT with and without a dispersion correction (either the D3 or the non-local correction). The fully optimized geometry of each compound with each method is located to then the rotational constants are computed. Since this provides B_e values, he has computed the vibrational correction to each rotational constant for each molecule, in order to get “experimental” B_e values for comparisons.

Scheme 1.

Grimme first examines the basis set effect for vitamin C and aspirin using B3LYP-D3. He concludes that def2-TZVP or lager basis sets are necessary for reliable structures. However, the errors in the rotational constant obtained at B3LYP-D3/6-31G* is at most 1.7%, and even with CBS the error can be as large as 1.1%, so to my eye even this very small basis set may be completely adequate for many purposes.

In terms of the different functionals (using the DZVP basis set), the best results are obtained with the double hybrid B2PLYP-D3 functional where the mean relative deviation is only 0.3%; omitting the dispersion correction only increases the mean error to 0.6%. Common functionals lacking the dispersion correction have mean errors of about 2-3%, but with the correction, the error is appreciably diminished. In fact B3LYP-D3 has a mean error of 0.9% and B3LYP-NL has an error of only 0.6%. In general, the performance follows the Jacob’s Ladder hierarchy.

References

(1) Grimme, S.; Steinmetz, M. "Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase," Phys. Chem. Chem. Phys. 2013, 15, 16031-16042, DOI: 10.1039/C3CP52293H.

The click reaction has become a major workhorse of synthetic chemists since its proposal in 2001.¹ Despite its efficiencies, no clear-cut example of its use in nature has been reported until 2012, where Yu and co-workers speculated that it might be utilized in the biosynthesis of lycojaponicumin A and B.² Krenske, Patel, and Houk have examined the possibility of an enzyme activated click process in forming this natural product.³

First they examined the gas-phase intramolecular [3+2] reaction that takes 1 into 2.

They identified (at M06-2X/def2-TZVPP/M06-2X/6-31+G(d,p)) four different low-energy conformations of 1, of which three have the proper orientation for the cyclization to occur. The lowest energy conformer, the TS, and the product 2 are shown in Figure 1. The free energy activation barrier in the gas phase is 19.8 kcal mol^-1. Inclusion of water as an implicit solvent (through a TS starting from a different initial conformation) increases the barrier to 20.0 kcal mol^-1. Inclusion of four explicit water molecules, hydrogen bonded to the nitrone and enone, predicts a barrier of 20.5 kcal mol^-1. These values predict a slow reaction, but not totally impossible. In fact, Tantillo in a closely related work reported a theoretical study of the possibility of a [3+2] cyclization in the natural synthesis of flueggine A and virosaine, and found barriers of comparable size as here. Tantillo concludes that enzymatic activation is not essential.⁴

1

TS12

3

Table 1. M06-2X/6-31+G(d,p) optimized geometries of 1, TS12, and 2.

To model a potential enzyme, the Houk group created a theozyme whereby two water molecules act as hydrogen bond donors to the enone and the use of implicit solvent (diethyl ether) to mimic the interior of an enzyme. This theozyme model predicts a barrier of 15.3 kcal mol^-1, or a 2000 fold acceleration of the click reaction. The search for such an enzyme might prove quite intriguing.

References

(1) Kolb, H. C.; Finn, M. G.; Sharpless, K. B. "Click Chemistry: Diverse Chemical Function from a Few Good Reactions," Angew. Chem. Int. Ed. 2001, 40, 2004-2021, DOI: 10.1002/1521-3773(20010601)40:11<2004::AID-ANIE2004>3.0.CO;2-5.

(2) Wang, X.-J.; Zhang, G.-J.; Zhuang, P.-Y.; Zhang, Y.; Yu, S.-S.; Bao, X.-Q.; Zhang, D.; Yuan, Y.-H.; Chen, N.-H.; Ma, S.-g.; Qu, J.; Li, Y. "Lycojaponicumins A–C, Three Alkaloids with an Unprecedented Skeleton from Lycopodium japonicum," Org. Lett. 2012, 14, 2614-2617, DOI: 10.1021/ol3009478.

(3) Krenske, E. H.; Patel, A.; Houk, K. N. "Does Nature Click? Theoretical Prediction of an Enzyme-Catalyzed Transannular 1,3-Dipolar Cycloaddition in the Biosynthesis of Lycojaponicumins A and B," J. Am. Chem. Soc. 2013, 135, 17638-17642, DOI: 10.1021/ja409928z.

(4) Painter, P. P.; Pemberton, R. P.; Wong, B. M.; Ho, K. C.; Tantillo, D. J. "The Viability of Nitrone–Alkene (3 + 2) Cycloadditions in Alkaloid Biosynthesis," J. Org. Chem. 2014, 79, 432–435, DOI: 10.1021/jo402487d.

InChIs

1: InChI=1S/C16H21NO3/c1-11-8-12-10-14(18)13-4-2-6-17(20)7-3-5-16(12,13)15(19)9-11/h4,7,11-12H,2-3,5-6,8-10H2,1H3/b13-4-,17-7+
InChIKey=GVEYMXKHRRHCLV-KYGYAMEJSA-N

2: InChI=1S/C16H21NO3/c1-9-6-10-8-13(19)16-11(17-5-3-14(16)20-17)2-4-15(10,16)12(18)7-9/h9-11,14H,2-8H2,1H3/t9?,10-,11?,14?,15+,16-/m0/s1
InChIKey=QKFAOJHYKPBTKX-SGVNFLFUSA-N

The notion of tunneling control has been a topic of interest within this blog a number of times. As developed by Schreiner and Allen,^1,2 tunneling control is a third means for predicting (or directing) the outcome of a reaction, alongside the more traditionally recognized kinetic and thermodynamic control. Tunneling control occurs when tunneling through a higher barrier is preferred over tunneling through a lower barrier.

Kozuch and Borden propose another example of tunneling control, this time in the rearrangement of the noradamantyl carbene 1.³ This carbene can undergo a 1,2-carbon shift, driven by strain relief to form the alkene 2. The alternative as a 1,2-hydrogen shift that produces the alkene 3.

These two reaction pathways were explored using B3LYP/6-31G(d,p) computations coupled with canonical variational theory and small curvature tunneling corrections. Structures of the reactant 1 and the two transition states leading to the two products 2 and 3 are shown in Figure 1. The activation barrier at 300 K is 5.4 kcal mol^-1 leading to 2 and 8.6 kcal mol^-1 leading to 3. Tunneling is expected to be much more important for the hydrogen shift than for the carbon shift, but even including tunneling, the rate to form 2 is much faster than the rate to form 3 at 300 K.

1	TS 1→2	2
	TS 1→3	3

Figure 1. B3LYP/6 optimized structures of 1-3 and the transition states leading to 2 and 3.

The situation is reversed however at cryogenic temperatures (< 20 K). Tunneling is now the only route for the reactions to occur, and the rate for formation of 3 is dramatically greater than the rate of formation of 2, which is inhibited by the movement of the much heavier carbon atom. Perdeuteration of the methyl group of 1, which drastically slows the rate of tunneling in the path to 3, nonetheless still favors this pathway (forming d₃–3) over formation of d₃–2. Thus, at low temperatures the formation of 3 is the preferred product, a manifestation of tunneling control.

Kozuch and Borden end their paper with a hope that an experimentalist will examine this interesting case. I concur!

References

(1) Schreiner, P. R.; Reisenauer, H. P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. "Methylhydroxycarbene: Tunneling Control of a Chemical Reaction," Science 2011, 332, 1300-1303, DOI: 10.1126/science.1203761.

(2) 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.

(3) Kozuch, S.; Zhang, X.; Hrovat, D. A.; Borden, W. T. "Calculations on Tunneling in the Reactions of Noradamantyl Carbenes," J. Am. Chem. Soc. 2013, 135, 17274-17277, DOI: 10.1021/ja409176u.

InChIs

1: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h8-10H,3-7H2,1H3
InChIKey=CXFJINASYYTBBV-UHFFFAOYSA-N

2: InChI=1S/C11H16/c1-7-10-3-8-2-9(5-10)6-11(7)4-8/h8-10H,2-6H2,1H3
InChIKey=XDANPUSLLJWVEK-UHFFFAOYSA-N

3: InChI=1S/C11H16/c1-2-11-6-8-3-9(7-11)5-10(11)4-8/h2,8-10H,1,3-7H2
InChIKey=JHEPVTWREMDEMG-UHFFFAOYSA-N

The concept of antiaromaticity is an outgrowth of the well-entrenched notion or aromaticity. While 4n+2 π-electron systems are aromatic, 4n π-electron systems should be antiaromatic. That should mean that antiaromatic systems are unstable. The cyclopropenyl anion 1a has 4 π-electrons and should be antiaromatic. Kass has provided computational results that strongly indicate it is not antiaromatic!¹

Let’s first look at the 3-cyclopropenyl cation 1c. Kass has computed (at both G3 and W1) the hydride affinity of 1c-4c. The hydride affinities of the latter three compounds plotted against the C=C-C⁺ angle is linear. The hydride affinity of 1c however falls way below the line, indicative of 1c being very stable – it is aromatic having just 2 π-electrons.

A similar plot of the deprotonation enthalpies leading to 1a-4d vs. C=C-C^– angle is linear including all four compounds. If 1a where antiaromatic, one would anticipate that the deprotonation energy to form 1a would be much greater than expected simply from the effect of the smaller angle. Kass suggests that this indicates that 1a is not antiaromatic, but just a regular run-of-the-mill (very) reactive anion.

A hint at what’s going on is provided by the geometry of the lowest energy structure of 1a, shown in Figure 1. The molecule is non-planar, having C_s symmetry. A truly antiaromatic structure should be planar, really of D_3h symmetry. The distortion from this symmetry reduces the antiaromatic character, in the same way that cyclobutadiene is not a perfect square and that cyclooctatraene is tub-shaped and not planar. So perhaps it is more fair to say that 1a has a distorted structure to avoid antiaromaticity, and that the idealized D_3h structure, does not exist because of its antiaromatic character.

References

(1) Kass, S. R. "Cyclopropenyl Anion: An Energetically Nonaromatic Ion," J. Org. Chem. 2013, 78, 7370-7372, DOI: 10.1021/jo401350m.

InChIs

1a: InChI=1S/C3H3/c1-2-3-1/h1-3H/q-1
InChIKey=IBTMQWIWZUYLHW-UHFFFAOYSA-N

1c: InChI=1S/C3H3/c1-2-3-1/h1-3H/q+1
InChIKey=IPKCFGQXHZKYLH-UHFFFAOYSA-N

Naphthalene, phenanthrene and pyrene are all planar aromatic compounds. How can substituted version be chiral, with the chirality present in the aromatic portion of the molecule? The answer is provided by Yamaguchi and Kwon.¹ They prepared peri-substituted analogues with the bulky adamantly group as the substituents. This bulky requires one adamantyl group to be position above the aromatic plane and the other below the plane, as in 1 and 2.

These molecules and two other examples were prepared in their optically pure form. B3LYP/6-31G(d) computations were performed on both of these structures (shown in Figure 1), but computations are a minor component of the work. These structures do show the out-of-plane distortions at C₁ and C₈, also apparent in the crystal structures. Computations of naphthalene and 1,8-dimethylnaphthalene show a planar naphthalene backbone, but i­-propyl substitution does force the substituents out of plane.

1

2

Figure 1. B3LYP/6-31G(d) optimized structures of 1 and 2.

These types of systems continue to subject the notion of “aromaticity” to serious scrutiny.

References

(1) Yamamoto, K.; Oyamada, N.; Xia, S.; Kobayashi, Y.; Yamaguchi, M.; Maeda, H.; Nishihara, H.; Uchimaru, T.; Kwon, E. "Equatorenes: Synthesis and Properties of Chiral Naphthalene, Phenanthrene, Chrysene, and Pyrene Possessing Bis(1-adamantyl) Groups at the Peri-position," J. Am. Chem. Soc. 2013, 135, 16526-16532, DOI: 10.1021/ja407800e.

InChIs

1: InChI=1S/C30H36/c1-3-25-4-2-6-27(30-16-22-10-23(17-30)12-24(11-22)18-30)28(25)26(5-1)29-13-19-7-20(14-29)9-21(8-19)15-29/h1-6,19-24H,7-18H2
InChIKey=QNPJKZPPLCPHSS-UHFFFAOYSA-N

2: InChI=1S/C36H38/c1-2-27-4-5-28-6-7-30(35-15-21-8-22(16-35)10-23(9-21)17-35)34-31(14-29(3-1)32(27)33(28)34)36-18-24-11-25(19-36)13-26(12-24)20-36/h1-7,14,21-26H,8-13,15-20H2
InChIKey=DKRBDGNWYTWNHL-UHFFFAOYSA-N

2-deoxyribose 1 is undoubtedly one of the most important sugars as it is incorporated into the backbone of DNA. The conformational landscape of 1 is complicated: it can exist as an open chain, as a five-member ring (furanose), or a six-member ring (pyranose), and intramolecular hydrogen bonding can occur. This internal hydrogen bonding is in competition with hydrogen bonding to water in aqueous solution. Unraveling all this is of great interest in predicting structures of this and a whole host of sugar and sugar containing-molecules.

1

In order to get a firm starting point, the gas phase structures of the low energy conformers of 1 would constitute a great set of structures to use as a benchmark for gauging force fields and computational methods. Cocinero and Alonso¹ have performed a laser ablation molecular beam Fourier transform microwave (LA-MB-FTMW) experiment (see these posts for other studies using this technique) on 1 and identified the experimental conformations by comparison to structures obtained at MP2/6-311++G(d,p). Unfortunately the authors do not include these structures in their supporting materials, so I have optimized the low energy conformers of 1 at ωB97X-D/6-31G(d) and they are shown in Figure 1.

1a (0.0)	1b (4.7)
1c (3.3)	1d (5.6)
1e (8.9)	1f (9.4)

Figure 1. ωB97X-D/6-31G(d) optimized structures of the six lowest energy conformers of 1. Relative free energy in kJ mol^-1.

The computed spectroscopic parameters were used to identify the structures responsible for the six different ribose conformers observed in the microwave experiment. To give a sense of the agreement between the computed and experimental parameters, I show these values for the two lowest energy conformers in Table 1.

Table 1. MP2/6-311++G(d,p) computed and observed spectroscopic parameters for the two lowest energy conformers of 1.

This is yet another excellent example of the symbiotic relationship between experiment and computation in structure identification.

References

(1) Peña, I.; Cocinero, E. J.; Cabezas, C.; Lesarri, A.; Mata, S.; Écija, P.; Daly, A. M.; Cimas, Á.; Bermúdez, C.; Basterretxea, F. J.; Blanco, S.; Fernández, J. A.; López, J. C.; Castaño, F.; Alonso, J. L. "Six Pyranoside Forms of Free 2-Deoxy-D-ribose," Angew. Chem. Int. Ed. 2013, 52, 11840-11845, DOI: 10.1002/anie.201305589.

InChIs

1a: InChI=1S/C5H10O4/c6-3-1-5(8)9-2-4(3)7/h3-8H,1-2H2/t3-,4+,5-/m0/s1
InChIKey=ZVQAVWAHRUNNPG-LMVFSUKVSA-N

I have not discussed any papers that utilize computations to confirm chemical structure in a while, so here are two recent examples.

Grabow has utilized MP2 and M06-2x computations to confirm the lowest energy conformation of (-)-lupinine 1.¹ The interesting structural aspect of this compound is the possibility of an intramolecular hydrogen bond linking the hydroxyl group with the amine.

1

Using molecular mechanics, the authors identified 57 structures within 50 kJ mol^-1 of each other. These geometries were reoptimized at MP2/6-311++G(d,p) and M06-2x/6-311++G(d,p).
The lowest energy structures had the expected trans ring fusion, with a trans relationship between the hydrogen on the bridgehead carbon (C9) and the hydroxymethyl group. This corresponds to either the (R,R) or (S,S) isomer. The three lowest energy structures are shown in Figure 1. Unfortunately, the geometry for the lowest energy isomer provided in the Supporting Materials is wrong, and the authors did not supply the geometries of the other isomers. This situation is unacceptable! Reviewers and editors must do a better job in policing the Supporting Materials; there is no excuse for not including all of the optimized structures, and better yet, in a more usable format that what has been done here. I have reoptimized these structures at M06-2x/6-31G(d). The lowest energy conformer 1a does possess the expected internal hydrogen bond.

1a (0.0)
1b (10.4)	12 (11.5)

Figure 1. M06-2x/6-31G(d) optimized structures of the three lowest energy conformers of 1, with relative free energies in kJ mol^-1.

Table 1 provides a comparison of the MP2 computed values of important structural parameters along with the experimental values obtained from a microwave experiment. The agreement with the computed values for 1a provides strong evidence that this is the structure of (-)-lupinine.

Table 1. Comparison of MP2 and experimental structural parameters of 1.^a

^aRotational constants (A, B, C) in MHz, centrifugal distortion constants (Δ_J, Δ_JK, Δ_K) in kHz, and nuclear quadrupole coupling tensor elements (χ_aa, χ_bb, χ_cc) in MHz.

The second study utilizes computed NMR chemical shifts to discriminate potential diastereomeric structures. Laurefurenyne A was first assigned the structure 2 based on 1D and 2D NMR experiments. However, based on potential biochemical analogy to other compounds, Paton and Burton² had doubts about this structure. In addition to synthesizing the natural material, they performed an extensive computational study of the chemical shifts of the diastereomers. For each of the 32 possible diastereomers, they performed a Monte Carlo search of the conformational space using molecular mechanics. The structures of all isomers within 10 kJ mol^-1 of the lowest energy structure were reoptimized at ωB97X-D/6-31G(d) with PCM (CHCl₃) and chemical shifts obtained at mPW1PW91/6-311G(d,p). Final chemical shifts were obtained using a Boltzmann weighting. The computed values for 2 were quite off from the experimental values, with a mean unsigned error of 1.5 ppm. A better assessment was provided with the DP4 method, which indicated that 3 has the highest probability of being the correct structure, a structure consistent with the likely biosynthetic pathway.

References

(1) Jahn, M. K.; Dewald, D.; Vallejo-López, M.; Cocinero, E. J.; Lesarri, A.; Grabow, J.-U. "Rotational Spectra of Bicyclic Decanes: The Trans Conformation of (-)-Lupinine," J. Phys. Chem. A 2013, DOI: 10.1021/jp407671m.

(2) Shepherd, D. J.; Broadwith, P. A.; Dyson, B. S.; Paton, R. S.; Burton, J. W. "Structure Reassignment of Laurefurenynes A and B by Computation and Total Synthesis," Chem. Eur. J. 2013, 19, 12644-12648, DOI: 10.1002/chem.201302349.

InChIs

(-)-Lupinine 1: InChI=1S/C11H21NO/c1-11-6-2-3-7-12(11)8-4-5-10(11)9-13/h10,13H,2-9H2,1H3/t10-,11+/m0/s1
InChIKey=WVDUAOYJLFVEMW-WDEREUQCSA-N

Laurefurenyne A 3: InChI=1S/C14H20O4.C2H6/c1-3-4-5-6-12-11(16)8-14(18-12)13-7-10(15)9(2)17-13;1-2/h1,4-5,9-16H,6-8H2,2H3;1-2H3/b5-4-;/t9-,10-,11-,12+,13-,14+;/m1./s1
InChIKey=ZYESDGGYHKCHMJ-SKFGUVSTSA-N

Suppose you are looking at the reaction aA + bB → cC + dD. You can compute each of these molecules at two computational levels; lets call these M1 and M2. Then the reaction energy is

Now, if the two computational methods are reasonably complete, then ΔE^M1 ≈ ΔE^M2. This can also be true if the reaction has been selected such that one might expect very good cancellation of errors. In this case, the overall problems in computing the reactants are similar to the problems computing the products, and so these problems (i.e., errors) will cancel off. So, if we have the latter condition (a reaction constructed to obtain excellent cancellation of errors), then we might be able to exploit this idea in order to obtain energies of large molecules with a large method while avoiding to actually have to do these very large computations!

How does this work? Let’s suppose the largest molecule in the reaction is molecule C. Since

then

and so

So, we can get the energy of the big molecule C at the big method M1 by computing the energy of the big molecule C at the smaller method M2 along with computing all of the other molecules at both levels. If these other molecules are significantly smaller than molecule C, there can be considerable time savings here. This is the idea presented in a recent article by Raghavachari.¹

The key element here is a systematic means for generating appropriate reactions, ones that (a) involve small molecules other than the molecule of interest and (b) get good cancellation of errors. Raghavachari comes up with a systematic way of creating a reaction with ever larger reference molecules. This is analogous with the methodology presented by Wheeler, Schleyer and Allen.² Basically, the method decomposes the molecule of interest into smaller molecules that preserve the immediate chemical environment around each heavy atom, a method they call CBH-2 (connectivity-based hierarchy). The reaction below is an example of the CBH-2 decomposition reaction for methionine. (Note that CBH-2 is essentially a homodesmotic reaction and CBH-3 is essentially the group equivalent reaction I defined years ago.³)

They apply the concept towards computing the energy of larger molecules (having 6-13 heavy atoms) at CCSD(T)/6-31+G(d,p) by only having to compute these large molecules at MP2/6-31+G(d,p). For a set of 30 molecules, the error in the energy of the extrapolated energy vs. the actual CCSD(T) energy is 0.35 kcal mol^-1.

One of the advantages of this approach is that the small molecules are used over and over again, but they need be computed only twice, once at CCSD(T) and once at MP2.

This is certainly an approach that has been implicitly employed by many people for a long time, but here is made explicit and points towards ways to apply it even more widely.

References

(1) Ramabhadran, R. O.; Raghavachari, K. "Extrapolation to the Gold-Standard in Quantum Chemistry: Computationally Efficient and Accurate CCSD(T) Energies for Large Molecules Using an Automated Thermochemical Hierarchy," J. Chem. Theor. Comput. 2013, ASAP DOI: 10.1021/ct400465q.

(2) Wheeler, S. E.; Houk, K. N.; Schleyer, P. v. R.; Allen, W. D. “A Hierarchy of Homodesmotic Reactions for Thermochemistry,” J. Am. Chem. Soc. 2009, 131, 2547-2560, DOI: 10.1021/ja805843n.

(3) Bachrach, S. M. “The Group Equivalent Reaction: An Improved Method for Determining Ring Strain Energy,” J. Chem. Ed. 1990, 67, 907-908, DOI: 10.1021/ed067p90.

Can one identify a labile bond in a molecule without computing activation barriers? Markopoulos and Grunenberg suggest that examination of the bond length and its associated relaxed force constant might provide some guidance.¹

The relaxed force constant comes from identifying the force constant for some coordinate while allowing for other coordinates to relax. Badger’s rule relates the (normal) force constant to bond distance (k = a/(r_eq – d)³). For a series of 36 molecules, covering 71 C-C single bonds, Badger’s rule fits the data well, except for a set of molecules which undergo rapid Cope rearrangements (like bullvalene and semibullvalene). For these molecules, the relaxed force constants are much lower than Badger’s rule predicts, and indicates a weakened bond. This gives rise to their low activation barriers.

Another example is provided with the highly strained polycyclic hydrocarbon 1. This compound is predicted (B3LYP/6-31G(d)) to undergo a [1,2]-shift to give the carbene 2 (see Figure 1), and this is extremely exothermic: -105.7 kcal mol^-1, reflecting the enormous strain of 1. The barrier, through TS1 (Figure 1), is only 6.7 kcal mol^-1. This rearrangement was predicted by examining the relaxed force constants which identified a very weak bond, despite a short bond distance of 1.404 Å. It is unlikely that without this guidance, one would have predicted that this short bond is likely to rupture and produce this particular product.

1	2
TS1

Figure 1. B3LYP/6-31G(d) optimized structures of 1, 2, and TS1.

References

(1) Markopoulos, G.; Grunenberg, J. "Predicting Kinetically Unstable C-C Bonds from the Ground-State Properties of a Molecule," Angew. Chem. Int. Ed. 2013, 52, 10648-10651, DOI: 10.1002/anie.20130382.

InChIs

1: InChI=1S/C14H12/c1-2-8-11-5-3-9-7(1)10(9)4-6-12(8,11)14(8,11)13(7,9)10/h1-6H2
InChIKey=LNBZAENQMFDBJW-UHFFFAOYSA-N

2: InChI=1S/C14H12/c1-3-11-12-4-2-9-7-8(1,9)10(9)5-6-13(11,12)14(10,11)12/h1-6H2
InChIKey=UKVODHRLGFPZPT-UHFFFAOYSA-N

Sorry I missed this paper from much earlier this year – it’s from a journal that’s not on my normal reading list. Anyways, here is another fantastic work from the Schreiner lab demonstrating the concept of tunneling control (see this post).¹ They prepare the t-butylhydroxycarbene 1 at low temperature to look for evidence of formation of possible products arising from a [1,2]-hydrogen shift (2), a [1,2]-methyl shift (3) or a [1,3]-CH insertion (4).

Schreiner performed CCSD(T)/cc-pVDZ optimizations of these compounds along with the transition states for the three migrations. The optimized geometries and relative energies are shown in Figure 1. The thermodynamic product is the aldehyde 2 while the kinetic product is the cyclopropane 4, with a barrier of 23.8 kcal mol^-1 some 3.5 kcal mol^-1 lower than the barrier leading to 2.

1 (0.0)	TS2 (27.3)	2 (-53.5)
	TS3 (31.0)	3 (-41.0)
	TS4 (23.8)	4 (-28.3)

Figure 1. CCSD(T)/cc-pVDZ optimized structures of 1-4 and the transition states for the three reaction. Relative energies in kcal mol^-1.

At low temperature (11 K), 1 is found to slowly convert into 2 with a half-life of 1.7 h. No other product is observed. Rates for the three reactions were also computed using the Wentzel-Kramers-Brillouin (WKB) method (which Schreiner and Allen have used in all of their previous studies). The predicted rate for the conversion of 1 into 2, which takes place at 11 K solely through a tunneling process, is 0.4h, in quite reasonable agreement with experiment. The predicted rates for the other two potential reactions at 11 K are 10³¹ and 10⁴⁰ years.

This is clearly an example of tunneling control. The reaction occurs not across the lowest barrier, but through the narrowest barrier.

References

(1) Ley, D.; Gerbig, D.; Schreiner, P. R. "Tunneling control of chemical reactions: C-H insertion versus H-tunneling in tert-butylhydroxycarbene," Chem. Sci. 2013, 4, 677-684, DOI: 10.1039/C2SC21555A.

InChI

1: InChI=1S/C5H10O/c1-5(2,3)4-6/h6H,1-3H3
InChIKey=ZGFKBRGJTPEEOC-UHFFFAOYSA-N

2: InChI=1S/C5H10O/c1-5(2,3)4-6/h4H,1-3H3

3: InChI=1S/C5H10O/c1-4(2)5(3)6/h6H,1-3H3
InChIKey=BZAZNULYLRVMSW-UHFFFAOYSA-N

4: InChI=1S/C5H10O/c1-5(2)3-4(5)6/h4,6H,3H2,1-2H3
InChIKey=MWWQKEGWQLBJBJ-UHFFFAOYSA-N