Inverted carbon atoms, where the bonds from a single carbon atom are made to four other atoms which all on one side of a plane, remain a subject of fascination for organic chemists. We simply like to put carbon into unusual environments! Bremer, Fokin, and Schreiner have examined a selection of molecules possessing inverted carbon atoms and highlights some problems both with experiments and computations.¹

The prototype of the inverted carbon is propellane 1. The ­C_inv-C_inv bond distance is 1.594 Å as determined in a gas-phase electron diffraction experiment.² A selection of bond distance computed with various methods is shown in Figure 1. Note that CASPT2/6-31G(d), CCSD(t)/cc-pVTZ and MP2 does a very fine job in predicting the structure. However, a selection of DFT methods predict a distance that is too short, and these methods include functionals that include dispersion corrections or have been designed to account for medium-range electron correlation.

CASPT2/6-31G(d) CCSD(T)/cc-pVTZ MP2/cc-pVTZ MP2/cc-pVQZ B3LYP/6-311+G(d,p) B3LYP-D3BJ/6-311+G(d,p) M06-2x/6-311+G(d,p)	1.596 1.595 1.596 1.590 1.575 1.575 1.550

Figure 1. Optimized Structure of 1 at MP2/cc-pVTZ, along with C_inv-C_inv distances (Å) computed with different methods.

Propellanes without an inverted carbon, like 2, are properly described by these DFT methods; the C-C distance predicted by the DFT methods is close to that predicted by the post-HF methods.

The propellane 3 has been referred to many times for its seemingly very long C_inv-C_inv bond: an x-ray study from 1973 indicates it is 1.643 Å.³ However, this distance is computed at MP2/cc-pVTZ to be considerably shorter: 1.571 Å (Figure 2). Bremer, Fokin, and Schreiner resynthesized 3 and conducted a new x-ray study, and find that the C_inv-C_inv distance is 1.5838 Å, in reasonable agreement with the computation. This is yet another example of where computation has pointed towards experimental errors in chemical structure.

Figure 2. MP2/cc-pVTZ optimized structure of 3.

However, DFT methods fail to properly predict the C_inv-C_inv distance in 3. The functionals B3LYP, B3LYP-D3BJ and M06-2x (with the cc-pVTZ basis set) predict a distance of 1.560, 1.555, and 1.545 Å, respectively. Bremer, Folkin and Schreiner did not consider the ωB97X-D functional, so I optimized the structure of 3 at ωB97X-D/cc-pVTZ and the distance is 1.546 Å.

Inverted carbon atoms appear to be a significant challenge for DFT methods.

References

(1) Bremer, M.; Untenecker, H.; Gunchenko, P. A.; Fokin, A. A.; Schreiner, P. R. "Inverted Carbon Geometries: Challenges to Experiment and Theory," J. Org. Chem. 2015, 80, 6520–6524, DOI: 10.1021/acs.joc.5b00845.

(2) Hedberg, L.; Hedberg, K. "The molecular structure of gaseous [1.1.1]propellane: an electron-diffraction investigation," J. Am. Chem. Soc. 1985, 107, 7257-7260, DOI: 10.1021/ja00311a004.

(3) Gibbons, C. S.; Trotter, J. "Crystal Structure of 1-Cyanotetracyclo[3.3.1.1^3,7.0^3,7]decane," Can. J. Chem. 1973, 51, 87-91, DOI: 10.1139/v73-012.

InChIs

1: InChI=1S/C5H6/c1-4-2-5(1,4)3-4/h1-3H2
InChIKey=ZTXSPLGEGCABFL-UHFFFAOYSA-N

3: InChI=1S/C11H13N/c12-7-9-1-8-2-10(4-9)6-11(10,3-8)5-9/h8H,1-6H2
InChIKey=KTXBGPGYWQAZAS-UHFFFAOYSA-N

I remain amazed at how regularly I read reports of structure determinations of what seem to be simple molecules, yet these structures have eluded determination for decades if not centuries. An example is the recently determined x-ray crystal structure of L-phenylalanine;¹ who knew that growing these crystals would be so difficult?

The paper I want to discuss here is on the gas-phase structure of carbonic acid 1.² Who would have thought that preparing a pure gas-phase sample would be so difficult? Schreiner and co-workers prepared carbonic acid by high-vacuum flash pyrolysis (HVFP) of di-tert-butyl carbonate, as shown in Scheme 1.

Scheme 1

Carbonic acid can appear in three difference conformations, shown in Figure 1. The two lowest energy conformations are separated by a barrier of 9.5 kcal mol^-1 (estimated by focal point energy analysis). These conformations can be interconverted using near IR light. The third conformation is energetically inaccessible.

1cc (0.0)	1ct (1.6)	1tt (10.1)
2cc		2cc

Figure 1. CCSD(T)/cc-pVQZ optimized structures of 1 (and the focal point relative energies in kcal mol^-1) and the CCSD(T)/cc-pVTZ optimized structures of 2.

The structures of these two lowest energy conformations were confirmed by comparing their experimental IR spectra with the computed spectra (CCSD(T)/cc-pVTZ) and their experimental and computed rotational constants.

An interesting added component of this paper is that sublimation of the α- and β-polymorphs of carbonic acid do not produce the same compound. Sublimation of the β-isomorph does produce 1, but sublimation of the α-isomorph produces the methylester of 1, compound 2 (see Figure 1). The structure of 2 is again confirmed by comparison of the experimental and computed IR spectra.

References

(1) Ihlefeldt, F. S.; Pettersen, F. B.; von Bonin, A.; Zawadzka, M.; Görbitz, C. H. "The Polymorphs of L-Phenylalanine," Angew. Chem. Int. Ed. 2014, 53, 13600–13604, DOI: 10.1002/anie.201406886.

(2) Reisenauer, H. P.; Wagner, J. P.; Schreiner, P. R. "Gas-Phase Preparation of Carbonic Acid and Its Monomethyl Ester," Angew. Chem. Int. Ed. 2014, 53, 11766-11771, DOI: 10.1002/anie.201406969.>

InChIs

1: InChI=1S/CH2O3/c2-1(3)4/h(H2,2,3,4)
InChIKey=BVKZGUZCCUSVTD-UHFFFAOYSA-N

2: InChI=1S/C2H4O3/c1-5-2(3)4/h1H3,(H,3,4)
InChIKey=CXHHBNMLPJOKQD-UHFFFAOYSA-N

Twistane 1 is a more strained isomer of adamantane 2. The structure of 1 is shown in Figure 1.

1

Figure 1. B3LYP/6-31G(d) optimized structure of 1.

Adamantane is the core structure of diamond, which can be made by appending isobutene groups onto adamantane. In an analogous fashion, twistane can be extended in a linear way by appending ethano groups in a 1,4-bridge. Allen, Schreiner, Trauner and co-workers have examined this “polytwistane” using computational techniques.¹ They examined a (CH)₂₃₆ core fragment of polytwistane, with the dangling valences at the edges filled by appending hydrogens, giving a C₂₃₆H₂₄₂ compound. This compound was optimized at B3LYP/6-31G(d) and shown in Figure 2a. (Note that I have zoomed in on the structure, but by activating Jmol – click on the figure – you can view the entire compound.) A fascinating feature of polytwistane is its helical structure, which can be readily seen in Figure 2b. A view down the length of this compound, Figure 2c, displays the opening of this helical cylinder; this is a carbon nanotube with an inner diameter of 2.6 Å.

(a)

(b)

(c)

Figure 2. B3LYP/6-31G(d) structure of the C₂₃₆H₂₄₂ twistane. (a) A zoomed in look at the structure. This structure links to the Jmol applet allowing interactive viewing of the molecule – you should try this! (b) a side view clearly showing its helical nature. (c) A view down the twistane showing the nanotube structure.

Though the molecule looks quite symmetric, each carbon is involved in three C-C bonds, and each is of slightly different length. The authors go through considerable detail about addressing the symmetry and proper helical coordinates of polytwistane. They also estimate a strain energy of about 1.6 kcal mol^-1 per CH unit. This modest strain, they believe, suggests that polytwistanes might be reasonable synthetic targets.

References

(1) Barua, S. R.; Quanz, H.; Olbrich, M.; Schreiner, P. R.; Trauner, D.; Allen, W. D. "Polytwistane," Chem. Eur. J. 2014, 20, 1638-1645, DOI: 10.1002/chem.201303081.

InChIs

1: InChI=1S/C10H16/c1-2-8-6-9-3-4-10(8)5-7(1)9/h7-10H,1-6H2
InChIKey=AEVSQVUUXPSWPL-UHFFFAOYSA-N

2: InChI=1S/C10H16/c1-7-2-9-4-8(1)5-10(3-7)6-9/h7-10H,1-6H2
InChIKey=ORILYTVJVMAKLC-UHFFFAOYSA-N

Schreiner provides another beautiful example of the important role that dispersion plays, this time in a biological system.¹ The microbe Candidatus Brocadia Anammoxidans oxidizes ammonia with nitrite. This unusual process must be done anaerobically and without allowing toxic side products, like hydrazine to migrate into the cellular environment. So this cell has a very dense membrane surrounding the enzymes that perform the oxidation. This dense membrane is home to some very unusual lipids, such as 1. These lipids contain the ladderane core, a highly strained unit. Schreiner hypothesized that these ladderane groups might pack very well and very tightly due to dispersion.

1

The geometries of the [2]- through [5]-ladderanes and their dimers were optimized at MP2/aug-cc-pVDZ, and the binding energies corrected for larger basis sets and higher correlation effects. The dimers were oriented in their face-to-face orientation (parallel-displaced dimer, PDD) or edge-to-edge (side-on dimer, SD). Figure 1 shows the optimized structures of the two dimeric forms of [4]-ladderane.

[4]-PDD

[4]-SD

Figure 1. MP2/aug-cc-pVDZ optimized geometries of the dimers of [4]-ladderane in the PDD and SD orientations.

The binding energies of the ladderane dimers, using the extrapolated energies and at B3LYP-D3/6-311+G(d,p), are listed in Table 1. (The performance of the B3LYP-D3 functional is excellent, by the way.)The binding is quite appreciable, greater than 6 kcal mol^-1 for both the [4]- and [5]-ladderanes. Interestingly, these binding energies far exceed the binding energies of similarly long alkanes. So, very long alkyl lipid chains would be needed to duplicate the strong binding. Nature appears to have devised a rather remarkable solution to its cellular isolation problem!

References

(1) Wagner, J. P.; Schreiner, P. R. "Nature Utilizes Unusual High London Dispersion
Interactions for Compact Membranes Composed of Molecular Ladders," J. Chem. Theor. Comput. 2014, 10, 1353-1358, DOI: 10.1021/ct5000499.

InChIs

1: InChI=InChI=1S/C20H30O2/c21-15(22)7-5-3-1-2-4-6-11-10-14-16(11)20-18-13-9-8-12(13)17(18)19(14)20/h11-14,16-20H,1-10H2,(H,21,22)/t11-,12-,13+,14-,16+,17+,18-,19-,20+/m0/s1
InChIKey=ZKKJRZDMLYQUNK-QIPWGTBCSA-N

[2]-ladderane: InChI=1S/C6H10/c1-2-6-4-3-5(1)6/h5-6H,1-4H2/t5-,6+
InChIKey=YZLCEXRVQZNGEK-OLQVQODUSA-N

[3]-ladderane: InChI=1S/C8H12/c1-2-6-5(1)7-3-4-8(6)7/h5-8H,1-4H2/t5-,6+,7+,8-
InChIKey=YTZCZYFFHKYOBJ-SOSBWXJGSA-N

[4]-ladderane: InChI=1S/C10H14/c1-2-6-5(1)9-7-3-4-8(7)10(6)9/h5-10H,1-4H2/t5-,6+,7+,8-,9-,10+
InChIKey=VZHFDSXKIJOCAY-UXAOAXNSSA-N

[5]-ladderane: InChI=1S/C12H16/c1-2-6-5(1)9-10(6)12-8-4-3-7(8)11(9)12/h5-12H,1-4H2/t5-,6+,7-,8+,9+,10-,11-,12+
InChIKey=CWUAAECPDWVJSU-SBBGGFAWSA-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

Schreiner has expanded on his previous paper¹ regarding alkanes with very long C-C bonds, which I commented upon in this post. He and his colleagues report² now a series of additional diamond-like and adamantane-like sterically congested alkanes that are stable despite have C-C bonds that are longer that 1.7 Å (such as 1! In addition they examine the structures and rotational barriers using a variety of density functionals.

For 2, the experimental C-C distance is 1.647 Å. A variety of functionals all using the cc-pVDZ basis predict distances that are much too long: B3LYP, B96, B97D, and B3PW91. However, functionals that incorporate some dispersion, either through an explicit dispersion correction (Like B3LYP-D and B2PLYP-D) or with a functional that address mid-range or long range correlation (like M06-2x) or both (like ωB97X-D) all provide very good estimates of this distance.

On the other hand, prediction of the rotational barrier about the central C-C bond of 2 shows different functional performance. The experimental barrier, determined by ¹H and ¹³C NMR is 16.0 ± 1.3 kcal mol^-1. M06-2x, ωB97X-D and B3LYP-D, all of which predict the correct C-C distance, overestimate the barrier by 2.5 to 3.5 kcal mol^-1, outside of the error range. The functionals that do the best in getting the rotational barrier include B96, B97D and PBE1PBE and B3PW91. Experiments and computations of the rotational barriers of the other sterically congested alkanes reveals some interesting dynamics, particularly that partial rotations are possible by crossing lower barrier and interconverting some conformers, but full rotation requires passage over some very high barriers.

In the closing portion of the paper, they discuss the possibility of very long “bonds”. For example, imagine a large diamond-like fragment. Remove a hydrogen atom from an interior position, forming a radical. Bring two of these radicals together, and their computed attraction is 27 kcal mol^-1 despite a separation of the radical centers of more than 4 Å. Is this a “chemical bond”? What else might we want to call it?

A closely related chemical system was the subject of yet another paper³ by Schreiner (this time in collaboration with Grimme) on the hexaphenylethane problem. I missed this paper somehow near
the end of last year, but it is definitely worth taking a look at. (I should point out that this paper was already discussed in a post in the Computational Chemistry Highlights blog, a blog that acts as a journals overlay – and one I participate in as well.)

So, the problem that Grimme and Schreiner³ address is the following: hexaphenylethane 3 is not stable, and 4 is also not stable. The standard argument for their instabilities has been that they are simply too sterically congested about the central C-C bond. However, 5 is stable and its crystal structure has been reported. The central C-C bond length is long: 1.67 Å. But why should 5 exist? It appears to be even more crowded that either 3 or 4. TPSS/TZV(2d,2p) computations on these three compounds indicate that separation into the two radical fragments is very exoergonic. However, when the “D3” dispersion correction is included, 3 and 4 remain unstable relative to their diradical fragments, but 5 is stable by 13.7 kcal mol^-1. In fact, when the dispersion correction is left off of the t-butyl groups, 5 becomes unstable. This is a great example of a compound whose stability rests with dispersion attractions.

3: R₁ = R₂ = H
4: R₁ = tBu, R₂ = H
5: R₁ = H, R₂ = tBu

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

(2) Fokin, A. A.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Dahl, J. E. P.; Carlson, R. M. K.; Schreiner, P. R. "Stable Alkanes Containing Very Long Carbon–Carbon Bonds," J. Am. Chem. Soc., 2012, 134, 13641-13650, DOI: 10.1021/ja302258q

(3) Grimme, S.; Schreiner, P. R. "Steric Crowding Can tabilize a Labile Molecule: Solving the Hexaphenylethane Riddle," Angew. Chem. Int. Ed., 2011, 50, 12639-12642, DOI: 10.1002/anie.201103615

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.

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

As we have noted in many previous posts, Schreiner has observed tunneling in hydroxycarbenes that is either very rapid (1a-c) or not at all (1d-f).^1-4 In a recent paper his group investigates whether cyclopropylhydroxycarbene 2 might have an intermediate lifetime due to the π-donating effect of the three-member ring.⁵

Schreiner makes this carbene in his usual manner: flash pyrolysis of the cyclopropylglyoxylic acid. Let’s now consider three possible rearrangements of carbene 2. The hydrogen can migrate (Scheme 1, path a) to give cyclopropylcarboxyaldehyde 3 similar to what was observed with the related hydroxycarbenes. Carbon can migrate (Scheme 1, path b), opening up the three-member ring to give the cyclobutenol 4. This ring could open to the diene 5 and tautomerize to the ketone 6. Lastly, a hydrogen migration from carbon (Scheme 1, path c) would lead to 7. The relative energies of these species computed at CCSD(T)//cc-pVTZ//M06-2x//6-311++G(d,p) are shown in Scheme 1.

Scheme 1. Relative energies in kcal mol^-1.

The computed barriers for the initial step of each pathway is +30.4 kcal mol^-1 for path a, +21.9 kcal mol^-1 for path b and +35.8 kcal mol^-1 for path c. Thus, one might expect to see only the reaction along path b at low temperature and mostly along b at high temperature with some small percent along path a. So what actually occurs?

After capturing the flash pyrolysis product in an Ar matrix, besides the unreacted cyclopropylglyoxylic acid, 6, 3, and 2 are observed in an approximate 8:5:1 ratio. 2 is identified on the basis of the nice agreement between the experimental and computed IR frequencies. Irradiation of 2 in the matrix leads to clean conversion to 4, also identified by comparison of the observed and computed IR frequencies. This is all consistent with the computed activation barriers. In the pyrolysis, at high T, 6 is the major product and 3 is the minor product. At very low T (11 K), irradiation of 2 produces 4 (crossing only the lowest barrier) and not continuing further along the rearrangement path to 6.

What is perhaps most exciting is that 2 disappears slowly in the dark at both 11 K and 20 K, converting at the same rate to 3. The half life is 17.7 h, much longer than for the alkyl and aryl substituted hydroxycarbenes 1a-c. This confirms the stabilization effect of the cyclopropyl group, as does its large singlet-triplet gap. The computed tunneling half-life using the WKB approach is 16.6 h, in excellent agreement with experiment. And as expected for a tunneling phenomenon, the dueterated analog has a much longer half-life, computed to be 10⁵ years. Experimentally, 2-d persists with no conversion to 3-d observed.

As with methylhydroxycarbene, we see here an example of tunneling control vs kinetic control. At high T, the reaction crosses the lowest barrier (shown in Figure 1a), proceeding to 4 and subsequent rearrangement products. At low T, the reaction crosses a higher barrier (shown in Figure 1b), but this path involves tunneling of the very light hydrogen atom only, producing 3.

TS 2 → 3

TS 2 → 4

Figure 1. M06-2X/6-311++G(d,p) optimized geometry of the transition states connecting 2 to (a) 3 and (b) 4.

References

(1) Schreiner, P. R.; Reisenauer, H. P.; Pickard Iv, F. C.; Simmonett, A. C.; Allen, W. D.; Matyus, E.; Csaszar, A. G., "Capture of hydroxymethylene and its fast disappearance through tunnelling," Nature, 2008, 453, 906-909, DOI: 10.1038/nature07010.

(2) Schreiner, P. R.; Reisenauer, H. P., "Spectroscopic Identification of Dihydroxycarbene," Angew. Chem. Int. Ed., 2008, 47, 7071-7074, DOI: 10.1002/anie.200802105

(3) Gerbig, D.; Reisenauer, H. P.; Wu, C.-H.; Ley, D.; Allen, W. D.; Schreiner, P. R., "Phenylhydroxycarbene," J. Am. Chem. Soc., 2010, 132, 7273-7275, DOI: 10.1021/ja9107885

(4) 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.

(5) Ley, D.; Gerbig, D.; Wagner, J. P.; Reisenauer, H. P.; Schreiner, P. R., "Cyclopropylhydroxycarbene," J. Am. Chem. Soc., 2011, 133, 13614-13621, DOI: 10.1021/ja204507j

Another remarkable piece of science from the Schreiner and Allen groups has appeared demonstrating the critical importance of combining experiment with computations.¹ (This one will surely be in the running for computational chemistry paper of the year.) Once again they examine tunneling from a carbene intermediate, but this time with an amazing conclusion that will have impact on chemistry textbooks!

Schreiner and Allen have previously examined a number of hydroxycarbenes (see these posts: A, B, C) and have found tunneling to be the main exit channel from these carbenes. The tunneling passes through barriers that are as large as 30 kcal mol^-1, and as expected, the deuterium labeled analogues have tunneling half lives that are exceptionally long, like 4000 years.

Now they examine methylhydroxycarbene 1,¹ which is interesting because there are two possible exit channels, leading to acetaldehyde 2 or vinyl alcohol 3. Previous gas-phase pyrolysis of pyruvic acid suggested the intermediacy of 1, which rearranges to 2 much more rapidly than to 3. However, G1 computations predict the barrier to 3 is smaller than the barrier to 2,² which should mean that 2 is the kinetic product!

Methylhydroxycarbene 1 was prepared by flash pyrolysis of pyruvic acid with capture of the products in an argon matrix. The carbene 1 was characterized by IR. The predicted frequencies (CCSD(T)/cc-pCVTZ – with corrections for anharmonicity) of 9 of the 11 bands of 1 are within 8 cm^-1 of the experimental frequencies. The OH and OD stretches, the ones not in agreement, are likely to be perturbed by the matrix. The predicted (MRCC/aug-cc-pVTZ) and experimental UV spectrum are also in close agreement.

Holding the matrix at 11 K and following the spectra of 1-3 led to the following important kinetic results: the half-life for formation of 2 is 66 min with no 3 observed to form. In addition, the rate for the deuterium labeled carbene to form 2 was too long for measuring, but was 196 minutes in Kr and 251 minutes in Xe. CCSD(T)/cc-pCVCZ computations followed by focal point methods gives the barrier to form acetaldehyde from 1 as 28.0 kcal mol^-1 while that to form vinyl alcohol 3 is much lower: 22.6 kcal mol^-1. (The structures of these three molecules and the transition states connecting them are shown in Figure 1.) Apparently, the reaction passes through or over the higher barrier in large preference over passing through or over the lower barrier!

1
TS12	2
TS13	3

Figure 1. CCSD(T)/cc-pCVTZ optimizes structures of 1-3 and the transition states connecting 1 to 2 and 1 to 3.

Precise mapping of the intrinsic reaction path at CCSD(T)/cc-pCVTZ allows for computing the WKB tunneling probabilities. This leads to the prediction of the half-life for the reaction 1 → 2 as 71 minutes, in excellent agreement with experiment. The computed half-life for the deuterium labeled reaction of 400 years and the computed half-life for 1 → 3 of 190 days are both in fine agreement with experiment.

Why does the reaction preferentially tunnel through the higher barrier? Well, the tunneling rate is dependent on the square root of the barrier height and linearly on the barrier width. The width is much smaller for the rearrangement to 2. The hydrogen needs to move a shorter amount in proceeding from 1to 2 than to 3, and in the rearrangement to vinyl alcohol a second hydrogen must migrate downwards to form the planar vinyl group. Basically, width beats out the height.

The important conclusion from this paper is the following: in addition to reactions being under kinetic or thermodynamic control, we must now consider a third options – a reaction under tunneling control!

A nice perspective on this paper and its implications has been written by Carpenter, who points out how this adds to our general notion of significant limitations to transition state theory.³

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) Smith, B. J.; Nguyen Minh, T.; Bouma, W. J.; Radom, L., "Unimolecular rearrangements connecting hydroxyethylidene (CH₃-C-OH), acetaldehyde (CH₃-CH:O), and vinyl alcohol (CH₂:CH-OH)," J. Am. Chem. Soc., 1991, 113, 6452-6458, DOI: 10.1021/ja00017a015

(3) Carpenter, B. K., “Taking the High Road and Getting There Before You,” Science, 2011, 332, 1269-1270, DOI: 10.1126/science.1206693.

InChIs

1: InChI=1/C2H4O/c1-2-3/h3H,1H3
InChIKey=JVKQHDUTAFISFX-UHFFFAOYAN

2: InChI=1/C2H4O/c1-2-3/h2H,1H3
InChIKey=IKHGUXGNUITLKF-UHFFFAOYAB

3: InChI=1/C2H4O/c1-2-3/h2-3H,1H2
InChIKey=IMROMDMJAWUWLK-UHFFFAOYAT