Archive for the 'Tunneling' Category

The structure of gauche-1,3-butadiene

Sometimes you run across a paper that is surprising for a strange reason: hasn’t this work been done years before? That was my response to seeing this paper on the structure of gauche-1,3-butadiene.1 Surely, a molecule as simple as this has been examined to death. But, in fact there has been some controversy over whether the cis or gauche form is the second lowest energy conformation. Computations have indicated that the cis form is a transition state for interconverting the two gauche isomers, but experimental confirmation was probably so late in coming due to the small amount of the gauche form present and its small dipole moment.

This paper describes Fourier-transform microwave (FTMW) spectroscopy using two variants: cavity-enhanced FTMW combined with a supersonic expansion and chirped-pulse FTMW in a cryogenic buffer gas cell. In addition, computations were done at CCSD(T) using cc-pCVTZ through cc-pCV5Z basis sets and corrections for perturbative quadruples. The computed structure is shown in Figure 1. In addition to confirming this non-planar structure, with a C-C-C-C dihedral angle of 33.8°, they demonstrate the tunneling between the two mirror image gauche conformations, through the cis transition state.

Figure 1. Computed geometry of gauche-1,3-butadiene.


1. Baraban, J. H.; Martin-Drumel, M.-A.; Changala, P. B.; Eibenberger, S.; Nava, M.; Patterson, D.; Stanton, J. F.; Ellison, G. B.; McCarthy, M. C., "The Molecular Structure of gauche-1,3-Butadiene: Experimental Establishment of Non-planarity." Angew. Chem. Int. Ed. 2018, 57, 1821-1825, DOI: 10.1002/anie.201709966.


1,3-butadiene: InChI=1S/C4H6/c1-3-4-2/h3-4H,1-2H2

Tunneling Steven Bachrach 24 Apr 2018 1 Comment

Isotope Controlled Selectivity

I seem to be recently flooded with papers dealing with tunneling in organic systems. Well, here’s one more! Kozuch, Borden, Schreiner and co-workers seek out systems whereby isotopic substitution might lead to reaction selectivity.1 Their base system is cyclopropylmethylcarbene 1, which can undergo three different reactions: (a) the ring can expand to give 1-methylcyclobut-1-ene 2, (b) a hydrogen can shift from the terminal methyl group to give vinylcyclopropane 3, or (c) the methane hydrogen can shift to produce ethylidenecyclopropane 4. This last option can be neglected since its barrier (20.5 kcal mol-1) is so much higher than for the other two, 7.5 kcal mol-1 for the ring expansion and 12.1 kcal mol-1 for the [1,2]H-shift converting 13.

At high temperature, the ring expansion to 2 will dominate, but at low temperature the hydrogen shift to 3 might dominate by tunneling through the barrier due to the low mass and short distances involved. The reaction rates were computed using B3LYP/6-31G(d,p) and small-curvature tunneling. At low temperature, the rate for the hydrogen shift is 10 orders of magnitude faster than the ring expansion. Thinking that deuterium substitution of the terminal methyl group might slow down the rate of the [1,2]-shift, they computed the rates for the reactions of 1-d3, and in fact the rate of this shift does reduce by 104 but it is still much faster than the rate for ring expansion. What is needed is a system where the rate for ring expansion is slower than the rate for hydrogen migration but faster than the rate of deuterium migration.

They examine a number of different substituents that may help to lower the barrier for the ring expansion. The methoxy derivative 5 turns out to suit the bill perfectly. The methoxy group reduces the barrier for ring expansion from 7.5 kcal mol-1 with 1 to 2.5 kcal mol-1 with 5. With hydrogenated 5, the [1,2]H-shift is 103 times faster than ring expansion, but with deuterated 5, ring expansion is twice as fast as the deuterium migration.

The authors call this isotope controlled selectivity (ICS), and this is the first example of this type of control.


1. Nandi, A.; Gerbig, D.; Schreiner, P. R.; Borden, W. T.; Kozuch, S., Isotope-Controlled Selectivity by Quantum Tunneling: Hydrogen Migration versus Ring Expansion in Cyclopropylmethylcarbenes. J. Am. Chem. Soc. 2017, 139, 9097-9099, DOI: 10.1021/jacs.7b04593.


1: InChI=1S/C5H8/c1-2-5-3-4-5/h5H,3-4H2,1H3

2: InChI<=1S/C5H8/c1-5-3-2-4-5/h3H,2,4H2,1H3

3: InChI=1S/C5H8/c1-2-5-3-4-5/h2,5H,1,3-4H2

4: InChI=1S/C5H8/c1-2-5-3-4-5/h2H,3-4H2,1H3

5: InChI=1S/C6H10O/c1-3-6(7-2)4-5-6/h4-5H2,1-2H3

6: InChI<=1S/C6H10O/c1-5-3-4-6(5)7-2/h3-4H2,1-2H3

7: InChI<=1S/C6H10O/c1-3-6(7-2)4-5-6/h3H,1,4-5H2,2H3

Borden &Isotope Effects &Schreiner &Tunneling Steven Bachrach 22 Jan 2018 No Comments

Heavy-atom tunneling

Though recognized to occur in organic systems, the breadth of involvement of heavy-atom tunneling has not been established. Doubleday, Greer and coworkers have examined 13 simple organic reactions sampling pericyclic reactions, radical rearrangements and SN2 reactions for heavy-atom tunneling.1 A few of these reactions are shown below.

Reaction rates were obtained using the small curvature tunneling approximation (SCT), computed using Gaussrate. Reaction surfaces were computed at B3LYP/6-31G*. The tunneling correction to the rate was also estimated using the model developed by Bell: kBell = (u/2)/sin(u/2) where u = hν/RT and ν is the imaginary frequency associated with the transition state. The temperature was chosen so as to give a common rate constant of 3 x 10-5 s-1. Interestingly, all of the examined reactions exhibited significant tunneling even at temperatures from 270-350 K (See Table 1). The tunneling effect estimated by Bell’s equation is very similar to that of the more computationally demanding SCT computation.

Table 1. Tunneling contribution to the rate constant


% tunneling





CN + CH3Cl → CH3CN + Cl (aqueous)


This study points towards a much broader range of reactions that may be subject to quantum mechanical tunneling than previously considered.

(Note: The original post had swapped some of the values in Table 1. These have now been corrected. My thanks to Drs. Greer and Doubleday for bringing this to my attention.)


1. Doubleday, C.; Armas, R.; Walker, D.; Cosgriff, C. V.; Greer, E. M., "Heavy-Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial, and Bell’s Formula Closely Approximates Multidimensional Tunneling at ≥250 K." Angew. Chem. Int. Ed. 2017, 56, 13099-13102, DOI: 10.1002/anie.201708489.

Tunneling Steven Bachrach 04 Dec 2017 1 Comment

Perspective on Tunneling Control

Over the past nine years the Schreiner group, often in collaboration with the Allen group, have produced some remarkable studies demonstrating the role of tunneling control. (I have made quite a number of posts on this topics.) Tunneling control is a third mechanism for dictating product formation, in tandem with kinetic control (the favored product is the one that results from the lowest barrier) and thermodynamic control (the favored product is the one that has the lowest energy). Tunneling control has the favored product resulting from the narrowest mass-considered barrier.

Schreiner has written a very clear perspective on tunneling control. It is framed quite interestingly by some fascinating quotes:

It is probably fair to say that many organic chemists view the concept of tunneling, even of hydrogen atoms, with some skepticism. – Carpenter 19832

Reaction processes have been considered as taking place according to the laws of classical mechanics, quantum mechanical theory being only employed in calculating interatomic forces. – Bell 19333

Schreiner’s article makes it very clear how critical it is to really think about reactions from a truly quantum mechanical perspective. He notes the predominance of potential energy diagrams that focus exclusively on the relative energies and omits any serious consideration of the reaction coordinate metrics, like barrier width. When one also considers the rise in our understanding of the role of reaction dynamics in organic chemistry (see, for example, these many posts), just how long will it take for these critical notions to penetrate into standard organic chemical thinking? As Schreiner puts it:

It should begin by including quantum phenomena in introductory textbooks, where they are, at least in organic chemistry, blatantly absent. To put this oversight in words similar to those used much earlier by Frank Weinhold in a different context: “When will chemistry textbooks begin to serve as aids, rather than barriers, to this enriched quantum-mechanical perspective?”4


1) Schreiner, P. R., "Tunneling Control of Chemical Reactions: The Third Reactivity Paradigm." J. Am. Chem. Soc. 2017, 139, 15276-15283, DOI: 10.1021/jacs.7b06035.

2) Carpenter, B. K., "Heavy-atom tunneling as the dominant pathway in a solution-phase reaction? Bond shift in antiaromatic annulenes." J. Am. Chem. Soc. 1983, 105, 1700-1701, DOI: 10.1021/ja00344a073.

3) Bell, R. P., "The Application of Quantum Mechanics to Chemical Kinetics." Proc. R. Soc. London, Ser. A 1933, 139 (838), 466-474, DOI: 10.1098/rspa.1933.0031.

4) Weinhold, F., "Chemistry: A new twist on molecular shape." Nature 2001, 411, 539-541, DOI: 10.1038/35079225.

Schreiner &Tunneling Steven Bachrach 13 Nov 2017 No Comments

Heavy atom tunneling in semibullvalene

Another prediction made by quantum chemistry has now been confirmed. In 2010, Zhang, Hrovat, and Borden predicted that the degenerate rearrangement of semibullvalene 1 occurs with heavy atom tunneling.1 For example, the computed rate of the rearrangement including tunneling correction is 1.43 x 10-3 s-1 at 40 K, and this rate does not change with decreasing temperature. The predicted half-life of 485 s is 1010 shorter than that predicted by transition state theory.

Now a group led by Sander has examined the rearrangement of deuterated 2.2 The room temperature equilibrium mixture of d42 and d22 was deposited at 3 K. IR observation showed a decrease in signal intensities associated with d42 and concomitant growth of signals associated with d22. The barrier for this interconversion is about 5 kcal mol-1, too large to be crossed at this temperature. Instead, the interconversion is happening by tunneling through the barrier (with a rate about 10-4 s-1), forming the more stable isomer d22 preferentially. This is exactly as predicted by theory!


1. Zhang, X.; Hrovat, D. A.; Borden, W. T., "Calculations Predict That Carbon Tunneling Allows the Degenerate Cope Rearrangement of Semibullvalene to Occur Rapidly at Cryogenic Temperatures." Org. Letters 2010, 12, 2798-2801, DOI: 10.1021/ol100879t.

2. Schleif, T.; Mieres-Perez, J.; Henkel, S.; Ertelt, M.; Borden, W. T.; Sander, W., "The Cope Rearrangement of 1,5-Dimethylsemibullvalene-2(4)-d1: Experimental Evidence for Heavy-Atom Tunneling." Angew. Chem. Int. Ed. 2017, 56, 10746-10749, DOI: 10.1002/anie.201704787.


1: InChI=1S/C8H8/c1-3-6-7-4-2-5(1)8(6)7/h1-8H

d42: InChI=1S/C10H12/c1-9-5-3-7-8(4-6-9)10(7,9)2/h3-8H,1-2H3/i5D

d22: InChI=1S/C10H12/c1-9-5-3-7-8(4-6-9)10(7,9)2/h3-8H,1-2H3/i7D

Borden &Tunneling Steven Bachrach 02 Nov 2017 No Comments

Conformationally selective tunneling

The Schreiner group has again reported an amazing experimental and computational study demonstrating a fascinating quantum mechanical tunneling effect, this time for the trifluoromethylhydroxycarbene (CF3COH) 2.1 (I have made on a number of posts discussing a series of important studies in this field by Schreiner.) Carbene 2 is formed, in analogy to many other hydroxycarbenes, by flash vapor pyrolysis of the appropriate oxoacid 1 and capturing the products on a noble gas matrix.

Carbene 2t is observed by IR spectroscopy, and its structure is identified by comparison with the computed CCSD(T)/cc-pVTZ frequencies. When 2t is subjected to 465 nm light, the signals for 2t disappear within 30s, and two new species are observed. The first species is the cis conformer 2c, confirmed by comparison with its computed CCSD(T)/cc-pVTZ frequencies. This cis conformer remains even with continued photolysis. The other product is determined to be trifluoroacetaldehyde 3. Perhaps most interesting is that 2t will convert to 3 in the absence of light at temperatures between 3 and 30 K, with a half-life of about 144 h. There is little rate difference at these temperatures. These results are quite indicative of quantum mechanical tunneling.

To aid in confirming tunneling, they computed the potential energy surface at CCSD(T)/cc-pVTZ. The trans isomer is 0.8 kcal mol-1 lower in energy that the cis isomer, and this is much smaller than for other hydroxycarbenes they have examined. The rotational barrier TS1 between the two isomer is quite large, 26.4 kcal mol-1, precluding their interchange by classical means at matrix temperatures. The barrier for conversion of 2t to 3 (TS2) is also quite large, 30.7 kcal mol-1, and insurmountable at 10K by classical means. No transition state connecting 2c to 3 could be located. These geometries and energies are shown in Figure 1.






Figure 1. Optimized geometries at CCSD(T)/cc-pVTZ. Relative energies (kcal mol-1) of each species are listed as well.

WKB computations at M06-2X/6-311++G(d,p) predict a half-life of 172 h, in nice agreement with experiment. The computed half-life for deuterated 2t is 106 years, and the experiment on the deuterated analogue revealed no formation of deuterated 3.

The novel component of this study is that tunneling is conformationally selective. The CF3 group stabilizes the cis form probably through some weak HF interaction, so that the cis isomer can be observed, but no tunneling is observed from this isomer. Only the trans isomer has the migrating hydrogen atom properly arranged for a short hop over to the carbon, allowing the tunneling process to take place.


1) Mardyukov, A.; Quanz, H.; Schreiner, P. R., "Conformer-specific hydrogen atom tunnelling in trifluoromethylhydroxycarbene." Nat. Chem. 2017, 9, 71–76, DOI: 10.1038/nchem.2609.


1: =1S/C3HF3O3/c4-3(5,6)1(7)2(8)9/h(H,8,9)

2: InChI=1S/C2HF3O/c3-2(4,5)1-6/h6H

3: InChI=1S/C2HF3O/c3-2(4,5)1-6/h1H

carbenes &Schreiner &Tunneling Steven Bachrach 07 Feb 2017 2 Comments

Tunneling within a phenylnitrene

Reva and McMahon report a very nice experimental and computational study implicating hydrogen atom tunneling in the rearrangement of the nitrene 1 into the ketene 2.1 The reaction is carried out by placing azide 3 in an argon matrix and photolyzing it. The IR shows that at first a new compound A is formed and that over time the absorptions of A erode and those of a second compound B grow in. This occurs whether the photolysis continues or not over time.

IR spectra were computed at B3LYP/6-311++G(d,p) for compounds 31 and 2 and they match up very well with the recorded spectra of A and B, respectively. The triplet state of nitrenes are typically about 20 kcal mol-1 lower in energy than the singlet states. The EPR spectrum confirms that 1 is a triplet.

So how does the conversion of 31 into 2 take place, especially at 10 K? The rate constant for this conversion at 10 K is estimated as 1 x 10-5 s-1, which implies a barrier from classical transition state theory of only 0.2 kcal mol-1. That low a barrier seems preposterous, and suggests that the reaction may proceed via tunneling. This notion is supported by the experiment on the deuterated analogue, which shows no conversion of 1D into 2D.

The authors propose that 31 undergoes a hydrogen migration on the triplet surface through transition state 34 to give 32, which then undergoes intersystem crossing to give singlet 2. The structures of these critical points calculated at B3LYP/6-311++G(d,p) are shown in Figure 1. The computed activation barrier is 20.7 kcal mol-1. (The barrier height ranges from 16.7 to 23.0 with a variety of different computational methods.) This large barrier precludes a classical over-the-top reaction and points towards tunneling. The barrier width is estimated at about 2.1 Å. WKB computations estimate the tunneling half time of about 21 min, somewhat smaller than in the experiments, and the estimate for the deuterated species is 150,000 years.




Figure 1. B3LYP/6-311++G(d,p) optimized structures of 31, 32, and the TS 34.


1) Nunes, C. M.; Knezz, S. N.; Reva, I.; Fausto, R.; McMahon, R. J., "Evidence of a Nitrene Tunneling Reaction: Spontaneous Rearrangement of 2-Formyl Phenylnitrene to an Imino Ketene in Low-Temperature Matrixes." J. Am. Chem. Soc. 2016, 138, 15287-15290, DOI: 10.1021/jacs.6b07368.


1: InChI=1S/C7H5NO/c8-7-4-2-1-3-6(7)5-9/h1-5H

2: InChI=1S/C7H5NO/c8-7-4-2-1-3-6(7)5-9/h1-4,8H

Tunneling Steven Bachrach 15 Dec 2016 No Comments

Domino Tunneling

A 2013 study of oxalic acid 1 failed to uncover any tunneling between its conformations,1 despite observation of tunneling in other carboxylic acids (see this post). This was rationalized by computations which suggested rather high rearrangement barriers. Schreiner, Csaszar, and Allen have now re-examined oxalic acid using both experiments and computations and find what they call domino tunneling.2

First, they determined the structures of the three conformations of 1 along with the two transition states interconnecting them using the focal point method. These geometries and relative energies are shown in Figure 1. The barrier for the two rearrangement steps are smaller than previous computations suggest, which suggests that tunneling may be possible.






Figure 1. Geometries of the conformers of 1 and the TS for rearrangement and relative energies (kcal mol-1)

Placing oxalic acid in a neon matrix at 3 K and then exposing it to IR radiation populates the excited 1tTt conformation. This state then decays to both 1cTt and 1cTc, which can only happen through a tunneling process at this very cold temperature. Kinetic analysis indicates that there are two different rates for decay from both 1tTt and 1cTc, with the two rates associated with different types of sites within the matrix.

The intrinsic reaction paths for the two rearrangements: 1tTt1cTt and → 1cTc were obtained at MP2/aug-cc-pVTZ. Numerical integration and the WKB method yield similar half-lives: about 42 h for the first reaction and 23 h for the second reaction. These match up very well with the experimental half-lives from the fast matrix sites of 43 ± 4 h and 30 ± 20 h, respectively. Thus, the two steps take place sequentially via tunneling, like dominos falling over.


(1) Olbert-Majkut, A.; Ahokas, J.; Pettersson, M.; Lundell, J. "Visible Light-Driven Chemistry of Oxalic Acid in Solid Argon, Probed by Raman Spectroscopy," J. Phys. Chem. A 2013, 117, 1492-1502, DOI: 10.1021/jp311749z.

(2) Schreiner, P. R.; Wagner, J. P.; Reisenauer, H. P.; Gerbig, D.; Ley, D.; Sarka, J.; Császár, A. G.; Vaughn, A.; Allen, W. D. "Domino Tunneling," J. Am. Chem. Soc. 2015, 137, 7828-7834, DOI: 10.1021/jacs.5b03322.


1: InChI=1S/C2H2O4/c3-1(4)2(5)6/h(H,3,4)(H,5,6)

focal point &Schreiner &Tunneling Steven Bachrach 11 Aug 2015 1 Comment

Hypercoordinated carbon revisited

Last year I wrote a post on the possibility of a stable hypercoordinated carbon in the C(CH3)5+ molecule as proposed by Schleyer and Schaefer.1 Kozuch has re-examined this molecule with an eye towards examining the lifetime of this proposed “fleeting” molecule.2

The computed barriers for either (1) loss of a methane molecule leaving behind the (CH3)2C+CH2CH3 cation or (2) loss of an ethane molecule leaving behind the t-butyl cation are small: 1.65 and 1.37 kcal mol-1, respectively. Kozuch employed canonical variational theory with and without small curvature tunneling (SCT). Without the tunneling correction, the pentamethylmethyl cation is predicted to have a long (millennia) lifetime at very low temperatures (<20 K). However, when tunneling is included, the half-life is reduced to 6 and 40 μs for degradation along the two pathways. Clearly, this is not a fleeting molecule – its lifetime is really too short to consider it as anything.

Interestingly, perdeuterating the molecule ((CD3)5C+) substantially increases the half-life to 4 ms, a thousand-fold increase. Tritium substitution would further increase the half-life to 0.2 s – a long enough time to really identify it and perhaps justify the name “molecule”. What is perhaps the most interesting aspect here is that H/D substitution has such a large effect on the tunneling rate even though no C-H bond is broken in the TS! This results from a mass effect (a CH3 vs. a CD3 group is migrating) along with a zero-point vibrational energy effect.


(1) McKee, W. C.; Agarwal, J.; Schaefer, H. F.; Schleyer, P. v. R. "Covalent Hypercoordination: Can Carbon Bind Five Methyl Ligands?," Angew. Chem. Int. Ed. 2014, 53, 7875-7878, DOI: 10.1002/anie.201403314.

(2) Kozuch, S. "On the tunneling instability of a hypercoordinated carbocation," Phys. Chem. Chem. Phys. 2015, 17, 16688-16691, DOI: 10.1039/C5CP02080H.


C(CH3)5+: InChI=1S/C6H15/c1-6(2,3,4)5/h1-5H3/q+1

Isotope Effects &Tunneling Steven Bachrach 14 Jul 2015 No Comments

QM reflection off a barrier

Organic chemists are beginning to recognize that tunneling may be more pervasive than previously thought. This blog has noted a number of interesting occurrences of tunneling, and here’s one more, by Karmakar and Datta.1

The barrier for the intramolecular earrangement (Reaction 1) taking the carbene 1 into 2 is estimated to be 44.1 kcal mol-1 at M06-2X/6-31+G(d,p), prohibitively large. However, the intermolecular rearrangement (Reaction 2) has a much smaller barrier of 11.4 kcal mol-1. The structures of the transition states for these two reactions are shown in Figure 1.



Figure 1. M06-2X/6-31+G(d,p) optimized transition states for Reactions 1 and 2.

Given that the barrier width is likely to be very small for the intramolecular route, perhaps tunneling may play a role. The rate predicted with canonical variational transition-state theory (CVT) and small curvature tunneling (SCT) at 298K is negligible. However, for the intermolecular process, the rate at 298K including tunneling is 3.56 x 104 s-1, more than 10 times great than predicted with CVT alone, and tunneling makes a dramatically larger difference at lower temperatures.

The intermolecular barrier for the rearrangement of 3 into 4 is very small, only 1.6 kcal mol-1.
This manifests in a very interesting rate prediction: the reaction is actually predicted to be slower at temperatures above 150K when tunneling is included than when tunneling is omitted. This is a result of quantum mechanical reflection off of the barrier, and this becomes noticeable with the very small barrier. In addition, the kinetic isotope effects are smaller than expected when D is substituted in for H. These predictions await experimental confirmation.


(1) Karmakar, S.; Datta, A. "Tunneling Assists the 1,2-Hydrogen Shift in N-Heterocyclic Carbenes," Angew. Chem. Int. Ed. 2014, 53, 9587-9591, DOI: 10.1002/anie.201404368.


1: InChI=1S/C3H6N2/c1-2-5-3-4-1/h4-5H,1-2H2

2: InChI=1S/C3H6N2/c1-2-5-3-4-1/h3H,1-2H2,(H,4,5)

3: InChI=1S/C3H2F2N2/c4-2-3(5)7-1-6-2/h6-7H

4: InChI=1S/C3H2F2N2/c4-2-3(5)7-1-6-2/h1H,(H,6,7)

Tunneling Steven Bachrach 27 Oct 2014 No Comments

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