On the tunneling instability of a hypercoordinated carbocation

Kozuch, S. Phys. Chem. Chem. Phys. 2015, 17, 16688-16691
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

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⁺CH₂CH₃cation 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.

References

(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.

InChIs

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

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Dynamics and a Unified Understanding of Competitive [2,3]- and [1,2]-Sigmatropic Rearrangements Based on a Study of Ammonium Ylides

Biswas, B.; Collins, S. C.; Singleton, D. A. J. Am. Chem. Soc. 2014, 136, 3740-3743
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

While the [2-3]-sigmatropic rearrangement is well known and understood as allowed under the Woodward-Hoffmann rules, [1,2]-sigmatropic are much more rare, perhaps because they are forbidden by the same orbital symmetry arguments. It is perhaps surprising that these two rearrangements may sometimes be found in competition. Singleton has applied many of his tried-and-true techniques, namely, careful normal abundance kinetic isotope effect (KIE) analysis and molecular dynamics computations, to this problem.¹

Reaction 1 takes place exclusively through a [2,3]-rearrangement; the principle evidence is the lack of any crossover reaction. However, the slightly more substituted analogue shown in Reaction 2 gives rise to two products: that obtained from a [2,3]-rearrangement 6 and that obtained from a [1,2]-rearrangement 7.

The KIE for the rearrangement of 2 is large for the carbon breaking the bond with nitrogen, while it is small at the carbons that are forming the new bond. This becomes a metric for judging the transition state obtained with computations. With the computed TS and canonical variational transition state theory (VTST) including small curvature tunneling, the KIE can be computed from a computed structures and frequencies. This imposes a range of reasonable distances for the forming C-C bond of 2.6-2.9 Å – much longer that a typical distance in the TS of similar pericyclic reactions.

Crossover experiments for Reaction 2 are understood in terms of a reaction model whereby some fraction of the reactants undergo a concerted rearrangement to form 6, and 7 is formed by first breaking the C-N bond, forming two radicals, that either recombine right away or form isolated radicals that then collapse to product.

The interesting twist here is that one would expect two different transition states, one for the concerted process 8 and one to cleave the bond 9. Both do exist and are shown in Figure 1. However, VTST predicts that the concerted process should be 25-50 times faster than cleavage, and that does not match up with experiments. Amazingly, molecular dynamics trajectories started from the concerted TS 8 leads to cleavage about 20% of the time using UMO6-2X with a variety of basis sets. Thus, as Singleton has noted many times before, a single TS is crossed that leads to two different products! An argument based on entropy helps explain why the second (cleavage) pathway is viable.

8

9

Figure 1. UMO6-2x/6-31G* optimized structures of TS 8 and 9.

References

(1) Biswas, B.; Collins, S. C.; Singleton, D. A. "Dynamics and a Unified Understanding of Competitive [2,3]- and [1,2]-Sigmatropic Rearrangements Based on a Study of Ammonium Ylides," J. Am. Chem. Soc.2014, 136, 3740-3743, DOI: 10.1021/ja4128289.

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Entropic Intermediates and Hidden Rate-Limiting Steps in Seemingly Concerted Cycloadditions. Observation, Prediction, and Origin of an Isotope Effect on Recrossing

O. M. Gonzalez-James, E. E. Kwan, D. A. Singleton  Journal of the American Chemical Society 2012, 134, 1914 (Paywall)
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

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, 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.

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. 2011, 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.


This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.