Wes Borden has been exploring reactions where tunneling is operational. These studies have been inspired by Bill Doering’s¹ statement regarding tunneling in 1,5-sigmatropic shifts: “The tunneling effect is likely, in the opinion of some, to remain relegated to the virtual world of calculations”. Borden’s first two papers dealt with the kinetic isotope effects for the [1,5]-H shift in 1,3-cyclopentadiene and 5-methyl-1,3-cyclopentadiene.^2,3

His latest article examines carbon tunneling,⁴ which, due to the much heavier mass of the carbon nucleus relative to a proton, is likely to play a minimal role at best. Borden looked at the ring opening of cyclopropylcarbinyl radical 1 to 3-butene-1-yl radical 2, passing through transition state TS1-2. The B3LYP/6-31G(d) optimized structures are shown in Figure 1.

1		2
1	TS1-2	2

Figure 1. B3LYP/6-31G(d) optimized geometries of 1, 2, and TS1-2.⁴

The predicted rate of the reaction at 298 K using canonical variational transition state theory is increased by about 50% when small-curvature tunneling is included. This predicted rate is a bit smaller than the experimental value. Experiments also shows a linear Arrhenius plot, and Borden’s calculations agree until one reaches very low temperatures. Below 150 K the Arrhenius curve begins to deviate from linearity, and below 20 K the curve is flat – the rate is no longer temperature dependent! Thus, at cryogenic temperatures, the tunneling rate far exceeds traditional crossing of the variational barrier. Borden hopes that experimentalists will reinvestigate this problem (and hopefully confirm his predictions).

References

(1) Doering, W. v. E.; Zhao, X., "Effect on Kinetics by Deuterium in the 1,5-Hydrogen Shift of a Cisoid-Locked 1,3(Z)-Pentadiene, 2-Methyl-10-methylenebicycloJ. Am. Chem. Soc., 2006, 128, 9080-9085, DOI: 10.1021/ja057377v.

(2) Shelton, G. R.; Hrovat, D. A.; Borden, W. T., "Tunneling in the 1,5-Hydrogen Shift Reactions of 1,3-Cyclopentadiene and 5-Methyl-1,3-Cyclopentadiene," J. Am. Chem. Soc., 2007, 129, 164-168, DOI: 10.1021/ja0664279.

(3) Shelton, G. R.; Hrovat, D. A.; Borden, W. T., "Calculations of the Effect of Tunneling on the Swain-Schaad Exponents (SSEs) for the 1,5-Hydrogen Shift in 5-Methyl-1,3-cyclopentadiene. Can SSEs Be Used to Diagnose the Occurrence of Tunneling?," J. Am. Chem. Soc., 2007, 129, 16115-16118, DOI: 10.1021/ja076132a.

(4) Datta, A.; Hrovat, D. A.; Borden, W. T., "Calculations Predict Rapid Tunneling by Carbon from the Vibrational Ground State in the Ring Opening of Cyclopropylcarbinyl Radical at Cryogenic Temperatures," J. Am. Chem. Soc., 2008, 130, 6684-6685, DOI: 10.1021/ja801089p.

InChIs

1: InChI=1/C4H7/c1-4-2-3-4/h4H,1-3H2

2: InChI=1/C4H7/c1-3-4-2/h3H,1-2,4H2

I concluded the subchapter on pseudopericyclic reaction (Chapter 3.4) with a discussion of the controversy concerning the nature of the electrocyclization of 7-azahepta-1,2,4,6-tetraene 1. Quickly summarizing form the book, based on which data one deems important, the reaction can be seen as either pericyclic or pseudopericyclic.

However, I offered David Birney’s opinion as perhaps the proper way to interpret this reaction. David suggested that the TS has both pericyclic and pseudopericyclic character. I wrote that “what we have is a continuum from pericyclic to pseudopericyclic character, analogous to the S_N1 to S_N2 continuum for nucleophilic substitution”.

Duncan has revisited this reaction,¹ employing both B3LYP and CASSCF(10,9) computations. He concludes that the reaction is “neither purely pericyclic nor pseudopericyclic” – just as Birney had indicated. Duncan does offer the possibility of a secondary orbital interaction involving the nitrogen lone pair. But it is nice to see confirmation of the interpretation that David originated for my book!

References

(1) Duncan, J. A.; Calkins, D. E. G.; Chavarha, M., "Secondary Orbital Effect in the Electrocyclic Ring Closure of 7-Azahepta-1,2,4,6-tetraene – A CASSCF Molecular Orbital Study,", J. Am. Chem. Soc., 2008, 130, 6740-6748, DOI: 10.1021/ja074402j.

InChIs

1: InChI=1/C6H7N/c1-2-3-4-5-6-7/h3-7H,1H2/b5-4-,7-6+
InChIKey=VCEMZTODUGWAPF-SCFJQAPRBS

2: InChI=1/C6H7N/c1-6-4-2-3-5-7-6/h2-5,7H,1H2
InChIKey=JGSLKNWXPRDWBA-UHFFFAOYAH

The search for the elusive hypervalent carbon atom took an interesting turn for the positive with the report of the synthesis and characterization of 1 and especially its dication 2.¹ The x-ray structure was obtained for both compounds along with computing their B3PW91/6-31G(d) geometries. These computed geometries are shown in Figure 1.

1	2
1	2

Figure 1. B3PW91/6-31G(d) optimized geometries of 1 and 2.¹

The allene fragment is bent in both structures: 168.5° (169.9° at B3PW91) in 1 and 166.8° (172.7° at B3PW91) in 2. The distances between the central carbon atom of the allene and the four oxygen atoms are 2.66 to 2.82 Å, and computed to be a little longer. Interestingly, these distance contract when the dication 2 is created; ranging from 2.64 to 2.75 Å (again computed to be a little longer). These distances, while significantly longer than normal covalent C-O bonds, are less than the sum of the C and O van der Waals radii. But are they really bonds?

This is not a trivial answer to solve. The authors opt to employ topological electron density analysis (Bader’s atoms-in-molecules approach). Using the electron density from both the high resolution x-ray density map and from the DFT computations, bond paths between the central allene carbon and each oxygen are found, though with, as expected, low values of ρ. The Laplacian of the density at the critical point are positive, indicative of ionic interactions. So according to Bader’s model, the existence of a bond path in a ground state molecule is the necessary and sufficient condition for bonding.

The others conclude by proposing that O^…C intermolecular interactions with separations of around 2.6 to 2.8 Å may also suggest hypervalent cases. They note that about 2000 structures in the Cambridge crystallographic database fit this criterion.

References

(1) Yamaguchi, T.; Yamamoto, Y.; Kinoshita, D.; Akiba, K.-y.; Zhang, Y.; Reed, C. A.; Hashizume, D.; Iwasaki, F., "Synthesis and Structure of a Hexacoordinate
Carbon Compound," J. Am. Chem. Soc., 2008, 130, 6894-6895, DOI: 10.1021/ja710423d.

InChIs

1: InChI=1/C31H24O4S2/c1-32-20-9-5-13-24-28(20)18(29-21(33-2)10-6-14-25(29)36-24)17-19-30-22(34-3)11-7-15-26(30)37-27-16-8-12-23(35-4)31(19)27/h5-16H,1-4H3
InChiKey= RJBVLFYVIBCWKW-UHFFFAOYAD

2: InChI=1/C33H30O4S2/c1-34-22-11-7-15-26-30(22)20(31-23(35-2)12-8-16-27(31)38(26)5)19-21-32-24(36-3)13-9-17-28(32)39(6)29-18-10-14-25(37-4)33(21)29/h7-18H,1-6H3/q+2
InChIKey= MVHOSIVPHPDYJJ-UHFFFAOYAM