Following up on his previous studies of isotope effects on the ring opening of cyclopropylcarbinyl radical 1 to give 2 (see my previous post), Borden now reports on its kinetic isotope effect (KIE).¹

Using the small-curvature tunneling approximation along with structures and frequencies computed at B3LYP/6-31G(d), he finds a negligible KIE at C₁, consistent with little motion of C₁ in the transition vector. The KIE for substitution at C₄ is large (k(¹²C/¹⁴C)=5.46), also consistent with its large motion in the transition vector. What is surprising is the KIE for deuterium substitution at C₁: 0.37. This is a large inverse isotope effect!

Analysis of the vibrational frequencies that involve the C₁ hydrogens provides an explanation. In going to the TS for the ring opening, both the torsional motion about the C₁-C₂ bond (making the double bond) and the pyramidal motion increase in frequency. This leads to a higher activation barrier for H than D, and the inverse isotope effect.

References

(1) Zhang, X.; Datta, A.; Hrovat, D. A.; Borden, W. T., “Calculations Predict a Large Inverse H/D Kinetic Isotope Effect on the Rate of Tunneling in the Ring Opening of Cyclopropylcarbinyl Radical,” J. Am. Chem. Soc., 2009, 131, 16002-16003, DOI: 10.1021/ja907406q.

I missed this when it came out, but Quast, Sander and Borden have made the very interesting non-Kekule diradical 1.¹

³1

The EPR spectra shows the characteristic six-line signal, with zero-field splitting parameters consistent with related triplet diradicals. The Curie-Weiss plot is linear from 4.6 to 22.9 K. These data suggest a triplet ground state. CASSCF(14,14)/6-31G* computations indicate that the triplet lies 8.5 kcal mol^-1 below the singlet. The optimized triplet geometry is shown in Figure 1. The triplet ground state is consistent with the Borden-Davidson rules for radicals.²

31

Figure 1. CASSCF(14,14)/6-31G* optimized structure of triplet 1.

References

(1) Quast, H.; Nudling, W.; Klemm, G.; Kirschfeld, A.; Neuhaus, P.; Sander, W.; Hrovat, D. A.; Borden, W. T., "A Perimidine-Derived Non-Kekule Triplet Diradical," J. Org. Chem. 2008, 73, 4956-4961, DOI: 10.1021/jo800589y.

(2) Borden, W. T.; Davidson, E. R., "Effects of electron repulsion in conjugated hydrocarbon diradicals," J. Am. Chem. Soc. 1977, 99, 4587-4594, DOI: 10.1021/ja00456a010.

InChIs

1: InChI=1/C20H27N3/c1-19(2,3)13-8-12-9-14(20(4,5)6)11-16-17(12)15(10-13)22-18(21-7)23-16/h8-11H,1-7H3,(H2,21,22,23)/f/h22-23H
InChIKey=XAKUHDACNAUAAB-PDJAEHLQCL

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-methylenebicyclo<[4.4.0]dec-1-ene: Evidence for Tunneling?," J. 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