Calculations Predict a Large Inverse H/D Kinetic Isotope Effect on the Rate of Tunneling in the Ring Opening of Cyclopropylcarbinyl Radical Page: 16,003
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calculated increases are 380.1-101.8 cm-1 = 278.3 cm-1 for C1D2
torsion and 561.4-414.1 cm-1 = 147.3 cm-1 for C1D2 pyramidal-
ization. Consequently, the net increase in the ZPEs for these two
vibrations on going from 1 to the TS for ring opening to 2 is 212.8
cm- = 0.61 kcal/mol for C1D2. Thus, the sum of the increases in
these two ZPEs is smaller by 0.25 kcal/mol for C1D2 than for C1H2.
The calculated increases in the unscaled harmonic frequencies
in going from 1 to the TS for its ring opening to 2 occur in
vibrational coordinates that are orthogonal to the reaction coordinate.
Therefore, the effect of the change in either frequency on the
difference between the ZPEs in 1 and the TS for ring opening can
be depicted schematically as in Figure 1.
Figure 1. Schematic depiction of the effect on AHo*, the effective height
of the barrier through which tunneling must occur, of a vibration, orthogonal
to the reaction coordinate, which increases in frequency in going from the
reactant to the TS. If the increase in the ZPE that is associated with this
vibration is greater for H than for D, and if motion of H and D along the
reaction coordinate is negligible, an inverse H/D KIE on tunneling can occur,
since AHo*(H) is greater than AHo*(D).
For passage over the reaction barrier, the difference between
AH0o(H) and AH0o(D) gives rise to a temperature-dependent,
secondary, H/D KIE. In the rearrangement of 1 to 2 the difference
between the calculated, zero-point-inclusive barrier heights for H2
and for D2 at C1 is 0.24 kcal/mol, which is almost the same as the
0.25 kcal/mol sum of the differences between the changes in ZPEs
for torsion about the bond between C1 and C2 and for pyramidal-
ization at C1. At 20 K the effect of the 0.24 kcal/mol difference
between the effective barrier heights for H and D gives rise to a
very large, inverse, CVT KIE at C1 of k(H)/k(D) = 0.0023 for
passage over the barrier.13 As shown in Table 1, the same difference
in effective barrier heights is calculated to give rise to a smaller,
inverse KIE at C1 of k(H)/k(D) = 0.37 on the rate of tunneling.
Isotopic substitution at C2, C3, and C4 affects the KIEs for
tunneling in two ways. The substitution of a heavier for a lighter
isotope not only increases the effective tunneling mass but also, as
shown schematically in Figure 1, alters the effective barrier height
through which tunneling occurs. For example, rehybridization of
C3 on ring opening results in a 0.06 kcal/mol decrease in the
effective barrier height upon substitution of D2 for H2 at this carbon.
This decrease, coupled with the small amount of motion of C3 in
the transition vector,11 causes the H/D KIE for substitution of D2
for H2 at C3 to be inverse, rather than normal, unlike the isobaric
substitution of 14C for 12C at this carbon.
Obtaining experimental ratios of rate constants that would be
precise enough to compare with the predicted KIEs in Table 1 might
be difficult, due to the differences between the rates at which
molecules at different types of sites react in matrix isolation.'4
However, the ratios of the KIEs at C3 and C4 in Table 1 predict
whether it is the isotopically substituted or unsubstituted C-C bond
in 1 that preferentially cleaves. After chemical trapping of 2,
accurate measurements of the ratio of isotopes at these two carbons
could be made. Assay of the distribution of 13C at C3 and C4 in the
product by natural-abundance 13C NMR should be particularly easy.
Such experiments are underway, and the results will be reported
in due course.15
Supporting Information Available: The optimized UB3LYP/6-
31G(d) geometries and energies for 1, 2, and the transition structure
connecting them; the CVT and SCT rate constants for ring opening of
1 to 2; and complete lists of authors for refs 9 and 10. This material is
available free of charge via the Internet at http://pubs.acs.org.
Acknowledgment. We thank the National Science Foundation
and the Robert A. Welch Foundation for support of this research.
Some of the results reported here were obtained on computers,
purchased with funds provided by the National Science Foundation
under Grant CHE-0741936.
(1) Reviews:(a) Bell, R. P. The Tunneling Effect in Chemistry; Chapman and
Hall: London and New York, 1980. (b) Isotope Effects in Chemistry and
Biology; Kohen, A. Limbach, H.-H., Eds.; Taylor and Francis: Boca Raton,
FL, 2006. (c) Hynes, J. T., Klinman, J. P., Limbach, H.-H., Schowen, R. L.
Hydrogen Transfer Reactions, Vols. 1-4; Wiley-VCH: Weinhein, 2007.
(d) Sheridan, R. S. In Reviews in Reactive Intermediate Chemistry; Moss,
R. A., Platz, M. S., Jones, M. J., Jr., Eds.; John Wiley & Sons: New York,
2007; pp 415-64.
(2) (a) Newcomb, M.; Glenn, A. G. J. Am. Chem. Soc. 1989, 111, 275. (b)
Maillard, B.; Forrest, D.; Ingold, K. U. J. Am. Chem. Soc. 1976, 98, 7024.
(c) Beckwith, A. L. J.; Bowry, V. W.; Moad, G. J. Org. Chem. 1988, 53,
(3) Datta, A.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2008, 130,
(4) (a) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (b) Lee, C.; Yang, W.;
Parr, R. G. Phys Rev. B 1988, 37, 78. (c) Miehlich, B.; Savin, A.; Stoll,
H.; Preuss, H. Chem. Phys. Lett. 1989, 157, 200.
(5) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213.
(6) Truhlar, D. G.; Garrett, B. C. Annu. Rev. Phys. Chem. 1984, 35, 159.
(7) Fernandez-Ramos, A.; Ellingson, B. A.; Garrett, B. C.; Truhlar, D. G. In
Reviews in Computational Chemistry, 23; Lipkowitz, K. B., Cundari, T. R.,
Eds.; Wiley-VCH: Hoboken, NJ, 2007; pp 125-232.
(8) Corchado, J. C.; Chuang, Y.-Y.; Coitino, E. L.; Truhlar, D. G. GAUSSRATE-
version 9.5; University of Minnesota: Minneapolis, MN, 2007.
(9) Frisch, M. J.; Gaussian 03, revision D.02; Gaussian, Inc.: Wallingford,
(10) Corchado, J. C.; POLYRATE, version 9.5; University of Minnesota:
Minneapolis, MN, 2007.
(11) An animation of the transition vector for conversion of 1 to 2 is available
(12) The change in ZPE of 1.69 kcal/mol between 1 and 2 for these modes is,
as expected, larger.
(13) However, at 20 K the rate constant for passage of 1 over the barrier is
calculated to be k = 2.54 x 10-72 s-, compared to k = 2.22 10-2 s-1
for tunneling through the barrier.3 Therefore, at 20 K, no molecules actually
do react by passage over the barrier.
(14) See, for example: Sponsler, M. B.; Jain, R.; Comns, F. D.; Dougherty, D. A.
J. Am. Chem. Soc. 1989, 111, 2240.
(15) James, O.; Hrovat, D. A., Borden, W. T., Singleton, D. A. To be submitted
J. AM. CHEM. SOC. VOL. 131, NO. 44, 2009 16003
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Zhang, Xue; Datta, Ayan; Hrovat, David A. & Borden, Weston T. Calculations Predict a Large Inverse H/D Kinetic Isotope Effect on the Rate of Tunneling in the Ring Opening of Cyclopropylcarbinyl Radical, article, October 15, 2009; [Washington, DC]. (digital.library.unt.edu/ark:/67531/metadc71808/m1/2/: accessed January 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.