Secondary deuterium kinetic isotope effects in the rotations of alkenes and allyl Radicals: Theory and experiment

Article abstract of DOI:10.1021/ja952046b

Secondary deuterium kinetic isotope effects (KIEs) associated with restricted rotation about the C-C bonds of ethylene, propene, and allyl radical substituted by H or D were calculated. Geometries and force constants of ground states and transition states

Full text of DOI:10.1021/ja952046b

886
J. Am. Chem. Soc. 1996, 118, 886-892
Secondary Deuterium Kinetic Isotope Effects in the Rotations
of Alkenes and Allyl Radicals: Theory and Experiment
Leif P. Olson,† Satomi Niwayama,† Hi-Young Yoo,† K. N. Houk,*,†
Nathan J. Harris,§ and Joseph J. Gajewski§
Contribution from the Department of Chemistry and Biochemistry, UniVersity of California,
Los Angeles, California 90095, and the Department of Chemistry, Indiana UniVersity,
Bloomington, Indiana 47405
ReceiVed June 22, 1995X
Abstract: Secondary deuterium kinetic isotope effects (KIEs) associated with restricted rotation about the C-C
bonds of ethylene, propene, and allyl radical substituted by H or D were calculated. Geometries and force constants
of ground states and transition states were obtained by ab initio MCSCF calculations with the 6-31G* and/or 6-311G**
basis sets. The KIEs were then calculated from the partition functions for the Bigeleisen equation. The “rotational”
KIEs are predicted to be larger than typical secondary KIEs. For simple alkenes, predicted kH/kD values range from
1.32-1.46 at 25 °C to 1.15-1.25 at 275 °C. Predicted values are compared with existing experimental results. As
a test of our prediction that high-temperature alkene isomerizations should display large KIEs, samples of cis-
stilbene and R,R′-dideuterio-cis-stilbene were pyrolyzed; the measured KIE was a remarkable kH/kD2 ) 1.47 ( 0.13
(σn) at 287 °C.
Introduction
Secondary deuterium kinetic isotope effects which were
interpreted as arising mainly from rotational motions of isotopic
substituents have been observed in a number of reactions.
Examples are product-determining KIEs in the formation of
methylenecyclopropanes from partially deuterated trimethylene-
methane biradicals1 and large rate effects on the {1,3} sigma-
tropic shifts of vinylcyclopropanes,2 cyclopropylallene,3 and
vinylcyclobutanes4 upon deuteration of exo-methylene groups.
In a few cases, the experiments were accompanied by semiem-
pirical quantum mechanical calculations.
Figure 1. The Caldwell et al. reaction for which kH/kD ) 2.5
theoretically by Halevi and Wolfsberg using an AM1/CI method
(kH/kD4 ) 1.17 at 220 ˚C).9
Recently, Perrin et al. measured deuterium KIEs upon C-N
rotation in a series of substituted formamides.10 Their experi-
ments were stimulated in part by the surprisingly large
magnitude of the experimental and theoretical KIEs reported
by Caldwell et al.5 The amide KIEs were smaller (at least
within a given temperature range) than those seen in alkenes;
this supported Perrin’s hypothesis that either Caldwell’s trans-
cycloalkene might be a nonrepresentative case or that the alkene
experiments might be in error. We carried out ab initio
theoretical studies of rotation of formamides11 and obtained
results in good agreement with experiments.
In order to better compare the amide and alkene rotational
isotope effects, it is desirable to study KIEs of alkene rotation
theoretically using ab initio methods. As pointed out by Perrin
et al.,10 amides remain closed-shell species throughout C-N
bond rotation, and these KIEs are therefore well-represented
by restricted Hartree-Fock methods. However, such calcula-
tions inadequately describe singlet biradicals, such as the 1,2-
biradicals encountered in thermal cis-trans isomerizations of
alkenes. In this work, we have employed MCSCF ab initio
methods12 to calculate the geometries and force constants of
open-shell species encountered in alkene and allyl radical bond
rotation. MCSCF calculations have been previously reported
Caldwell et al. observed kH/kD ) 2.0 at 25 °C in the thermal
isomerization of the transient trans-2-deuterio-1-phenylcyclo-
hexene (Figure 1);5 MNDO calculations on a model trisubsti-
tuted alkene predicted an isotope effect of kH/kD ) 1.85. Large
secondary KIEs were observed6 experimentally (kH/kD2 ) 1.4
and kH/kD12 ) 1.5 at 25 ˚C) by Courtney et al. and calculated7
by Negri and Orlandi using a QCFF/PI method (kH/kD2 ) 1.4
- 1.7 and kH/kD12 ) 1.2-1.7 depending on the nature of the
assumed transition state) for the photochemical isomerization
of trans-stilbenes. Product-determining rotational KIEs (kH/
kD4 ) 1.15-1.20 at 220 ˚C) were encountered in cycloadditions
of allene performed by Dolbier and Dai8 and investigated
† University of California, Los Angeles.
§ Indiana University.
X Abstract published in AdVance ACS Abstracts, January 1, 1996.
(1) (a) Crawford, R. J.; Cameron, D. M. Tokunaga, H. Can. J. Chem.
1974, 52, 4025. (b) Gajewski, J. J.; Chou, S. K. J. Am. Chem. Soc. 1977,
99, 5696.
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Soc. 1989, 111, 6717. (c) Baldwin, J. E.; Villarica, K. A. Tetrahedron Lett.
1994, 35, 7905.
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(4) Gajewski, J. J.; Paul, G. C. J. Org. Chem. 1991, 56, 1986.
(5) Caldwell, R. A.; Misawa, H.; Healy, E. F.; Dewar, M. J. S. J. Am.
Chem. Soc. 1987, 109, 6869.
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(b) Dai, S. H.; Dolbier, W. R., Jr. J. Am. Chem. Soc. 1972, 94, 3946.
(9) Halevi, E. A.; Wolfsberg, M. J. Chem. Soc., Perkin Trans. 2 1993,
1493.
(10) Perrin, C. L.; Thoburn, J. D.; Kresge, A. J. J. Am. Chem. Soc. 1992,
114, 8800.
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Levy, D. H.; Fleming, G. R. J. Chem. Phys. 1988, 89, 6697.
(7) Negri, F.; Orlandi, G. J. Phys. Chem. 1991, 95, 748.
(11) Olson, L. P.; Li, Y.; Houk, K. N.; Kresge, A. J.; Schaad, L. J. J.
Am. Chem. Soc. 1995, 117, 2992.
0002-7863/96/1518-0886$12.00/0 © 1996 American Chemical Society

KIEs in Rotations of Alkenes and Allyl Radicals
J. Am. Chem. Soc., Vol. 118, No. 4, 1996 887
for both ethylene and allyl radical. Yamaguchi et al. calculated
the geometries and frequencies of planar and perpendicular
ethylene, using a 2-electron, 2-orbital (2e-/2o) active space and
a double-ú basis set.13 Also, 3-electron, 3-orbital (3e-/3o)
MCSCF calculations of planar allyl radical have been done,
including frequency calculations,14a,b and the barrier to -CH2
rotation in allyl radical has been calculated using UHF, MP4,
and CISD calculations with a variety of basis sets.14c,d Fre-
quency calculations of twisted allyl radical appear only to have
been done using UHF methods, however, and no zero-point
energy correction was applied to the rotational barrier. It
appears that no KIE calculations using MCSCF ab initio
geometries and force constants have been previously reported
for ethylene or allyl radical thermal isomerizations.
Figure 2. CASSCF/6-311G** [2e/2o] structures of ethylene: ground
state (left); transition state (right).
Structures of Ground States and Transition States
Ethylene calculations were carried out in D2h (ground state)
and D2d (transition state) symmetry (Figure 2; Tables 1 and 2),
using the 6-31G* and 6-311G** basis sets. The ground-state
geometries are in satisfactory agreement with experiment.20 The
transition state is 60.8 kcal/mol (6-31G* basis set) or 61.5 kcal/
mol (6-311G** basis set) higher in energy than the ground state
after zero-point energy correction, which is in good agreement
with experiment.21 Interestingly, previous calculations using a
similar method but different basis set predicted a 45-kcal/mol
barrier.13
As a complement to our theoretical studies, we have studied
the rate of alkene isomerization experimentally. cis-Stilbene
has been shown to isomerize to the trans isomer in a first-order,
unimolecular fashion in the gas phase.15 We have measured
the KIE upon gas-phase thermal isomerization of cis-stilbene
and R,R′-dideuterio-cis-stilbene. This was done in order to test
theoretical predictions concerning the magnitude and nature of
alkene rotational KIEs.
Computational Methods
Propene calculations were carried out in Cs symmetry for both
the ground state and transition state (Figure 3, Tables 1 and 2),
and also in C1 symmetry for the transition state, using the
6-31G* basis set. Both the ground-state geometry and the
barrier to rotation (62 kcal/mol) are in good agreement with
experimental values.22,23 The Cs transition structure of propene
(Figure 3) is a second-order saddle point. There is a large (1337i
cm-1) imaginary frequency associated with CdC bond rotation
and a second, smaller (195i cm-1) imaginary frequency that
corresponds to a pyramidalization of the radical at C2. The
methyl group in the transition state is staggered with respect to
the C1-C2 bond; when the methyl group is eclipsed with the
C1-C2 bond, there is an additional imaginary frequency
associated with this motion. Relaxation of the symmetry
constraint gives a transition structure (Figure 4) which is
pyramidalized at the central carbon by 18° (the angle formed
by the C-H bond with the C-C-C plane). The -CH2
terminus is pyramidalized by about 8° in both the C1 and Cs
structures. On a vibrationless energy surface, the C1 structure
is calculated to be 0.2 kcal/mol lower in energy than the Cs
structure; the Cs structure is the saddle point for interconversion
of the C1 structure shown in Figure 4 with its enantiomer.
However, after zero-point energy corrections are applied, the
Cs structure is lower in energy than the C1 structure by 0.3 kcal/
mol. The Cs structure probably better represents the “true”
transition-state structure, but KIEs were calculated for the C1
transition structure as well.
Ab initio calculations were performed using GAMESS16a or Gaussian
94.16b UHF Natural Orbital Analysis17 indicated a [2e-/2o] active space
for ethylene and propene and a [3e-/3o] active space for allyl radical.
In allyl radical, orbitals ψ10 and ψ11 were reordered in the ground state
species, so that ψ10 (a π orbital) was included and ψ11 (a σ orbital)
was excluded from the active space; if these reorderings were not done,
the calculations failed to reach self-consistency. No orbital reordering
was necessary for twisted allyl radical. When necessary, force constant
matrix contaminants resulting from molecular translation and rotation
were removed by use of internal rather than Cartesian coordinates for
frequency calculations. The CASSCF geometries and force constants
were used as input to QUIVER,18 which calculates the partition
functions for the Bigeleisen equation.19 In one test case, isotope effects
were calculated from free energies of activation calculated in Gaussian
94.16b
(12) (a) Hehre, W. J.; Radom, L.; v. R. Schleyer, P.; Pople, J. A. Ab
Initio Molecular Orbital Theory; Wiley-Interscience: New York, 1986. (b)
Roos, B. O. In Methods in Computational Molecular Physics; Diercksen,
G. H. F., Wilson, S., Eds.; D. Reidel Publishing: Dordrecht, The
Netherlands, 1983; pp 161-187. (c) Werner, H. J. In AdVances in Chemical
Physics; Lawley, K. P., Ed.; Wiley Interscience: New York, 1987; Vol.
69, pp 1-62. (d) Shepard, R. Ibid., pp 63-200.
(13) Yamaguchi, Y.; Osamura, Y.; Schaefer, H. F., III J. Am. Chem.
Soc. 1983, 105, 7506.
(14) (a) Takada, T.; Dupuis, M. J. Am. Chem. Soc. 1983, 105, 1713. (b)
Szalay, P. G.; Csa´za´r, A. G.; Fogarasi, G.; Karpfen, A.; Lischke, K. J. Chem.
Phys. 1990, 93, 1246. (c) Peeters, D.; Leroy, G.; Matagne, M. THEOCHEM
1988, 43, 267. (d) Hammons, J. H.; Coolidge, M. B.; Borden, W. T. J.
Phys. Chem. 1990, 94, 5468.
Allyl radical was calculated in C2V symmetry (ground state)
and Cs symmetry (transition state), using the 6-31G* basis set
(Figure 5). The geometry of the ground state is in reasonable
agreement with experiment,24 although the bond lengths are not
very close. This lack of close agreement may be attributable
to the use of electron diffraction to obtain internuclear distances.
The calculated barrier to rotation is 13.7 kcal/mol after zero-
point energy correction, which is in good agreement with the
experimental value.25
(15) (a) Kistiakowsky, G. B.; Smith, W. R. J. Am. Chem. Soc. 1934, 56,
638. (b) Schmiegel, W. W.; Lett, F. A.; Cowan, D. O. J. Org. Chem. 1968,
33, 3334.
(16) (a) GAMESS: Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.;
Koseki, S.; Jensen, J. H.; Gordon, M. S.; Nguyen, K. A.; Windus, T. L.;
Elbert, S. T. QCPE Bull. 1990, 10, 52. (b) Gaussian 94 (Revision A.1), M.
J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M.
A. Robb, J. R. Cheeseman, T. A. Keith, G. A. Petersson, J. A. Montgomery,
K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B.
Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe,
C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E. S.
Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J. Defrees,
J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez, and J. A. Pople;
Gaussian, Inc.: Pittsburgh, PA, 1995.
(17) Pulay, P.; Hamilton, T. P. J. Chem. Phys. 1988, 88, 4926.
(18) Saunders, M.; Laidig, K. E.; Wolfsberg, M. J. Am. Chem. Soc. 1989,
111, 8989.
(19) (a) Bigeleisen, J.; Wolfsberg, M. AdV. Chem. Phys. 1958, 1, 15. (b)
Bigeleisen, J.; Goeppert-Mayer, M. J. Chem. Phys. 1947, 15, 261.
(20) Kuchitsu, K. J. Chem. Phys. 1966, 44, 906.
(21) Douglas, J. E.; Rabinovitch, B. S.; Looney, F. S. J. Chem. Phys.
1955, 23, 315.
(22) Lide, D. R.; Christensen, D. J. Chem. Phys. 1961, 35, 1374.
(23) Flowers, M. C.; Jonathan, N. J. Chem. Phys. 1969, 50, 2805.
(24) Vajda, E.; Tremmel, J.; Rozsondai, B.; Hargittai, I.; Maltsev, A.
K.; Kagramanov, N.; Nefedov, O. M. J. Am. Chem. Soc. 1986, 108, 4352.

888 J. Am. Chem. Soc., Vol. 118, No. 4, 1996
Table 1. Optimized Ground-State Structures
Olson et al.
molecule
ethylene
ethylene
propene
allyl radical
MCSCF calculation
symmetry
[2e/2o]/6-31G*
D2h
-78.06025
31.2
[2e/2o]/6-311G**
D2h
-78.08247
30.8
[2e/2o]/6-31G*
Cs
-117.09927
48.1
[3e/3o]/6-31G*
C2v
-116.48359
39.6
energy (hartrees)
zero-point energy
(kcal/mol; scaled)
selected bond distances (Å)
and angles (deg)a
C1-C2
1.3382
1.3368 (1.330)
1.3389 (1.336)
1.5040 (1.501)
1.0766 (1.091)
1.0752 (1.081)
1.0785 (1.090)
121.78 (120.5)
121.59 (121.5)
118.89 (119.0)
124.94 (124.3)
1.3899 (1.428)
same
C2-C3
Hcis-C1
1.0756
(same)
(same)
121.73
(same)
(same)
1.0764 (1.076)
(same)
(same)
121.63 (121.7)
(same)
(same)
1.0749 (1.069)
1.0732 (1.069)
1.0780 (1.069)
121.21 (120.9)
121.44 (120.9)
117.68 (118.2)
124.65 (124.6)
Htrans-C1
H-C2
Hcis-C1-C2
Htrans-C1-C2
C1-C2-H
C1-C2-C3
a Experimental data (parentheses) are taken from refs 20 and 22.
Table 2. Optimized Transition-State Structures
molecule
ethylene
ethylene
propene
propene
allyl radical
MCSCF calculation
symmetry
[2e/2o]/6-31G*
D2d
-77.95570
26.4
[2e/2o]/6-311G**
D2d
-77.97772
26.5
[2e/2o]/6-31G*
Cs
-116.99377
44.2
[2e/2o]/6-31G*
C1
-116.99405
44.7
[3e/3o]/6-31G*
Cs
-116.46214
38.9
energy (hartrees)
zero-point energy
(kcal/mol; scaled)
selected bond distances
(Å) and angles (deg)
C1-C2a
1.4692
1.4709
1.4720
1.5028
1.0767
1.0759
121.27
119.26
121.56
7.31
1.4741
1.5038
1.0769, 1.0756
1.0778
121.21, 121.14
118.15
120.92
7.65
18.32
1.4765
1.3058
1.0827
1.0923
120.18
116.31
124.96
19.80
C2-C3
H-C1
1.0754
(same)
121.32
(same)
1.0762
(same)
121.22
(same)
H-C2
H-C1-C2
C1-C2-H
C1-C2-C3
pyram. at C1b
pyram. at C2b
Hcis-C3-C2
Htrans-C3-C2
0.0
(same)
0.0
(same)
0.0
0.0
121.77
121.53
a Where C1 is the radical carbon, in the case of allyl radical. b Pyramidalization at that carbon, i.e., the improper angle.
Figure 3. CASSCF/6-31G* [2e/2o] structures of propene: ground state
(left); transition state (right).
Figure 4. Two views of the CASSCF/6-31G* [2e/2o] structures of
propene (C1 symmetry; see text). Note the pyramidalization at the
central carbon atom. The compound isotope effects for atoms HA and
HB, designated on the view at right, were essentially the same (∆KIE
< 0.02).
Frequencies of Ground States and Transition States
The vibrational frequencies of ground-state ethylene26 and
propene27 are reasonably reproduced by the MCSCF calculations
when scaled12a (Table 3; the frequencies of isotopomers of
ethylene and propene in both ground states and transition states
are tabulated in the supporting information). As shown in Table
3, one ground-state vibrational mode is entirely lost in the
transition state, becoming an imaginary frequency, but other
modes are reduced in magnitude as well. Aside from the
reaction coordinate motion, the most striking reduction in
vibrational frequencies is seen in the out-of-plane wagging
motions of the methylene groups, which are far looser in the
transition state than in the reactant state. The reduction in these
frequencies is about 700 cm-1 in these two cases. Other
vibrations associated with C-H bonds are reduced by 30-300
cm-1
.
In propene, an out-of-plane bending mode at C2 of the twisted
species has an imaginary frequency if the C-H bond is held
coplanar with the carbon skeleton. Although with a zero-point
energy correction the planar geometry is the lowest-energy
species, the out-of-plane motion is a very loose vibration with
negligible associated zero-point energy.
(25) Korth, H.-G.; Trill, H.; Sustmann, R. J. Am. Chem. Soc. 1981, 103,
4483.
(26) Shimanouchi, T. Tables of Molecular Vibrational Frequencies,
Consolidated Volume; National Bureau of Standards: Washington, DC,
1972; NSRDS-NBS 39.
(27) Silvi, B.; Labarbe, P.; Perchard, J. P. Spectrochim. Acta, Part A
1973, 29A, 263.

KIEs in Rotations of Alkenes and Allyl Radicals
J. Am. Chem. Soc., Vol. 118, No. 4, 1996 889
Table 4. MCSCF/6-31G* Vibrational Frequencies (cm-1) of Allyl
Radicala,b
ground state freq
transition-state freq
CH2 rock
416 (-)
CH2 twist
222i
374
499
526
803
924
936
996
1073
1287
1422
1458
1611
3009
CCC bend
CCC oop bend
CH2 wag
CH2 wag
CH2 oop bend
CH2 wag
CCC stretch
CCC stretch
CCC stretch
CH2 scissor
CCC stretch
CCC stretch
CH stretch
502 (502-510)
CCC bend
CCC oop bend
CH2 wag
CH wag
CH2 wag
CCC bend
CCC bend
C-C stretch
CCC stretch
532 (-)
636 (-)
651 (801-802)
917 (-)
Figure 5. CASSCF/6-31G* [3e/3o] structures of allyl radical: ground
state (left); transition state (right).
937 (983-985)
994 (-)
1092 (-)
1232 (1242)
Table 3. MCSCF/6-311G** Vibrational Frequencies (cm-1) of
Ethylenea,b
1395 (1388-1389) CH2 scissor
1483 (1463)
1507 (1477)
ground-state freq
803 (826)
transition-state freq
CH2 scissor
CdC stretch
CH2 rock
CH2 wag
CH2 wag
CH2 twist
CH2 wag
1611i
160
162
3013 (3016-3019) CH stretch
830 (943)
867 (949)
CH2 asym stretch 3041 (-)
CH2 sym stretch
CH2 asym stretch 3124 (3105-3107) CH2 asym stretch 3089
CH2 sym stretch 3136 (-) CH2 sym stretch 3115
CH2 asym stretch 3018
CH2 wag
3055 (3048-3051) CH2 asym stretch 3033
CH2 twist
CH2 rock
1011 (1023)
1238 (1236)
1324 (1342)
1474 (1444)
1622 (1623)
3024 (2989)
3040 (3026)
3094 (3103)
3120 (3106)
CH2 wag
CH2 wag
938
948
CH2 scissor
CH2 scissor
CC stretch
CH2 sym stretch
CH2 asym stretch
CH2 asym stretch
CH2 sym stretch
CC stretch
CH2 scissor
CH2 scissor
CH2 stretch
CH2 stretch
CH2 stretch
CH2 stretch
1079
1444
1475
3027
3034
3118
3122
a Experimental values in parentheses are from ref 28. b Calculated
frequencies scaled by 0.91.
ZPE represents the KIE due to differences in zero-point
energy changes for H and D. EXC gives the contributions due
to different populations of excited vibrational levels for H and
D. VP, the vibrational product, and the ratio of imaginary
frequencies come from the replacement of the MMI term, which
gives translational and rotational contributions to the KIE.19
Isotope effects calculated using scaled frequencies are given
in Tables 5 and 6 for temperatures ranging from 25 to 400 °C.
The components of the isotope effects from the Bigeleisen
equation are given in the tables.
The calculated isotope effect for rotation of ethylene at room
temperature (Table 5) is large (kH/kD ) 1.32). The contribution
of zero-point energy differences (1.35) is somewhat larger than
the net values, because the excitation term is inverse. The
temperature dependence of the KIE is mainly due to the
Arrhenius behavior arising from differences in activation
energies.
a Experimental values in parentheses are from ref 26. b Calculated
frequencies scaled by 0.93.
The scaled MCSCF frequencies of the ground-state allyl
radical reasonably reproduce experimental values.28 In contrast
to ethylene and propene, the simple disappearance of a single
torsional mode is a good approximation of the changes in
vibrational frequency associated with the rotational process. The
magnitude of the imaginary frequency (221i cm-1) is also far
lower than in the alkenes (1291i to 1611i cm-1).
Calculated Kinetic Isotope Effects
The Bigeleisen equation,19
q
νi(H)
kH
kD
Isotope effects for both the Cs and C1 structures of twisted
propene are provided in Table 5. The ratio of imaginary
frequencies makes a significant contribution. ZPE factors are
also large; for alkenes, they are larger than the total KIE, because
the EXC factors are inverse or near unity. Although there is a
component of the KIE which can reasonably be ascribed to
rehybridization (especially in lower-frequency out-of-plane C-H
vibrations), the magnitudes of the isotope effects are larger than
secondary isotope effects typically encountered upon simple
)
q‚VP‚EXC‚ZPE
νi(D)
expresses the isotope effect in terms of the ratio of imaginary
frequencies and three terms, each of which is a function of the
ground-state and transition-state vibrational frequencies:
3n-6
3nq-7
VP )
ν
n(D)/νn(H)
/
νn(D)q/νn(H)
q
∏
∏
•
n
n
rehybridization. Adding a -CH3 (or -CH2 group, see Table
6) on the terminus of the double bond opposite from the side
of the deuterium substituent increases kH/kD. The 1-deutero-
priopene isotope effect is 1.22 at 473 K. Adding a -CH3 to
the same terminus of the double bond has little effect. The
EXC )
3n-6
3nq-7
q
q
1 - e-u (H)/1 - e-u (D)
/
1 - e-u (H) /1 - e-u (D)
n
n
n
n
∏
∏
n
•
n
kH/kD becomes 1.19 (at 473 K); adding a -CH2 to form
2-deuterioallyl decreases kH/kD to 1.05 (at 473 K). The
particularly small KIE in the case of the 2-deuterioallyl radical
indicates that rotation is centered mainly on C1.
3n-6
3nq-7
q
q
ZPE )
e(u (H)/2)/e(u (D)/2)
/
e(u (H) /2)/e(u (D) /2)
n
n
n
n
∏
∏
n
n
In the 1-deuterioallyl radical, there are two different types of
methylene rotation, one involving rotation of the CHD, the other
involving rotation of CH2. The deuterium slows the rotation
of the methylene group to which it is attached, but it speeds up
the rotation of the opposite methylene. There is a small
fractionation-factor preference for deuterium to be on an olefinic
site, since the bending force constants are larger for olefin than
for allyl radical sp2 carbon-hydrogen bonds.29
where un ) hυn/κT, and υn are the fundamental vibrational
frequencies. The isotope effect can also be corrected for
tunneling (see below).
(28) (a) Maltsev, A. K.; Korolov, V. A.; Nefedov, O. M. Bull. Acad.
Sci. USSR, Chem. Ser. 1982, 31, 2131. (b) Maier, G.; Reisenauer, H. P.;
Rohde, B.; Dehnicke, K. Chem. Ber. 1982, 16, 732.

890 J. Am. Chem. Soc., Vol. 118, No. 4, 1996
Olson et al.
Table 5. Kinetic Isotope Effects (kH/kD) upon Alkene Rotation
Ethylene-1-d (MCSCF/6-311G**)
Table 6. MCSCF/6-31G* Kinetic Isotope Effects of Allyl Radical
Rotation.
2-Deuterioallyl Radical
H
D
D
H
H
H
CH2
•
q
T (K)
υHq/υD
VP
1.052
EXC
ZPE
KIE
H
298
373
473
573
673
1.068
0.872
0.868
0.869
0.872
0.874
1.347
1.269
1.206
1.168
1.150
1.322
1.240
1.180
1.147
1.129
q
T (K)
υHq/υD
VP
EXC
ZPE
KIE
298
373
473
573
1.020
0.984
0.991
0.990
0.990
0.952
1.089
1.071
1.055
1.046
1.082
1.062
1.048
0.998
2-Deuteriopropene Rotation (Cs) MCSCF/6-31G*
1-Deuterioallyl Radical (Average of exo and endo)
D
H
H
CH3
D
CH2
H
•
H
υHq/υD
VP
EXC
ZPE
KIE
q
T (K)
q
T (K)
υHq/υD
VP
EXC
ZPE
KIE
298
373
473
573
673
1.088
0.837
0.986
0.999
1.016
1.032
1.053
1.505
1.370
1.282
1.228
1.191
1.352
1.246
1.186
1.154
1.142
298
373
473
573
1.165
0.855
1.034
1.041
1.052
1.067
1.284
1.224
1.173
1.141
1.318
1.270
1.234
1.215
1-Deuterioallyl Radical (Average of exo and endo)
1-Deuteriopropene Rotation (Cs average of cis and trans)
MCSCF/6-31G*
H
H
H
D
C
•
D
H
H
CH3
H
q
T (K)
υHq/υD
VP
EXC
ZPE
KIE
q
T (K)
υHq/υD
VP
EXC
ZPE
KIE
298
373
473
573
1.005
0.994
1.021
1.024
1.026
1.027
0.946
0.956
0.965
0.972
0.965
0.980
0.991
0.998
298
373
473
573
673
1.095
0.920
0.910
0.920
0.936
0.949
0.952
1.512
1.391
1.297
1.239
1.210
1.385
1.290
1.222
1.185
1.161
Table 7. Calculated Isotope Effects of Variously Substituted
Alkenes
Deuteriopropene Rotations (C1) (MCSCF/6-3G*)
KIE (tunnel
corrected)
2-deuteriopropene
1-deuteriopropene
molecule
νqH/νq
KIE (H/D)
D
D
H
H
H
-1599/-1394 ) 1.147 1.330 at 300 °C 1.657 at 300 °C
-1337/-1099 ) 1.217 1.396 at 300 °C 1.678 at 300 °C
-1108/-807 ) 1.373 1.580 at 300 °C 1.871 at 300 °C
-1337/-1335 ) 1.001 1048 at 25 °C
H
D
CH3
CH3
D
H
D
CH3
H
H
T (K)
KIE
KIE
298
373
473
573
673
1.313
1.235
1.179
1.115
1.099
1.386
1.288
1.204
1.169
1.157
D
M
D
CH3
D
H
D
CD3
a Average of cis-propene-1-d going to H8 or H9 and trans-propene-
1-d going to H8 or H9; all give essentially the same result.
H
M
H
CH3
-830/-631 ) 1.315 1.632 at 25 °C 2.363 at 25 °C
M
D
The effects of varying the masses of substituents and the
location of deuterium substituents are further explored in Table
7. One notable example is 3,3,3-trideuteriopropene; even at
25 °C, kH/kD3 is only 1.048 (using the Cs transition structure)
or 1.036 (using the C1 transition structure), which is only 1.012-
1.016 per D. These atoms are only indirectly involved in the
reaction coordinate and have little effect on the KIE. The small
effect is due to an increase in hyperconjugation involving the
interaction of the methyl group with the radical center at C2 in
the transition state. Also in Table 7 are KIEs for a series of
deuterated olefins, with various masses added. M signifies a
hypothetical hydrogen of mass ) 15 to simulate the mass effect
of a methyl group.5 Adding mass to the alkene increases the
overall KIE per D; more reaction coordinate motion resides in
the remaining hydrogens as heavier substituents are added to
the double bond.
We tested whether the change in translational and rotational
partition functions upon deuteration had any substantial influ-
ence on the isotope effects. For this purpose, UHF/6-31G*
calculations on ground-state and D2d ethylene were performed.
When ∆Gq values were calculated from the translational,
rotational, and vibrational partition functions, only the vibra-
tional terms are significantly different in the undeuterated and
deuterated compounds.
The large tunnel corrections30 reported in Table 7 should be
looked on with skepticism, since the single Bell correction is
not expected to be accurate for such cases.
(29) (a) Houk, K. N.; Gustafson, S. M.; Black, K. A. J. Am. Chem. Soc.
1992, 114, 8565. (b) Gajewski, J. J.; Olson, L. P.; Tupper, K. J. J. Am.
Chem. Soc. 1993, 115, 4548.

KIEs in Rotations of Alkenes and Allyl Radicals
J. Am. Chem. Soc., Vol. 118, No. 4, 1996 891
the calculations do not support the notion that only one -CH2
torsional vibration is affected in the transition state for methylene
rotation.1b,5 Rather, a number of modes are involved in creating
the large KIE. Nonetheless, the predicted significant loss of
zero-point energy1b,5 is borne out by the calculations on alkenes.
Allyl radical, on the other hand, has a much smaller loss of
zero-point energy in its rotation process. Still, from Table 6,
the ·PE term is quite significant.
In alkene rotations, similar mass effects to those observed in
amide rotations10,11 are seen; the terminus of the rotating bond
with the heavier substituents has less motion in the transition
state. This leads to a smaller KIE with deuterium on the more
heavily-substituted terminus relative to the KIE with deuterium
on the less-substituted terminus. For example, the KIE is largest
with deuterium on C1 of propene.
Figure 6. Experimental study.
Table 8. Experimental Kinetic Isotope Effects for Thermal
Isomerization of cis-Stilbene and R,R′-Dideuterio-cis-stilbene at 287
( 3 °C.a
b
run no.
KIE (kH/kD2)
A1
A2
A3
A4
B1
B2
B3
B4
B5
B6
1.25
1.60
1.41
1.53
1.45
1.61
1.59
1.39
1.29
1.64
A1-A4 av: 1.45
B1-B6 av: 1.50
No KIEs for allyl radical isomerizations seem to have been
reported; however allyl radical is a model for a number of
reactions with putative allyl-radical-like intermediates or transi-
tion states, where methylene rotation must occur in order for
the reaction (e.g., ring closure) to occur. The [1,3] shifts of
vinylcyclopropanes and vinylcyclobutanes may involve transi-
tion states or intermediates resembling an allyl radical tethered
to another radical site. The observed KIEs at approximately
300 °C are kH/kD2 ) 1.14-1.18 for vinylcyclopropane rear-
rangements2 and kH/kD2 ) 1.07 for a vinylcyclobutane rear-
rangements4 when the methylene termini are deuterated. These
values are significantly lower than kH/kD2 ) 1.46, which we
predict for allyl radical rotation at that temperature. These
reactions, however, consist of considerable nuclear motion aside
from simple hydrogen motion, and almost certainly a certain
degree of carbon rehybridization, depending on the degree of
bond formation. Nonetheless, the source of the observed kinetic
isotope effect in these cases should be similar in principle to
that of allyl radical, and substantial KIEs should be observed
even at elevated temperatures in many reactions where rotational
motion of hydrogen through space is an important component
of the reaction coordinate. These KIEs could be partly caused
by fractionation between vinyl and allyl carbon.
overall av: 1.47 ( 0.13 (σn)
a 560 ( 3 K. b KIEs corrected for incomplete deuterium incorpora-
tion, assuming the following: (kH/kD)2 ) kH/kD2; (fraction D0) ) (%
H/100)2; and (fraction D1) ) 1 - [(fraction D2) + (fraction D0); and
(fraction D2) ) (% D/100)2.
Figure 7. MCSCF KIE for propene and allyl.
Experimental Measurements of Stilbene Rotational KIE
In order to test several of our general theoretical predictions
concerning alkene isomerization KIEs, we pyrolyzed cis-
stilbenes (Figure 6). Two sets of KIE data were obtained (Table
8), with the samples in each set synthesized, purified, pyrolyzed,
and analyzed independently from the other set, by different
investigators.
Another interesting point is observed in the calculations:
methylene twisting (as experienced by C1) is a similar process
in propene and allyl radical (Figure 7). Despite significant
differences in the rotational barriers as well as the magnitude
of various terms in the Bigeleisen equation, the calculated KIEs
are nearly the same; the MCSCF calculation of doublet allyl
radical provides a similar KIE result to that of singlet biradical
propene.
The two sets of data have been corrected for incomplete
deuterium incorporation in the deuterated samples (94% D
incorporation in samples A1-A4; 88% D incorporation in
samples B1-B6). Overall, the two sets of data agree with each
other very well. Despite careful pretreatment of the pyrolysis
tubes, the greatest source of error in the measured KIEs is
probably due to residual surface catalysis which might affect
one sample more than the other in any given run; this error
should be random, however. Presumably, the experimental error
in the KIE could be reduced by taking extreme care to eliminate
all surface catalysis; nonetheless, the essential result is clear:
even at its lower bound, the KIE is substantial. The large
experimental KIE in this case (kH/kD2 ) (1.47 ( 0.13) (σ) at
287 °C) agrees with the calculated KIE for a model cis-
disubsituted alkene (entry 3, Table 7; kH/kD2 ) 1.58 at 300 ˚C).
Deuterium has a pronounced effect on the isomerization rate
even at the elevated temperature of 287 °C.
Three distinct features become apparent from inspection of
Tables 5-7. (i) Even at a high temperature, significant KIEs
are predicted. The calculations suggest that this is primarily a
consequence of the large zero-point energy terms and the large
ratios of imaginary frequencies in the Bigeleisen equation. The
loss or diminution of several ground-state modes and the
considerable hydrogen motion required for twisting about the
CdC bond are reflected here. (ii) The KIE per deuterium is
predicted to increase with increased substituent mass, because
the zero-point energy term becomes more sensitiVe to each
deuterium substituent when there are fewer hydrogens overall
which are involved in the reaction coordinate. As examples,
note the increase in KIEs in Table 7 along the series dideute-
rioethylene, propene, and butene (simulated). In the experiment
of Caldwell et al.5 as well as our own (Table 8) the masses
connected to the twisting double bond are considerable. (iii)
Large KIEs are predicted in the CdC rotation of normal,
unstrained alkenes (as was also predicted by Caldwell et al.5).
Using the hypothetical trisubstituted alkene (entry 5 in Table
Discussion
Large KIEs are calculated for rotation about the restricted
C-C bonds of alkenes and allyl radical. In the case of alkenes,
(30) Bell, R. P. Trans. Faraday Soc. 1959, 55, 1.

892 J. Am. Chem. Soc., Vol. 118, No. 4, 1996
Olson et al.
(8 mL), and dry ethyl ether (8 mL). The activated zinc was then
resuspended in 4 mL of CH3OD/D2O (5:3 v/v). Diphenylacetylene
(0.10 g, 0.56 mmol) was added to the suspension, and it was stirred
under argon at room temperature for 16 h; then the mixture was refluxed
for 6 h (at which point no starting material was detectable by thin-
layer chromatography (UV detection; hexane/silica gel)). The mixture
was filtered, and most of the solvent was evaporated. The product
was extracted with pentane (3 × 20-mL portions) and dried (MgSO4).
After evaporation of solvent, the residue was distilled (bulb-to-bulb,
90 °C/3 Torr) and purified by chromatography on silica gel (hexane).
Bulb-to-bulb distillation was then repeated twice to give 73 mg of
product (68% yield), >99% pure by capillary GC. Deuterium
incorporation was 88% in one sample and 94% in the other, as
determined by careful collection (20-s pulse delays) and integration of
7), where 2-deuteriopropene has been substituted at C1 with
two hydrogens of mass ) 15 (M), the calculated KIE is 1.632
at 25 °C; with a tunneling correction31 applied, this value
increases to 2.365 (based on an imaginary frequency of 830i
cm-1 for the nondeuterated and 631i cm-1 for the deuterated
species). With or without the tunneling correction, the calcu-
lated value compares reasonably well with the experimental
value of 2.0,5 considering the difference between the hypotheti-
cal trisubstituted alkene and trans-1-phenylcyclohexene. Ex-
periment also showed that kH/kD3 for trans-cis isomerization
of 2,6,6-trideuteriophenylcyclohexene differed little from kH/
kD for isomerization of 2-deuteriophenylcyclohexene.5 This is
consistent with our calculations, which show that there is only
a small KIE associated with the isomerization of 3,3,3-
trideuteriopropene (Table 7).
1
the H NMR spectra. 1H NMR (360 MHz, acetone-d6): δ 6.64 (br s,
0.12H), 7.22-7.30 (m, 10H).
Pyrolysis. The pyrolysis tubes were cleaned with concentrated
chromic acid, rinsed with distilled water, soaked overnight in 1 M
HNO3, rinsed with distilled water, soaked for 3 days in a dilute solution
of Na2EDTA, rinsed with distilled water and concentrated ammonium
hydroxide, and then oven-dried. The interior surfaces were wetted with
freshly distilled Me2SiCl2; after evaporation of the silane, the tubes
were rinsed with ethyl acetate, dried, rinsed with dilute ammonium
hydroxide and glass-distilled water, and dried in an oven (120 °C) for
two days.
Samples of purified cis-stilbene (3 µL) were vacuum-sealed after
two cycles of freeze-pump-thaw degassing in the pyrolysis tubes.
Pyrolyses were carried out using a tube furnace equilibrated at 287 (
3 °C. Fine temperature control was not used, because the quantity of
interest was the ratio of rate constants, which should vary little over
this small temperature range. The furnace was fitted with a large Pyrex
sleeve (sealed at one end and loosely packed with glass wool at the
other end) into which the pyrolysis tubes were inserted. Deuterated
and nondeuterated samples were inserted and removed simultaneously,
and the large Pyrex sleeve was rotated several times during pyrolysis
to ensure a homogeneous temperature environment. Pyrolysis was
carried out over 0.5 to 2 half-lives of isomerization, that is, from 30
min to 2 h in different runs. Analysis of stilbenes was by capillary
gas chromatography, with several determinations of each sample
averaged to determine the cis-trans ratio. No significant side products
were observed by gas chromatography.
Conclusions
Our experiments with cis-stilbenes (Table 8) demonstrate the
points (i, ii, and iii) discussed above: at a high temperature, an
unstrained alkene with ponderous substituents exhibits a large
secondary deuterium KIE on thermal isomerization.
We also conclude that the results of Caldwell et al.5 are not
due to a spurious effect caused by trace catalysts in the
nondeuterated sample or trace inhibitors in the deuterated
sample, as has been suggested.10 Furthermore, the description
of the alkene rotational KIE as a “quasi-primary” isotope effect5
seems appropriate; although there is not simply a single torsion
which is lost in the transition state, the considerable hydrogen
motion and the loss of zero-point energy in the rotational process
are indeed reminiscent of primary KIEs.
We also predict large rotational KIEs in the isomerization of
allyl radicals substituted with deuterium at the radical termini.
This is a testable hypothesis.
Experimental Section
cis-Stilbene was obtained from Aldrich. 1H NMR spectra were
recorded at 360 MHz using a Bruker AM360 spectrometer. Capillary
gas chromatography was performed using a Hewlett-Packard HP-1
methylsilicone column (25 m × 0.2 mm id) installed in a Hewlett-
Packard 5890 Series II chromatograph equipped with flame ionization
detection (FID). cis- and trans-stilbenes were assumed to have the
same FID sensitivity factor.
Acknowledgment. We are grateful to the National Science
Foundation for financial support of this research.
Supporting Information Available: Tables of MCSCF/6-
311G** frequencies (11 pages). This material is contained in
many libraries on microfiche, immediately follows this article
in the microfilm version of the journal, can be ordered from
the ACS, and can be downloaded from the Internet; see any
current masthead page for ordering information and Internet
access instructions.
(Z)-1,2-(2H)-Diphenylethene. This procedure is a slightly modified
version of a published method31 for selective reduction of alkynes to
cis-alkenes. A zinc-copper-silver couple was prepared as follows:
Cu(OAc)2‚H2O (70 mg) was added to a stirred suspension of Zn dust
(0.7 g) in 4 mL of D2O. After 15 min, AgNO3 (70 mg) was added.
After an additional 15 min, the suspension was filtered, and the filtrant
was washed successively with D2O (5 mL), CH3OD (5 mL), dry acetone
(31) Avignon-Tropis, M.; Pougny, J. R. Tetrahedron Lett. 1989, 30, 4951.
JA952046B