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?

Article abstract of DOI:10.1021/ja057377v

Prompted by extensive theoretical interest in the role of tunneling in the intramolecular 1,5-hydrogen shift in 1,3(Z)-pentadienes and the large uncertainty in the published values of the theoretically relevant kinetic deuterium-isotope effect and its dependence on temperature, we have examined a degenerate bicyclic version, 2-methyl-10-methylenebicyclo[4.4.0]dec-1-ene, which is locked into the rearrangement-competent cisoid conformation, in the hope of obtaining more precise and accurate values. From rate constants determined over a range of 33 °C from 167.7 to 201.6 °C, Arrhenius parameters, E _a = 32.8 ± 0.4 kcal mol^-1 and log A = 11.1 ± 0.2, were obtained. An average kinetic isotope effect of 4.2 ± 0.5 obtained from all values for k_H/k_D and k _-H/k_-D may be compared with a value of 5.0 ± 0.3, recalculated from data in the pioneering publication of Roth and Koenig. From a highly problematic extrapolation of the temperature dependence, a value of k_H/k_D of 16.6 (standard error between 6.5 and 43) is calculated for the kinetic isotope effect at 25 °C (Roth and Koenig: 12.2). With curvature in Arrhenius plots being one of the three types of experimental evidence considered indicative of tunneling, the kinetic study of the previously published rearrangement of 1-phenyl-5-p-tolyl-1,3(Z)-pentadiene has been extended over a period of 339 days to a range of 108 °C (77-185 °C) without discerning any deviation from a straight-line Arrhenius plot: E_a = 28.7 ± 0.5 (kcal mol^-1) and log A = 9.41 ± 0.30.

Full text of DOI:10.1021/ja057377v

Published on Web 06/22/2006
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?
William von E. Doering* and Xin Zhao
Contribution from the Department of Chemistry and Chemical Biology, HarVard UniVersity,
Cambridge, Massachusetts 02138-2902
Received October 28, 2005; Revised Manuscript Received March 22, 2006; E-mail: doering@chemistry.harvard.edu
Abstract: Prompted by extensive theoretical interest in the role of tunneling in the intramolecular 1,5-
hydrogen shift in 1,3(Z)-pentadienes and the large uncertainty in the published values of the theoretically
relevant kinetic deuterium-isotope effect and its dependence on temperature, we have examined a
degenerate bicyclic version, 2-methyl-10-methylenebicyclo[4.4.0]dec-1-ene, which is locked into the
rearrangement-competent cisoid conformation, in the hope of obtaining more precise and accurate values.
From rate constants determined over a range of 33 °C from 167.7 to 201.6 °C, Arrhenius parameters, E
a
32.8 ( 0.4 kcal mol- and log A ) 11.1 ( 0.2, were obtained. An average kinetic isotope effect of 4.2
1
)
(
H D
0.5 obtained from all values for k /k and k-H/k-D may be compared with a value of 5.0 ( 0.3, recalculated
from data in the pioneering publication of Roth and K o¨ nig. From a highly problematic extrapolation of the
temperature dependence, a value of k /k of 16.6 (standard error between 6.5 and 43) is calculated for the
H
D
kinetic isotope effect at 25 °C (Roth and K o¨ nig: 12.2). With curvature in Arrhenius plots being one of the
three types of experimental evidence considered indicative of tunneling, the kinetic study of the previously
published rearrangement of 1-phenyl-5-p-tolyl-1,3(Z)-pentadiene has been extended over a period of 339
days to a range of 108 °C (77-185 °C) without discerning any deviation from a straight-line Arrhenius plot:
-
1
E ) 28.7 ( 0.5 (kcal mol ) and log A ) 9.41 ( 0.30.
a
Introduction
Several theoreticians have shown interest for a third of a
century in the strongly concerted, thermally activated 1,5-
hydrogen shift undergone by 1,3(Z)-penta-1,3-diene as a reaction
in which tunneling may play a significant role.1 The at-
tractiveness of this example has stemmed not merely from the
high value of 5.3, reported by Roth and K o¨ nig for its deuterium
kinetic isotope effect (KDIE), but more from its extrapolation
to a value of 12.2 at room temperature by means of the ratio of
the Arrhenius equations for kH and kD (Figure 1).7 The elegant
elucidation of the stereochemistry of the reaction, also by Roth
-6
a
8
and K o¨ nig, in full confirmation of the original proposal by
Figure 1. Thermal rearrangement of 1,1-dideuterio-1,3(Z)-pentadiene is
depicted, as are the relative, statistically determined concentrations expected
at equilibrium in the absence of secondary deuterium isotope effects.
(
1) Bingham, R. C.; Dewar, M. J. S. J. Am. Chem. Soc. 1972, 94, 9107-
112; Dewar, M. J. S.; Merz, K. M., Jr.; Stewart, J. J. P. J. Chem. Soc.
9
Chem. Commun. 1985, 166-168; Dewar, M. J. S.; Healy, E. F.; Ruiz, J.
M. J. Am. Chem. Soc. 1988, 110, 2666-2667.
(2) Hess, B. A., Jr.; Schaad, L. J.; Pancir, J. J. Am. Chem. Soc. 1985, 107,
Wolinsky and co-workers9a (later given theoretical support by
1
49-154.
(3) Dormans, G. J. M.; Buck, H. M. J. Am. Chem. Soc. 1986, 108, 3253-
Woodward and Hoffmann) has contributed in no small measure
to the attractiveness of this reaction for theoretical exploration.9b
Critical to the evaluation of the quantitative predictions from
theoretical investigations is the availability of reliable experi-
mental observations for direct comparison. The only report in
3
258.
(
4) Jensen, F.; Houk, K. N. J. Am. Chem. Soc. 1987, 109, 3139-3140.
(
5) Chantranupong, L.; Wildman, T. A. J. Am. Chem. Soc. 1990, 112, 4151-
4
154.
(
6) Liu, Y.-P.; Lynch, G. C.; Truong, T. N.; Lu, D.-h.; Truhlar, D. G.; Garrett,
B. C. J. Am. Chem. Soc. 1993, 115, 2408-2415.
(
7) (a) Roth, W. R.; K o¨ nig, J. Liebigs Ann. Chem. 1966, 699, 24-32. (b) K o¨ nig,
J. Zum Mechanismus nichtkatalysierter WasserstoffVerschiebung, Ph.D.
Dissertation, Universit a¨ t zu K o¨ ln, 1967 (examined by Prof. Wolfram
Grimme).
(9) (a)Wolinsky, J.; Chollar, B.; Baird, M. D. J. Am. Chem. Soc. 1962, 84,
2775-2779. (b) Woodward, R. B.; Hoffmann, R. J. Am. Chem. Soc. 1965,
87, 2511-2513.
(8) Roth, W. R.; K o¨ nig, J.; Stein, K. Chem. Ber. 1970, 103, 426-439.
9080
9
J. AM. CHEM. SOC. 2006, 128, 9080-9085
10.1021/ja057377v CCC: $33.50 © 2006 American Chemical Society

1,5-Hydrogen Shift of a 1,3(Z)-Pentadiene
A R T I C L E S
7
Table 1. Specific Rate Constants and Derived Arrhenius Parameters (including Recalculations) Reported in Roth and K o¨ nig for the
Disappearance of 1,1-Dideuterio-1,3(Z)-pentadiene (kH) and 5,5,5-Trideuterio-1,3(Z)-pentadiene (kD)
T °C
185.0
1.38
190.1
190.2
1.80
195.1
200.0
205.3
210.6
2.26
a
kH
3.13
0.600
5.22
4.47
0.90
4.97
7.10
1.38
5.14
a
kD
0.394
kH/kD
4.57
1
1
b
-1
R/K
recalcd
R/K
kH ) 2.8 × 10 exp(-36 300 ( 500) /RT sec
c
c
11 -1
kH ) 2.19 × 10 exp(-36 100 ( 2 160)/RT sec (log A ) 11.34 ( 1.00)
11 -1
kD ) 2.4 × 10 exp(-37 700 ( 500)/RT sec
11
-1
recalcd
kD ) 2.36 × 10 exp(-37 670 ( 680)/RT sec (log A ) 11.37 ( 0.31)
a
In units of 10 sec-1; no estimates of experimental uncertainties given,7a nor are any available in K o¨ nig’s dissertation.7b b (1300 cal mol-1 in K o¨ nig’s
-6
c
dissertation. Uncertainties are standard errors as provided by the Anova regression analysis in Microsoft Excel.
the literature on the paradigm, 1,3(Z)-pentadiene, comes from
the investigation of Roth and K o¨ nig. Although their ratios of
kH to kD (KDIE) in the temperature range, 190.2-205.3 °C,
5
.0 ( 0.3, seem quite reliable, as noted in a recent examination
of the effect of radical-stabilizing phenyl substituents on the
,5-hydrogen shift,10 their specific rate constants and derived
1
Arrhenius parameters for the KDIE are of insufficient precision
for extrapolation to room temperature to serve as a reliable basis
for comparison with theory.11 This inadequacy is fully to be
understood in light of having only 60 MHz NMR at their
disposal and, consequently, being limited to a study of the
disappearance of their educts, 1,1-dideuterio-1,3(Z)-pentadiene
and 5,5,5-trideuterio-1,3(Z)-pentadiene, rather than a full study
as outlined in Figure 1. From the tabulation of their data and
calculations in Table 1, the limitations are clear.
Figure 2. Interconversion by thermal 1,5-hydrogen shift is shown in the
two sets of the three isotopomers of 2-methyl-10-methylenebicyclo[4.4.0]-
dec-1-ene deuterium-labeled, respectively, in the methylene group and the
methyl group.
As reported by Roth and K o¨ nig, temperature dependence of
kH/kD can be estimated from the ratio of the Arrhenius
expressions in Table 1 (rows five and seven), whence ln(kH/kD)
Scheme 1
)
0.154 + (1400 ( 700)/RT [(kH/kD)25°C ) 12.4 (3.8 to 41);
AH/AD ) 1.17], or from the recalculated kinetic results given in
rows six and eight: ln(kH/kD) ) -0.14 ( 1.60 + (1570 ( 2400)/
RT [(kH/kD)25°C ) 12.3; AH/AD ) 0.94]. Calculation directly from
the ratios of kH/kD at the four temperatures collected in the fourth
row of Table 1 affords ln(kH/kD) ) (4.45 ( 2.28) + (-1340 (
interconversions among all three isotopomers. Each has a
different statistical factor that sets a theoretical ratio of 1:3:6 at
equilibrium (in explicit neglect of secondary isotopic perturba-
tions on the position of equilibrium). These factors stem from
the three possible ways of arranging the atoms in both the
monodeuterio- and dideuteriomethyl groups and the two ar-
rangements possible in the monodeuteriomethylene group
1
070)/RT. Here, also, the uncertainties in the calculated value
for kH/kD are too large for a credible extrapolation to room
temperature: kH/kD ) 8.9 (1.5-54 in neglect of any uncertainty
in the constant, ln(AH/AD) ) 4.45).
Stimulus for the present paper stems less from a desire to
confirm the experimental values for the ratios of kH/kD at the
higher temperatures than from a hope to provide a more reliable
basis for extrapolation of the ratio to room temperature. For
this study, deuterated 2-methyl-10-methylenebicyclo[4.4.0]dec-
(Figure 1).
Preparation
Preparation was accomplished by the unexceptional sequence
shown in Scheme 1, starting from bicyclo[4.4.0]decan-2,10-
dione (fully enolized). Methylation of the diketone, although
presumably a reaction of its anion, proceeded satisfactorily with
methylmagnesium iodide. But note how weakly acidic the
1
-ene (1 and 1′ of Figure 2) has been chosen. By its bicyclic
constitution, it is the first 1,3(Z)-pentadiene to be fully locked
into the cisoid conformation essential for the realization of the
1,5-hydrogen shift and, therefore, freed of any need to consider
the complicating factor introduced by the rearrangement-
incompetent, usually thermochemically more stable transoid
conformation of the acyclic paradigm.12
Given the vastly increased analytical power of currently
available NMR spectroscopy, we have aspired to elucidate the
13
enolizable diketones fixed in the cis configuration are. For
the conversion of 2-methylbicyclo[4.4.0]dec-1-en-10-one to
2
-methyl-10-methylenebicyclo[4.4.0]-dec-1-ene, the procedure
pioneered by Petasis that employs dimethyl titanocene offered
14
a substantial improvement over the classical Wittig procedure.
(
10) Doering, W. v. E.; Keliher, E. J.; Zhao, X. J. Am. Chem. Soc. 2004, 126,
4206-14216.
11) Although Chantranupong and Wildman, for example, have noted explicitly
that “...the error in the slope (of ln k /k ) is about 50% according to Roth
(We did not explore an improved method introduced by
Hasselmann.) The deuterium analogues, 1 and 1′ of Figure 2,
were prepared by the same sequences by employing trideute-
riomethyl reagents.
1
15
(
H
D
-1
and K o¨ nig (1.4 ( 0.7 kcal mol ),” they have little alternative but to
-1
conclude that a “frequency of 390 cm provides reasonable agreement
with experiment.”5 Liu et al. have concluded that “tunneling can indeed
account for the strong temperature dependence observed experimentally
as well as for the magnitude of the KIEs.”6
(13) Stetter, H.; Milbers, U. Chem. Ber. 1958, 91, 977-983.
(14) Petasis, N. A.; Bzowej, E. I. J. Am. Chem. Soc. 1990, 112, 6392-6394.
(15) Hasselmann, D. Chem. Ber. 1974, 107, 3486-3493.
(12) Saettel, N. J.; Wiest, O. J. Org. Chem. 2000, 65, 2331-2336.
J. AM. CHEM. SOC.
9
VOL. 128, NO. 28, 2006 9081

A R T I C L E S
Doering and Zhao
Table 2. Specific Rate Constants for the 1,5-Hydrogen Shift in 2-Methyl-10-dideuteriomethylenebicyclo[4.4.0]dec-1-ene (1) and
-Methylene-10-trideuteriomethylbicyclo[4.4.0]dec-1-ene (1′)
2
2-Methyl-10-dideuteriomethylenebicyclo[4.4.0]dec-1-ene (1)
a,b
3k
H
k
-H
2k
D
k
-D
201.6 ( 0.2 °C
c,d
c,d
9
.73 ( 0.16 (1.61)
3.29 ( 0.13 (3.80)
3.43 ( 0.078 (2.28)
1.73 ( 0.043 (2.46)
1.66 ( 0.024 (1.44)
1.00 ( 0.038 (3.75)
0.90 ( 0.020 (2.25)
1
0.01 ( 0.10 (0.98)
184.4 ( 0.25 °C
c,d
2
2
.70 ( 0.032 (1.20)
0.911 ( 0.028 (3.09)
0.925 ( 0.026 (2.85)
0.425 ( 0.010 (2.23)
0.419 ( 0.011 (2.57)
0.249 ( 0.009 (3.63)
0.226 ( 0.010 (4.33)
c,d
.65 ( 0.034 (1.29)
167.9 ( 0.2 °C
c,d
c,d
0
0
.691 ( 0.008(1.11)
0.245 ( 0.006 (2.42)
0.251 ( 0.007 (2.79)
0.104 ( 0.002 (1.71)
0.090 ( 0.002 (1.96)
0.060 ( 0.0016 (2.74)
0.0494 ( 0.0017(3.37)
.697 ( 0.009(1.31)
2-Methylene-10-trideuteriomethylbicyclo[4.4.0]dec-1-ene (1′)
3k
D
k
-D
2k
H
k
-H
1
67.7 ( 0.2 °C
d,e
0
.135 ( 0.0011(0.8)
0.0461 ( 0.0015 (3.2)
0.430 ( 0.012 (2.9)
0.386 ( 0.022(5.8)
0.202 ( 0.0067 (3.3)
0.185 ( 0.013 (6.8)
d,f
0.131 ( 0.0023(1.7)
0.0433 ( 0.0030(6.9)
a
For the definition of the specific rate constants, see Figure 2. b Specific rate constants, in units of 10-5 sec-1, are calculated from the corrected data
c
given in Table SI-5. Values in italics are based on NMR measurements of the methyl groups: CH3 1.81, CH2D 1.78, CHD2 1.76 ppm (δ) (method a); those
d
in plain type are based on the methyl group: CH3 1.81, the dCH2 group 5.01 and 4.78, and the dCHD group 5.00 and 4.76 ppm (δ) (method b). Values
e
1
in parentheses are uncertainties at the 95% confidence level in %. Analytical results for 1′ are based on H NMR signals (method c) in Table SI-4 as
f
corrected in Table SI-5. Analytical results by method d (Tables SI-4 and SI-5)).
Kinetics
Rates of the disappearance of 1 and the appearance of 2 and
of the two sets of values to fully overlap within acceptable
uncertainties points to a lower accuracy.
A further worry concerns the possibility that side products
initiated by a second-order, ethene-ethene union to a 1,8-octa-
1
(E and Z)-3 are followed by H NMR analysis on a 600-MHz
instrument, but even at this strong field, the resolving capacities
are stretched to the limit. Two sets of results in Tables SI-1,
SI-2, and SI-3 of the Supporting Information relating changes
in concentration with time at three temperatures are based on
the signals given in Table 2, footnote c. In both methods of
analyses, baseline separation is nearly, but not completely,
achieved. We favor method a because quantitative evaluation
by the second method b of the relative intensity of the two
stereoisomeric hydrogen atoms in the methylene group falls
short of equality by 10%, despite extensive variation of the
relevant operating parameters of the NMR apparatus and the
use of the 500-MHz instrument as well. This arcane phenom-
enon persists in three other examples, which will be discussed
2,6-diene diyl diradical may be corrupting analyses at the longer
times of reaction. The activation energy of that type of
-1 19
bimolecular reaction is estimated to be ∼24 kcal mol , which
is substantially lower than the activation energy of 36.3 kcal
mol reported for the unimolecular 1,5-hydrogen shift.7
Toward the end of each kinetic series, when no further
significant change in relative concentrations was to be seen,
the theoretical, symmetry-based values of 0.100, 0.300, and
-1
0
.600 had not been reachedsa possible warning of a compro-
mised accuracy or the impact of nontrivial secondary isotope
effects. At 201.6 °C, values of approach to equilibrium were
0
.107, 0.326, 0.567, and 0.112, 0.312, 0.578; at 184.4 °C, 0.109,
0.331, 0.560, and 0.115, 0.310, 0.579; at 167.9 °C, 0.108, 0.328,
.564, 0.114, 0.314, 0.572 (Tables SI-1, SI-2, and SI-3), and
16
at greater length in the future. The possibility that the
phenomenon is related to the use of NMR tubes made of
borosilicate glass has been explored by substituting soft glass
tubes. The small differences in concentrations at 201.6 °C for
reaction times of 112 and 205 h are not significant within
experimental uncertainties (Table SI-6 in Supporting Informa-
tion).
0
from 1′, 0.109, 0.285, 0.606, 0.112, 0.293, 0.595 (Table SI-4).
On average, these values differ from the statistical by +11, +3.5,
and -4%, respectively. A presentation in terms of specific rate
constants is given in columns 2 and 3 of Table 3. These
shortfalls weigh on the determination of kH/kD adversely.
From the resulting specific rate constants collected in Table
2, values for the ratios of kH/kD starting with 1 may be obtained
from the values for 3kH/2kD (italics; propagation of errors): 3.75
Specific rate constants are calculated by numerical integration
17
by the program KINETIK of Dr. R. Fink. This program
employs a Runge-Kutta procedure of fourth order, allows up
to seven components to be handled by ad libitum kinetic
schemes, and incorporates the estimation of errors for the
(
0.11 at 201.6 °C, 4.24 ( 0.11 at 184.4 °C, and 4.44 ( 0.09
at 167.9 °C, and from 1′, 4.78 ( 0.14 at 167.7 °C (Table 3).
These values are uniformly larger than those obtained from
k-Hk-D: 3.28, 3.66, 4.10, and 4.38, respectively.
individual rate constants at the 95% confidence level by the
method of Marquardt.18 Results from methods a and b of
analysis are collected in Table 2. Although the precision of the
four calculated specific rate constants is about as good as it
gets with NMR (2-4% at the 95% confidence level), the failure
Discussion
The rearrangement of 1 is not exceptional in being degenerate
and requiring either racemization or isotopic labeling for its
observation, but it is unique to our knowledge in being locked
(
16) This vexing aspect of the quantitative study of the kinetics of the 1,5-
hydrogen shift will be addressed in greater detail in a forthcoming paper
by Doering and Keliher.
(17) Roth, W. R.; Fink, R. Unpublished.
(19) Doering, W. v. E.; Belfield, K. D.; He, J.-n. J. Am. Chem. Soc. 1993, 115,
5414-5421.
(18) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431-441.
9082 J. AM. CHEM. SOC.
9
VOL. 128, NO. 28, 2006

1,5-Hydrogen Shift of a 1,3(Z)-Pentadiene
A R T I C L E S
Table 3. Degree of Approach to the Statistical Equilibrium, and Values of KDIEs (kH/kD) for the 1,5-Hydrogen Shift in
-Methyl-10-dideuteriomethylenebicyclo[4.4.0]dec-1-ene (1) and 2-Methylene-10-trideuteriomethylbicyclo[4.4.0]dec-1-ene (1′) (Figure 2)
2
2
-Methyl-10-dideuteriomethylenebicyclo[4.4.0]dec-1-ene (1)a
T,
°
C
approach to equilibrium
kinetic deuterium isotope effectsa
3k
H -H
/k
D
2k /k
-D
(2/3)(3k
H
/2k
D
)
k
/k
-H -D
H -D
(1/3)(3k /k )
201.6
201.6
184.4
184.4
167.9
167.9
2.96
2.94
2.97
2.87
2.82
2.78
1.73
1.84
1.71
1.86
1.73
1.83
3.75 ( 0.11
4.05 ( 0.07
4.24 ( 0.11
4.22 ( 0.12
4.44 ( 0.09
5.16 ( 0.16
3.28 ( 0.18
3.80 ( 0.12
3.66 ( 0.17
4.09 ( 0.21
4.10 ( 0.15
5.09 ( 0.22
3.24 ( 0.13
3.71 ( 0.09
3.61 ( 0.14
3.91 ( 0.18
3.84 ( 0.11
4.70 ( 0.17
2-methylene-10-trideuteriomethylbicyclo[4.4.0]dec-1-ene (1′)
T,
°
C
approach to equilibrium
kinetic deuterium isotope effectsa
3k
D
/k
-D
2k
H
/k
-H
(3/2)(2k
H
/3k k /k
D
)
-H -D
1
67.7
2.93
3.03
2.13
2.09
4.78 ( 0.14
4.42 ( 0.27
4.38 ( 0.20
4.27 ( 0.42
167.7
a
Based on the specific rate constants given in Table 2 (data in italics and plain type have the same significance as in footnote c of Table 2). b Propagation
of errors in the specific rate constants of Table 2.
Scheme 2
5), and an overall average of 4.2 ( 0.5. Another estimate may
be made by combining the data in Table 2 at 167.9 °C for 3kH
from 1 with that at 167.7 °C for 3kD from 1′. The resulting
values of kH/kD, 5.12 ( 0.10 and 5.32 ( 0.12 (propagation of
errors), are in good, possibly accidental, agreement with the
value, 4.91 ( 0.36, derived from the combined values of kH/kD
of Roth and K o¨ nig obtained over the temperature range, 190.1-
2
05.3 °C (Table 1). (Kloosterziel and ter Borg report a value
of 5.0 in their study of the interconversion of 1,3,6- and 1,3,5-
cyclooctatriene at 120 °C and a secondary isotope effect of 1.02
2
1
into the cisoid conformation indispensable to the occurrence of
the intramolecular 1,5-hydrogen shift in 1,3(Z)-pentadienes (see
Scheme 2). Although compound 1 is perturbed in other ways
as well sa certain rigidity imposed by its octalin configuration;
by being tri-alkyl substituted at the 2, 3, and 4 positionssit
nevertheless offers the opportunity of a comparison of enthalpy
of activation with that of the paradigm, without including the
equilibrium constant governing s-trans and s-cis (K in Scheme
( 0.02.) A value for kH/kD of ∼4.5 ( 0.5 appears trustworthy.
The closest our design comes to freedom from secondary
isotope effects is in the ratio (1/3)(3k /k-D) (see Figure 2). The
resulting values are as widely spread as those derived from (2/
3)(3k /2k ) (see Table 2).
H
20
H
D
Temperature dependence of the KDIE is one of three
generally accepted, operational criteria bearing on a role for
tunneling. An unexpected increase in the KDIE at lower
temperatures should become observable in a range of temper-
atures where the temperature-independent tunneling component
is comparable to the temperature-dependent component of the
overall rate. Of the four sets of values at 201.6, 184.4, and
67.7 °C, two are from column 4 of Table 3, 3.75, 4.24, 4.44,
and 4.05, 4.24, 5.16, and two more are from column 5, 3.28,
.66, 4.10, and 3.80, 4.09, 5.09. Whether the increase at lower
temperature in reality exceeds that expected from the higher
enthalpy of activation of kDs is the question. That the precision
of these data is insufficient to warrant extrapolation to room
temperature emerges starkly from calculation of the temperature
dependence of kH/kD from the eight values in Table 3 (column
22
2
).
The Arrhenius parameters calculated from the rate constants
for 3kH listed in Table 2, which are the most precise, are Ea )
-1
3
2.8 ( 0.4 kcal mol and log A ) 11.1 ( 0.2. These parameters
are the first defining the 1,5-hydrogen shift in a cisoid-locked
,3(Z)-pentadiene. Comparison with the values given by Roth
23
1
1
-
1
and K o¨ nig for the paradigm, Ea ) 36.3 ( 0.5 kcal mol and
log A ) 11.45, reveals a difference of 3.5 kcal mol (in neglect
3
-1
of experimental uncertainties), which compares well with the
-1
difference of 3.7 kcal mol in heat of formation of the transoid
and cisoid conformations of 1,3(Z)-pentadiene calculated by
Saettel and Wiest.12
Values of KDIE and their response to changes in temperature
constitute one of the prominent manifestations of the tunneling
effect. The KDIE of deuterium-perturbed compounds 1 and 1′
at the higher temperatures (201.6, 184.4, and 167.9 °C), where
specific rate constants are conveniently accessible within
comfortable lengths of times of measurement, are collected in
Table 3 as values of kH/kD [(2/3)(3kH/2kD)] and k-H/k-D. They
vary over a disappointingly large range of 3.28-5.16 but have
average values of 4.14, 4.48 (column 4), and 3.68, 4.33 (column
4
0
). The resulting Arrhenius equation, ln(kH/kD) ) (-1.10 (
.62) + (1170 ( 280)/RT (standard errors at the 95% confidence
level errors are ( 1.52 and ( 690 cal/mol, respectively), leads
to a value extrapolated to room temperature of 16.8 (2-67!)
(21) Kloosterziel, H.; ter Borg, A. P. Rec. TraV. Chem. 1965, 84, 1305-1314.
(
22) (a) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall: New
York, 1980. (b) Melander, L.; Saunders, W. H. Reaction Rates of Isotopic
Molecules; Wiley: New York, 1980. (c) Baldwin, J. E.; Reddy, P. V. J.
Am. Chem. Soc. 1988, 110, 8223-8228.
(
23) With tunneling, (kobs
expected to be very much smaller than (ktun
(-E /RT) + (ktun ]/[A exp(-E /RT)]; only at temperatures where A
exp(-E will (kobs
)
H
) A
H
exp(-E
a
/RT) + (ktun
)
H
)
. Because (ktun
)
D
exp-
is
)
H
, (kobs
H
/(kobs ) [A
)
D
H
(
20) Not being up to a discussion with significant conclusions, we cite a
a
)
H
)
H
D
a
)
D
H
model: Glass, D. S.; Boikess, R. S.; Dewar, M. J. S. Tetrahedron Lett.
a
)
H
/RT) becomes comparable in magnitude to (ktun
begin to reflect tunneling.
)
H
)
H
/
1
966, 7, 999-1008.
(kobs
)
D
J. AM. CHEM. SOC.
9
VOL. 128, NO. 28, 2006 9083

A R T I C L E S
Doering and Zhao
for kH/kD at 25 °C.24 Although this value falls in the same range
as the value of 12.2 advanced by Roth and K o¨ nig for the
paradigm and agrees with the value of 10.3 projected by Baldwin
and Reddy for a related 1,7-hydrogen shift (note the drastically
different geometry of the transition region),2 we believe the
present effort has no more succeeded than that of Roth and
K o¨ nig in providing experimental values of kH/kD of sufficiently
high accuracy to serve theoreticians as a reliable check on their
calculations of the low-temperature KDIE and the tunneling
component in the 1,5-hydrogen shift. Along with Hayase, Hrovat
and Borden in footnote 11 of their recent paper,25 we note that
the good agreements of the value of 36.6 calculated by Saettel
neling.28 For most organic chemists, the deliberate slowing of
reactions by lowering temperatures seems without question a
step in the wrong direction! None the less, we look forward to
predictions from the calculational and theoretical community
of a range of temperature within which the two components of
the experimental rates of the 1,5-hydrogen shift become
comparable and attention to the tunneling component is
demanded. Above such ranges of temperature, the tunneling
effect is likely, in the opinion of some, to remain relegated to
the virtual world of calculation.
2b
Experimental Section
General Procedures. NMR spectra, H (400 MHz) and 13C (100.6
1
1
2
and Wiest and those of Jiao and Schleyer of 36.9 and 34.9
-
1 26
7
3
MHz), were measured in CDCl and, unless otherwise noted, on a
kcal mol
with the experimental value of Roth and K o¨ nig
1
13
Varian Mercury 400 instrument, whereas H (500 MHz) and C (125.7
MHz) spectra were measured on a Varian Unity/Inova 500 instrument.
Chemical shifts are reported in ppm relative to tetramethylsilane (δ)
of 36.3 kcal mol-1 for s-trans-1,3(Z)-pentadiene were obtained
in neglect of a tunneling component.
Curvature in the Arrhenius plot constitutes a third, closely
with respect to residual C D H (7.15 ppm for H and 128.0 ppm for
1
6
5
2
7
13
related criterion advanced as a manifestation of tunneling.
C). Spin-lattice relaxation times (T
inversion-recovery method in benzene-d
1
) were determined by the
. Preparative GC on a Varian
Indeed Chantranupong and Wildman note, “Because the Ar-
rhenius plots for hydrogen transfer show no indication of
curvature, it might seem that this reaction can be described in
6
Aerograph A90-P3 instrument employed a 3-m column of 20%
Carbowax 20M on Anachrom AS with He as a carrier gas. Analytical
gas chromatography was conducted on a Hewlett-Packard (HP) 5890A
gas chromatograph equipped with a J&W Scientific, Inc. DB-225
5
terms of a conventional, thermally activated process.” This
criterion has now been pursued more searchingly by adding to
the published kinetic study of the kinetics of rearrangement of
(cyanopropylphenyldimethylpolysiloxane) megabore column (0.53 mm
i.d. × 30 m, 1 µm film thickness) and an HP 3393A integrator.
Bicyclo[4.4.0]decane-2,10-dione. A solution of ethyl 4-(3-oxocy-
clohexyl)-butyrate (1.2 g, 5.65 mmol, prepared according to the
1
-p-tolyl-5-phenyl-1,3(Z)-pentadiene10 an extension to lower
temperatures over a necessarily much longer period of time.
After 339 days (29 289 600 s), we can now report reliable
29
literature ) and sodium hydride (0.29 g, 12 mmol, 60% in mineral
oil) in 15 mL of anhydrous benzene was boiled under reflux for 15 h.
To the solution cooled in an ice bath, 20 mL of a 10% solution of
9
-1
specific rate constants of 3.58 ( 0.20 × 10- s and 2.82 (
8
-1
0
.14 × 10- s at 77.1 °C and 98.4 °C, respectively (95%
KH
ether extract, which was washed with water, dried over anhydrous Na
SO , filtered, concentrated, and subjected to column chromatography
silica gel, hexane/ethyl acetate, 20:1) to give 0.8 g (85% of theoretical
2 4
PO was added. Extraction twice with ether (30 mL each) gave an
confidence level). When combined with the published rate
constants at 153.7 and 185.2 °C,10 these new data give a straight-
2
-
4
line Arrhenius plot with no sign of curvature over the 108 °C
range of temperature. The resulting Arrhenius equation has the
(
1
yield) of the dione as pale-yellow crystals: H NMR 0.84-0.89 (m,
parameters: ln k ) (21.7 ( 0.7 - (14,420 ( 265)/T; Ea )
1
H), 1.14-1.25 (m, 3H), 1.61-1.71 (m, 2H), 1.82-1.93 (m, 3H), 2.34-
q
2
8.7 ( 0.5; and log A ) 9.41 ( 0.3 (∆H (404.3K) ) 27.9). These
2.46 (m, 4H), 16.17 (br s, 1H); 13C NMR 21.67, 29.92, 33.96, 35.98,
values remain little changed from those reported earlier on the
110.76, 190.89.
basis of rate constants at the two higher temperatures (Ea )
2-Hydroxy-2-methylbicyclo[4.4.0]decan-10-one. To a solution of
methylmagnesium iodide (prepared from 0.44 g of magnesium sus-
pended in 15 mL of anhydrous ether under argon and 2.6 g of methyl
iodide in 5 mL of anhydrous ether), 1.0 g (6 mmol) of bicyclo[4.4.0]-
decane-2,10-dione in 6 mL of anhydrous ether was added slowly at 0
-
1
3
0.1 ( 0.9 kcal mol and log A ) 10.14 ( 0.9). Attention is
q
directed to a value for ∆H recently calculated by Hayase,
Hrovat, and Borden for 1,5-diphenyl-1,3-(Z)-pentadiene of 32.6
kcal mol (no estimate of uncertainty given). The discrepancy
-
1
°
C. After being stirred overnight at room temperature, the reaction
mixture was quenched with saturated aqueous NH Cl, neutralized with
0% aqueous HCl, and extracted with 80 mL of ether. The ethereal
extract was washed with water, dried over anhydrous Na SO , filtered,
-
1
of 4.7 kcal mol is probably not due to the presence of one
4
p-methylphenyl group in place of the second phenyl.
1
At least over this 108 °C range of temperature, there is no
indication of a curvature that might indicate a tunneling effect.
Even though there is an experimentally verifiable contribution
from tunneling, the temperature-dependent Arrhenius component
of the rate is still too large at our lowest temperature relative to
the rate of the putative, temperature-independent tunneling
component to make an experimental observation of an increase
in the KDIE possible.27 In the investigations of Platz and co-
workers, by contrast, hydrogen abstraction by diphenylcarbene
at very low temperatures gives convincing evidence for tun-
2
4
concentrated, and subjected to column chromatography (silica gel,
hexane/ethyl acetate, 10:1 to 3:1) to give 0.57 g (52% of theoretical
yield) of 2-hydroxy-2-methylbicyclo[4.4.0]decane-10-one as a pale-
yellow oil: 1H NMR (500 mHz, CDCl
) 1.15-1.21 (m, 2H), 1.33-
3
1
3
2
2
2
.06 (m, 14H), 2.24-2.29 (m, 1H), 2.37-2.41 (m, 1H); C NMR
2.35, 22.51, 24.80, 32.65, 34.56, 40.34, 40.71, 42.38, 63.80, 71.75,
14.24.
2
-Methylbicyclo[4.4.0]dec-1-en-10-one. A solution of 0.57 g (3.1
mmol) of 2-hydroxy-2-methylbicyclo[4.4.0]decan-10-one in 30 mL of
benzene containing 100 mg of p-toluenesulfonic acid in a 50-mL, round-
bottomed flask fitted with a Dean-Stark trap was boiled under reflux
(
24) At room temperature (298.15 K) and in neglect of the uncertainties in ln
A, k
H
/k
D
) 16.6 but ranges from 6.5 to 43 at the level of standard error
(28) (a) Platz, M. S.; Senthilnathan, V. P.; Wright, B. B.; McCurdy, C. W., Jr.
J. Am. Chem. Soc. 1982, 104, 6494-6501. (b) Hadel, L. M.; Platz, M. S.;
Scaiano, J. C. J. Am. Chem. Soc. 1983, 105, 283-287. (c) Shaffer, M. W.;
Leyva, E.; Soundararajan, N.; Chang, E.; Chang, D. H. S.; Capuano, V,;
Platz, M. S. J. Phys. Chem. 1991, 95, 7273-7277.
(29) Knochel, P.; Berk, M. C. P. Y. S.; Talbert, J. J. Org. Chem. 1988, 53,
2392-2394.
and from 1.6 to 168 at the 95% confidence level!
(
25) Hayase, S.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2004, 126,
1
0028-10034.
(
(
26) Jiao, H.; Schleyer, P. v. R. J. Am. Chem. Soc. 1988, 110, 8223-8228.
27) The Arrhenius plot of ln[(kobs ] ) ln(A /A ) - [(E - (E ]/RT
is no longer linear when (ktun is added to the expression for (kobs
)
H
)
/(kobs
H
)
D
H
D
a
)
H
a
)
D
) .
H
9084 J. AM. CHEM. SOC.
9
VOL. 128, NO. 28, 2006

1,5-Hydrogen Shift of a 1,3(Z)-Pentadiene
A R T I C L E S
for 2.5 h. The cooled reaction mixture was washed successively with
saturated aqueous NaHCO , water, and brine to give a benzene solution,
which was dried over anhydrous Na SO , filtered, concentrated, and
subjected to column chromatography (silica gel, hexane/ethyl acetate,
0:1) to give 0.31 g (61% of theoretical yield) of 2-methylbicyclo-
precipitate, which was removed by filtration. Concentration gave a crude
product, which was subjected to column chromatography (basic
aluminum, hexane), and a final purification by GC on the preparative
column at 66 °C to afford 0.17 g (42.9%) of 2-trideuteriomethyl-10-
methylenebicyclo[4.4.0]dec-1-ene as a colorless oil: H NMR (500
6
MHz, benzene-d ) 1.07-1.14 (m, 2H), 1.38-1.49 (m, 2H), 1.56-1.60
3
2
4
1
1
1
[4.4.0]dec-1-en-10-one as a colorless oil: H NMR 1.18-1.24 (m, 1H),
1.31-1.44 (m, 2H), 1.61-1.70 (m, 2H), 1.80-1.96 (m, 6H), 2.05-
2
.08 (m, 2H), 2.22-2.30 (m, 2H), 2.43-2.48 (m, 1H); 13C NMR 21.53,
21.99, 23.95, 31.01, 33.20, 33.98, 39.36, 43.19, 135.03, 143.57, 204.65.
(m, 1H), 1.66-1.72 (m, 3H), 1.89-1.92 (m, 2H), 1.99-2.05 (m, 2H),
2.27-2.31 (m, 1H), 4.77 (q, J ) 1.47 Hz, 1H), 5.00 (d, J ) 2.44 Hz,
1H); 13C NMR (benzene-d
6
) 22.05, 27.73, 31.92, 32.49, 35.56, 37.41,
2
2
-Methyl-10-methylene-d -bicyclo[4.4.0]dec-1-ene (1). Trideute-
39.82, 111.12, 127.17, 135.75, 148.24; exact mass HRMS (EI) calcd
riomethyllithium (22 mL of a 0.5 M solution in diethyl ether; 11 mmol)
was added dropwise to a suspension of bis-cyclopentadiene titanium
dichloride (1.25 g, 5 mmol) under argon at 0 °C. After 1 h, the mixture
for C12
H
15
D
3
165.1594, found 165.1586.
1
Kinetics. All analyses were by H NMR in benzene-d at 600 MHz
6
on a Unity/Varian Inova 600 instrument. Even with this resolving
power, baseline separation of the isotopomers in Figure 2 was not
always achievable. To better separate the two sets of three signals used
in the acquisition of the data-relating concentration and time of reaction
(Table 2), the data were processed by using resolution enhancement
by 1.0 Hz and Gauss apodization by 0.4 s. Samples were prepared by
was quenched with cold D
2
O and separated. The ethereal layer was
4
, filtered, and concentrated to give orange
dried over anhydrous Na SO
2
crystals of bis-cyclopentadiene dimethyltitanium. This material was
dissolved in 10 mL of anhydrous toluene and treated with the sample
of 2-methylbicyclo[4.4.0]dec-1-en-10-one above in 5 mL of toluene.
The reaction mixture was stirred at 75 °C in the dark for 46 h. The
addition of hexane at room temperature precipitated solid material,
which was removed by filtration. Concentration of the hexane phase
and chromatography on basic alumina (hexane as eluant) afforded 0.17
placement in NMR tubes with benzene-d as the solvent and by being
6
sealed under vacuum after three freeze-dry cycles. Heating was in the
vapors of boiling liquids: acetophenone, average temperature: 201.6
( 0.2 °C; diethyl oxalate, 184.42 ( 0.24 °C; tert-butylbenzene, 167.7
( 0.2 °C. At 201.6 °C, two sets of NMR measurements were obtained
at 15 time intervals ranging from 0.5 and 1.0 h at the beginning of a
run to 110 and 205 h, respectively, at the end. A similarly large number
of points was taken at the other temperatures. Acquisition times were
4.00 s; relaxation time delay was 40 s; and the number of accumulated
determinations was 16.
To confirm that the borosilicate glass of the NMR tubes used as
reaction vessels was not interfering with accuracy by acid-catalysis of
undesired constitutional changes, two experiments were conducted in
soft-glass tubes using p-xylene-d10 as solvent at 201.6 °C for 112 h
(403 200 s) and 205 h (738 000 sec). Analysis of compounds 1, 2, and
(E + Z)-3 (See Figure 2), as described above, revealed concentrations
that did not differ from the comparable runs in NMR tubes within
experimental uncertainties: i.e., (5% (Table SI-6).
g (54%) of 2-methyl-10-methylene-d
2
-bicyclo[4.4.0]dec-1-ene as a pale-
yellow oil: H NMR (500 MHz, benzene-d ) 1.07-1.14 (m, 2H), 1.38-
.46 (m, 2H), 1.56-1.60 (m, 1H), 1.64-1.71 (m, 3H), 1.80 (t, J )
.98 Hz, 3H), 1.90-1.92 (m, 2H), 2.00-2.09 (m, 2H), 2.26-2.31 (m,
1
6
1
0
1
3
1
3
H); C NMR (125.7 MHz, benzene-d
2.59, 35.58, 37.32, 39.85, 127.28, 135.70, 148.06; exact mass HRMS
164.1532, found 164.1524.
-Trideuteriomethylbicyclo[4.4.0]dec-1-en-10-one. To a solution
of bicyclo-[4.4.0]decane-2,10-dione (1.0 g, 6 mmol) in 10 mL of
anhydrous diethyl ether under argon at 0 °C, methyl-d -magnesium
6
) 21.11, 22.08, 27.75, 31.94,
(EI) calcd for C12H D
16 2
2
3
iodide (18 mL, 1.0 M in diethyl ether, 18 mmol, Aldrich, 99 atom %
D) was added dropwise. After being warmed to room temperature, the
reaction mixture was stirred overnight, then quenched with saturated
aqueous NH
extracted with diethyl ether (2 × 30 mL). The combined extracts were
washed with water, dried over anhydrous Na SO , filtered, and
4
Cl, neutralized with aqueous HCl (10%), and then
Analysis of the kinetics of the rearrangement of compound 1′ requires
correction for a weak absorption (∼11%) at 1.76 ppm (see uncorrected
data in Table SI-4). A simple correction is made on the assumptions
that the impurity is dideuteriomethyl 1 formed by partial exchange of
deuterium by hydrogen during the preparation of 2-methylbicyclo[4.4.0]-
dec-1-en-10-one, and that its contributions to the raw data at the various
2
4
concentrated. The residue was dissolved in 40 mL benzene in a 100-
mL, round-bottomed flask fitted with a Dean-Stark device. p-
Toluenesulfonic acid (0.2 g) was added, and the mixture was heated
under reflux for 2 h. After being cooled to room temperature, the
reaction mixture was washed successively with saturated aqueous
30
times of reaction can be calculated on the basis of the approximate
NaHCO
Na SO , filtered, concentrated, and subjected to column chromatography
silica gel, hexane-diethyl ether: 15:1) to give 0.47 g (47%) of
-trideuteriomethylbicyclo[4.4.0]dec-1-en-10-one as a pale-yellow
3
, water, and brine. The organic phase was dried over anhydrous
rate constants obtained for compound 1. These values are then
subtracted to produce the corrected values in Table SI-5. The resulting
specific rate constants are those given in Table 3.
2
4
(
2
1
oil: H NMR 1.18-1.27 (m, 1H), 1.32-1.48 (m, 2H), 1.67-1.76 (m,
Acknowledgment. We express our warmest thanks and
appreciation to Dr. Edmund J. Keliher for his assistance. This
work has been fully supported by the Norman Fund in Organic
Chemistry in memory of Ruth Alice Norman Weil Halsband
and Edward A. Norman. We thank Professor Wolfram Grimme,
Universit a¨ t zu K o¨ ln, and Professor Dieter Hasselmann, Ruhr
Universit a¨ t Bochum, for their critical scrutiny of the manuscript.
2
2
1
H), 1.84-2.00 (m, 3H), 2.07-2.17 (m, 2H), 2.25-2.34 (m, 2H), 2.46-
.52 (m, 1H); C NMR 21.53, 23.94, 31.02, 33.19, 33.91, 39.34, 43.17,
35.08, 143.50, 204.61.
13
2-Trideuteriomethyl-10-methylenebicyclo[4.4.0]dec-1-ene (1′). Me-
thyllithium (9.4 mL, 1.6 M solution in diethyl ether, 15 mmol, Aldrich)
was added dropwise to a suspension of bis-cyclopentadiene titanium
dichloride (1.74 g, 7.0 mmol) in 5 mL anhydrous diethyl ether under
argon at 0 °C. After 1 h, the mixture was quenched with water. The
ether layer was separated, dried over anhydrous Na SO , filtered, and
2 4
concentrated. The resulting orange crystals were dissolved in 15 mL
of anhydrous toluene, and 2-trideuteriomethylbicyclo [4.4.0]dec-1-en-
Supporting Information Available: Seven tables giving
concentration/time data. This material is available free of charge
via the Internet at http://pubs.acs.org.
1
0-one (0.4 g 2.4 mmol) in 5 mL of anhydrous toluene was added
under argon. The reaction mixture was stirred at 70 °C in the dark for
0 h and cooled to room temperature. Addition of hexane produced a
JA057377V
4
(30) Frey, H. M.; Solly, R. K. Trans. Faraday Soc. 1968, 64, 1858-1865.
J. AM. CHEM. SOC.
9
VOL. 128, NO. 28, 2006 9085