Effect of deuterium on the kinetics of 1,5-hydrogen shifts: 5-Dideuteriomethylene-2,4,6,7,9-pentamethyl-11,11a-dihydro-12H-naphthacene

Article abstract of DOI:10.1021/ja066018c

To obtain a more reliable temperature dependence of the kinetic deuterium isotope effect in a 1,5-hydrogen shift, the title compound has been designed to repress compromising side reactions, arguably arising from second-order ene-ene unions. The values of

Full text of DOI:10.1021/ja066018c

Published on Web 02/09/2007
Effect of Deuterium on the Kinetics of 1,5-Hydrogen Shifts:
5-Dideuteriomethylene-2,4,6,7,9-pentamethyl-11,11a-
dihydro-12H-naphthacene
William von E. Doering* and Edmund J. Keliher
Contribution from the Department of Chemistry and Chemical Biology, HarVard UniVersity,
Cambridge, Massachusetts 02138-2902
Received August 18, 2006; E-mail: doering@chemistry.harvard.edu
Abstract: To obtain a more reliable temperature dependence of the kinetic deuterium isotope effect in a
1,5-hydrogen shift, the title compound has been designed to repress compromising side reactions, arguably
arising from second-order ene-ene unions. The values of kH/kD, 4.58-5.15, in the range 185.8-153.8 °C,
on extrapolation by the derived Arrhenius equation, lead to 8-14 at 25 °C. Another goal is the evaluation
of the effect on rates of the free rotation available to the phenyl groups in 2,4-diphenyl-1,3(Z)-pentadiene
compared to the constraint to coplanarity of the phenyl groups in the title compound. The effect is
insignificant. Incidental to the presence of the sterically effective methyl groups in the title compound,
participation of the hydrogen atoms of an aromatic methyl group as part of the 1,3(Z)-pentadienyl system
has been uncovered in 6,8-dimethyl-1-methylene-1,2,3,4-tetrahydronaphthalene. The rate of the rear-
rangement is too slow to compromise the kinetics of the hydrogen shifts in the title compound. A
reassessment of the conventional procedure for estimating uncertainties in Arrhenius parameters based
on a small number of rate constants has led to the proposal of an alternative procedure based on the
statistically more significant uncertainties associated with the individual rate constants.
Scheme 1
Introduction
The pioneering work of Roth and Ko¨nig on the kinetic
deuterium isotope effect (KDIE) in the thermal 1,5-hydrogen
shift in 1,3(Z)-penta-1,3-diene at 185-201 °C revealed a large
value of 5.7 and a dramatic increase to 12.2 on extrapolation to
25 °C.1 Taken with the definitive establishment of the stereo-
chemistry of the rearrangement,2 their work prompted theoretical
interest in the possible role for tunneling in the mechanism of
the thermal 1,5-hydrogen shift.3 As already cautioned,4 the
Arrhenius parameters providing the basis for the temperature
dependence of the KDIE were of insufficient precision to justify
their acceptance as experimentally assured points for comparison
with theoretical results (Scheme 1). In the hope of obtaining
more reliable results, Doering and Zhao studied an example
frozen in the reaction-competent cis conformation of the diene
without achieving a satisfactory improvement (2, Scheme 1).5
Disturbing complications were unsatisfactory levels of recovery
over time and a persistent failure to reach the statistically
expected ratios among the three products at long times of
reaction.
(1) Roth, W. R.; Ko¨nig, J. Liebigs Ann. Chem. 1966, 699, 24-32.
(2) Roth, W. R.; Ko¨nig, J.; Stein, K. Chem. Ber. 1970, 103, 426-439.
(3) (a) Liu, Y.-p.; Lynch, G. C.; Truong, T. N.; Lu, D.-h.; Truhlar, D. G.;
Garnett, B. C. J. Am. Chem. Soc. 1993, 115, 2408-2415. (b) Chantran-
upong, L.; Wildman, T. A. J. Am. Chem. Soc. 1990, 112, 4151-4154. (c)
Dewar, M. J. S.; Healy, E. F.; Ruiz, J. M. J. Am. Chem. Soc. 1988, 110,
2666-2667. (d) Jensen, F.; Houk, K. N. J. Am. Chem. Soc. 1987, 109,
3139-3140.
The present work was undertaken to obtain a more accurate
value for the temperature dependence of the KDIE in a 1,5-
hydrogen shift and to compare 2,4-diphenyl-1,3(Z)-pentadienes
(3) with previously published work on 1-p-tolyl-5-phenyl-1,3-
(Z)-pentadiene.4
(4) Doering, W. v. E.; Keliher, E. J.; Zhao, X. J. Am. Chem. Soc. 2004, 126,
14206-14216.
(5) Doering, W. v. E.; Zhao, X. J. Am. Chem. Soc. 2006, 128, 9080-9085.
9
2488
J. AM. CHEM. SOC. 2007, 129, 2488-2495
10.1021/ja066018c CCC: $37.00 © 2007 American Chemical Society

Effect of Deuterium on Kinetics of 1,5-Hydrogen Shifts
A R T I C L E S
Table 1. Specific First-Order Rate Constants for 1,5-Hydrogen
Shifts
a,e
3kH
b,e
c,e
d,e
T,
°
C
3kH
3kH
3kD
201.5
185.0
169.5
154.0
118.0
97.3
27.0
6.91
2.08
15.4f
4.14
63.0 ( 0.6g
95.7 ( 2.5g
29.3 ( 0.76g
1.46 ( 0.05g
5.24 ( 0.06g
aIn 1,1-dideuterio-2,4-diphenylpenta-1,3(Z)-diene. b In 1-phenyl-5-p-
tolylpenta-1,3(Z)-diene. c In 2-methyl-10-methylenebicyclo[4.4.0]dec-1-ene.
d In penta-1,3(Z)-diene. e All values of k in units of 10-6 s-1 f Calculated
.
from Arrhenius equation (experimental: 13.4 at 200.0 °C).4 g 95%
confidence level.
Scheme 2
Figure 1. Preparation from dypnone of 3-1,1-d2 and its thermal rearrange-
ment to 3-5,5-d2 and 3-1,5-d2 are shown. The shifts in the 1H NMR spectrum
of the hydrogen atoms used in the analysis of the kinetics are shown in
ppm (δ).
Results
Preparation of 1,1-dideuterio-2,4-diphenyl-1,3(Z)-pentadiene
(3-1,1-d2) from (E)-dypnone6 involved methylenation (conversion
of the carbonyl group to methylene) following the method of
Petasis and Bzowej employing dimethyltitanocene (Figure 1).
006
7
169.5 °C. That behavior is consistent with the prediction of a
lower energy of activation for loss of monomer through ene-
ene union.
Early in the study of the kinetics of 3-1,1-d2, a steady decline
in recovery with time of reaction made the achievement of
reliable results problematic. As an illustration, recovery of
deuterium isotopomers at 118 °C after 815 h was only 50%,
while the 1,5-hydrogen shift had itself proceeded barely 50%
toward equilibrium (Table S1).
The kinetics of deuterium exchange was followed at four
1
temperatures, analysis being by 600-MHz H NMR spectros-
copy. Two sets of signals relating concentration to time were
employed: the first, those of the methyl groups; the second,
the CH3 at 1.81, the dCH2 group at 5.01 and 4.78, and the
dCHD group at 5.00 and 4.76 ppm (δ) (Figure 1). By both
methods, baseline separation was nearly, but not completely,
achieved. There was no obvious basis for choosing between
the two methods of analysis.
A likely culprit was thought to be the competitive formation
of dimeric side products initiated by an ene-ene union to a
1,4-diradical (Scheme 2). This type of dimerization had been
estimated to have an activation energy of 24.0 kcal mol-1 in
the paradigm, butadiene (experimental: 26 kcal mol-1).8
Enhancement of stabilization in the allylic radical moieties by
two phenyl groups could amount to 6.6-4.3 kcal mol-1 by one
phenyl group and 2.3 kcal mol-1 by the second.9 Mulzer had
indeed reported an activation enthalpy of 12.4 kcal mol-1 for
the dimerization of 1,3-diphenylbuta-1,3-diene in fine agreement
with a predicted value of 11.4 kcal mol-1 (24.6 - 2 × 6.6 kcal
mol-1).10 However, a traditional plot of the reciprocal of
concentration against time to confirm second-order kinetics was
not linear. Nor did a doubling of the concentration of starting
material improve recovery by more than 20%. Even if the effect
of byproducts on the kinetics might have been handled credibly
by introducing an extra irreversible second-order step, the effect
on the accuracy of analysis by NMR would have remained
difficult to estimate. It is noted that the relative ratios of
hydrogen shift to loss of material is smallest at the lowest
temperature, 118.0 °C, and largest at the highest temperature,
Rate constants for the conversion of 3-1,1-d2 to 3-5,5-d2 have
been obtained by extrapolation to zero time of the tangents to
the plot of data relating concentration and time given in Table
S1 in the Supporting Information. These are summarized in
Table 1 along with the corresponding rate constants for
1-phenyl-5-p-tolyl-1,3(Z)-penta-1,3-diene. 4 The ratios of those
from the 2,4-diphenyl isomer 3 to the 1-phenyl-5-p-tolyl are
4.4, while the Arrhenius parameters are Ea ) 30.6 ( 3.4 kcal/
mol-1, log A ) 11.05 ( 0.14, and Ea ) 30.1 ( 0.9 kcal/mol-1
,
log A ) 10.14 ( 0.9, respectively. These values may be
compared with those of Ea ) 36.1 ( 2.2 and log A ) 11.34 (
1.0 reported for the paradigm by Roth and Ko¨nig.1 The
corresponding values of enthalpies of activation, 29.7 and 29.3
kcal/mol-1, respectively, compare very well with the B3LYP
calculational results of Hayase, Hrovat, and Borden: 28.8 and
28.8 kcal/mol-1, respectively.11,12 These authors discuss ex-
haustively the steric and electronic factors that may account
for the ∼7-kcal/mol-1 differences to the paradigm. Electronic
stabilization was in any event not expected to contribute more
than that seen in the comparison of allyl radical with cinnamyl
or the 1,3-diphenylallyl radical. These are of the same magnitude
as the loss of electronic stabilization by steric forcing out of
coplanarity of phenyl groups and conventional steric repulsions
in the cis and trans starting materials. Whether the “aromatic”
transition region is especially resistant to electronic stabilization
by substituents is not clear.
(6) Muzart, J. Synthesis 1982, 60-61.
(7) Petasis, N. A.; Bzowej, E. I. J. Am. Chem. Soc. 1990, 112, 6392-6394.
(8) Doering, W. v. E.; Belfield, K. D.; He, J. J. Am. Chem. Soc. 1993, 115,
5414-5421.
(9) Doering, W. v. E.; Benkhoff, J.; Shao, L. J. Am. Chem. Soc. 1999, 121,
962-968.
(10) Mulzer, J.; Ku¨hl, U.; Huttner, G.; Evertz, K. Chem. Ber. 1988, 121, 2231-
2238.
(11) Hayase, S.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2004, 126,
10028-10034.
(12) In footnote 11 of ref 11, attention is directed to the success of the
calculations in the absence of inclusion of a tunneling component.
9
J. AM. CHEM. SOC. VOL. 129, NO. 9, 2007 2489

A R T I C L E S
Scheme 3
Doering and Keliher
Scheme 4
1,5-Hydrogen Shift in Naphthacenes. Forcing the phenyl
groups in 3 into coplanarity with the sterically vulnerable
methylene group was deemed a reasonable way to fix the
pentadiene in the cisoid conformation, to slow dimerization
relative to hydrogen transfer, and to limit loss of electronic
stabilization by non-coplanarity. The consequent tetracyclic
structure 7 was prepared from the known 5,6-dioxo-5,5a,6,11,-
11a,12-hexahydronaphthacene (4) (Scheme 3).13Of the various
conditions mentioned in that reference for the conversion of
(dibenzylmethyl)malonic acid to 4, polyphosphoric acid/
phosphorus pentoxide afforded variable yields accompanied by
a deep red product of dehydrogenation, proposed to be 6-hy-
droxy-12H-naphthacen-5-one (5). Gupte and co-workers had
noted the appearance of a red, non-enolizable R,â-unsaturated
diketone in the cyclization of di-R-naphthylmethylmalonic acid
following a procedure of Clar and co-workers.14
shown by X-ray diffraction analysis to be that of 10. Further
support is thereby given to the structure proposed for 5, the
analogue without the four methyl groups (Scheme 3). Paren-
thetically this oxidation, if by hydride abstraction, would be
favored by a direct coupling with the enolized â-diketone
depicted in an extreme electronic form in 9′ of Scheme 4.
Specific rate constants have been calculated by numerical
integration by use of the program KINETIK of Dr. R. Fink,
which employs a Runge-Kutta procedure of fourth order, allows
up to seven components to be handled by ad libitum kinetic
schemes, and provides errors at the 95% confidence interval
for individual rate constants by incorporation of the method of
Marquardt.15,16
Although the change from acyclic 3-1,1-d2 to cyclic 7 did
improve recovery somewhat, the ratio of 1,5-hydrogen shift to
recovery remained too unfavorable to hold promise of affording
reliable kinetics.
The rearrangement of the tetramethylnaphthacene analogue
12-1,1-d2 of the unsubstituted 7 is clean. Recovery remains
undiminished over the entire length of the kinetic study. In the
previous work on the KDIE of the 1,5-hydrogen shift4 and now
with 12-1,1-d2, the equilibrium ratios among the three isomers
at long times of reaction deviate slightly from those predicted
in neglect of secondary deuterium isotope effects, 0.100:0.300:
0.600 (Scheme 1). The experimental ratios at each of the three
temperatures are 0.098, 0.308, and 0.594 (see Table SI-3 in the
Supporting Information). These deviations are consistent with
the difference in bond strengths between the relatively weaker
sp2 and stronger sp3 carbon deuterium bonds.17 This factor
increases the equilibrium concentration of the methylene-
dideuteriomethyl isotopomer, 12-5,5-d2, relative to the other two
(Figure 2).
In a final effort to suppress the competitive formation of
frustrating byproducts, a further increase in steric shielding was
introduced by the addition of ortho methyl groups as in
compound 12 of Scheme 4. For convenience in synthesis, 3,5-
dimethylbenzyl magnesium bromide was employed instead of
3-methylbenzyl magnesium bromide in order to avoid the
formation of several unwanted constitutional isomers. The
structure of 12 was confirmed by X-ray diffraction analysis.
Although it could be assumed that the two superfluous methyl
groups remaining in the para positions would not constitute a
perturbation of disturbing magnitude, the presence of the ortho
methyl groups opened the possibility of a competing 1,5-
hydrogen shift.
In this preparation, a red impurity is formed in variable
amount when the diacid chloride and aluminum trichloride as
catalyst are used but can be avoided by the use of stannic
chloride as the Lewis acidic catalyst. Its structure has been
(15) Roth, W. R.; Fink, R., unpublished.
(16) Marquardt, D. W. J. Soc. Ind. Appl. Math. 1963, 11, 431-441.
(17) Sunko, D. E.; Humski, K.; Molojcic, R.; Borcic, S. J. Am. Chem. Soc.
1970, 92, 6534-6538. Barborak, J. C.; Chari, S.; Schleyer, P. v. R. J. Am.
Chem. Soc. 1971, 93, 5275-5277. Gu¨nther, H.; Pawliczek, J. B.; Ulmen,
J.; Grimme, W. Angew. Chem., Int. Ed. Engl. 1972, 11, 517-518. Gajewski,
J, J.; Conrad, N. D. J. Am. Chem. Soc. 1979, 101, 6693-6704.
(13) Gupte, S. D.; Nabar, D. P.; Sunthankar, S. V. J. Sci. Ind. Res. 1960, 19B,
411-412.
(14) Clar, E.; Kemp, W.; Stewart, D. G. Tetrahedron 1958, 3, 325-333.
9
2490 J. AM. CHEM. SOC. VOL. 129, NO. 9, 2007

Effect of Deuterium on Kinetics of 1,5-Hydrogen Shifts
A R T I C L E S
The second compares the obligatorily cisoid 2 and the
equilibrated transoid and cisoid pair, 2,4-diphenylpenta-1,3(Z)-
11
diene 3, in which the cisoid conformation is favored. After
calculation by means of the reported Arrhenius equation, the
specific rate constants estimated for 2 at 169.5 °C (6.91 × 10-6
s-1) and 154.0 °C (2.08 × 10-6 s-1) are found to be slower
than those of 3 at the same temperatures by factors of 13.9 and
14.1, respectively. The radical-stabilizing effect of the two
phenyl groups can be expressed at the 1- and 3-positions of an
allyl radical but not at the 2- and 4- positions of a pentadienyl
radical (nodal positions) as depicted in Figure 4. In this
comparison the transoid/cisoid complication is avoided. The
conjugative stabilization of the phenyl groups in the starting
material has been more than overcome in the transition region
consistent with a compromised conformation behaving substan-
tially like a relatively insensitive “aromatic” system (Figure 4).
Note that the effect of radical-stabilizing substituents in the two
5-positions of the Cope rearrangement are much larger because
they operate on a simple secondary radical, not on an already
well stabilized allyl or pentadienyl radical.
Figure 2. Kinetic scheme for the interconversions starting from 12-1,1-d2
are shown along with the 1H NMR signals employed in the analyses of
concentrations versus time.
The thermodynamic (equilibrium) isotope effect is likely also
to compromise the values of KDIE evaluated from 2/3(3kH/2kD)
and k-H/k-D to the extent that it has begun to take effect in the
transition region. In the former, 3kH will be slightly accelerated
and 2kD slightly decelerated, while, in k-H/k-D, k-H will be
decelerated, and k-D, accelerated in comparison to the nonob-
servable rates in the all-protium and all-deuterium analogues.
This effect may contribute to the higher values of KDIE in
column six of Table 2 vis-a`-vis the lower values in column seven
but cannot provide the entire explanation. The thermodynamic
The third is a comparison of 3 and 12-1,1-d2, in which the
phenyl groups are rigidly confined to coplanarity with the
rearranging pentadienyl system. The surprising closeness of the
specific rate constantssat 169.5 °C, 95.7 and 81.4 × 10-6 s-1
,
and at 154.0 °C, 29.3 and 23.4 × 10-6 s-1, respectivelyssuggest
almost identical interaction of the two phenyl groups in the
starting materials and transition regions.
1
isotope effect is reduced in the ratios /3(3kH)/k-D and 2(k-H)/
If the rearrangement of the hydrogen atom in the aromatic
methyl group of 13-1,1-d2 at a temperature as low as 258 °C
seemed surprising, Grimme and his co-workers have established
in several examples that benzo-annelation in a transition state
leads to an increase in free energy of activation in the range
10-12 kcal mol-1, a value much less than that expected if the
entire resonance energy of benzene was to have been lost in
the transition region.18 Among other examples quoted in that
reference, fusion of a benzene ring with one of the double bonds
in the 1,7-hydrogen shift has been extensively examined by the
late Hans Schmid and his co-workers.19 Their rate constant may
be compared, if imperfectly, with that of the acyclic 1,7-
hydrogen shift studied by Baldwin and Reddy.20 The result is a
ratio of 210 000 at 225 °C (∆∆Gq ) 12.1 kcal mol-1) between
the acyclic and benzo-fused trienes. Also of note is a ratio of
∼270 000 (∆∆Gq ) 11.5 kcal mol-1) for the hydrogen shifts
in cyclopentadiene and indene calculated from the data of
Roth.21
In our initial attempts to extrapolate in the accepted manner
the KDIE of the naphthacene 12-1,1-d2 from the higher temper-
atures to the much lower temperature of 25 °C, plotting the
natural logarithms of the three values of the ratio, (3kH/2kD)
(2/3) (as they were first calculated) against the reciprocal of
temperature revealed an almost perfect straight line! The fortuity
of this linearity prompted us to rethink the uncertainties
associated with the conventional evaluation by least-squares of
an Arrhenius equation based on a small number of specific rate
constants! (Uncertainty in the slope and intercept is, of course,
indeterminate by this approach when only two data are
available.) Individual rate constants fall randomly within an error
2kD (columns eight and nine of Table 2, respectively).
Questioning the validity of the assumption that the ortho
methyl groups in 12 would not engage in a 1,5-hydrogen shift,
we prepared a truncated version (13) of 12 and examined it
enough to demonstrate that at higher temperatures the hydrogen
shift did occur, but at a rate too slow to be a disturbing factor
at the temperatures of the study of 12 (see Figure 3). At 258.4
( 0.2 °C, 13-1,1-d2 rearranged cleanly in tubes of lead-potash
glass to 13-1,5-d2 and 13-5,5-d2, presumably reversibly, but
demonstrably without contaminating rearrangement to 1,6,8-
trimethyl-3,4-dihydronaphthalene. A rough rate constant, 3.1 ×
10-6 s-1 at 258 °C, was estimated by extrapolation to zero time
of a first-order plot of the data in Table S4 for the disappearance
of 13-1,1-d2. As was to be expected, the two hypothetical non-
benzenoid intermediates could not be detected.
The specific rate constant for 13-1,1-d2 (3.1 × 10-6 s-1 at
258 °C) may be compared to the values for 2 and 12-1,1-d2
extrapolated to the same temperature: 4.1 × 10-3 s-1 and
2.5 × 10-2 s-1, respectively. The resulting factors, 1300 and
8000 (∆∆Gq258°C ) 9500 cal/mol), respectively, are compatible
with expectation (vide infra).18
Discussion
To begin, three comparisons may be of interest. The first is
that between the equilibrated pair, transoid and cisoid penta-
1,3(Z)-diene 1, in which the transoid is favored by ∼3.5 kcal
mol-1, and the rigidly cisoid 2-methyl-10-methylenebicyclo-
[4.4.0]dec-1-ene 2. The latter reacts faster at both 201.5 and
185.0 °C by a factor of ∼6 (∆Ea ∼3-4 kcal mol-1). This point
has been discussed recently at length.5
(18) Grimme, W.; Grommes, T.; Roth, W. R.; Breuckmann, R. Angew. Chem.,
Int. Ed. Engl. 1992, 31, 872-874. Grommes, T. Ph.D. Dissertation,
“Pericyclic Reactions with Participation of a Double Bond of Benzene,”
University of Cologne, 1991.
(19) Heimgartner, H.; Hansen, H.-J.; Schmid, H. HelV. Chim. Acta 1970, 52,
173-176.
(20) Baldwin, J. E.; Reddy, V. P. J. Am. Chem. Soc. 1988, 110, 8223-8228.
(21) Roth, W. Tetrahedron Lett. 1964, 1009-1013.
9
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A R T I C L E S
Doering and Keliher
1/3(3kH)/k-
2(k-H)/2kD
D
Table 2. Specific Rate Constantsa of the Thermal Rearrangements of
5-Dideuteriomethylene-2,4,6,7,9-pentamethyl-11,11a-dihydro-12H-naphthacene (12-1,1-d2) (Figure 2)
T,
°
C
3kH
k-
H
2kD
k-
D
2/3(3kH/2kD)
k-H/k-
D
185.8 ( 0.3
169.2 ( 0.3
153.8 ( 0.3
27.62
(0.20
(0.72%
8.144
(0.0763
(0.94%
2.342
(0.0343
(1.46%
8.649
4.019
2.091
4.582
4.136
4.403
(0.073
(1.65%
4.609
(0.105
(2.27%
4.819
(0.167
(3.47%
4.304
(0.152
(1.76%
2.602
(0.0561
(2.16%
0.721
(0.0425
(1.06%
1.116
(0.0157
(1.41%
0.303
(0.0311
(1.49%
0.589
(0.0122
(2.07%
0.162
(0.059
(1.28%
4.865
(0.082
(1.69%
5.153
(0.095
(2.31%
4.418
(0.132
(2.99%
4.451
(0.088
(2.05%
4.663
(0.120
(2.58%
4.759
(0.0245
(3.39%
(0.0063
(2.09%
(0.051
(3.15%
(0.131
(2.55%
(0.206
(4.63%
(0.190
(3.98%
Arrhenius and Eyring Parametersb
30.25 ( 0.62
Ea
30.01 ( 0.20
31.37 ( 0.15
31.05 ( 0.17
10.11 ( 0.09
30.17 ( 0.18
log A
∆Hq
∆Sq
10.74 ( 0.10
29.13 ( 0.21
10.35 ( 0.31
10.55 ( 0.07
30.49 ( 0.19
29.37 ( 0.63
-13.95
-12.17
-13.04
-15.05
a All specific rate constant in units of 10-5 s-1; uncertainties at the 95% confidence level. b Ea and ∆Hq in kcal mol-1; standard error in the conventional
manner - linear regression on the three specific rate constants.
Figure 4. A compromise between two extreme representations of the
transition region for the 1,5-hydrogen shift in 2,4-diphenyl-1,3(Z)-pentadiene
is depicted.
Figure 3. Preparation and kinetic profile of 6,8-dimethyl-1-dideuteriom-
ethylene-1,2,3,4-tetrahydronaphthalene are depicted. The 1H NMR used in
quantitative analysis are give in ppm (δ) above the relevant groups.
and the higher value of the error bar of the second datum,
(kT1 - ∆) and (kT2 + ∆). From the differences between the
original Arrhenius parameters and the additional pair of Arrhe-
nius parameters, error bars for the energy of activation and the
A factor are obtained. By this method, for example, for 3kH
(k1 ) 27.62 ( 0.20 × 10-5 s-1 at 185.8 °C and k2 ) 2.341 (
0.035 × 10-5 s-1 at 153.8 °C [Table 2]), Ea ) 30028 ( 265
(0.9%) and log A ) 10.755 ( 0.109/-0.145 (1.2%) are
obtained. This method produces generous values for the
uncertainties and can perhaps be refined to give statistically more
valid uncertainties. Implicit in this approach is the assumption
that the unknowable true value of a specific rate constant falls
within its error bar with a probability related to the specification
of the error bar (95% confidence limit in the example above:
19 out of 20 measurements).22
Extrapolation of the KDIEs from the range of temperature
185.8-153.8 °C to 25.0 °C is accomplished by calculation of
the two sets of three specific rate constants, each from the two
sets of the three Arrhenius equations, for 3kH and 2kD,
respectively.23 The extrapolated value of kH/kD [2/3(3kH/2kD)]
from 12-1,1-d2 is 10.6 (+3.3/-2.4); that is, the true value should
bar that is assumed to include their unknowable true value. The
error bar in the slope of such a plot of a small number of
observed rate constants against the reciprocal of temperature
reflects the randomness of the points comprising that particular
sample. The error bar does not reflect the uncertainty in
temperature but only the happenstance within that collection
of points.
In an alternative approach to the estimation of error in the
translation to the Arrhenius parameters, the rate constants at
the two extreme temperaturessthe original van’t Hoff methods
are employed, each with its associated error bar. The error bar
((∆) associated with each specific rate constant is based on a
dozen or more observations of concentration versus time (t) and
has some statistical significance by the usual method of least-
squares. Recall that the error bar in k contains the responses of
the rates to random fluctuations in temperature during their
determination. In addition to the Arrhenius parameters derived
from the specific rate constants (kT1, kT2), customarily as far
apart in temperature as is experimentally convenient, two
additional two-point Arrhenius equations are then created: the
one from the higher value of the error bar of the first datum
and the lower value of the error bar of the second datum (or
last, if more than two), (kT1 + ∆) and (kT2 - ∆); the other, the
reverse, from the lower value of the error bar of the first datum
(22) In respect to experimental design, when, for example, four determinations
of k were contemplated, uncertainties in Ea would be lower if two
measurements were made each at the highest and lowest temperature rather
than four measurements equally spaced in 1/T.
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2492 J. AM. CHEM. SOC. VOL. 129, NO. 9, 2007

Effect of Deuterium on Kinetics of 1,5-Hydrogen Shifts
A R T I C L E S
distilled from lithium aluminum hydride, 5 mL of a 1.6 M solution of
methyllithium in diethyl ether were added at 0 °C. After 3 h of standing,
5 mL of water were added, and the reaction mixture was worked up in
the usual way to yield 0.8 g (96%) of dimethyltitanocene as an orange
solid.
lie between 8.2 and 13.9 at the 95% confidence interval. The
spread is large despite the satisfactory level of uncertainties in
the rate constants and their ratio because of amplification by
the large extent of the extrapolation.
To a solution of 0.62 g of dimethyltitanocene in 5 mL of toluene,
200 mg of dypnone were added. The reaction mixture was heated for
18 h at 65 °C. Purification by column chromatography (1 cm × 15
cm, alumina; 14:1 petroleum ether/ethyl acetate) afforded 150 mg of
2,4-diphenyl-1,3(Z)-pentadiene 3 as a colorless oil: 1H NMR (cyclo-
hexane-d12) 7.40 (d, J ) 7.61 Hz, 2H), 7.37 (d, J ) 7.32 Hz, 2H), 7.21
(q, J ) 7.61 Hz, 4H), 7.15 (t, J ) 7.32 Hz, 2H), 6.50 (s, 1H), 5.57 (d,
J ) 1.47 Hz, 1H), 5.15 (s, 1H), 2.07 (d, J ) 1.17 Hz, 3H); 13C NMR
145.7, 143.4, 140.9, 137.9, 129.0, 128.31, 128.28, 127.6, 127.4, 126.6,
125.6, 115.4, 17.6.
1,1-Dideuterio-2,4-diphenyl-1,3(Z)-pentadiene (3-1,1-d2). The same
procedure as that above was followed but for the substitution of di-
(trideuteriomethyl)titanocene for dimethyltitanocene. Dichlorotitanocene
(1.22 g)7 was converted in the usual way with trideuteriomethyllithium
(28 mL of a 1.6 M ethereal solution; Aldrich Co.) to 1.28 g of di-
(trideuteriomethyl)titanocene, which was then allowed to react with
dypnone (300 mg).
Kinetics of Thermal Rearrangement of 1,1-Dideuterio-2,4-
diphenyl-1,3(Z)-pentadiene (3-1,1-d2). Kinetics were effected as already
described.4 Samples were prepared by placement in NMR tubes with
benzene-d6 as solvent and sealing under a vacuum after three freeze-
dry cycles. Heating was in the vapors of boiling liquids: acetophenone,
average temperature: 201.6 ( 0.2 °C; diethyl oxalate, 184.4 (
0.3 °C; tert-butylbenzene, 167.7 ( 0.2 °C. 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 s). Analysis of compounds 3-1,1-d2, 3-1,5-d2, and 3-5,5-d2, (Figure
1) revealed concentrations that did not differ from the comparable runs
in conventional NMR tubes within experimental uncertainties: i.e.,
(5% (Table SI-2).
For quantitative analysis, acquisition times were 4.00 s, the relaxation
time delay was 40 s, and the number of accumulations was 16. Even
at 600 MHz, baseline separation of the isotopomers in Figure 1 was
not always achievable. In order to achieve better separation, the data
were processed by using resolution enhancement by 1.0 Hz and Gauss
apodization by 0.4 s. The first of two sets of signals relating
concentration to time was based on the methyl groups CH3, 1.81; CH2D,
1.78; and CHD2, 1.76 ppm (δ); the second, on the methyl group CH3,
1.81; the dCH2 group, 5.01, 4.78; and the dCHD group, 5.00, 4.76
ppm (δ). The raw data are given in Table S1.
Conclusion
A discussion of the conventional basis for estimating uncer-
tainties in Arrhenius parameters determined from a small number
of rate constant/temperature data has been opened by proposing
an alternative procedure based on the more significant uncer-
tainties usually achieved in specific rate constants.
The experimental determination of the dependence of the
KDIE on temperature initiated by Roth and Ko¨nig, and furthered
by Doering and Zhao, has now been brought to a more
satisfactory level of reliability. The value of kH/kD for the system
12-1,1-d2 (Figure 2) is 4.6 ( 0.1 at the highest temperature
(185.8 °C) and considerably higher, 10.6 (+3.3, -2.4), on
extrapolation to the lower temperature of 25 °C. Whether this
increase in KDIE at 25 °C constitutes compelling support for
the case that tunneling is a significant contributor to the rate of
the hydrogen shift even at this low temperature, which is not
realistically accessible to kinetic observation, we leave to
theoreticians to conclude.12 A more precise explication of the
criteria to the satisfaction of which an experimentalist could
and should aspire would be welcome.
The extrapolation to 25 °C is, of course, linear. Were
tunneling to be an increasingly important component of the rate
constants as temperature decreased, the line would become a
curve and kH/kD would be larger than the value linearly
extrapolated from the higher range of temperature.24 With the
extrapolated rate constants having t1/2 ∼4000 years, only were
tunneling to increase dramatically over this range of temperature
would its effect become observable as a statistically valid
curvature departure from the Arrhenius, over-the-barrier linear
plot and nonvirtual to the practicing mechanistic organic chemist
of realistic lifespan.
Experimental Section
General Procedures. All 1H NMR spectra were measured on a
Varian Unity/Inova 600 instrument at 600 MHz in CDCl3, unless
otherwise noted; 1H NMR (400 MHz) spectra were measured on a
Varian Mercury 400 instrument; 13C NMR(125.7 MHz) spectra were
measured in CDCl3 on a Varian Unity 500 instrument. Chemical shifts
are reported in ppm relative to tetramethylsilane (δ) with respect to
residual C6D5H (7.15 ppm for 1H and 128.0 ppm for 13C). Spin-lattice
relaxation times (T1) were determined by the inversion-recovery
method in benzene-d6. Preparative GC on a Varian 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 (0.53 mm i.d. × 30-m,
1 µm film thickness) megabore column and an HP 3393A integrator.
2,4-Diphenyl-1,3(Z)-pentadiene (3). (E)-Dypnone (200 mg) was
prepared by the procedure of Wayne and Adkins.25 Dimethyltitanocene
was prepared following a procedure of Petasis and Bzowej:7 to a stirred
solution of 1.0 g of dichlorotitanocene in 45 mL of diethyl ether freshly
Dibenzylmethylmalonic Acid. Following the procedure of Kim and
co-workers,26 to a solution of benzylmagnesium chloride (from 4.2 g
of benzyl chloride) in ether was added diethyl ethoxymethylenemalonate
(3.69 g). Conventional workup afforded 6.3 g of crude product, which
was purified by evaporative distillation at 1 mmHg and 185° to afford
5.0 g (76%) of diethyl dibenzylmethylmalonate of 96% of purity by
NMR: 1H NMR 7.28 (t, J ) 7.32 Hz, 4H), 7.19 (m, 6H), 4.18 (q, J )
5.86 Hz, 4H), 3.39 (d, J ) 4.39 Hz, 1H), 2.79 (dd, J ) 5.62, 12.45 Hz,
2H), 2.67 (m, 3H), 1.28 (t, J ) 7.32 Hz, 6H).
This ester was hydrolyzed in 2.5 mL of 25% NaOH and 30 mL of
methanol to give 3.95 g (94% of theoretical yield) of dibenzylmeth-
ylmalonic acid as a colorless solid: 1H NMR 11.15 (br s, 2H), 7.29 (t,
J ) 7.61 Hz, 4H), 7.20 (m, 6H), 3.66 (d, J ) 3.54 Hz, 1H), 2.91-2.85
(m, 2H), 2.80-2.73 (m, 3H); 13C NMR (100.6 MHz) 174.6, 139.4,
129.2, 128.5, 126.5, 52.3, 43.3, 37.2.
(23) Alternatively, the equivalent calculation of the three Arrhenius equations
from the high and low temperature values of kH/kD in Table 2, column 6,
including the extremes of + and -, and - and + of the estimated
uncertainties.
(24) Kohen, A., Limbach, H.-H., Eds. Isotope Effects in Chemistry and Biology;
CRC Press: 2006.
(25) Wayne, W.; Adkins, H. Org. Syn. Col. Vol. III 1955, 367-369.
6-Hydroxy-11a,12-dihydro-11H-naphthacen-5-one (4). Cyclization
of the diacid above (2.7 g) was effected by treatment with polyphos-
(26) Kim, Y. M.; Kwon, T. W.; Chung, S. K.; Smith, M. B. Synth. Commun.
1999, 29, 343-350.
9
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A R T I C L E S
Doering and Keliher
phoric acid (60 mL) at 75 °C for 15 min. Quenching with ice, diluting
further with water, and extraction with ether gave an ethereal extract,
which, when washed with aqueous NaHCO3 and brine, dried with Na2-
SO4, and concentrated, afforded 1.3 g of 4: 1H NMR 16.55 (s, 1H),
8.03 (d, J ) 7.62 Hz, 2H), 7.46 (t, J ) 7.42 Hz, 2H), 7.38 (t, J ) 7.42
Hz, 2H), 3.05 (m, 6H), 7.26 (t, J ) 7.42 Hz, 2H), 3.05 (m, 3H), 2.80
(t, J ) 14.14 Hz, 2H); 13C NMR (100.6 MHz) 180.2, 140.2, 132.3,
131,3, 127.8, 127.1, 125.9, 107.0, 35.6, 30.1.
of 540 mg of 9 (46% of theoretical yield): 1H NMR (500 MHz) 17.61
(s, 1H), 6.95 (s, 2H), 6.89 (s, 2H), 2.89 (dd, J ) 14.42, 4.95 Hz, 2H),
2.79 (m, 1H), 2.69 (s, 6H), 2.67 (t, J ) 13.45 Hz, 2H), 2.33 (s, 6H);
13C NMR 182.8, 141.7, 141.4, 139.7, 131.8, 127.3, 126.4, 109.5, 36.9,
30.1, 22.7, 21.4.
6-Hydroxy-2,4,7,9-tetramethyl-12H-naphthacen-5-one (10). Phos-
phorus pentachloride (0.59 g) was added to bis(3′,5′-dimethylbenzyl)-
methylmalonic acid (300 mg) suspended in 50 mL of benzene. To this
solution, having been stirred for 3 h at room temperature, freshly
sublimed aluminum trichloride (0.37 g) was added. The mixture was
heated at 35 °C for 17 h (reflux condenser), cooled, and extracted with
ether (3 × 15 mL each). This extract was dried over Mg2SO4, filtered,
and concentrated to 221 mg of a dark brown solid, which was
crystallized from 0.5 mL of THF at room temperature to give 76 mg
of deep red needles. Recrystallization afforded a sample suitable for
X-ray crystallographic analysis: 1H NMR 15.55 (s, 1H), 7.27 (s, 1H),
7.07 (s, 1H), 7.04 (s, 1H), 7.02 (s, 1H), 7.01 (s, 1H), 4.33 (s, 2H), 2.98
(s, 3H), 2.83 (s, 3H), 2.44 (s, 3H), 2.39 (s, 3H); 13C NMR 192.1, 166.6,
143.1, 142.1, 139.5, 139.0, 138.6, 134.4, 132.0, 129.9, 128.5, 127.5,
126.8, 124.4, 121.2, 115.5, 111.8, 33.6, 24.9, 24.2, 21.6, 21.5.
2,4,6,7,9-Pentamethyl-11a,11-dihydro-12H-naphthacen-5-one (11).
To a cooled (0 °C) solution of compound 9 (0.87 g) in 20 mL of THF
in a flame-dried, 50-mL round-bottomed flask, 5.0 mL of a 1.6 M
ethereal solution of methyl lithium were added. Stirring under argon
of the dark green solution was continued for 14 h. Analysis by TLC
(5:1 hexane/ethyl acetate) revealed three spots, Rf ) 0.43, 0.32, and
0.22 (starting material: Rf ) 0.51). Diluted with 10 mL of water and
30 mL of ether, the mixture was washed with 70 mL of 10% aqueous
HCl and 100 mL of brine. The separated ethereal solution was dried
over MgSO4 and concentrated to a residue (0.57 g). Dissolved in 15
mL of benzene, the residue was transferred to a 25-mL flask fitted
with a Dean-Stark trap, treated with a few crystals of p-toluenesulfonic
acid, and boiled under reflux for 2 h. Cooled to 25 °C and diluted with
diethyl ether, the reaction mixture was washed successively with
aqueous NaHCO3 (2 × 70 mL) and brine (2 × 70 mL), dried over
MgSO4, and concentrated. The residue was chromatographed (3 cm ×
22 cm silica gel column:10:1 hexane/ethyl acetate) to afford 0.45 g of
11 as an orange solid: 1H NMR (500 MHz) 6.94 (s, 1H), 6.93 (s, 1H),
6.88 (s, 1H), 6.87 (s, 1H), 2.89 (dd, J ) 14.89, 4.15 Hz, 1H), 2.72 (m,
5H), 2.59 (s, 3H), 2.54 (m, 2H), 2.45 (s, 3H), 2.33 (s, 3H), 2.31 (s,
3H); 13C NMR 191.3. 146.3, 141.5, 141.4, 139.4, 138.9, 137.7, 135.9,
135.7, 135.2, 132.6, 131.7, 131.3, 125.7, 125.2, 37.6, 34.7, 34.4, 23.0,
22.0, 21.7, 21.4, 21.0.
From the NaHCO3 washes, 1.4 g. of unreacted dicarboxylic acid
was recovered (1H NMR).
6-Methyl-11a,12-dihydro-11H-naphthacen-5-one (6). To a solution
of 200 mg of 4 in 10 mL of anhydrous THF, 2.5 mL of a 1.6 M solution
of methyllithium in diethyl ether were added with stirring at 0 °C under
argon. Worked up in the usual manner, 230 mg (76%) of 6 were
obtained as a viscous oil: 1H NMR 8.01 (d, J ) 7.62 Hz, 1H), 7.62 (d,
J ) 7.91 Hz, 1H), 7.46 (t, J ) 7.32 Hz, 1H), 7.36 (t, J ) 7.32 Hz,
1H), 7.31 (m, 2H), 7.23 (t, J ) 7.31 Hz, 2H), 3.02 (m, 1H), 2.96 (m,
1H), 2.89 (m, 2H), 2.77 (d, J ) 1.76 Hz, 3H), 2.76 (t, J ) 13.18 Hz,
1H); 13C NMR 189.5, 145.8, 141.0, 136.7, 136.5, 135.8, 132.5, 132.1,
129.0, 127.7, 127.4, 127.1, 127.0, 126.9, 125.8, 36.0, 35.1, 34.4, 17.3.
12-Methyl-11-methylene-5,5a,6,11-tetrahydro-naphthacene (7).
Dimethyltitanocene (0.8 g) was dissolved in 20 mL of toluene and added
to 0.3 g of 6. After 6 h of being heated at 65 °C, the reaction mixture
was diluted with 20 mL of petroleum ether, filtered, concentrated, and
subjected to column chromatography (2 cm × 15 cm, alumina, 15:1
petroleum ether/ethyl acetate) to yield 140 mg (45%) of 7: 1H NMR
7.58 (d, J ) 7.62 Hz, 1H), 7.51 (d, J ) 7.62 Hz, 1H), 7.34-7.30 (m,
3H), 7.27-7.23 (m, 3H), 5.73 (d, J ) 1.17 Hz, 1H), 5.45 (d, J ) 1.17
Hz, 1H), 2.97 (dd, J ) 4.25, 13.91 Hz, 2H), 2.92 (dd, J ) 3.22, 12.89
Hz, H), 2.88-2.75 (m, 3H), 2.45 (d, J ) 1.46 Hz, 3H); 13C NMR (100.6
MHz) 144.1, 139.4, 137.1, 137.0, 136.7, 135.9, 127.4, 127.3, 127.1,
127.0, 126.6, 126.5, 126.4, 124.3, 123.9, 115.4, 35.8, 35.7, 35.1, 16.2.
Bis-(3′,5′-dimethylbenzyl)methylmalonic Acid. Following a pro-
cedure adapted from Baldwin and O’Neill,27 a Grignard reagent was
prepared from 1.41 g of Mg shavings (0.06 mol) in 50 mL of ether
and 10.0 g (0.05 mol) of R-bromomesitylene in 40 mL of ether. To
this solution, diethyl ethoxymethylenemalonate (10 g in 30 mL of ether)
was added over a period of 30 min. After being boiled under reflux
for 18 h, the cooled reaction mixture was quenched with 10 mL of
saturated aqueous NH4Cl and separated into an ether and aqueous layer,
which was diluted with 70 mL of saturated aqueous NH4Cl, extracted
three times with 40-mL portions of ether, dried over MgSO4, and
concentrated. Purification of the 10.4-g residue by column chroma-
tography (silica gel, 5:1 hexane/ethyl acetate) afforded 4.46 g of diethyl
bis(3′,5′-dimethylbenzyl)methylmalonate.
This diethyl ester was hydrolyzed by treatment with 2.5 mL of 25%
aqueous NaOH and 30 mL of methanol at reflux for 4 h. Addition of
50 mL of water, extraction with ether (3 × 20 mL each), acidification
with dilute HCl to pH 2, and extraction with ether (3 × 30 mL each)
gave an ethereal solution, which was dried over MgSO4 and concen-
trated to yield 3.71 g of the malonic acid: 1H NMR 6.83 (s, 2H), 6.80
(s, 4H), 3.54 (d, J ) 6.78 Hz, 1H), 2.72 (m, 5H), 2.28 (s, 12H); 13C
NMR 174.8, 139.3, 137.9, 128.0, 127.1, 52.4, 43.0, 37.1, 21.3.
6-Hydroxy-2,4,7,9-tetramethyl-11a,12-dihydro-11H-naphthacen-
5-one (9). A 100-mL, three-necked, round-bottomed flask containing
1.30 g of the malonic acid above was fitted with a Tygon tube charged
with 1.89 g of PCl5. After evacuation and three cycles with argon,
benzene (40 mL) and the PCl5 were added. After 18 h of stirring, stannic
chloride (1.3 mL) was added. Stirring was continued for 14 h. Diluted
with 150 mL of water, the mixture was extracted five times with 30
mL each of CH2Cl2. The combined extracts were dried (MgSO4),
filtered, and concentrated to 1.54 g of a dark residue, which was
dissolved in 1.1 mL of THF and cooled at -78 °C for 4 h to give 360
mg of orange plates. A second crop (180 mg) was obtained for a total
5-Methylene-2,4,6,7,9-pentamethyl-11,11a-dihydro-12H-naph-
thacene (12-d0). A solution of dimethyltitanocene (1.22 g, 6.0 mmol)
in toluene (10 mL) was added to ketone 11 (600 mg, 2.0 mmol) under
argon and stirred at 60 °C for 60 h following the procedure of Petasis
and Bzowej.7 A solution of the cooled reaction mixture and 20 mL of
pentane were filtered and evaporated to a concentrate, from which
column chromatography (1′′ × 15′′ alumina, 14:1 petroleum ether/
ethyl acetate) afforded 100 mg of 5-methylene-2,4,6,7,9-pentamethyl-
11,11a-dihydro-12H-naphthacene 12-d0, which was purified by recrys-
tallization from pentane (90 mg): 1H NMR (benzene-d6) 6.84 (s, 1H),
6.79 (s, 1H), 6.74 (s, 1H), 6.72 (s, 1H), 5.45 (d, J ) 2.13 Hz, 1H),
5.37 (d, J ) 2.05 Hz, 1H), 2.94 (dd, J ) 14.35, 7.15 Hz, 1H), 2.74 (m,
1H), 2.50 (t, J ) 14.86 Hz, 1H), 2.42 (s, 3H), 2.40 (dd, J ) 14.42,
2.78 Hz, 1H), 2.35 (s, 3H), 2.30 (d, J ) 2.05 Hz, 3H), 2.24 (dd, J )
14.28, 4.10 Hz, 1H), 2.17 (s, 3H), 2.15 (s, 3H); 13C NMR 142.5, 141.6,
138.5, 137.8, 136.7, 136.1, 135.5, 135.3, 134.3, 132.7, 130.9, 129.5,
126.2, 125.3, 116.5, 37.1, 35.1, 34.9, 22.9, 21.0, 20.8, 20.3, 20.2.
5-Dideuteriomethylene-2,4,6,7,9-pentamethyl-11,11a-dihydro-
12H-naphthacene (12-1,1-d2). A solution of di(trideuteriomethyl)-
titanocene (1.61 g) in toluene (10 mL) is added to the ketone 11 (300
mg, 0.9 mmol) under argon and stirred at 60 °C for 60 h following the
procedure above for 12-d0. The yield of recrystallized 12-1,1-d2 was 80
mg. Its 1H NMR spectrum was identical to that of 12-d0 except for the
(27) Baldwin, S. W.; O’Neill, T. H. Synth. Commun. 1976, 6, 109-112.
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2494 J. AM. CHEM. SOC. VOL. 129, NO. 9, 2007

Effect of Deuterium on Kinetics of 1,5-Hydrogen Shifts
A R T I C L E S
absence of the signals at 5.45 and 5.37 ppm and two slightly different
coupling constants at 2.40 and 2.94 ppm: 1H NMR (benzene-d6) 6.84
(s, 1H), 6.79 (s, 1H), 6.74 (s, 1H), 6.72 (s, 1H), 2.94 (dd, J ) 14.35,
7.25 Hz, 1H), 2.74 (m, 1H), 2.50 (t, J ) 14.86 Hz, 1H), 2.42 (s, 3H),
2.40 (dd, J ) 14.46, 2.74 Hz, 1H), 2.35 (s, 3H), 2.30 (d, J ) 2.05 Hz,
3H), 2.24 (dd, J ) 14.31, 4.10 Hz, 1H), 2.17 (s, 3H), 2.15 (s, 3H).
Kinetics of the Thermal Rearrangement of 5-Dideuteriometh-
ylene-2,4,6,7,9-pentamethyl-11,11a-dihydro-12H-naphthacene (12-
1,1-d2). Individual samples in ampoules of lead-potash glass of 12-1,1-
d2 (6 mg in 0.7 mL of benzene-d6) were prepared from a stock solution
consisting of 75.9 mg of 12-1,1-d2 in 0.4 mL of benzene-d6. The
ampoules were degassed three times by freeze-thaw cycles prior to
being sealed under a vacuum. Heating was provided by the vapors of
freshly distilled compounds boiling under reflux: anisole, bp 153.8 (
0.3 °C; tert-butylbenzene, bp 169.2 ( 0.5 °C; and diethyl oxalate, bp
185.8 ( 0.3 °C. For analysis, the ampoules were opened and their
contents were transferred to Pyrex NMR tubes, which were examined
by 1H NMR spectroscopy (600 MHz with the aid of a resolution-
enhancing Gaussian function set to 0.4 and line-broadening to -1.0).
Two sets of signals were used to determine relative concentrations:
method A: 2.30, 2.27, and 2.29 ppm; method B: 2.30, 5.46, 5.38,
5.44, and 5.36 ppm (see Figure 2). Following analysis, the samples
were transferred to soft-glass (lead-potash) ampoules, sealed under a
vacuum, and returned to the heating bath. The unrefined data are given
in Table S3 of the Supporting Information.
6,8-Dimethyl-3,4-dihydro-2H-naphthalen-1-one. This compound
was prepared as a mixture with the 5,8-dimethyl isomer following the
procedure of Jung and Koreeda for p-xylene, but employing m-xylene
instead.28 The pure compound (not obtained by Jung and Koreeda) was
obtained by preparative gas chromatography (2.7 m × 6 mm column
of 20% Carbowax 20M on Anakrom AS (50-60 mesh) at 180 °C)
(0.43 g from 4.0 g of γ-butyrolactone and 40 mL of m-xylene): 1H
NMR 2.06 (quin, J ) 6.74 Hz, 2H), 2.32 (s, 3H), 2.62 (m, 5H), 2.91
(t, J ) 6.15 Hz, 2H), 6.90 (s, 1H), 6.91 (s, 1H); 13C NMR 21.4, 23.0,
23.2, 31.0, 41.0, 127.3, 128.8, 131.4, 141.6, 142.8, 145.8, 199.9.
6,8-Dimethyl-1-methylene-1,2,3,4-tetrahydronaphthalene 13. A
solution of 1.25 g of dimethyltitanocene in 6 mL of toluene was added
to 250 mg of 6,8-dimethyl-3,4-dihydro-2H-naphthalen-1-one in 2 mL
of toluene. The reaction mixture was stirred for 60 h at 60 °C under
argon, cooled, diluted with 5 mL of pentane, and filtered though a pad
of alumina. The resulting pentane/toluene solution was concentrated
to 100 mg of an oil, which was separated into three fractions by GC
(1.7 m × 6 mm column of 5% OV-225 on 50-60 mesh Anakrom
ABS at 97 °C): 6.3-10.3 min, compound 13; 10.3-15 min, a mixture;
and 15-20 min, 1,2-dihydro-4,5,7-trimethylnaphthalene. (A solution
obtained by extraction of the alumina pad with ether was concentrated
to give 121 mg of starting ketone, determined by 1H NMR.) 6,8-
Dimethyl-1-methylene-1,2,3,4-tetrahydronaphthalene 13 : 1H NMR
1.86 (quin, J ) 6.44 Hz, 2H), 2.27 (s, 3H), 2.43 (s, 3H), 2.47 (t, J )
6.74 Hz, 2H), 2.72 (t, J ) 6.74 Hz, 2H), 5.07 (s, 1H), 5.23 (d, J )
1.46 Hz, 1H), 6.80 (s, 1H), 6.90 (s, 1H); 13C NMR 20.9, 21.0, 23.9,
30.2, 34.1, 113.3, 126.6, 129.9, 133.7, 134.8, 136.0, 139.1, 143.5. When
this sample was allowed to stand for 48 h at room temperature, the
spectrum had changed to that of 1,2-dihydro-4,5,7-trimethylnaphtha-
lene:29 1H NMR 2.09 (m, 2H), 2.22, (d, J ) 1.46 Hz, 3H), 2.30 (s,
3H), 2.47 (s, 3H), 2.64 (t, J ) 7.45 Hz, 2H), 5.96 (t, J ) 4.50 Hz, 1H),
6.87 (s, 1H), 6.89 (s, 1H).
6,8-Dimethyl-1-dideuteriomethylene-1,2,3,4-tetrahydronaphtha-
lene (13-1,1-d2). This dideuterium isotopomer was prepared as described
above for 13: 1H NMR 1.68 (tt, J ) 6.66, 6.74, 6.48 Hz, 2H), 2.14 (s,
3H), 2.34 (t, J ) 6.70 Hz, 2H), 2.40 (s, 3H), 2.57 (t, J ) 6.55 Hz, 2H),
6.68 (s, 1H), 6.81 (s, 1H).
Heating 6,8-Dimethyl-1-dideuteriomethylene-1,2,3,4-tetrahy-
dronaphthalene 13-1,1-d2. A solution of 2.3 mg of the hydrocarbon in
40 mL of benzene-d6 was split into two portions, each of which was
placed in a soft glass (lead-potash) tube, subjected to three freeze-
evacuate-thaw cycles, and sealed under a vacuum. Immediately prior
to insertion into a bath of the vapors of diphenyl ether boiling under
reflux (258.4 ( 0.2 °C) to be heated for 24 and 90 h, respectively, the
tubes were warmed for 1.5 min at 185 °C (vapors above boiling diethyl
oxalate). The contents of a cooled tube were transferred to an NMR
tube, diluted with 0.66 mL of benzene-d6, and analyzed by methods A
(the signals of the three methyl group) and B (CH3 and methylenes
CHD and CH2) (see Figure 4). The contents of the 90-h tube were
transferred to a soft-glass tube, concentrated by a slow stream of natural
gas, and prepared for heating an additional 90 h as described above.
The resulting data are given in Table S4.
Acknowledgment. We express our gratitude to the Norman
Fund in Organic Chemistry in memory of Ruth Alice Norman
Weil Halsband and Edward A. Norman for its generous support
of this work. Our gratitude goes to Dr. Richard Staples for
executing the X-ray diffraction studies of compounds 10 and
12. We are especially grateful to emeritus Professor Wolfram
Grimme, Universita¨t zu Ko¨ln, for his many constructive
suggestions, including the treatment of uncertainty in our
evaluation of Arrhenius energies of activation.
Supporting Information Available: Four tables of kinetic
data. This material is available free of charge via the Internet
at http://pubs.acs.org.
(28) Jung, K.-Y.; Koreeda, M. J. Org. Chem. 1989, 54, 5667-5675.
(29) Heimgartner, H.; Zsindely, J.; Hansen, H. J.; Schmid, H. HelV. Chim. Acta
1973, 56, 2924-2945.
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