Elucidation, by scanning microcalorimetry, of the detailed mechanism of the thermal rearrangement of [18]annulene into benzene and 1,2-benzo-1,3,7-cyclooctatriene. Determination and interpretation of the thermochemical and kinetic parameters of the three consecutive reactions implicated

Article abstract of DOI:10.1021/jp000443p

The thermograms Q_r(T) recorded for the thermal rearrangement of [18]annulene 1 have been reinvestigated using an iterative method (CALIT-3 program) based on the numerical integration of the kinetic equations established for the following reaction mechanism: [18]annulene 1 →k₁ tetracyclic intermediates 2 →k₂ transbicyclo[6.4.0]dodeca-2,4,6,9,11-pentaene 3 + benzene 5; 3 → k₃ 1,2-benzo-1,3, 7-cyclooctatriene 4. Independent ¹³C-NMR experiments indicate that three chiral tetracyclic intermediates 2a, 2b, and 2c are implicated in the reaction. They are considered to play the same role in the mechanism and are therefore considered as a single compound 2 in the kinetic equations. A programmed differential microcalorimeter with linearly increasing temperature was used for producing the thermograms. The reaction enthalpies Δ_r,_iH of each individual reaction (: i = 1, 2, or 3 as well as the Arrhenius parameters E_a,i, log A_i, and the activation thermodynamic quantities ΔH^?_i, ΔS^?_i, and ΔG^?_i (at 298.2 K) have been established by the iterative numerical simulation of the thermograms. These results are discussed. The enthalpy of formation of [18]annulene 1, as well as the stabilization and π-bond delocalization energies of this molecule have been deduced: ΔH°_f(1, g, 298.2 K) = 123.4 ± 3.7 kcal mol^-1; ΔH_stab(1) = -37.6 ± 4.5 kcal mol^-1; ΔH_deloc(π-bonds in 1) ? -120.5 kcal mol^-1. The stabilization enthalpy ΔH_stab(1) has been used for discussing the activation enthalpy of the conformational mobility in 1 previously reported. The pathway multiplicities deduced from the detailed mechanisms for each individual reaction are discussed in view of the interpretation of the large activation entropies found. Of special interest is the discussion of the mechanism of the two suprafacial 1,5 hydrogen shifts implied in the reaction 3 → k₃ 4 and of the high activation entropy observed. In independent measurements, the rate of disappearence of the [18]annulene 1 has been followed by UV spectroscopy in order to obtain the kinetic parameters for the first reaction. The results of these independent measurements are in good agreement with those obtained by the analysis of the thermograms. The reported investigation points to the fact that the thermograms recorded with our calorimetric method constitute very precise data and that their correct analysis allows the elucidation of complex reaction mechanisms.

Full text of DOI:10.1021/jp000443p

7980
J. Phys. Chem. A 2000, 104, 7980-7994
Elucidation, by Scanning Microcalorimetry, of the Detailed Mechanism of the Thermal
Rearrangement of [18]Annulene into Benzene and 1,2-Benzo-1,3,7-cyclooctatriene.
Determination and Interpretation of the Thermochemical and Kinetic Parameters of the
Three Consecutive Reactions Implicated
Jean F. M. Oth*,†
Laboratory for Organic Chemistry, Swiss Federal Institute of Technology, CH-8006 Zu¨rich, Switzerland
Jean-Marie Gilles‡
Physics Department, Faculte´s UniVersitaires N.-D. de la Paix, B-5000 Namur, Belgium
ReceiVed: February 3, 2000
The thermograms Q4 r(T) recorded for the thermal rearrangement of [18]annulene 1 have been reinvestigated
using an iterative method (CALIT-3 program) based on the numerical integration of the kinetic equations
k1
k2
established for the following reaction mechanism: [18]annulene 1
98 tetracyclic intermediates 2 98 trans-
k3
bicyclo[6.4.0]dodeca-2,4,6,9,11-pentaene 3 + benzene 5; 3
98 1,2-benzo-1,3, 7-cyclooctatriene 4. Indepen-
dent 13C-NMR experiments indicate that three chiral tetracyclic intermediates 2a, 2b, and 2c are implicated
in the reaction. They are considered to play the same role in the mechanism and are therefore considered as
a single compound 2 in the kinetic equations. A programmed differential microcalorimeter with linearly
increasing temperature was used for producing the thermograms. The reaction enthalpies ∆r,iH of each individual
reaction (i ) 1, 2, or 3) as well as the Arrhenius parameters Ea,i, log Ai and the activation thermodynamic
quantities ∆Hq , ∆Sq , and ∆Gq (at 298.2 K) have been established by the iterative numerical simulation of
i
i
i
the thermograms. These results are discussed. The enthalpy of formation of [18]annulene 1, as well as the
stabilization and π-bond delocalization energies of this molecule have been deduced: ∆H°(1, g, 298.2 K) )
f
123.4 ( 3.7 kcal mol-1; ∆Hstab(1) ) - 37.6 ( 4.5 kcal mol-1; ∆Hdeloc(π-bonds in 1) = - 120.5 kcal mol-1.
The stabilization enthalpy ∆Hstab(1) has been used for discussing the activation enthalpy of the conformational
mobility in 1 previously reported. The pathway multiplicities deduced from the detailed mechanisms for each
individual reaction are discussed in view of the interpretation of the large activation entropies found. Of
special interest is the discussion of the mechanism of the two suprafacial 1,5 hydrogen shifts implied in the
k3
reaction 3
98 4 and of the high activation entropy observed. In independent measurements, the rate of
disappearence of the [18]annulene 1 has been followed by UV spectroscopy in order to obtain the kinetic
parameters for the first reaction. The results of these independent measurements are in good agreement with
those obtained by the analysis of the thermograms. The reported investigation points to the fact that the
thermograms recorded with our calorimetric method constitute very precise data and that their correct analysis
allows the elucidation of complex reaction mechanisms.
I. Introduction
tion program to simulate thermograms observed for successive
first-order reactions or for successive and parallel first-order
The thermal rearrangement of [18]annulene 1 has been
investigated by one of us by scanning calorimetry,1 and the final
products have been identified as benzene 5 and 1,2-benzo-1,3,7-
cyclooctatriene 4. The analysis of the thermograms recorded
allowed the determination of the enthalpy of formation and the
stabilization energy of [18]annulene 1, but the details of the
rearrangement mechanism were not elucidated.
The thermograms were analyzed as being the result of a one-
step first-order reaction (program CALIT-2 2) since their habitus
is in accordance with this interpretation, although we have
recognized the implication of tetracyclic intermediate(s) in the
reaction mechanism. The development of an iterative computa-
reactions (program CALIT-3 3) led us to reinvestigate the
thermograms.
We report here on the mechanism of the thermal rearrange-
ment of [18lannulene elucidated via the simulation of the
thermograms, the iterative computations being conducted with
the CALIT-3 program considering three successive first-order
reactions. Further kinetic measurements were undertaken that
substantiate the results of this ultimate analysis of the thermo-
grams. These results lead us to the following conclusion:
A thermogram measured with our calorimeter gives the value
of the reactions heat flux Q4 r as a function of the sample
temperature, which is increased linearly with time. It consists
of a great number of data points and contains very precise kinetic
information. Even when its shape does not exhibit direct
† Tannenweg 8, CH-8908 Hedingen, Switzerland.
‡ Rue de Namur 13, B-1435 Mont-St-Guibert, Belgium.
10.1021/jp000443p CCC: $19.00 © 2000 American Chemical Society
Published on Web 08/09/2000

Thermal Rearrangement of [18]Annulene
J. Phys. Chem. A, Vol. 104, No. 34, 2000 7981
evidence of the complexity of the reaction mechanism, the
thermogram, when properly analyzed, allows the elucidation
of the mechanism of the rearrangement investigated and the
determination of the thermochemical and kinetic parameters
characterizing each individual reaction implicated.
II. The Thermal Rearrangement of [18]Annulene
In our calorimetric technique,4 the compound to be investi-
gated is in solution in a deuterated solvent, the solution being
introduced in an ampoule made of 8 mm o.d. precision NMR
tube and sealed under vacuum (45 mm length). The purity of
the compound is checked by NMR before the thermolysis, the
ampule being introduced in a 10 mm NMR tube and the
temperature of the NMR probe being adequately selected. The
nature of the reaction product(s) is determined in the same
manner after completion of the calorimetric measurement. Figure
1 reproduces the spectra recorded before and after run 105 in
the calorimeter.
The spectrum recorded at -30 °C before the run in the
calorimeter confirms the high purity of the [18]annulene 1; the
spectrum measured after pyrolysis indicates the formation of
benzene 5 and of 1,2-benzo-1,3,7-cyclooctatriene 4. The spec-
trum of 1,2-benzo-1,3,7-cyclooctatriene was known to us from
our studies on [12]annulene:5 upon photolysis at λ ) 350 nm
and -70 °C, [12]annulene gives trans-bicyclo[6.4.0]dodeca-
2,4.6,9,11-pentaene 3, which rearranges thermally in 1,2-benzo-
Figure 1. 1H-NMR spectra of a solution of [18]annulene in tetrahy-
drofuran-d8 before (spectrum at -30 °C) and after (spectrum at
+30 °C) run 105 in the calorimeter (100 MHz, TMS as reference
signal).
1,3,7-cyclooctatriene 4.6 In a first step we have analyzed the
thermograms according to the reaction represented in Scheme
1.3
Figure 2 reproduces thermogram 105 recorded with 0.423
deg/min heating rate. The thermogram was simulated, after
Figure 2. Experimental (105) and calculated thermograms for the thermolysis of [18]annulene. The iteratve calculations were performed assuming
a single first-order reaction. The experimental recording displays both the linearly increasing block temperature and the temperature difference
(T1 - T2) between the reference and sample cells as a function of time.

7982 J. Phys. Chem. A, Vol. 104, No. 34, 2000
Oth and Gilles
iterative computations using the program CALIT-2, assuming
one single first-order reaction (Scheme 1). As can be seen in
Figure 2, the errors Q4 exp - Q4 calc are not statistically distributed;
this indicates that the proposed kinetic mechanism (Scheme 1)
is not correct.
The intermediate compound(s) 2 must have one of the three
possible structures 2a, 2b, or 2c (c ) cis ring fusion; t ) trans).
SCHEME 1
2a
2b
2c
These structures are the only ones compatible with the
following observations:
1
(a) H-NMR spectrum (Figure 4) and decoupling experi-
ments,8 IR and MS spectra (molecular peak at m/e ) 234);
(b) photochemical rearrangement of 2 carried out at
-100 °C in THF-d8 (λ ) 350 nm) gives benzene and
[12]annulene;6,7
(c) catalytic hydrogenation of 2 indicates the presence of six
double bonds in the molecule; the MS of the fully hydrogenated
derivative(s) (molecular peak m/e ) 246) indicates a tetracyclic
saturated C18-hydrocarbon.7
We have therefore simulated the thermograms using the
CALIT-3 program, considering two succesive first-order reac-
tions (rate constants k1 and k2) according to the reaction given
in Scheme 2.
4
1
5
In order to elucidate the mechanism of the thermal transfor-
mation of 1 into 4 and 5, we have followed, as a function of
time, the composition of a solution of [18]annulene heated at
92 °C. The composition of the solution was deduced from the
1
recorded H-NMR spectra; the concentrations of 1, 4, and 5
are reported, as function of time, in Figure 3.3
This figure shows that one (or more) intermediate(s) is (are)
implicated in the thermal rearrangement, the maximum con-
centration of the intermediate(s) occuring after ca. 24 h
thermolysis. In an independent experiment, we have isolated
the intermediate(s) and could show that it corresponds to one
or more tetracyclic structures 2 of molecular formula C18H18.7
The 1H-NMR spectrum of the isolated intermediate(s) 2 as well
as the spectrum of the hydrogenated product(s) are represented
in Figure 4.1,8
SCHEME 2
1
2
4
5
According to these simulations, the total quadratic error
2
tot. quad. error )
(Q˙ exp - Q˙ calc)
∑
all points
resulting from the iterative calculations is smaller than the
corresponding error as obtained from the iterative calculations
assuming a single reaction. This can be seen from Table 2. Here
also, as for the simulation assuming one single reaction, the
errors Q4 exp - Q4 calc are not statistically distributed, indicating
that the kinetic approach is not yet satisfactory (see Figure 5).
We have therefore isomerized a solution of [18]annulene in
THF-d8 (in a sealed 5 mm NMR tube) at 92 °C and for 24 h,
that is, under conditions where the concentration of the
intermediate(s) should be the highest, and then recorded the 1H-
Figure 3. Concentration of the different compounds 1, 2 + 3, 4 and
5 present in the solution as a function of the time of thermolysis at
92 °C: b, [18]annulene 1; $, 1,2-benzo-1,3,7-cyclooctatriene 4;
., benzene; /, tetracyclic intermediates 2a, 2b, 2c and trans-bicyclo-
[6.4.0]dodeca-2,4,6,9,11-pentaene 3.
Figure 4. 1H-NMR spectra of the intermediate C18H18 tetracyclic
compound(s) 2 (in cyclohexane-d12, 100 MHz, 30 °C) and of its fully
hydrogenated derivative(s) C18H30 (in benzene-d6, 100 MHz, 30 °C).10
Figure 5. Simulation of thermogram 105 by iterative computations
(CALIT-3) assuming two consecutive first-order reactions (Sheme 2).
The errors distribution is not statistical.

Thermal Rearrangement of [18]Annulene
J. Phys. Chem. A, Vol. 104, No. 34, 2000 7983
Figure 6. 1H noise decoupled 13C-NMR spectrum of a solution of [18]annulene in THF-d8 thermolized at 92 °C during 24 h (Varian spectrometer
XL-300, 75 MHz; lock signal, TMS-d12; chemical shift reference (δ ) 0), C6H6; temperature, 23.2 °C). Top: Only the aliphatic region is represented
here. Bottom: Only the olefinic region is represented here.
noise-decoupled 13C-NMR spectrum (at 30 °C). This spectrum,
reproduced in Figure 6 (aliphatic domain and olefinic domain),
clearly indicates that, next to quadricyclic intermediate com-
pounds 2a, 2b, and 2c, the precursor of 4, i.e., trans-bicyclo-
[6.4.0]dodeca-2,4,6,9,11-pentaene 3, also accumulates in the
reaction mixture.
heats, we do not introduce the corrections for polymerization
of 4 as we have postulated and introduced in ref 1.
We have therefore simulated the thermograms with the
CALIT-3 program,3 considering three successive reactions
according to the reaction in Scheme 3 in which the identification
of the rate constants is the following:
This observation led us to modify our interpretation of the
diagram represented in Figure 3; the data marked by * do not
correspond to the concentration of 2 exclusively, but rather to
2 and 3 (the proton signals of these compounds are superposed).
Furthermore, the fact that the curves marked by . (benzene 5)
and by $ (1,2-benzo-1,3,7-cyclooctatriene 4) are still separated
after 210 h reaction means that the reaction is not completed (1
is still present) and is not due to polymerization of 4, as we
initially thought. Therefore, in the interpretation of the reaction
k1 for reaction 1 f 4
k2 for reaction 2 f 3 + 5
k3 for reaction 3 f 4
The simulation of the thermograms, after CALIT-3 iter-
ative computations considering three consecutive reactions,
gives optimal fit of the experimental data. The total quadratic
error is smaller than those obtained considering only one
(Scheme 1) or two reactions (Scheme 2) as indicated in

7984 J. Phys. Chem. A, Vol. 104, No. 34, 2000
Oth and Gilles
TABLE 1: Experimental Conditions of the Three
Thermograms Recorded for the Thermal Rearrangement of
[18]Annulene 1
SCHEME 3
[18]annulene
solvent
progr. rate
run no. w0 (mg) n0 (mmol) chemical w (mg) T˙ B (deg/min)
101
104
105
22.65
18.57a
19.40a
96.65
79.24
82. 78
toluene-d8
THF-d8
THF-d8
550
441
582
0.532
0.532
0. 423
5
1
2
3
a Freshly recrystallized sample.
employed to perform, the temperature corrections10 are indicated
below this table.
4
The Arrhenius parameters Ea and log A obtained from the
analysis of the three thermograms and for each individual
reaction are reported in Table 5. These parameters, averaged
over the three thermograms, are utilized in Table 6 to calculate
the entalpies, the entropies, and the free energies of activation
of the individual reactions. These thermodynamical parameters
are given for the standard temperature of 298.15 K, but the rate
constants ki (i ) 1, 2, 3) are quoted for the temperature of 150
°C, that is, for the mean temperature of the thermograms.
IV. Discussion of the Enthalpy Change for the Overall
Reaction 1 f 4 + 5
IVa. The Enthalpy of Formation of [18]Annulene 1 in the
Gas Phase at 298.15 K. The enthalpy of formation ∆H°(1, g,
f
298 K) of [18]annulene in the gas phase at 298.15 K can now
be derived as
Figure 7. Simulation of thermogram 105 by iterative computations
(CALIT-3) assuming three consecutive first-order reactions (Scheme
3). The errors distribution is statistical.
∆H°(1, g, 298 K) ) ∆H°(4, g, 298 K) +
f
f
Table 2. The distribution of the errors Q4 exp - Q4 calc is now
statistical as shown in Figure 7; this indicates that the reaction
mechanism adopted (Scheme 3) is the correct one.
∆H°(5, g, 298 K) - ∆rH(1 fff 4 + 5, g, 298 K)
f
The thermochemical and kinetic results of the analysis of the
thermograms performed according to the mentioned mechanism
(Scheme 3) are reported as tables below (Tables 3-6); their
interpretation will be discussed.
The enthalpy of formation of benzene 5 is known; the
recommended value9 is
∆H°(5, g, 298 K) ) 19.81 ( 0.13 kcal mol-1
f
III. The Numerical Results of the Simulations of
Thermograms 101, 104, and 105, the Computations Being
Performed with the CALIT-3 Program, Three
Consecutive Reactions Are Considered (Scheme 3)
The enthalpy of formation ∆H°(4, g, 298 K) of 1,2-benzo-
f
1,3,7-cyclooctatriene 4 can be estimated with confidence,
resorting to the group increment methods.10,11,12,13 The value
adopted is ∆H°(4, g, 298 K) ) 53.5 + 0.5 kcal mol-1 (cf.
f
The experimental conditions used for the investigation by
scanning calorimetry of the thermal rearrangement of [18]-
annulene 1 are listed in Table 1; three thermograms were
measured.
Table 2 gives the total quadratic errors obtained after the the
iterative simulations of the thermograms considering one
reaction (Scheme 1), two reactions (Scheme 2) and, ultimately,
three consecutive reactions (Scheme 3). This table displays the
obvious improvement achieved in the quality of the fittings when
considering three successive reactions.
Table 7).
The enthalpy of formation of [18]annulene 1 is then
∆H°(1, g, 298 K) ) 50.05 + 19.81 + 53.5 )
f
123.4 + 3.7 kcal mol-1
This value is much larger than the one reported by Beezer et
al.14 deduced from heat of combustion measurements. The value
reported, ∆H°(1, g, 298 K) ) 67 + 6 kcal mol-1, is certainly
f
In Table 3 we report, for each thermogram, the results of the
measured total reaction heat (Qr tot), the total enthalpy change
∆rH(1, sol., 415 K) for the rearrangement of 1 mol of
[18]annulene in solution, and the enthalpies changes of the three
individual reactions.
The averaged values of these enthalpy changes are then
reduced to standard conditions (i.e., 298.15 K and gas phase)
and are reported in Table 4. The required enthalpies of
sublimation and of vaporization9 as well as the methods
incorrect and much too small since oxidation of [18]annulene
in the bomb prior to combustion is unavoidable; the heat of
combustion of the oxidized annulene would then be much
smaller than the “correct” value, and, therefore, the enthalpy of
formation reported also should be much too small. The
evaluation of the enthalpy of formation of [18]annulene
∆H°(1, g, 298 K) as well as the signification of the stabiliza-
f
tion (resonance) and of the π-bonds delocalization energies are
summarized in Figure 8.

Thermal Rearrangement of [18]Annulene
J. Phys. Chem. A, Vol. 104, No. 34, 2000 7985
TABLE 2: Total Quadratic Error after the Iterative Simulation of the Thermograms Considering One, Two, or Three
Consecutive Reactions
1 reaction
2 reactions
3 consecutive reactions
experiment
no.
no. of
exptl points
k1
k1
k2
k1
k2
k3
1
98 4 + 5
1
9
8 2
98 4 + 5
1
98 2
98 3 + 5
98 4 + 5
101
104
105
70
68
79
0.1372
0.1451
0.1360
0.0626
0.0970
0.0517
0.0556
0.0832
0.0463
a The total quadratic error is calculated as tot. quadr. error ) ∑all points(Q4 exp - Q4 calc)2.
TABLE 3: Molar Reaction Enthalpies of the Three Individual Reactions As Obtained by the Iterative Fitting (CALIT-3) of the
Three Thermograms Considering Three Consecutive Reactions
∆rH(sol., 415 K) for each reaction indicated (in kcal mol-1
)
w0 (mg)
w (mg)
Qr tot
k1
k2
k3
98 4
run no.
[18]annul.
solvent
(cal)
1 fff 4 + 5
1
9
8 2
2
9
8 3 + 5
3
101
104
105
22.65
18.57c
19.40c
350a
441b
582b
-4.59
-3.81
-4.00
-47.49
-48.08
-48.32
-5.86
-5.34
-5.16
-12.52
-12.18
-12.49
-29.11
-30.56
-30.67
average:
-47.96
(0.60
-5.45
(0.35
-12.39
(0.30
-30.12
(1.10
statistical errorsd
a Toluene-d8. b Tetrahydrofuran-d8. c Freshly recrystallized sample. d The statistical error on the mean value of three measurements is
2js ) 2[(n2 - n)-1∑(xj - xi)2]1/2
.
TABLE 4: Enthalpies of the Three Consecutive Reactions Reduced to Standard Conditions (298.2 K, Gas Phase, in kcal mol-1
)
∆rH(sol., 415 K)
(kcal mol-1
correction
vap. + subl.
∆rH(g, 415 K)
(kcal mol-1
temperature
corrections
∆rH(g, 298.2 K)
(kcal mol-1
reaction
1 f 2
)
)
)
-5.45 ( 0.35
-12.39 ( 0.30
-30.12 ( 1.10
-47.96 ( 0.60
0.0
-5.45 ( 0.35
-18.29 ( 2.80
-30.12 ( 1.10
-53.86 ( 3.1
1.50
2.47
-0.16
3.82
-3.95 ( 0.35
-15.82 ( 2.80
-30.28 ( 1.10
-50.05 ( 3.1
2 f 3 + 5
-5.9 ( 2.5
3 f 4
1 ff 4 + 5
0.0
-5.9 ( 2.5
∆
∆
∆
∆
∆
subH(1) ) 28 ( 1.25 kcal mol-1
subH(2) ) 28 ( 1.25 kcal mol-1
vapH(3) ) 14 ( 1.25 kcal mol-1
vapH(4) ) 14 ( 1.25 kcal mol-1
vapH(5) ) 8.09 ( 0.01 kcal mol-1
temperature corrections:
f ∆rH(g, 298 K) ) ∆rH(g, 415 K) - (415 - 298.2)∆CP
∆CP ) ∑CP(products) - ∑CP(reagents) (the CP taken at 356 K)
f ∆rH(g, 298 K) ) ∆rH(g, 415 K) - ∑{(H°415 - H°) - (H° - H°)}prod. + ∑{(H°415 - H°) - (H° - H°)}reag
.
0
298
0
0
298
0
TABLE 5: Arrhenius Parameters Deduced from the Iterative Analyses of the Thermograms 101, 104, and 105, the Three
k1
k2
k3
Consecutive Reactions 1
98 2, 2
98 3 + 5, and 3
98 4 Being Taken into Consideration
k1
k2
k3
reaction 1
quadr. errors Ea (kcal mol-1
98 2
reaction 2
log A Ea (kcal mol-1
9
)
8 3 + 5
reaction 3
9
8 4
log A
w0 (mg)
no. of
tot.
run no. [18]annulene exptl points T˙ B (K min-1
)
)
log A Ea (kcal mol-1
)
101
22.65
18.57
19.40
70
68
79
0.532
0.532
0.423
0.0556
0.0832
0.0463
36.63
36.62
16.245
16.268
16.274
16.262
34.83
34.61
34.48
34.64
(0.20
16.209
16.309
16.478
16.332
(0.157
33.59
33.22
33.38
33.39
(0.21
16.335
16.317
16.353
16.335
104
105
36.62
mean values
36.625
(0.006
statistical errors 2js ) 2 [(n2 - n)-1 ∑(xj - xi)2]1/2
(0.017
(0.020
TABLE 6: Averaged Values of the Kinetic Parameters for Each of the Three Consecutive Reactions
values at 298.15 K
reaction
Ea (kcal mol-1
)
log10
A
ki(150 °C) (s-1
2.22 × 10-3
2.76 × 10-2
1.23 × 10-1
)
∆Hq (kcal mol-1
36.03 ( 0.01
34.05 ( 0.2
)
∆Sq (cal mol-1 K-1
13.88 ( 0.08
14.20 ( 1.0
)
∆Gq (kcal mol-1
31.89 ( 0.01
29.82 ( 0.2
)
k1
98 2
36.625 ( 0.006
34.64 ( 0.20
33.39 ( 0.21
16.2624 ( 0.017
16.3317 ( 0.16
16.3348 ( 0.020
1
2
3
k2
9
8 3 + 5
k3
32.90 ( 0.21
14.22 ( 0.13
28.56 ( 0.21
98 4
IVb. The Stabilization (Resonance) Energy of [18]Annu-
lene. The Activation Enthalpy of the Conformational Mobil-
ity in [18]Annulene. The stabilization energy due to the
resonance in the π-system, according to the definition by
Mortimer,15 is the difference between the enthalpy of formation
1k is readily calculated from thermochemical tables giving
the enthalpy of formation of groups. The value adopted is
(cf. Table 7)
∆H°(1k, g, 298 K) ) 161 ( 0.8 kcal mol-1
f
∆H°(1, g, 298 K) of [18]annulene (1, D6h) and the enthalpy of
f
The stabilization energy due to the resonance in the π-system
of [18]annulene is therefore
formation ∆H°(1k, g, 298 K) of the hypothetical planar Ke´kule´
f
structure 1k (symmetry D3h) with alternating single and double
bonds at their normal lengths.
∆Hstab(1) ) 123.4 - 161 ) -37.6 ( 4.5 kcal mol-1
∆Hstab(1) ) ∆H°(1, g, 298 K) - ∆H°(1k, g, 298 K)
f
i.e., a value very close to the corresponding quantity found for
The enthalpy of formation of the hypothetical Ke´kule´ annulene
benzene (-36.0).15

7986 J. Phys. Chem. A, Vol. 104, No. 34, 2000
Oth and Gilles
TABLE 7: Estimation, Using Three Group Increment Methods, of the Enthalpy of Formation of the Different Compounds 4,
1k, 2 ) 2a, 2b, 2c , 3 Implied in the Discussion of the Reaction Enthalpies of the Three Successive Reactions
tables used
Franklin10,11
Wiberg12
Benson13
adopted value
benzocyclooctatriene 4
Ke´kule´ [18]annulene 1k
tetracyclic intermediates
2 ) (2a + 2b + 2c)/3
trans-bicyclopentaene 3
53.07
(163.62)
52.51
161.4
53.99
160.62
53.5 ( 0.5
161.0 ( 0.8
118.14
85.02a
123.5
116.74
84.94
119.1 ( 3.0
84.33 ( 1.2
83.04a
a The stabilization energy in the plane cis-s cis-cis-butadiene (in cyclohexadiene) is taken as -3.5 kcal mol-1, and in 1,3,5-cyclooctatriene as
-3.7 kcal mol-1 (value deduced from the heat of hydrogenation of COT9 and from the comparison of the deduced enthalpy of formation of
1,3,5-cyclooctatriene with the value calculated by using the group increments methods).
SCHEME 4: Possible Structures of the Transition State
Implied in the Conformational Mobility of [18]Annulene
1 with Their Symmetry Indicated
This estimation of the activation enthalpy for the conformational
mobility in [18]annulene is 11 kcal larger than the experimental
value ∆Hq ) 16.1 kcal mol-1. This implies either that only a
part of the stabilization energy of [18]annulene 1 is lost along
the conformational mobility pathway or that strain release effects
have to be invoked. Indeed, we have also to consider that angular
strain is present in [18jannulene 1 in order to relax the steric
repulsion between the six inner protons (cf. X-ray data20); this
strain disappears in the transition state structures, and this fact
has also to contribute to the reduction of the activation enthalpy
of the conformational mobility process.
IVc. The π-Bond Delocalization Energy. The delocalization
energy ∆Hdeloc(1) in [18]annulene is the difference between the
enthalpy of formation ∆H°(1, g, 298 K) of [18]annulene (1)
f
and the enthalpy of formation ∆H°(1k*, g, 298 K) of the
f
Figure 8. Determination of the enthalpy of formation ∆Hf°(1, g, 298.15
hypothetical planar Ke´kule´ structure 1k* (symmetry D6h) with
localized single and double bonds having lengths identical to
those in the real [18]annulene molecule 1.
K) of [18]annulene and of its stabilization (resonance) and its π-bonds
delocalization energies: (a) Cox and Pilcher;9 (b) calculated values using
group increment methods.10-13
To calculate the enthalpy of formation of the Ke´kule´ structure
1k* (D6h), we must therefore add to the estimated enthalpy of
Note that the Hu¨ckel resonance energy in [18]annulene (of
symmetry D18h) is equal to 5.35â while in benzene it is equal
to 2â.
formation ∆H°(1k, g, 298 K) the energy required for the
f
readjustment of the bond lengths as indicated here under
3 × σ-bond compression from 1.54 to 1.419 Å
6 × σ-bond compression from 1.54 to 1.382 Å
We now have to explain why the activation enthalpy ∆Hq )
16.1 ( 0.2 kcal mol-1 determined for the conformational
mobility of the [18]annulene 116-18 is much smaller than the
absolute value of the stabilization energy, although the mech-
anism of this mobility implies that the cyclic delocalization of
the π-bonds must be destroyed, since in the transition state three
trans double bonds or three butadiene residues of configuration
trans-s trans-trans must be perpendicular to the “mean” molec-
ular plane16 (the possible transition state structures for the
conformational mobility in [18]annulene 1 are represented in
Scheme 4). In fact each of the possible transition state structures
contains three planar butadiene residues with a stabilization
3 × double bond readjust from 1.34 to 1.419 Å
6 × double bond readjust from 1.34 to 1.382 Å
The bond lengths in [18]annulene 1 are known from an X-ray
study20 and are reported in Scheme 5 where [18]annulene 1 is
represented together with the hypothetical Ke´kule´ structures 1k
and 1k*. The relevant bond lengths and the point group of these
species are indicated (note that only the geometry of the
molecular skeleton is taken into account when considering the
point group of 1k*; the π-bond distribution is not considered).
Using known force constants for the C-C bond in ethane
and for the CdC bond in ethylene,21 a total energy change of
+83 kcal mol-1 is calculated for these bond length readjust-
energy per residue of - 3.5 kcal mol-1 19
.
The activation enthalpy for the conformational mobility
should therefore be calculated as follows
∆Hq ) |∆Hstab(1)| - 3|∆Hstab(C4H6)| )
37.6 - (3 × 3.5) ) 27 ( 4.5 kcal mol-1

Thermal Rearrangement of [18]Annulene
J. Phys. Chem. A, Vol. 104, No. 34, 2000 7987
SCHEME 5: Bond Lengths in [18]Annulene 1 and in
the Hypothetical Structures 1k and 1k*a
SCHEME 6: The Two Degenerate (in Symmetry and in
Energy) HOMO’s of [18]Annulene (1) Calculated by the
SCF-MNDO Methoda
a The symmetry of the species is indicated.
a The numeratation of the centers in the two HOMO’s is chosen in
order to avoid in the discussion the necessity to refer to different number
identifications in the two orbitals.
ments. The estimated enthalpy of formation of the Ke´kule´
[18]annulene 1k* is then
strain accumulated along the reaction pathway, as can be
visualized from molecular model manipulations. On the contrary,
the electrocyclization between centers such as 1-8 proceeding
in a HMO’s symmetry conservation fashion and leading to a
cis junction between one 8-member ring and one 12-member
ring, as well as the electrocyclization between centers such as
3-8 leading to a cis junction between one 6-member ring and
one 14-member ring, are realistic processes. The multiplicity R
(i.e., the number of identical or isodynamical23 pathways) of
each of these two types of ring closure is the following:
∆H°(1k*, g, 298 K) = 161 + 83 = 244 kcal mol-1
f
and the π-bond delocalization energy in [18]annulene 1 is
estimated to be (cf. Figure 8)
∆Hdeloc(bonds in 1) ) ∆H°(1) - ∆H°(1k*) =
f
f
-120.5 kcal mol-1
Similar considerations concerning the benzene molecule give
the following result:15
ring closure of type 1-8 giving a cis ring fusion
ring closure of type 3-8 giving a cis ring fusion
R ) 24
R ) 12
∆Hdeloc(bonds in 5) ) -63 kcal mol-1
Remark. If one considers the π-bond delocalization energy
as identical to the Hu¨ckel resonance energy, and that the Hu¨ckel
resonance energy in [18]annulene 1 is the same as in the
annulene with D18 perimeter, then we have the following
determinations of the â value:
Note: The value of the multiplicity of a reaction pathway R
is found by direct counting of the identical ways of performing
the reaction, or, better, by taking the ratio of the number of
isometric23 transition state structures to the number of isometric
ground state structures:
benzene 5
2â ) - 63 kcal mol-1, i.e.
â ) -31.5 kcal mol-1
R ) Nq/NGS
[18]annulene 1
5.35â ) - 120.5 kcal mol-1, i.e.
â ) -22.5 kcal mol-1
These numbers N (Nq or NGS) are calculated according to the
following formula:
V. Discussion of the Thermochemical and Kinetic
Parameters of the Three Individual Consecutive
Reactions
for an achiral species: N ) P/σ
for a chiral species:24 N ) 2P/σ
Va. The Transformation of [18]Annulene 1 into the
Quadricyclic Compounds 2a, 2b, and 2c. These reactions can
be explained formally by a series of successive or concomittant
symmetry allowed intramolecular electrocyclizations. We will
discuss the possible reaction pathways, their multipicity, and
their stereochemical implications,22 considering these electro-
cyclizations as consecutive reactions. We will consider the
electronic structures of the two highest occupied molecular
orbitals of [18]annulene calculated by the SCF-CNDO method.
They are degenerate in energy and symmetry and are represented
in Scheme 6.
The electrocyclization between two opposite centers such as
1-10 or 3-12 implying the cyclization of a 10 π-electron
polyene must proceed thermally in a disrotatory fashion leading
to a cis junction of the two rings formed, since the phases of
the atomic orbitals of such opposite centers are in all cases
identical and their H’s are both pointing either inside or outside
the ring. Such a process is practically excluded in view of the
in which P is the dimension of the permutation group of
Longuet-Higgins25 (feasible permutations) and σ the symmetry
number of the species considered,26,27 i.e., the number of distinct,
physically feasible ways of orienting the species in space to
give an indistinguishable configuration (σ is the dimension of
the subgroup of rotations of the point group characteristic of
the species).
For the ring closure of type 1-8 giving a cis ring fusion, we
have (cf. Scheme 7a)).
ground state symmetry:
6h (achiral)
transition state symmetry:
C1 (chiral)24
D
symmetry number: σ ) 12
permutation group dimension:
P ) 2 × 18
symmetry number: σ ) 1
permutation group dimension:
P ) 2 × 18
NGS ) (2 × 18)/12 ) 3
Nq ) (2 × 2 × 18)/1 ) 72
The reaction path multiplicity is then R ) Nq/NGS
)
72/3 ) 24.

7988 J. Phys. Chem. A, Vol. 104, No. 34, 2000
Oth and Gilles
For the ring closure of type 3-8 giving a cis ring fusion, we
In view of the difficulties encountered in these calculations such
as the estimation of the contribution of adjacent aliphatic CH
groups and of the conjugation effects between double bonds,
this adopted value is somewhat uncertain.
have (cf. Scheme 7b)
ground state symmetry:
D6h (achiral)
transition state symmetry:
Cs (achiral)
The calculated reaction enthalpy, using this value
symmetry number: σ ) 12
permutation group dimension:
P ) 2 × 18
symmetry number: σ ) 1
permutation group dimension:
P ) 2 × 18
∆rH(1 f 2, g, 298 K) ) ∆H°(2, g, 298 K) -
f
NGS ) (2 × 18)/12 ) 3
Nq ) (2 × 18)/1 ) 36
∆H°(1, g, 298 K) ) 119.1 - 123.4 ) -4.3 kcal mol-1
f
The reaction path multiplicity is then R ) Nq/NGS
)
36/3 ) 12.
is, however, in excellent agreement with the experimental
reaction enthalpy reported in Table 4:
SCHEME 7: Symmetry of Possible Structures along the
Reaction Path toward the Transition States for the Two
Types of Electrocyclization of [18]Annulene 1 Discusseda
∆rH(1 f 2, g, 298 K) ) -3.95 kcal mol-1
These considerations constitute a further support for the validity
of the reported value for the enthalpy of formation of [18]-
annulene 1.
Vb. The Decomposition of the Tetracyclic Compounds 2a,
2b, and 2c to Benzene 5 and trans-Bicyclopentaene 3.28 Each
of the structures 2a, 2b, and 2c contains a four-membered ring
fused in cis fashion to a cyclohexadiene residue. Such a system
decomposes thermally via a biradical that is stabilized by
conjugation with the double bonds connected to the four
membered ring. The activation enthalpy of this ring opening is
easily estimated by considering the activation enthalpy of the
decomposition of cyclobutane to two ethylenes (Ea ) 62.5 kcal
mol-1, ∆Hq ) 61.9 29) and the stabilization enthalpy of the allyl
radical (∆Hstab ) - 13.5 30). If two allyl (or allyl and
pentadienyl) resonance energies are gained in the biradical, then
the activation enthalpy of the C4-ring opening would be
a The conformations of the 12-member ring and of the 14-member
ring are not correctly represented; the planar structures are represented
in order to emphasize their configurations.
The other ring closure steps leading to the tetracyclic
compounds 2a, 2b, and 2c are illustrated in Figure 9. It can be
seen, using molecular models, that the formation of 2a, and 2b
is easier than the formation of 2c, the strain required to form
the last rings in 2c being greatest and the reaction path
multiplicity being reduced in this last case. This explains why
the relative abundances of 2a and of 2b are greater than that of
2c (cf. Figure 6; note that in these figures the signals marked a
designate signals of 2a or 2b, and the b signals designate
compound 2b or 2a). One can also realize that the number of
13C-NMR olefinic signals marked c for 2c is not 12 but
smaller: the molecule has local symmetry such that 6 olefinic
C atoms have pairwise the same chemical shift giving 3 signals
with double the intensity of the 6 other olefinic C atoms; the 6
aliphatic C atoms give 4 13C-NMR signals with relative
intensities 2:2:1:1 for the same reason.
It is interesting that the multiplicity of the overall reaction
1 f 2a, 2b, and 2c is responsible for a large part of the reported
activation entropy ∆Sq ) 13.88 eu. If one assumes that all the
ring closures are concomitant, the contribution of the multiplicity
to ∆Sq is estimated to be R ln(48 + 48 + 24) ) 9.51 eu (cf.
Figure 9). If the different ring closures implicated in the
formation of the compounds 2a, 2b, and 2c are not concomitant,
intermediates are implied and the interpretation of the activation
entropy of the reaction 1 f 2 in terms of reaction path
multiplicity would have to be revised; the coefficients of
transmission through the different barriers would have to be
taken into account.
∆Hq(2 f biradical) ) 61.9 - (2 × 13.5) ) 34.9 kcal mol-1
This value is in very good agreement with the observed enthalpy
of activation of the reaction 2 f 3 + 5 reported in Table 6.
This agreement implies that the biradical is in fact the transition
state, or close to it, along the reaction path and that the splitting
of benzene 5 takes place along the second part of the reaction
path with continuous energy decay toward benzene 5 and trans-
bicyclopentaene 3.
The entropy of activation of the reaction is large, as is also
the case for the activation entropy of the reaction, of 1,2-cis-
dimethylcyclobutane giving two propene molecules (∆Sq ) 10.9
eu at 298 K29). This is explained by the appearance of torsion
modes of vibration around the residual C-C bond of the
previous C4 ring. For the reaction 2 f 3 + 5 discussed here,
the value ∆Sq ) 14.2 ( 1 eu is larger than 11 eu; this could
mean that, in the biradical, the C-C bond is already weakened
and has a lower stretching frequency than in the transition state
for the decomposition of 1,2-cis-dimethylcyclobutane in two
propene molecules.
The Reaction Enthalpy ∆rH(2 f 3 + 5, g, 298 K). The
enthalpy change associated with the reaction 2 f 3 + 5 can be
estimated as
The Reaction Enthalpy ∆rH(1 f 2a + 2b + 2c, g, 298 K).
The concentrations of compounds 2a, 2b, and 2c being
controlled kinetically and not thermodynamically, we will
calculate, by group increment methods, the enthalpies of
formation of the three compounds and consider the average of
these values as representative of the enthalpy of formation of 2
(cf. Table 7). The adopted value for the enthalpy of formation
of 2 is, in these conditions
∆rH(2 f 3 + 5, g, 298 K) ) ∆H°(5, g, 298 K) +
f
∆H°(3, g, 298 K) - ∆H°(2, g, 298 K)
f
f
The enthapies of formation of 5 and of 2 are known (see section
V.a) and the enthalpy of formation of 3 is estimated by the
group increments methods (cf. Table 7). One obtains
∆rH(2 f 3 + 5, g, 298 K) ) 84.33 + 19.81 - 119.1 )
-14.96 kcal mol-1
∆H°(2, g, 298 K) ) 119.1 ( 3.0 kcal mol-1
f

Thermal Rearrangement of [18]Annulene
J. Phys. Chem. A, Vol. 104, No. 34, 2000 7989
Figure 9. Hypothetic mechanisms proposed in order to establish the stereochemistry of 2a, 2b, and 2c and to determine the multiplicity of the
different rearrangements. If the ring fusions leading to each of compounds 2a, 2b, or 2c are concomitant, then we have the following reaction path
multipicities: 1 f 2a R ) 48, 1 f 2b R ) 48, 1 f 2c R ) 24, i.e., overall 1 f 2 R ) 120. The contribution of the multiplicities to the activation
entropy is R ln 120 ) 9.51 eu.
SCHEME 8: Choice of the Reaction Coordinates To
Establish the Energy Hypersurface Computed in View of
the Elucidation of the Mechanism of the Reaction 3 f 4
a value in perfect agreement with the experimental result
reported in Table 4:
∆rH(2 f 3 + 5, g, 298 K) ) -15.82 ( 2.8 kcal mol-1
Vc. The Transformation of trans-Bicyclopentaene 3 in
Benzocyclooctatriene 4 as the Result of Two Consecutive
Suprafacial 1,5-Hydrogen Shifts. In our studies on the [12]-
annulene,5 the thermal rearrangement 3 f 4 was also studied
using the first version of our scanning differential calorimeter.31
The reaction was not found to be perfectly reproducible and
was recognized to be sensitive to traces of water (acid-catalyzed
reaction). Reproducible thermograms could finally be obtained
by treating the Pyrex ampule with NH3 vapor and using
deuterated pyridine as solvent. The reaction was found to be
first order, and no intermediate such as bicyclo[6.4.0]dodeca-
1,3,6,9,11-pentaene 3a could be detected.6,32 All the parameters
(thermochemical and kinetic) found for this reaction and
reported in the present work (Tables 4 and 6) are in perfect
accord with those deduced from these earlier measurements.
To obtain a better understanding of the mechanism of this
reaction, we have established the reaction energy hypersurface,
the reaction coordinates chosen being indicated in Scheme 8.
The geometries have been optimized for all the values chosen
for these parameters.32 The computations were done, using a
modified version of the program MOPN33 that treats closed-
shell molecules by the SCF-UHF method.34 Since the UHF
determinant is not an eigenfunction of the S2 operator but reflects
a mixture of different spin states, spin-annihilation35 or spin-
projection36 techniques have been applied. The energy hyper-
surface is reproduced in Figure 10.
According to these computations, the two hydrogen shifts
are not taking place synchronously but rather consecutively. The

7990 J. Phys. Chem. A, Vol. 104, No. 34, 2000
Oth and Gilles
TABLE 8: Enthalpy of Formation ∆H°(g, 298 K) of the Species 3, 3a, 4 and of the Transition States TSdirect, TS1, and TS2 with
f
the Geometries Found in the Computed Hypersurfacec
∆H°(kcal mol-1
)
f
species
state
G.S.
strained
G.S.
symmetry
experiment
83.78 ( 1.6a
group incr.
UHF-MINDO-3 spin projection
83.3
3
3
3a
4
C1
C2
C1
Cs
C2
C2
C1
C1
84.33 ( 1.2
87.4 ( 2.5
81.4 ( 1.3
53.5 ( 0.5
57.9 ( 1.5
79.2
57.6
59.4
182.7
127.8
112.3
G.S.
4
strained
q (3 f 4)
q(3 f 3a)
q(3a f 4)
TSdirect
TS1
TS2
116.7 ( 1.8b
a Value found from the enthalpy of the reaction ∆rH(3 f 4, g, 298 K) ) -30.28 ( 1.1 and from the enthalpy of formation ∆H°(4, g, 298 K)
f
) 53.5 ( 0.5 kcal mol-1 calculated by the group increments methods (cf. Table 7). b ∆H°(TS1, 298 K) ) ∆H°(4, g, 298 K) - ∆rH(3 f 4), g, 298
f
K) + ∆Hq(k3, 298 K) ) 116.7 ( 1.8 kcal mol-1
.
c For species 3 and 4 a second geometfry is reported that is discussed in the text.
energy in the quasi-planar triene is gained. The estimation of
∆H°[3(C2)] - ∆H°[3(C1)] amounts to 3-4 kcal mol-1. The
f
f
synchronous shift of the two hydrogen atoms would occur in
this conformation, the C2 symmetry axis remaining preserved
in the complete dynamic process as well as in the product 4,
which would then relax in the achiral Cs geometry.
The second condition is clearly verified, the reaction enthalpy
being equal to
∆rH(3 f 4) ) -30.28 kcal mol-1
The third condition is not fulfilled, although the strain ac-
cumulated in the C2 conformation of TSdirect is only slightly
larger than in the transition states TS1 and TS2 with the C1
conformations.
The occurrence of synchronous two-bond-breaking in chemi-
cal processes is unlikely; accumulating the energy required to
break two bonds specifically in two vibrational modes prior to
energy redistribution to all the other degrees of freedom of the
molecule is hardly possible.
Figure 10. Potential energy surface computed in order to elucidate
the mechanism of the double 1-5 hydrogen shift in trans-bicyclo-
[6.4.0]dodeca-2,4,6,9,11-pentaene 3 giving 1,2-benzo-1,3,7-cyclooc-
tatriene 4. The diagonal 3 f TSdirect f 4 corresponds to the synchronous
shift of the two hydrogen atoms; the two off-diagonal paths 3 f TS1
f 3a f TS2 f 4 represents the asynchronous mechanism (multiplicity
2).
Let us now interpret the high positive value of the activation
entropy of the reaction 3 f 4 ∆Sq ) 14.22 ( 0.13 eu. For
each enantiomer of 3 (C1 symmetry), there are two isodynamic
pathways for the 1-5 H-shift process, i.e., a contribution of
R‚ln 2 ) 1.38 eu to the entropy of activation. But the most
important contribution to the activation entropy is due to the
motion of the migrating H atom; this motion accounted as a
translation mode along one coordinate contributes to the entropy
of activation by a quantity of 8.67 eu. Taking into account the
multiplicity R ) 2, the total contribution amounts to 10.05 eu.
Note that for the synchronous mechanism, the contribution to
the activation entropy of the simultaneous translation of the two
H’s would be 17.34 eu.
implicated intermediate bicyclo[6.4.0]dodeca-1,3,6,9,11-pen-
taene 3a is not observed since the activation enthalpy for the
last reaction step 3a f 4 is lower than the one of the first step.
The enthalpies of formation of the species 3, 3a, and 4, observed
and computed, as well as the relevant activation enthalpies, are
reported in Table 8.
Dewar has considered the abstract possibility of synchronous
multibond-breaking reactions and has formulated the require-
ments for such mechanisms to occur.37 According to his
arguments, synchronous hydrogen shifts would be favored if
three conditions were satisfied:
We can now construct the full diagram representing the
enthalpy evolution when going from 1 to 4 + 5 along the
reaction pathways discussed (Figure 11).
(i) the transition state has to be aromatic;
(ii) the reaction has to be exothermic;
(iii) the amount of strain relieved in the transition state has
to be larger for the synchronous than for the asynchronous
pathway.
VI. Verification of the Validity of the Kinetic Data
Gained from the Reported Analysis of the Thermograms
The first condition is by far verified if one considers the
double H shift to occur in the C2 conformation of 3 since, upon
breaking the two C-H bonds, the π-system of benzene is
formed. The strain accumulated in the C2 conformation of 3
should be relatively small; in fact this C2 conformation
corresponds to the transition state of the isodynamic transforma-
tion of 3 (C1) into itself (inversion of the cyclooctatriene ring)
with retention of the absolute configuration. The energy cost
for this ring inversion is smaller than the 11 kcal mol-1 required
for the inversion of cyclooctatetraene17 since here the resonance
VIa. Direct Measurement of the Kinetic Parameters of
the First Reaction 1 f 2. We have followed, by UV
spectroscopy, the isothermal disappearance of [18]annulene as
a function of time at seven different temperatures (between 90
and 150 °C). The measurements were done by warming the
solution of annulene at constant temperature (oil bath) for
controlled periods of time in a UV cell specifically constructed
so that the solution could be degassed under high vacuum and
the cell sealed off. In order to optimize the experimental
conditions, we had to find the concentration of annulene to be

Thermal Rearrangement of [18]Annulene
J. Phys. Chem. A, Vol. 104, No. 34, 2000 7991
Figure 11. Enthalpies of formation of all the species involved in the thermal rearrangement of [18]annulene 1 into benzene 5 and 1,2-benzo-
1,3,7-cyclooctatriene 4 and of all the transition states implied by the three consecutive first-order reactions. All values are in kcal mol-1. Only the
enthalpies of formation of 4 and 3a (marked by *) are calculated by the group incement methods; all the other data are measured.
used, the optical path to be chosen for the cell, and the
absorption band of the annulene to be measured in order to
monitor the kinetic experiments. For these reasons, a preliminary
thermolysis experiment was conducted at 120 °C using cells
with different optical paths. The results are reported in Figure
12.
A cell with an optical path of 0.02 cm was chosen in order
to work with the realistic concentration of 7.04 mg of [18lan-
nulene in 100 mL of THF. i.e., 3.0 × 10-4 mol L-1. The optical
density of the absorption band at λ ) 384 nm measured at -100
°C on this stock solution is OD ) 1.75, a suitable value in order
to follow the disappearance of the annulene since the absorption
at this wavelength due to the reaction products is negligible
(OD = 0). The measurements were performed by quenching
the cell in a dry ice-methanol bath (-80 °C) after each time
of thermolysis and transferring the cell in a gas flow cryostat
with sapphire windows, the temperature of which was controlled
and maintained at -100 °C. The UV spectrometer is a Cary
17, modified in order to digitize the wavelengths and the OD
data and to transfer them to a desktop computer.
Figure 12. Preliminary measure of the rate of disappearance of [18]-
annulene at 120 °C. This measure was carried out in order to optimize
The rate constants kT were found by the linear regression of
the measured values of log[(OD0 - ODt)/OD0]t obtained at
different times. Finally the linear regression of log kT as a
function of 1000/T gave the following Arrhenius and thermo-
dynamic parameters:
the experimental conditions of the kinetic studies observed by UV
spectroscopy.
which are in very good agreement with the results reported in
Table 6 (reaction 1 f 2 ).
The Arrhenius regression line of these UV kinetic measure-
ments is represented (with the data points) in Figure 13, together
with the individual regression lines for the kinetic results for
the three processes k1, k2, and k3 as obtained from the
thermogram analysis. Also are represented, in this figure, the
rate constants k1(T) at two temperatures deduced from two
Ea ) 35.9 ( 0.2 kcal mol-1
∆Hq ) 35.3 ( 0.5 kcal mol-1
log A ) 16.03 ( 0.2 eu
k1(150 °C) ) 3.10 × 10-3 s-1
∆Sq ) 12.8 ( 0.8 eu
∆Gq ) 31.6 ( 0.5 kcal mol-1
kinetic measurements performed by H-NMR spectroscopy.
1

7992 J. Phys. Chem. A, Vol. 104, No. 34, 2000
Oth and Gilles
Figure 14. Mole fractions of compounds 1, 2, 3, and 4 as functions
of the temperature (or of time) as they are calculated and plotted after
the iterative simulation (CALIT-3) of the 105 thermogram. The mole
fraction of compound 5 is the sum of the mole fractions of 3 and 4.
A somewhat related test could be made by close inspection
1
of the H noise decoupled 13C-NMR spectra recorded for a
solution of [18]annulene in THF-d8 thermolyzed 24 h at 92 °C
(spectrum reported on Figure 6). We have to compare the mole
fractions of the constituents extracted from the spectra with those
computed with the kinetic parameters reported for each ther-
mogram in Table 5. This procedure allows us to avoid the
problem of the correlation between Ea and log A in determining
the average values and the dispersions of the rate constants and
of the mole fractions.
Figure 13. Regression lines according to the Arrhenius equation of
k1
the kinetic data for the reaction 1
98 2 studied by UV spectroscopy
(the data points are represented) and of the data for the three consecutive
reactions, as obtained from the iterative simulations of the three
thermograms (the data points are not represented here). Two data points,
1
deduced from H-NMR measurements, are also represented.
This figure emphasizes the fact that the Arrhenius regressions
According to the data of Table 5, we have, for the rate
constants at 92 °C
k1
k3
lines for the reactions 1
98 2 and 3 98 4 are reproducible in the
k2
three thermograms, the regression lines for the reaction 2
9
8 3
k1 ) (2.20 ( 0.11) × 10-6 s-1
k2 ) (4.4 ( 2.5) × 10-5 s-1
k3 ) (2.25 ( 0.75) × 10-4 s-1
+ 5 differing somewhat from one thermogram to the other. This
situation is demonstrated in Table 5, which shows that the
frequency factor for this second reaction is the least precisely
determined of all the kinetic parameters.
VIb. The Relative Concentrations of the Species 1, 2 (2a
+ 2b + 2c), 3, 4, and 5 as Functions of the Temperature (or
Time) in the Course of the Measurement of a Thermogram.
In the iterative process, controlled by the CALIT-3 program,
when the iteration is stopped i.e., when the total quadratic error
has reached its minimum value, the kinetic parameters of the
last iteration step are utilized to compute the evolution of the
relative concentration of each component present in the solution
(in mole fraction) as a function of the temperature (or of the
time) defined by the thermogram. These data are plotted in
graphic form as part of the computer output. Figure 14 represents
the graph giving the evolution of the composition of the solution
during its thermolysis in the calorimeter (thermogram 105) as
obtained at the end of the iterative computations.
and, at each reaction time
n1 + n2 + n3 + n4 ) n0
n5 ) n3 + n4
n0 is the number of moles of [18]annulene 1 introduced into
the ampule.
The integration of the kinetic equations gives formulae that
permit the calculation of the mole fractions of the different
components after a given time of pyrolysis at a specified
temperature (see section VIII below for the derivation and the
integration of the kinetic equations).
For 24 h of pyrolysis at 92 °C, we calculate the following
mole fractions of the different components:
With the aid of this graph, a very effective test of the validity
of the analysis of the thermograms could be envisaged: a new
calorimetric run with controlled amounts of [18]annulene +
solvent and with the same rate of temperature increase would
have to be started but should be stopped when a precise
temperatue, say 405 K (see Figure 14), would be reached. The
cell containing the ampule should be immediately quenched in
liquid nitrogen (the construction of the calorimeter easily allows
such a manipulation) and the solution in the ampule directly
analyzed by 13C-NMR spectroscopy. The mole fractions of the
different components would have to be measured and compared
to their values read on the graph (Figure 14) for the temperature
at which the thermogram was stopped. Unfortunately we could
not perform this ideal test, for the reason that we did not have
enough material to invest 20 mg in such an experiment.
n1/n0 ) 0.827 ( 0.007
n2/n0 ) 0.048 ( 0.021
n4/n0 ) 0.117 ( 0.027
n5/n0 ) 0.125 ( 0.027
n3/n0 ) 0.0081 ( 0.0012
In order to compare these calculated mole fractions with
experimental data, the intensities (i.e., heights) of the 13C-NMR
signals were measured on the original spectra. All the signals
due to a given species have been added; this total was converted,
by division by a suitable factor taking into account the number
of different magnetic sites in the species and its symmetry, to
obtain a quantity proportional to the number of moles of the
species considered. This was done separately for the signals in
the olefinic and in the alphatic regions. For each region, a

Thermal Rearrangement of [18]Annulene
J. Phys. Chem. A, Vol. 104, No. 34, 2000 7993
normalization procedure such that the mole fraction n5/n0 takes
the computed value was adopted. This amounts to a coherent
estimation of the number of moles n0 of the [18]annulene
involved in the thermolysis. This normalization number is
different for the two regions, since the corresponding spectra
are recorded with different sensitivity conditions. The results
obtained are the following:
Ea and A are then refined by simulating the thermogram through
numerical integration of the kinetic equation and determining
parameter changes that optimize the simulation. The optimiza-
2
tion is stopped when the quadratic error ∑all points(Q4 exp - Q4 calc
)
ceases to decrease.
Program CALIT-33,4 is a generalization of CALIT-2 to the
case of successive isomerization reactions. It is also possible
to include parallel isomerization reactions. A model for the
kinetics must be assumed. For each reaction three parameters
must be found: the reaction heat Qr,i and the corresponding
Arrhenius parameters Ea,i and Ai (i ) reaction index). Initial
values of these parameters are estimated in a semiquantitative
way from the shape of the thermogram: the number and
importance of maxima and minima, areas between minima, and
so on. These values are used for launching an iterative simulation
procedure based on numerical integration of the kinetic equa-
tions. The optimization of the parameters ends when the total
quadratic error ceases to decrease. Owing to the complexity of
the problem, the optimization strategy is based upon the SPIRAL
algorithm proposed by Jones.38 This algorithm has been
implemented in CALIT-3 by Dr. J. Heinzer. At the end of the
iterative computation, the program CALIT-3 calculates and gives
in the output the following:
olefinic domain
aliphatic domain
n2a ) 540/12 ) 45
n2/n0 ) 0.0452 n2a ) 678/6 ) 113 n2/n0 ) 0.0435
n3 ) 250/(2×5) ) 25
n3/n0 ) 0.0251 n3 ) 124/2 ) 62
n3/n0 ) 0.0239
n4/n0 ) 0.1040
n4 ) 1050/(2×5) ) 105 n4/n0 ) 0.1055 n4 ) 540/2 ) 270
n5 ) 690/6 ) 115
ff
n5/n0 ) 0.1156
n1/n0 ) 0.8242
n3/n0 + n4/n0 ) n5/n0 ) 0.1279
ff nl/n0 ) 0.8286
n0 ) 995b
n0 ) 2595b
a n2 ) n2a + n2b + n2c. b The ratio 995/2595 is consistent with the
change in attenuation (AT) and in vertical scale (VS) of the plots (Figure
6): 995/2595 ) (0.75 × 1062)/(1 × 2075).
Considering the experimental errors, these results demonstrate
that the composition of a solution thermolyzed at 92 °C for a
period of 24 h is in good agreement with the composition that
one predicts using the kinetic parameters deduced from the
analysis of the thermograms, assuming three consecutive
reactions (CALIT-3). One has, however, to note that the mole
fraction of compound 3 is much too high with respect to the
calculated value (by a factor of 3!). Indeed the experimental
value n3/n0 does not fit with the relation n3/n0 ) n5/n0 - n4/n0.
Using this relation, it is possible to evaluate a value of n3/n0
that is compatible with the one predicted by the assumed
kinetics: by subtracting n4/n0 from n5/n0 one obtains n3/n0 )
0.0109 ( 0.0008, which is a value that is close to the predicted
figure. Note also that the progress of the reaction, measured as
1 - (n1/n0) ) 0.1736, is in excellent agreement with the
predicted value of 0.1730 in spite of the fact that the error for
the experimental value of nl/n0 is cumulative.
(1) the refined values of Qr,tot, Qr,i, Ea,i, log Ai, and, for
preselected temperatures, the values of ki, ∆Hq , ∆Sq , and ∆Gq ;
i
i
i
(2) a listing of the experimental Q4 exp and the calculated data
Q4 calc and a graphic in which the thermograms Q4 exp(T) and
Q4 calc(T) are plotted on a common temperature scale (sample
temperature T);
(3) a graphic in which the errors Q4 exp - Q4 calc (on an enlarged
scale) are plotted against T;
(4) a graphic representing the evolution of the mole fractions
of the different compounds implicated in the reaction mechanism
as a function of the sample temperature T.
The graphical representation of the errors allows one to
conclude whether the proposed mechanism governing the
kinetics is the correct one or not; the error distribution has to
be statistical.
VII. Short Description of the Simulation Programs
CALIT-2 and CALIT-3
The calorimeter used in this study is linearly programmed in
temperature and is of the differential type. Its description, its
calibration, all its research capabilities, and the exploitation of
the thermograms are presented in a book in preparation.4 We
will briefly indicate here the principles of the evaluation of the
thermograms.
VIII. The Kinetic Equations and Their Integration
Let us consider the reactions in Scheme 3. We will assume
that the “compound” 2 plays kinetically the role of a single
compound, although it consists of three enantiomeric pairs of
formulae 2a, 2b, and 2c.
The calorimeter construction is designed to allow a very
accurate mesurement of the heat transfer between the heating
block and the reference and sample cells. It is thus possible to
deduce the heat flux due to a chemical reaction Q4 r as a function
of time and, by a convenient correction, as a function of the
sample temperature T. Comparison of the experimental heat flux
due to the reaction(s) Q4 r(T) with theoretical values calculated
by integration of the kinetic equations requires a fixed model
for the kinetics.
Program CALIT-22,4 considers a single isomerization reaction.
Three parameters have to be determined: the total reaction heat
Qr,tot and the kinetic parameters Ea and A. The total heat is
obtained initially by total integration of the thermogram. The
rate constant k(T) can be estimated from partial integrations of
the thermogram. Initial values of Ea and A are obtained from a
Let us designate by n1, n2, n3, n4, and n5 the numbers of moles
of compounds 1 ... 5 and by n0 the number of moles of 1
involved in the thermolysis. The kinetic equations expressing
the time evolution of the number of moles of each compound
are
dn1/dt ) - k1n1
dn2/dt ) k1n1 - k2n2
dn3/dt ) k2n2 - k3n3
dn5/dt ) k2n2
dn4/dt ) k3n3
linear regression of log k(T) versus 1000/T. The parameters Qr,tot
,

7994 J. Phys. Chem. A, Vol. 104, No. 34, 2000
Oth and Gilles
(5) Oth, J. F. M.; Ro¨ttele, H.; Schro¨der, G. Tetrahedron Lett. 1970, 1,
61. Oth, J. F. M.; Gilles, J.-M. Tetrahedron Lett. 1970, 1, 67. Oth, J. F.
M.; Schro¨der, G. J. Chem. Soc. B 1971, 5, 904.
The integration of these equations between the limits t ) 0
and t gives, after transformations
(6) Oth, J. F. M. Unpublished results.
(7) Sto¨ckel, K.; Garrat, P. J.; Sondheimer, F.; de Julien de Ze´licourt,
Y.; Oth, J. F. M. J. Am. Chem. Soc. 1972, 94, 8644.
n1 ) n0 exp(-k1t)
(8) de Julien de Ze´licourt, Y.; Oth, J. F. M. Results reported in: de
Julien de Ze´licourt, Y. Ph.D. Thesis, ETH 5679, Zu¨rich, 1976.
(9) Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organo-
metallic Compounds; Academic Press: London and New York, 1970.
(10) Janz, G. J. Thermodynamic Properties of Organic Compounds;
Academic Press: New York and London, 1967.
k1
n2 ) n
[exp(-k1t) - exp(-k2t)]
0 k2 - k1
k1k2 exp(-k1t) - exp(-k3t)
k2 - k1
(11) Franklin, J. L. Ind. Eng. Chem. 1949, 41, 1070.
n3 ) n0
-
[
(12) Wiberg, K. B. Determination of Organic Structures by Physical
Methods; Academic Press: New York and Lodon, 1971; Vol. 3, p 207.
(13) Benson, S. W. Thermochemical Kinetics; John Wiley & Sons,
Inc.: New York, 1968.
(14) Beezer, A. E.; Mortimer, C. T.; Springall, H. D.; Sondheimer, F.;
Wolovsky, R. J. Chem. Soc. 1965, 216.
(15) Mortimer, C. T. Reaction Heats and Bond Strengths; Pergamon
Press: Oxford-London-New York-Paris, 1962; Chapter 4.
(16) Gilles, J.-M.; Oth, J. F. M.; Sondheimer, F.; Woo, E. P. J. Chem.
Soc. B 1971, 11, 2171.
(17) Oth, J. F. M. Pure Appl. Chem. 1971, 25 (3), 573-622.
(18) de Julien de Ze´licourt, Y.; Oth, J. F. M. To be published. The results
of the 13C-NMR study of the conformational mobility in [18]annulene are
reported in: de Julien de Zelicourt, Y. Ph.D. Thesis, #5679, ETH, Zu¨rich,
1976.
(19) Mortimer, C. T. Reaction Heats and Bond Strengths; Pergamon
Press: Oxford-London-New York-Paris, 1962; Chapter 3.
(20) Bregman, J.; Hirshfeld, F. L.; Rabinovich, D.; Schmidt, G. M. J.
Acta Crystallogr. 1965, 19, 227. Hirshfeld, F. L.; Rabinovich, D. Acta
Crystallogr. 1965, 19, 235.
(21) Cottrel, T. L. The strengths of the chemical bonds, 2nd ed.;
Butterworths: London, 1958. Wilson; Decius; Cross. Molecular Vibrations;
McGraw Hill: 1955; p 175.
(22) Woodward, R. B.; Hoffman, R. The ConserVation of Orbital
Symmetry; Verlag Chemie: Weinheim, 1971. Anh, N. T. Les re`gles de
Woodward-Hoffmann; Ediscience: Paris, 1970.
(23) The terms “isodynamic” and “isometric” were introduced by:
Altman, S. L. Proc. R. Soc. London, Ser. A 1967, 298, 184.
(24) Enantiomers with same nuclei labeling are counted as two isometric
structures.
k3 - k1
exp(-k2t) - exp(-k3t)
k3 - k2
]
k1k2 1 - exp(-k1t) 1 - exp(-k2t)
k2 - k1
n5 ) n0
n4 ) n0
-
[
]
k1
k2
k2k3
[1 - exp(-k1t)] -
{
(k2 - k1)(k3 - k1)
k1k3
[1 - exp(-k2t)] +
(k2 - k1)(k3 - k2)
k1k2
[1 - exp(-k3t)]
}
(k3 - k1)(k3 - k2)
A verification of these equations is made by ckecking that
they fulfill the following conditions:
n1 + n2 + n3 + n4 ) n0 and
n3 + n4 ) n5
Acknowledgment. We acknowledge, with gratitude, the
financial support of the Sweizerischer Nationalfonds zur
Fo¨rderung der Wissenschaftlichen Forschung and the computing
center of the Eidg. Techn. Hochschule Zu¨rich for the computing
time.
(25) Longuet-Higgins, H. C. Mol. Phys. 1963, 6, 445.
(26) Herzberg, G. Molecular Spectra and Molecular Structure; Van
Nostrand: Princeton, NJ, 1945.
(27) Salthouse, J. A.; Ware, M. J. Point group character tables and
related data, Cambridge University Press: New York, 1972.
(28) We will adopt shorter names to identify compounds 3 and 4.
(29) Benson, S. W.; O’Neal, E. H. Kinetic Data on Gas Phase
Unimolecular Reactions; NSRDS-NBS 21; National Bureau of Standards:
(Gaithersburg, MD) 1970; pp 268-272 and references cited therein.
(30) Neuman, M.; Roth, W. Data quoted and discussed in: Neuman M.
Ruhr Universita¨t Bochum, 1994.
References and Notes
(1) Oth, J. F. M.; Bu¨nzli, J.-C.; de Julien de Ze´licourt, Y. HelV. Chim.
Acta 1974, 57, 2276.
(2) Gilles, J.-M. Program CALIT-2 (Fortran), 1967.
(3) Gilles, J.-M. Program CALIT-3 (Fortran), 1970 and extended by
J. Heinzer in 1980 with the “spiral algorithm” as developped by A. Jones
(cf. ref 38).
(4) Technical details concerning our calorimeter and the thermogram
evaluation methods will appear in a book in preparation: Oth, Jean F. M.;
Gilles, Jean-Marie. Un calorime`tre a` tempe´rature programme´e permettant
la mesure rapide de la fonction capacite´ calorifique dHX/dT dans le domaine
des tempe´ratures comprises entre 100 K et 700 K ainsi que la mesure du
flux thermique duˆ a` la chaleur de re´actions chimiques et des parame`tres
cine´tiques qui les caracte´risent.
(31) Oth, J. F. M. Union Carbide ERA Tech. Memorandum, No. 27;
Union Carbide European Research Associates: Brussels, 1970.
(32) Baumann, H.; Cometta-Morini, C.; Oth, J. F. M. J. Mol. Struct.:
THEOCHEM 1986, 138, 229-237.
(33) Bischof, P. K. J. Am. Chem. Soc. 1976, 98, 6844.
(34) Pople, J. A.; Nesbet, R. K. J. Chem. Phys. 1954, 22, 571.
(35) Salotto, A. W.; Burnelle, L. J. Chem. Phys. 1970, 52, 2936.
(36) Philipps, D. H.; Schug, J. C. J. Chem. Phys. 1974, 61, 1031.
(37) Dewar, M. J. S. J. Am. Chem. Soc. 1984, 106, 209.
(38) Jones, A. Comput. J. 1970, 13, 301.