92 J. Am. Chem. Soc., Vol. 120, No. 1, 1998
Ikeda et al.
(4-BrC6H4)3N] indicate. Under PET conditions, a rapid BET38
from DCA•- to 2c•+ followed by the ring cleavage of 2c resulted
in the formation of 1c. In support of this assumption was the
product distribution ratio, d4-1c:d4-1c′, from d4-4c under PET
and direct irradiation conditions as mentioned later. It is thus
reasonably assumed that a similar BET process operates to form
d4-2 in the DCA-sensitized PET degenerate Cope of d4-1,
completing a CRCY-DRCL mechanism as shown in Scheme
1d.
Photoacoustic Calorimetric Analysis and Energetics of the
PET Degenerate Cope Rearrangement of d4-1. The direct
CR cleavage of d4-2•+ to d4-1•+ and d4-1′•+ does not compete
with BET from DCA•- to d4-2•+. A possible kinetic reason
for this observation is based on the reaction thermodynamics.
To determine the energetics of the CR cleavage, the enthalpy
of formation, ∆Hirp([2•+/DCA•-]), of the ion radical pair [2•+/
DCA•-] must be measured. For this, we applied nanosecond
time-resolved photoacoustic calorimetry (PAC), which is a
useful technique to determine energetics of various PET
reactions as have been reported previously.40 The deconvolution
of the experimental acoustic waveforms can provide the
amplitude and time evolution of heat that is emitted when the
Figure 2. Schematic diagram of PAC for the 1-DCA-BP system.
From several experiments, the deconvolution parameters, R1,
R2, and τ2 are determined to be 0.29 ( 0.03, 0.24 ( 0.05, and
194 ( 42 ns, respectively, for the 1c-DCA-BP system. ∆Hirp-
([2a-c•+/DCA•-]), i.e., energy difference between [2a-c•+/
DCA•-] and the ground states of 1a-c and DCA, were thus
determined to be 40.8 ( 5.3, 44.2 ( 5.4 and 43.6 ( 4.5 kcal/
mol for 2a, 2b, and 2c, respectively.42 For the 1c-NMQ+PF6
-
-
TOL system, the deconvolution parameters, R1, R2, and τ2 were
determined to be 0.57 ( 0.02, 0.27 ( 0.03, and 180 ( 55 ns,
respectively. From those values and numerous calibrations,
energy of the ion-radical pair [2c•+/NMQ•PF6-] was given by
the equation ∆Hirp([2c•+/NMQ•PF6-]) ) hν × (1 - R1) + 9
kcal/mol.43 Using the R1 value and photon energy (337 nm,
84.8 kcal/mol), ∆Hirp([2c•+/NMQ•PF6-]) was determined to be
45.6 ( 3.5 kcal/mol. The reliability of ∆Hirp values determined
for both systems was verified by taking into account the
excited sensitizer affords [2•+/sensitizer•-]. Experiments were
performed for both the 1a-c-DCA-BP and 1c-NMQ+PF6
-
-
TOL systems in acetonitrile according to the reported proce-
dure.41 In Figure 2, a schematic diagram for PAC is described
for the 1-DCA-BP system. Enthalpy of formation of [2•+/
DCA•-] can be expressed by eqs 1 and 2
∆Hirp([2•+/DCA•-]) ) hν(1 - R1 - R2)/φ
φ ) hν(1 - R1)/E([BP•+/DCA•-])
(1)
(2)
difference (0.05 V) in Ered between DCA14 and NMQ+PF6
-
1/2
(-0.90 V vs SCE in acetonitrile). Energy of the ion radical
pair ∆Hirp([2c•+/NMQ•PF6-]) can be compared with that of
[2c•+/DCA•-] by adding 1.2 kcal/mol. The resulting energy of
the ion-radical pair, 46.8 ( 3.5 kcal/mol, approximates to 43.6
( 4.5 kcal/mol within experimental errors. After all, ∆Hirp-
([2c•+/DCA•-]) was determined statistically to be 44.4 ( 4.5
kcal/mol as shown in Figure 3.
where hν, φ, and E([BP•+/DCA•-]) are photon energy (415 nm,
68.9 kcal/mol), the quantum yield to form [BP•+/DCA•-], and
the energy (66.2 kcal/mol) of [BP•+/DCA•-] determined from
redox potentials of BP and DCA, respectively.
(37) This calculation has been done on the assumption that Eox of 2c
1/2
is comparable with that of the cumyl radical. As one of the reviewers pointed
out, this estimation of ∆Gbet gives a lower limit because the Eox of 2c
By using the redox potentials of 1c and DCA, the free energy
changes of the formation of [1c•+/DCA•-] are calculated to be
60.6 kcal/mol. On the basis of our results21 of pulse radiolysis
for cyclization of d,l-2,5-bis(4-methoxyphenyl)-3,4-dimethyl-
1,5-hexadiene CR to trans-1,4-bis(4-methoxyphenyl)-2,3-dim-
ethylcyclohexane-1,4-diyl CR, the enthalpy of activation for
cyclization of 1c•+ to 2c•+ was assumed to be 3∼4 kcal/mol.
The energy barrier for the CR cleavage of 2c•+ is thus >19
kcal/mol as shown in Figure 3. This barrier seems to be too
high for d4-1c to undergo the degenerate Cope, especially at
-80 °C, in a CRCY-CRCL mechanism, and hence, 2c•+ enters
into the DR energy surface through the competing exothermic
BET process. Because ∆Hirp([2c•+/DCA•-]) and the ∆Gbet for
the BET from DCA•- to 2c•+ are ca. 44.4 ( 4.5 and ca. 25.6
kcal/mol, respectively, diyl 2c will lie ca. 18.8 kcal/mol higher
in energy than 1c and ca. 25.6 kcal/mol below [2c•+/DCA•-].37
The experimental PAC results demonstrate the endothermicity4
1/2
may be more negative. This was suggested from a significant electron
coupling between the cumyl cation and cumyl radical parts in 2c•+ that
cause the remarkable red shift of 2c•+ in the electronic absorption
spectroscopy. Unfortunately, however, it is difficult to evaluate the effect
of through-bond interaction upon redox potentials.
(38) By using the following equations (3, 4)39 and reported parameters
by Farid15c and Kikuchi,15d rate constant, kbet, of the BET in [2c•+/DCA•-
]
at 20 °C was estimated to be 1.9 × 109 s-1 and 4.9 × 1010 s-1, respectively,
in acetonitrile
(λs + ∆Gbet + ωhν)2
4λskbT
1/2
∞
4π3
e-sSω
2
kbet
)
|V|
exp -
∑
(
)
(
)
{
}
h2λskbT
ω!
ω)0
(3)
(4)
S ) λv/hν
2
where parameters |V| , λs, λv, and ν are, respectively, an electronic matrix
element squared, solvent reorganization energy, vibrational reorganization
energy, and single average frequency.
(39) Miller, J. R.; Beitz, J. V.; Huddleston, R. K. J. Am. Chem. Soc.
1984, 106, 5057-5068. Siders, P.; Marcus, R. A. J. Am. Chem. Soc. 1981,
103, 741-747, 748-752. Van Duyne, R. P.; Fischer, S. F. Chem. Phys.
1974, 5, 183-197. Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975, 63, 4358-
4368.
(40) Rothberg, L. J.; Simon, J. D.; Bernstein, M.; Peters, K. S. J. Am.
Chem. Soc. 1983, 105, 3464-3468. Goodman, J. L.; Peters, K. S. J. Am.
Chem. Soc. 1986, 108, 1700-1701. Ci, X.; da Silva, R. S.; Goodman, J.
L.; Nicodem, D. E.; Whitten, D. G. J. Am. Chem. Soc. 1988, 110, 8548-
8550. Zona, T. A.; Goodman, J. L. Tetrahedron Lett. 1992, 33, 6093-
6096. LaVilla, J. A.; Goodman, J. L. J. Am. Chem. Soc. 1989, 111, 712-
714.
(41) Rudzki, J. E.; Goodman, J. L.; Peters, K. S. J. Am. Chem. Soc.
1985, 107, 7849-7854. Herman, M. S.; Goodman, J. L. J. Am. Chem. Soc.
1989, 111, 1849-1854. Peters, K. S. In Kinetics and Spectroscopy of
Carbenes and Biradicals; Platz, M. S., Ed.; Plenum: New York, 1990; pp
37-49. Griller, D.; Wayner, D. D. M. Pure Appl. Chem. 1989, 61, 717-
724.
(42) Similarly, ∆Hirp([2c•+/NMQ•PF6-]) in 1,2-dichloroethane was de-
termined to be 45.1 ( 2.3 kcal/mol by using the following parameters; R1
) 0.32 ( 0.02, R2 ) 0.27 ( 0.02, and τ2 ) 233 ( 36 ns (averages from
five runs).
(43) Goodman, J. L. unpublished results.