1648 J . Org. Chem., Vol. 64, No. 5, 1999
Ikeda et al.
Ta ble 9. Decon volu tion F ittin g P a r a m eter sa of P AC
An a lyses for Deter m in a tion of En er gy of th e Ion Ra d ica l
P a ir , ∆Hir p ([a a C-21a •+/DCA•-])
∆Hirp([aaC-21a •+
/
sub
R1
R2
τ2 (ns)
DCA•-]) (kcal/mol)b
ZZ-3a
EE-3a
dl-4a
0.25 ( 0.02 0.24 ( 0.02 205 ( 25
0.26 ( 0.03 0.22 ( 0.02 160 ( 53
0.25 ( 0.01 0.26 ( 0.00 191 ( 16
44.9 ( 2.1
46.3 ( 1.5
43.0 ( 0.4
29.3 ( 1.5
trans-5a 0.28 ( 0.00 0.40 ( 0.01 219 ( 11
a
b
The errors are 1σ. Face values relative to each substrate and
DCA.
Upon prolonged irradiation n,cis-5b enters into a Cope
rearrangement cycle to give a Cope photostationary
mixture as shown in Table 7. The fact that direct
irradiation of x,cis-6b forms n,cis-5b exclusively supple-
ments a diradical closure mechanism shown in Scheme
7.
P h otoa cou stic Ca lor im etr ic An a lysis a n d En er -
getics of th e P h otoin d u ced Electr on -Tr a n sfer Cop e
Rea r r a n gem en ts of EE-3a a n d d l-4a . Nanosecond
time-resolved photoacoustic calorimetry (PAC)26 allows
for the simultaneous determination of dynamics and
energetics of various photoinduced electron-transfer
reactions.1a,15,27 In fact, our recent PAC experiments
demonstrated that a CRCY-DRCL mechanism (Scheme
1) is energetically most favorable for the photoinduced
electron-transfer degenerate Cope rearrangement of d4-
1.1a For further confirmation of this mechanism, we have
used PAC to investigate the Cope rearrangement of EE-
3a and dl-4a .
F igu r e 1. Potential energy diagram for the DCA-sensitized
PET Cope rearrangement of EE-3a and dl-4a . Relative energy
was represented in kcal/mol.
statistic value, 47.3 kcal/mol is used for ∆Hirp([aaC-21a •+
/
DCA•-]).
By using redox potentials of EE-3a , dl-4a , and DCA,
the energies of ion pair [EE-3a •+/DCA•-] and [dl-4a •+
/
DCA•-] are calculated to be 58.1 and 47.5 kcal/mol,
respectively. The CRCY of dl-4a •+ to aaC-21a •+ is thus
about 11 kcal/mol exothermic. In contrast, the energy of
[EE-3a •+/DCA•-] is close to that of [aaC-21a •+/DCA•-],
and hence the direct cleavage of aaC-21a •+ to EE-3a •+
seems to be energetically feasible but perhaps slower.
However, BET to form diyl aaC-21a is assumed to occur
faster than cleavage to EE-3a •+. To judge experimentally
whether cleavage of aaC-21a •+ to EE-3a •+ is operative,
aaC-21a •+ was independently generated from trans-5a ,
and temperature effects on product ratios from aaC-21a •+
were examined at low conversion in the temperature
range between 60 and -80 °C. The product ratios, dl-
4a :EE-3a , at low conversion does not depend on temper-
ature, and the average ratio is near 32:68.4 This obser-
vation suggests that cleavage of aaC-21a •+ to EE-3a •+ is
not thermally accelerated and thus unlikely to occur in
a Cope rearrangement sequence. Thus, aaC-21a •+ gener-
ated from EE-3a •+ and dl-4a •+ preferentially suffers BET
to give aaC-21a , through which EE-3a and dl-4a are
formed. Using ∆Gbet for the BET from DCA•- to aaC-21a •+
to be about 19 kcal/mol,20,23 aaC-21a is about 29 kcal/
mol higher in energy than EE-3a .
Experiments were done under DCA-BP-cosensitized
conditions in acetonitrile.1a,15,27e The enthalpy of forma-
tion of [aaC-21a •+/DCA•-] can be expressed by ∆Hirp([aaC-
21a •+/DCA•-]) ) hν(1 - R1 - R2)/φ and φ ) hν(1 - R1)/
E([BP•+/DCA•-]), where hν, R, φ, and E([BP•+/DCA•-]) are
the photon energy (415 nm, 68.9 kcal/mol), the deconvo-
lution parameters, 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. ∆Hirp was determined from several experi-
ments for EE-3a and dl-4a , and shown in Table 9
together with another deconvolution parameter, τ2. The
energy of ion radical pair, ∆Hirp([aaC-21a •+/DCA•-]),
relative to dl-4a and DCA is determined to be 43.0 ( 0.4
kcal/mol. By adding this value to the difference in heat
of formation between dl-4a and EE-3a , 6.0 ( 1.5 kcal/
mol, determined by differential scanning calorimetry,
∆Hirp([aaC-21a •+/DCA•-]) relative to EE-3a and DCA is
estimated to be 49.2 ( 1.9 kcal/mol which corresponds
to the experimental value, 46.3 ( 1.5 kcal/mol, obtained
from EE-3a within experimental errors. In Figure 1, the
Con clu sion . Observed stereospecificity and energetics
based on PAC support a CRCY-DRCL mechanism of the
Cope rearrangement for the title dienes. The initial
cyclization of the diene cation radicals occurs in the chair
conformation to give the chair 1,4-diaryl-2,3-dimethyl-
cyclohexane-1,4-diyl cation radical intermediates. Sub-
sequent cleavage of the chair 1,4-diaryl-2,3-dimethylcy-
clohexane-1,4-diyl intermediates regenerates the neutral
dienes. These two processes are connected by the highly
exothermic BET from DCA•- to the 1,4-diaryl-2,3-di-
methylcyclohexane-1,4-diyl cation radicals. A CRCY-
DRCL mechanism is thus a general rearrangement
sequence for the photoinduced electron-transfer Cope
rearrangement of the 2,5-diaryl-1,5-hexadiene system.
The chair intermediates interconvert with the boat
(24) Eox1/2 of the 4-methylcumyl radical is estimated by interpolation
from the correlation between the known Eox of 4-substituted cumyl
1/2
radicals25 and the substituent constants σ+.
(25) Sim, B. A.; Milne, P. H.; Griller, D.; Wayner, D. D. M. J . Am.
Chem. Soc. 1990, 112, 6635-6638.
(26) 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.
(27) (a) Rothberg, L. J .; Simon, J . D.; Bernstein, M.; Peters, K. S. J .
Am. Chem. Soc. 1983, 105, 3464-3468. (b) Goodman, J . L.; Peters, K.
S. J . Am. Chem. Soc. 1986, 108, 1700-1701. (c) Ci, X.; Silva, R. S. da;
Goodman, J . L.; Nicodem, D. E.; Whitten, D. G. J . Am. Chem. Soc.
1988, 110, 8548-8550. (d) LaVilla, J . A.; Goodman, J . L. J . Am. Chem.
Soc. 1989, 111, 712-714. (e) Zona, T. A.; Goodman, J . L. Tetrahedron
Lett. 1992, 33, 6093-6096.