Mapping the potential energy surfaces of the 1,6-diphenyl-1,3,5- hexatriene ground and triplet states

Article abstract of DOI:10.1021/ja982551j

The relative energies of the ground state isomers of 1,6-diphenyl- 1,3,5-hexatriene (DPH) in benzene are determined from the temperature dependence of the equilibrium isomer composition obtained with the use of diphenyl diselenide as isomerization catalyst. In the triplet state, DPH exists as an equilibrium mixture of all-trans (ttt), trans,cis,trans (tct), cis,trans,trans (ctt), and cis,cis,trans (cct) isomers. Under degassed conditions, photoisomerization of the triplets is primarily bimolecular, involving a quantum chain process. Oxygen eliminates the quantum chain process by efficient deactivation of DPH triplets thereby revealing the triplet state isomeric composition. The temperature dependencies of the fluorenone-sensitized photoisomerization quantum yields and photostationary states for DPH in air-saturated benzene provide two independent measures of the temperature dependence of the equilibrium contribution of the isomeric triplets. They reveal the relative energies of the DPH triplet isomers. Together with the known 34 kcal/mol triplet energy of ttt-DPH, these results define points on the potential energy surfaces of the ground and triplet states corresponding to the equilibrium geometries of the four observed DpH isomers. At these geometries the two surfaces roughly parallel each other. Complete equilibration of isomeric triplets within 100 ns requires that the energies of triplet biradical transition states be no higher than 40.3 kcal/mol. Estimated radical stabilization energies give 40.2 and 41.6 kcal/mol for the energies of biradical transition states for central and terminal bond isomerization, respectively, in the ground state of ttt-DPH.

Full text of DOI:10.1021/ja982551j

VOLUME 121, NUMBER 5
FEBRUARY 10, 1999
© Copyright 1999 by the
American Chemical Society
Mapping the Potential Energy Surfaces of the
1,6-Diphenyl-1,3,5-hexatriene Ground and Triplet States
Jack Saltiel,* Janell M. Crowder, and Shujun Wang
Contribution from the Department of Chemistry, The Florida State UniVersity,
Tallahassee, Florida 32306-4390
ReceiVed July 20, 1998
Abstract: The relative energies of the ground state isomers of 1,6-diphenyl-1,3,5-hexatriene (DPH) in benzene
are determined from the temperature dependence of the equilibrium isomer composition obtained with the use
of diphenyl diselenide as isomerization catalyst. In the triplet state, DPH exists as an equilibrium mixture of
all-trans (ttt), trans,cis,trans (tct), cis,trans,trans (ctt), and cis,cis,trans (cct) isomers. Under degassed conditions,
photoisomerization of the triplets is primarily bimolecular, involving a quantum chain process. Oxygen eliminates
the quantum chain process by efficient deactivation of DPH triplets thereby revealing the triplet state isomeric
composition. The temperature dependencies of the fluorenone-sensitized photoisomerization quantum yields
and photostationary states for DPH in air-saturated benzene provide two independent measures of the temperature
dependence of the equilibrium contribution of the isomeric triplets. They reveal the relative energies of the
DPH triplet isomers. Together with the known 34 kcal/mol triplet energy of ttt-DPH, these results define
points on the potential energy surfaces of the ground and triplet states corresponding to the equilibrium
geometries of the four observed DPH isomers. At these geometries the two surfaces roughly parallel each
other. Complete equilibration of isomeric triplets within 100 ns requires that the energies of triplet biradical
transition states be no higher than 40.3 kcal/mol. Estimated radical stabilization energies give 40.2 and 41.6
kcal/mol for the energies of biradical transition states for central and terminal bond isomerization, respectively,
in the ground state of ttt-DPH.
Introduction
common relaxed triplet is accessed from both isomers by
torsional displacement about the central bond to a perpendicular
The photophysical and photochemical events that follow
excitation of a molecule to its lowest electronically excited triplet
state are controlled, in large measure, by the shapes and
proximity of the potential energy surfaces of the ground and
triplet states. Unimolecular photoisomerizations occur through
geometry changes of the initially excited molecule that move it
along minimum energy paths to energy minima on the excited-
state surface from which intersystem crossing to the ground state
may access geometries favorable to product formation. The cis
h trans photoisomerizations of triplet olefins provide excellent
illustrations of such events. Two limiting cases have been
identified. The first is exemplified by the stilbenes for which a
3
3
geometry, p*. Decay from p* leads to partitioning of the
triplets between the two ground-state isomers.1 The second case
is exemplified by the 1-(2-anthryl)-2-phenylethenes (APEs).2
Here cis f trans photoisomerization in the triplet state occurs
as an adiabatic one-way process, 3c* f 3t*, with 3p* an energy
(1) For reviews see: (a) Saltiel, J.; D’Agostino, J.; Megarity, E. D.; Metts,
L.; Neuberger, K. R.; Wrighton, M.; Zafiriou, O. C. Org. Photochem. 1973,
3, 1-113. (b) Saltiel, J.; Charlton, J. L. Rearrangements in Ground and
Excited States; de Mayo, P., Ed.; Academic Press: New York, 1980; Vol.
3, pp 25-89. (c) Go¨rner, H.; Kuhn, H. J. AdV. Photochem. 1995, 19, 1-118.
(2) For reviews see: (a) Arai, T.; Tokumaru, K. Chem. ReV. 1993, 93,
23-39. (b) Tokumaru, K.; Arai, T. Bull. Chem. Soc. Jpn. 1995, 68, 1065-
1087.
10.1021/ja982551j CCC: $18.00 © 1999 American Chemical Society
Published on Web 01/20/1999

896 J. Am. Chem. Soc., Vol. 121, No. 5, 1999
Saltiel et al.
Table 1. DPH Isomer Compositions at Thermal Equilibriuma
maximum corresponding to the transition state for the reaction.
3
b
Unimolecular radiationless decay from t* or triplet excitation
T, °C
102fttt
102ftct
102fctt
102fcct
3
transfer from t* to cis-APE (the first step of a quantum chain
9.8
18.1
27.3
36.8
47.2
58.0
69.7
92.7
91.9
91.6
90.9
90.7
88.9
87.8
5.91
6.34
6.56
6.99
7.13
8.53
8.98
1.32
1.64
1.71
1.89
1.89
2.26
2.81
0.129
0.131
0.169
0.209
0.251
0.282
0.422
process) completes the cis f trans photoreaction.
In fluid solutions DPH triplets exist as an equilibrium mixture
of all-trans (ttt) trans,cis,trans (tct), cis,trans,trans (ctt) and, in
trace amount, cis,cis,trans (cct) isomers.3 Excitation of any one
of the DPH isomers to the triplet state rapidly gives a common
equilibrium mixture of triplet isomers whose decay leads to
product isomer formation. Thus, the initial isomerization occurs
adiabatically in the triplet state as in APE, but since, in this
case, it is reversible, it occurs in more than one direction as in
the stilbenes.
a Estimated uncertainties are (0.2 °C for T and (3% for the HPLC
analyses of tct- and ctt-DPH; a larger uncertainty ((20%) is expected
for cct-DPH (see text). b Calculated from fttt ) 1 - (ftct + fctt + fcct).
was thermally or photochemically (λ ) 530 nm) dissociated to
yield iodine atoms as catalysts for the isomerization of ttt-DPH
(1.08 × 10-3 M). Degassed and air-saturated 3 mL samples
were equilibrated at temperatures ranging from -10 to 160 °C.
At temperatures g100 °C erratic and irreproducible isomer
distributions were obtained and large losses of DPH were
observed, especially in the presence of air. Use of 250 nm as
the monitoring wavelength, instead of the normally employed
350 nm monitoring wavelength,3 revealed the formation of a
major and several minor side products. These products were
not observed in the absence of iodine. The yield of the major
product increases dramatically as the temperature is raised above
100 °C and is larger in the presence of air. Its identity was not
pursued and this equilibration approach was abandoned. Further
measurements were carried out on a benzene solution containing
5.1 × 10-4 M ttt-DPH and 5.0 × 10-3 M diphenyl diselenide.
Equilibrium mixtures were obtained by irradiating degassed 3
mL samples for 2 h at each temperature. HPLC analyses, with
anthracene as the internal standard, revealed no side products
and established that, within (1%, DPH isomers accounted for
all of the DPH present prior to equilibration at the two lowest
(9.8 and 18.1 °C) and the two highest (58.0 and 69.7 °C)
temperatures employed. Only 92% of the total DPH concentra-
tion was accounted for in both initial and final solutions,
probably due to ttt-DPH signal saturation. Inability of the HPLC
conditions to give baseline separation between ctt- and cct-DPH
introduces some uncertainty in the derived concentrations of
the latter, which is formed only in trace amounts. The area
registered for cct-DPH by the HPLC integrator was found to
be 10-25% lower than the area estimated by cutting and
weighing 6 enlarged Xerox copies of the HPLC trace. The
higher values were employed in the analysis. Equilibrium DPH
isomer compositions are reported in Table 1.
This paper reports the temperature dependencies of DPH
isomer compositions in the ground and triplet states. The
resulting ∆H’s between the DPH isomers in these states provide
anchor points for the construction of the respective potential
energy surfaces that control the photochemical behavior of this
system.
Experimental Section
Materials. Diphenyl diselenide (Aldrich, 98%) was used as received.
The sources and purification methods of the other materials were given
previously.3
Analytical Procedures. These were as previously described,3 except
that samples containing diphenyl diselenide were first passed through
a small column of silver nitrate coated alumina with the aid of 20 mL
of benzene eluent. This procedure retains all the diphenyl diselenide
on the column while allowing all DPH to pass without altering the
isomeric distribution. The step was essential because diphenyl diselenide
interferes with the HPLC analysis of the DPH isomers. Prior to the
HPLC analysis anthracene was added as internal standard.3 The benzene
was removed under reduced pressure and the residue was diluted to
approximately 3 mL with Fisher Optima hexane, which was also used
as eluent for the HPLC analyses.3 Analyses of successively diluted
samples assured selection of conditions of linear response of the HPLC
detection system. Even at the lowest concentrations employed some
saturation of the ttt-DPH signals is suspected. Sample preparation and
handling were performed under nearly complete darkness to avoid
unintentional isomerization.
Irradiation Procedures. Irradiation procedures were as previously
described3 except that the Osram HBO 200-W super high-pressure
mercury lamp was used in all experiments. A high-intensity Bausch
and Lomb monochromator was used to excite samples at 425 nm for
both diphenyl diselinide catalyzed (degassed benzene solutions, thermal)
and fluorenone-sensitized (air-saturated benzene solutions, triplet)
stationary state determinations. For quantum yield measurements in
the presence of air, excitation of the fluorenone sensitizer was at 435
nm. The rotating miniature merry-go-round was employed for these
measurements and samples were flame sealed at a constriction in the
presence of air. The sealing prevents any loss of solvent at the higher
temperatures but introduces some reduction and uncertainty in the
oxygen concentration. The aluminum merry-go-round and samples were
immersed in water in a dewar. Temperature control was provided by a
Neslab RTE-4DD refrigerated circulating bath connected to a copper
coil positioned about the merry-go-around in the dewar. Temperatures
were monitored by use of an Omega Engineering Model 199P2 RTD
digital thermometer equipped with a calibrated probe.
Photostationary States. Three milliliter aliquots of an air-
saturated benzene solution containing 3.93 × 10-3 M ttt-DPH
and 0.024 M fluorenone were pipetted into Pyrex test tubes, 13
mm o.d., fitted with Teflon tape covered rubber stoppers. Control
experiments established that irradiation of the stationary sample
at 425 nm for 4 h was sufficient to attain the photostationary
state at 10 °C, the lowest temperature used in our experiments.
Each sample was irradiated for 4 h at each temperature and the
experiment was repeated with a duplicate sample set. Analyses
were as reported above. Decomposition of the ctt/cct combined
peaks was achieved by assuming that the tail of the ctt peak is
identical to the tail of the tct peak. The cct content was too
small for the cutting and weighing procedure to be applied to
the 10.8 and 10.9 °C samples. Photostationary state DPH isomer
compositions are listed in Table 2.
Absorption Spectra. Absorption spectra were measured with the
use of a Perkin-Elmer Lambda-5 spectrophotometer interfaced with a
Dell Corp. 12 MHz 80286/87 microcomputer.
Results
Thermal Equilibrations. In initial experiments iodine (2.30
× 10-4 M in benzene or 2.21 × 10-4 M in tert-butylbenzene)
(3) Saltiel, J.; Wang, S.; Ko, D.-H.; Gormin, D. A. J. Phys. Chem. A
1998, 102, 5383-5392.
Quantum Yields. The fluorenone-sensitized photoisomer-
ization of trans-stilbene in benzene (φtfc ) 0.474) was employed
for actinometry. The actinometer’s quantum yield reflects its

1,6-Diphenyl-1,3,5-hexatriene Ground and Triplet States
J. Am. Chem. Soc., Vol. 121, No. 5, 1999 897
Table 2. Photostationary State Fractions for the
chosen so that conversions to the cis isomers were small,
ensuring that back-reaction corrections,5 based on interpolated
photostationary fractions from Table 2, did not significantly
affect the results (e2%).
Fluorenone-Sensitized Isomerization of DPHa
T, °C
102fttt
102ftct
102fctt
102fcct
10.8
10.9c
11.0
11.3
17.1
17.2
29.2
29.2
37.3
37.2
47.2
47.1
58.6
58.7
69.3
94.8
94.7
95.3
95.2
94.8
94.8
94.2
94.2
93.5
93.5
93.2
93.3
92.6
92.8
91.9
4.06
4.16
3.69
3.82
4.05
4.01
4.40
4.38
4.73
4.78
4.97
4.89
5.24
5.09
5.65
1.09
1.11
0.930
0.974
1.12
1.12
1.35
1.39
1.65
1.62
1.75
1.73
1.99
1.93
2.22
b
b
Discussion
0.0405
0.0390
0.0455
0.0392
0.0603
0.0745
0.0865
0.0763
0.111
0.103
0.151
0.118
0.194
The Ground State. Equilibration of the DPH isomers was
reported first by Lunde and Zechmeister.7 On the basis of UV
spectra it was shown that daylight lamp irradiation through Pyrex
of air-saturated hexane solutions of the pure ttt, tct, ctt, and cct
isomers in the presence of iodine gives identical isomer mixtures
dominated by the ttt isomer. Chromatographic separation of the
mixture obtained starting from ttt-DPH gave 93.9% ttt, 3.8%
ctt, and 1.8% tct.7 Exposure of the DPH isomers to light under
these conditions probably interfered with the goal of establishing
purely thermal equilibrium mixtures. In our experiments iodine
was excited selectively and the resulting mixtures were con-
sistently richer in the tct than in the ctt isomer. However, in
contrast to our observations on the iodine-catalyzed isomeriza-
tion of the stilbenes,8,9 DPH isomer distributions were irrepro-
ducible and side reactions were dominant for T g 100 °C.
Diphenyl diselenide was first used by Alfimov and co-workers
as an efficient catalyst for the equilibration of the stilbenes and
other olefins.10 Isomerization is promoted by reversible addition
of phenylselenium radicals to the double bond and regeneration
of the catalyst by coupling of phenylselenium radicals is the
only competing reaction. Lewis and co-workers have reported
successful use of this catalyst,11 and we had shown it to cleanly
isomerize the 1,4-diphenyl-1,3-butadiene isomers.12 The di-
phenyl diselenide catalyzed equilibration of the DPH isomers
proceeds smoothly and cleanly. The equilibrium constants for
a See footnotes a and b in Table 1. b Too small for accurate analysis.
c This sample was irradiated for 8 h; two identical samples irradiated
for 4 and 5 h gave ftct values of 0.0407 and 0.0408, respectively.
Table 3. Quantum Yields for the Fluorenone-Sensitized
Photoisomerization of ttt-DPH in Air-Saturated Benzene
T, °C
104[ttt],a M
102φctt
102φtct
φctt/φtct
8.7
2.78
3.75
5.56
8.32
11.1
13.9
2.74
3.70
5.48
8.21
11.0
13.7
2.70
3.64
5.40
8.09
10.8
13.5
2.65
3.58
5.31
7.95
10.6
13.3
2.61
3.52
5.21
7.81
10.4
13.0
0.267
0.313
0.405
0.474
0.551
0.695
0.286
0.373
0.449
0.559
0.650
0.701
0.553
0.649
0.748
0.805
1.16
1.20
1.50
1.91
2.23
2.54
3.04
1.32
1.72
2.05
2.52
2.98
3.07
2.11
2.52
2.97
3.13
4.37
4.32
2.43
2.98
3.28
4.03
4.84
4.70
2.50
2.97
3.61
4.33
5.24
5.33
0.219
0.208
0.213
0.213
0.217
0.229
0.217
0.217
0.219
0.222
0.218
0.228
0.262
0.257
0.252
0.257
0.266
0.256
0.272
0.281
0.272
0.272
0.280
0.283
0.301
0.300
0.306
0.304
0.310
0.340
20.0
32.2
45.5
60.0
Kctt
ttt y z ctt
Ktct
ttt y z tct
Kcct
ttt y z cct
(1)
(2)
(3)
1.11
0.662
0.837
0.892
1.10
1.36
1.33
0.753
0.891
1.11
1.32
1.63
are ratios of the fractions given in Table 1, e.g., Kctt ) fctt/fttt.
Plots of the data according to
∆H ∆S
ln K ) -
+
(4)
RT
R
are shown in Figure 1 and give the ∆H and ∆S values in Table
4. Within experimental uncertainty the ∆Hctt + ∆Htct sum equals
∆Hcct. The well-resolved vibronic structure of the spectrum of
tct-DPH7 suggests that the equilibrium geometry of this isomer
is planar, as is the case for ttt-DPH. It is pleasing, therefore,
that ∆Stct is close to 0 eu. Eliel et al. proposed that the
nonplanarity of cis-stilbene accounts for its slightly higher
entropy relative to trans-stilbene.8 Nonplanarity due to the
terminal cis double bonds may, similarly, cause the ctt- and
cct-DPH structures to explore larger ranges of torsional space
1.81
a Concentrations were corrected for the temperature dependence of
the density of benzene: d(t) ) 0.90034 - 0.001074t, where t is in
°C.6
intersystem crossing yield, φis ) 0.93,5 and a lower than unity
(0.92) efficiency of the excitation transfer step.4 Since fluorenone
is also the sensitizer for the photoisomerization of ttt-DPH, any
change in φis with temperature cancels. However, the quantum
yields listed in Table 3 are based on the assumptions that
excitation transfer efficiency to ttt-DPH is completely efficient
and that the efficiency of the excitation transfer step to trans-
stilbene is temperature independent. Irradiation times were
(6) The equation is based on 17 selected density values in the 0-80 °C
range compiled in: Timmermans, J. Physico-Chemical Constants of Pure
Organic Compounds; Elsevier: New York, 1950; Elsevier: New York,
1965; Vol. 2.
(7) Lunde, K.; Zechmeister, L. J. Am. Chem. Soc. 1954, 76, 2308-2313.
(8) Saltiel, J.; Ganapathy, S.; Werking, C. J. Phys. Chem. 1987, 91,
2755-2758.
(9) Eliel, E. L.; Engelsman, J. J. J. Chem. Educ. 1996, 73, 903-905.
(10) Ushakov, E. N.; Lednev, I. K.; Alfimov, M. V. Dokl. Acad. Nauk.
SSR 1990, 313, 903.
(4) (a) Caldwell, R. A.; Gajewski, R. P. J. Am. Chem. Soc. 1971, 93,
532-534. (b) Valentine, D., Jr.; Hammond, G. S. J. Am. Chem. Soc. 1972,
94, 3449-3454.
(5) Lamola, A. A.; Hammond, G. S. J. Chem. Phys. 1965, 43, 2129-
2135.
(11) Lewis, F. D.; Yoon, B. A.; Arai, T.; Iwasaki, T.; Tokumaru, K. J.
Am. Chem. Soc. 1995, 117, 3029-3036.
(12) Wharton, J. T.; Wang, S.; Saltiel, J. Unpublished results.

898 J. Am. Chem. Soc., Vol. 121, No. 5, 1999
Saltiel et al.
mechanism as shown below
1F
hν8 1F*
φis
9
9
8 3F*
(5)
(6)
kFqttt
3F* + 1ttt 8 1F + 3eet*
kFqtct
3F* + 1tct
3F* + 1ctt
3F* + 1cct
3F* + 3O2
8 1F + 3eet*
8 1F + 3eet*
(7)
kFqctt
(8)
kFqcct
8 1F + 3eet*
(9)
kFqox
8 1F + 1O/2
(10)
kqox
3eet* + 3O2
8 ꢀ1ctt + ú1tct + η1ctt + (1 - ꢀ - ú -
η)1ttt + 1O2* (11)
Figure 1. Thermal equilibrium constants defined in eqs 1-3 plotted
according to eq 4.
3
where eet* is the equilibrating set of planar DPH triplets:
Table 4. Enthalpy and Entropy Differences between Ground State
ttt-DPH and Its Isomersa
3
3eet* ≡ ctt* h 3ttt* h 3tct* h 3cct*
(12)
ttt h ctt
ttt h tct
ttt h cct
∆H, kcal/mol
2.24 (0.28)
1.49 (0.17)
3.95 (0.33)
3.53 (0.06)b
0.67 (1.06)
and the Greek letters in eq 11 are the effective decay fractions
to each ground-state isomer. Application of the steady-state
approximation on all excited species gives the following
photostationary state (PSS) expressions.
∆S, cal/(mol K)
-0.48 (0.90)
-0.24 (0.56)
-0.68 (0.18)b
a The numbers in parentheses are from the standard deviations of
the intercepts and slopes in Figure 1. b These values were obtained by
including the point (0, -0.36) in the data set (see text).
[tct]s
[ttt]s
kFqttt
ú
)
)
)
(13)
(14)
(15)
F
(
(
(
)(
)(
)(
)
)
)
1 - ꢀ - ú - η
kqtct
than in the planar ttt-DPH. However, this effect should be
moderated here by the greater importance of s-cis conformers
in ttt-DPH13 and small entropy differences were expected for
these two cis isomers. This is consistent with the experimental
∆Sctt and ∆Scct values which are also within experimental
uncertainty of zero. Forcing the intercept of the cct-DPH plot
to a value of ∆Scct, roughly equal to the ∆Stct + ∆Sctt sum,
reduces ∆Hcct by only 0.4 kcal/mol to 3.53 kcal/mol, Table 4.
The Triplet State. The significant differences between
stilbene triplets and DPH triplets were discussed recently.3
Extended conjugation afforded by the two additional double
bonds in DPH lowers the energies of planar relative to twisted
triplet conformations. Equilibrium compositions favor twisted
triplet geometries, 3p*, in stilbene, but they favor planar triplet
geometries in DPH.3 This geometry difference, for example,
accounts for the 1000-fold longer lifetime of DPH triplets
relative to stilbene triplets, despite the smaller T1 - S0 energy
gap in DPH.3 In degassed benzene solution, the DPH triplet
[ctt]s
[ttt]s
kFqttt
ꢀ
F
1 - ꢀ - ú - η
kqctt
[cct]s
[ttt]s
kFqttt
η
F
1 - ꢀ - ú - η
kqcct
These expressions require that photostationary DPH composi-
tions be DPH concentration independent as was established in
ref 3. The first factors on the right-hand side of eqs 13-15 are
ratios of two highly exothermic triplet excitation transfer steps
from fluorenone to each of two DPH isomers. Since such
processes are known to occur at or close to the diffusion-
controlled limit, the rate constant ratios should be close to unity
and temperature independent. Assuming that oxygen does not
differentiate between DPH triplets, eq 11 provides a snapshot
of the isomeric composition of the equilibrium mixture. This
means that the second factors on the right side of eqs 13-15
are the triplet equilibrium constants K/tct, Kc/ct, and Kc/ct, respec-
tively,
3
3
3
exists as an equilibrium mixture of isomeric ttt*, tct*, ctt*,
3
3
and cct* triplets, designated as eet*.3 Transient observations
have established that at infinite dilution at ambient temperature
(20-22 °C), the lifetime of the eet* is 59.3 ( 0.8 µs.3 Self-
3
[3tct*]
[3ttt*]
[3ctt*]
[3ttt*]
[3cct*]
[3ttt*]
quenching reduces the triplet lifetime to roughly 32 µs at 4 ×
10-3 M ttt-DPH.3 Under these conditions photoisomerization
occurs primarily via bimolecular quantum chain processes.3 The
equilibration of isomeric DPH triplets is complete even in air-
ú
K/tct
K/cct
K/cct
)
)
)
)
)
)
(16)
(17)
(18)
1 - ꢀ - ú - η
ꢀ
saturated solutions3 where essentially all eet* decay is via
3
1 - ꢀ - ú - η
oxygen quenching and the lifetime of 3eet* is thereby reduced
to 100 ns.14,15 The short lifetime eliminates quantum chain
photoisomerization events and simplifies the photoisomerization
η
1 - ꢀ - ú - η
(13) Saltiel, J.; Sears, D. F., Jr.; Sun, Y.-P.; Choi, J.-O. J. Am. Chem.
Soc. 1992, 114, 3607-3612.
(14) Go¨rner, H. J. Photochem. 1982, 19, 343-356.
(15) Chattopadhyay, S. K.; Das, P. K.; Hug, G. L. J. Am. Chem. Soc.
1982, 104, 4507-4514.
The temperature dependence of the photostationary state ratios,
Table 3, should therefore reveal the enthalpy differences between
the isomeric triplets. The fractions ꢀ and ú can also be obtained

1,6-Diphenyl-1,3,5-hexatriene Ground and Triplet States
J. Am. Chem. Soc., Vol. 121, No. 5, 1999 899
Figure 3. Triplet equilibrium constants defined in eqs 16 and 17 plotted
according to eq 4; plots forced to zero intercepts (see text).
Figure 2. Plots of tct- (open symbols) and ctt-DPH (closed symbols)
formation quantum yields for the fluorenone-sensitized photoisomer-
ization of ttt-DPH in aerated benzene at 8.7 (4) and 60.0 °C (O), based
on eqs 19 and 20.
Table 6. Enthalpy Differences between Triplet State ttt-DPH and
Its Isomersa
3ttt* h 3ctt*
3ttt* h 3tct*
∆H*, kcal/mol
3ttt* h 3cct*
Table 5. The Temperature Dependence of Equilibrium Fractions
3
and Constants for Triplet DPH Isomers Relative to ttt-DPH* a
T, °C
ꢀ
ú
102K/ctt
102K/tct
QY
3.80(31)
2.51(10)b
2.92(12)
2.49(4)b
2.27(12)
1.68(5)b
1.49(8)
1.66(3)b
8.7
20.0
32.2
45.5
60.0
0.0100(10)
0.0117(8)
0.0151(20)
0.0190(20)
0.0271(22)
0.0456(27)
0.0504(34)
0.0590(67)
0.0674(50)
0.0802(40)
1.06(11)
1.24(10)
1.63(22)
2.08(24)
3.03(27)
4.84(30)
5.37(39)
6.37(78)
7.38(60)
8.98(51)
PSS
5.52(28)
4.11(11)b
∆S*, eu
QY
4.33(100)
0.07 (30)b
1.40(40)
1.96(39)
0.03(13)b
-0.62(26)
0.00(10)b
a Values in parentheses are uncertainties in the last significant figures
shown.
PSS
4.53(90)
0.00(36)b
0.00(12)b
a Values shown in parentheses are uncertainties (standard deviations)
from the ttt-DPH isomerization quantum yields (QY) by using
in the last significant figures shown. b Intercepts fixed to ∆S* = 0.
the following expressions3
rate constant ratios (kFqctt/kqFttt) ) 1.09 ( 0.05 and (kqFtct/kFqttt) )
1.33 ( 0.05 that are close to unity and, within experimental
uncertainty, temperature independent. This rate constant order
for excitation transfer from fluorenone triplets to the DPH
isomers is the same as predicted earlier on the basis of results
at one temperature,3 but spans a somewhat narrower range:
kFqttt:kFqctt:kqFtct ) 1.00:1.09:1.33.
φis
kFqox[O2]
1
)
)
1 +
1 +
(19)
(20)
F
(
)
)
φtct
ú
kqttt[ttt]
φis
kFqox[O2]
1
F
(
φcct
ꢀ
kqttt[ttt]
The relationship of the [tct]s/[ttt]s ratio to temperature is given
by
where φis is the intersystem crossing yield of fluorenone. The
value of η could be obtained by use of the analogous expression
for φcct, but the φcct values were too small to measure. Plots for
the lowest and highest temperature quantum yields in Table 3,
Figure 2, illustrate the adherence of the data to eqs 19 and 20.
Equilibrium fractions ꢀ and ú, obtained from the inverse of the
intercepts of these plots, are collected in Table 5. Also shown
in Table 5 are equilibrium constants estimated from ꢀ/(1 - ꢀ -
ú) and ú/(1 - ꢀ - ú), since the η values are negligibly small
(see below). The adherence of these equilibrium constants to
eq 4 is very good, but least-squares plots give unexpectedly
high ∆S/ctt ) 4.3 ( 1.0 eu and ∆St/ct ) 2.0 ( 0.4 eu values.
Naturally, the ∆H* values are also high (3.8 ( 0.3 and 2.3 (
0.1 kcal/mol for ctt and tct, respectively). As pointed out for
the ground-state isomers, the entropy differences are expected
to be close to zero, consequently, as an alternative treatment,
the intercepts of these plots were forced to be nearly zero, Figure
3. Thermodynamic quantities with and without the ∆S* ) 0
assumption are shown in Table 6. The plots in Figure 3 were
used to calculate Kc/tt and Kt/ct values at the temperatures in
Table 2. As expected, the ratio of the equilibrium constants to
the photostationary state ratios in Table 2 give excitation transfer
[tct]s
[ttt]s
∆H/tct ∆S/
kFqttt
kFqtct
ln
) -
+
tct + ln
(21)
(
)
RT
R
and analogous expressions can be written for the [ctt]s/[ttt]s and
[cct]s/[ttt]s ratios. Thermodynamic quantities from these plots
are also shown in Table 6. Since no estimate of the kFqttt/kqFcct
ratio is available, it was assumed equal to (kFqttt)2/(kFqcttkqFtct). The
more precise PSS data give ∆S* values for tct and ctt that are
much closer to zero than the values obtained from the QY data.
Again as an alternative treatment, the plots in Figure 4 were
forced to zero intercepts, and the resulting ∆H* values are
shown in Table 6. It can now be seen that when the ∆S* = 0
condition is uniformly imposed, the enthalpy differences
obtained independently from the quantum yields and from the
photostationary states are in excellent agreement. As in the case
of the ground-state enthalpy differences the relationship ∆Hc/tt
+ ∆H/tct ) ∆Hc/ct is adhered to remarkably well. Furthermore,
the enthalpy differences between the DPH isomers in the ground
and triplet states are nearly identical./

900 J. Am. Chem. Soc., Vol. 121, No. 5, 1999
Saltiel et al.
of papers,23 they measured activation enthalpies for the thermal
isomerization of several related polyenes. These activation
enthalpies were used to evaluate the effect of additional
conjugated double bonds on the enthalpies of stabilization, SEn,
of polyenyl radicals of type H(CH)CH)nC˙ H2. The relative
energies of the coplanar polyenes were obtained by applying
an additive constant K ) 3.74 kcal/mol, the Kistiakowski unit,23a
for each conjugative interaction between successive double
bonds. Theory, at all levels employed thus far,24-26 predicts the
linear relationship between the enthalpy of conjugation and the
order of the polyene, but the value of K is empirically derived23a
from thermochemical data on butadiene27 and methyl deriva-
tives28 and on hexa-1,3,5-triene.29 Starting with an allyl
stabilization enthalpy, SE1 ) 13.5 kcal/mol,30 the increase in
stabilization was found to diminish with each successive double
bond.23 Namely, SE2, SE3, and SE4 are 16.9, 19.2, and 20.7
kcal/mol, respectively, such that even the first increment, SE2-
SE1, is a little smaller than K.
Figure 4. Photostationary ratios plotted according to eq 21 and forced
to ∆S* ) 0 intercepts (see text).
The enthalpy of conjugation for a phenyl-vinyl coplanar
interaction, K′ ) 3.5 kcal/mol, has been based on the difference
between the heats of hydrogenation of trans-2-butene and trans-
stilbene.31,32 This value is close to the barrier (∼3.3 kcal/mol)
calculated for the torsion of the phenyl group in trans-stilbene
at the ab initio 3-21G level of theory.33 Provided that K and K′
units be additive, conjugative stabilization energies of the
coplanar all-trans-R,ω-diphenylpolyenes, Ph(CHdCH)nPh, should
be given by 2K′ + (n - 1)K. Experimental validation of this
relationship rests on the stabilization energy of 1,4-diphenyl-
1,3-butadiene, 10.7 kcal/mol,31 which coincides with 2K′ + K
) 10.74 kcal/mol. We therefore take 14.5 kcal/mol as the
conjugative stabilization energy of ttt-DPH. The relative energies
of the biradical transition states for cis-trans isomerization about
a specific bond could be estimated if the stabilization energies
of the resulting pairs of radical moieties were known. The
conjugative stabilization energies of the benzyl, SEBz, and of
the 1-phenylallyl, SEPhA, radicals are required to estimate
ground-state biradical energies for stilbene, 1,4-diphenyl-1,3-
butadiene, and for central bond rotation in ttt-DPH. Recom-
mended CH bond energies34 for ethane and toluene give SEBz
) 12.6 kcal/mol for the benzyl radical, but there is no empirical
SEPhA value for the 1-phenylallyl radical. Figure 5 shows a plot
The Biradicals. The relaxed geometries of the triplet states
of the stilbenes,8,16,17 1,3-dienes,16-18 and related simple alkenes,
generally, correspond to twisted species with orthogonal 2p
orbitals at the relaxation site. They are close in energy and
geometry to the biradical transition states for thermal cis-trans
isomerization.8,17,19 The proximity between S0 and T1 surfaces
at these relaxed geometries leads to rapid T1 f S0 decays and
short triplet lifetimes in the nanosecond time scale. DPH triplets,
on the other hand, have global energy minima at planar
geometries. Decay from these geometries is subject to substantial
S0 - T1 energy gaps leading to a 103-fold longer triplet lifetime.3
The enthalpy differences determined in this work together with
the known 34.0 kcal/mol energy15,20-22 of 3ttt-DPH* locate the
relative energies of the ttt, ctt, tct, and cct isomers on the ground
and triplet energy surfaces. Complete equilibration3 of the
isomeric DPH triplets within the 100 ns triplet lifetime in air-
saturated benzene14,15 requires interconversion rate constants
greater than 108 s-1. Assuming a normal preexponential factor
of 1013 s-1 for these adiabatic unimolecular processes requires
that activation energies for the interconversions be no larger
than 6.9 kcal/mol. This corresponds to a limiting activation
enthalpy of 6.3 kcal/mol at 20 °C and places twisted triplets at
energies no higher than 40.3 kcal/mol relative to the ground
state of ttt-DPH.
(23) (a) Doering, W. von E.; Kitagawa, T. J. Am. Chem. Soc. 1991, 113,
4288-4297. (b) Doering, W. von E.; Birladeanu, L.; Cheng, X-h.; Kitagawa,
T.; Sarma, K. J. Am. Chem. Soc. 1991, 113, 4558-4563. (c) Doering, W.
von E.; Sarma, K. J. Am. Chem. Soc. 1992, 114, 6037-6043. (d) Doering,
W. von E.; Shi, Y.-q.; Zhao, D.-c. J. Am. Chem. Soc. 1992, 114, 10763-
10766.
(24) Heilbronner, E.; Bock, H. Das HMO-Modell und seine Anwendung;
Verlag Chemie: Weinheim, 1970; Vol. 3, pp 16-42.
(25) (a) Dewar, M. J. S.; Gleicher, G. J. J. Am. Chem. Soc. 1965, 87,
685-692. (b) Dewar, M. J. S.; de Liano, C. J. Am. Chem. Soc. 1969, 91,
789-802.
(26) (a) Hess, B. A., Jr.; Schaad, L. V. Pure Appl. Chem. 1980, 52, 1471-
1494. (b) Hess, B. A., Jr.; Schaad, L. J. J. Am. Chem. Soc. 1983, 105,
7500-7505.
(27) Kistiakowsky, G. B.; Ruhoff, J. R.; Smith, H. A.; Vaughan, W. E.
J. Am. Chem. Soc. 1936, 58, 146-153.
(28) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of
Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986.
(29) Turner, R. B.; Mallon, B. H.; Tichy, M.; Doering, W. von E.; Roth,
W. R.; Schro¨der, G. J. Am. Chem. Soc. 1973, 95, 8605-8610.
(30) Doering, W. von. E.; Roth, W. R.; Bauer, F.; Boenke, M.;
Breuckmann, R.; Ruhkamp, J.; Wortmann, O. Chem. Ber. 1991, 124, 1461-
1470.
Since activation enthalpies for tct f ttt and ctt f ttt
isomerizations are not available for DPH, the energies of the
singlet biradicals corresponding to the transition states of these
reactions are unknown. The energy of the symmetrical ortho-
gonal biradical derived by a 90° twist about the central double
bond of ttt-DPH can be estimated by reversing, in part, the
procedure used by Doering and co-workers. In an elegant series
(16) Hammond, G. S.; Saltiel, J.; Lamola, A. A.; Turro, N. J.; Bradshaw,
J. S.; Cowan, D. O.; Vogt, V.; Dalton, C. J. Am. Chem. Soc. 1964, 86,
3197-3217.
(17) Ni, T.; Caldwell, R. A.; Melton, L. A. J. Am. Chem. Soc. 1989,
111, 457-464.
(18) Saltiel, J.; Rousseau, A. D.; Sykes, A. J. Am. Chem. Soc. 1972, 94,
5903-5905.
(19) Unett, D. J.; Caldwell, R. A. Res. Chem. Intermed. 1995, 21, 665-
709.
(20) Heinrich, G.; Holzer, G.; Blume, H.; Schulte-Frohlinde, D. Z.
Naturforsch. 1970, 25b, 496.
(21) Evans, D. F.; Tucker, J. N. J. Chem. Soc., Faraday Trans. 2 1972,
68, 174.
(22) (a) Ramamurthy, V.; Caspar, J. V.; Corbin, D. R.; Schyler, B. D.;
Maki, A. H. J. Phys. Chem. 1990, 94, 3191-3193. (b) Ramamurthy, V.;
Caspar, J. V.; Eaton, D. F.; Kuo, E. W.; Corbin, D. R. J. Am. Chem. Soc.
1992, 114, 3882-3892.
(31) Williams, R. B. J. Am. Chem. Soc. 1942, 64, 1395-1404.
(32) Wheland, G. W. Resonance in Organic Chemistry; Wiley: New
York, 1955; p 80.
(33) Lhost, O.; Bre´das, J. L. J. Chem. Phys. 1992, 96, 5279-5288.
(34) Berkowitz, J.; Ellison, G. B.; Gutman, D. J. Phys. Chem. 1994, 98,
2744-2765.

1,6-Diphenyl-1,3,5-hexatriene Ground and Triplet States
J. Am. Chem. Soc., Vol. 121, No. 5, 1999 901
Scheme 1
Figure 5. Experimental stabilization energies for the polyenyl22c and
benzyl radicals plotted against Hu¨ckel MO π-delocalization energies.
of SEn values for the polyenyl radicals23c (n ) 1-4) against
the corresponding HMO DEπ values.35 The dependence of SEn
on DEπ is far from linear, but it is monotonic. Furthermore, the
point for the benzyl radical (DEπ ) 0.72â) falls nicely on the
same curve. A polynomial fit of all five points gives SEPhA
)
16.6 kcal/mol as an estimate of the stabilization energy of the
1-phenylallyl radical (DEπ ) 1.38â). Interestingly, this value
is nearly identical with the average of SE1 + K′ ) 17.0 kcal/
mol and SEBz + K ) 16.3 kcal/mol. The biradical obtained by
rotation about one of the terminal double bonds in DPH consists
of benzyl and 1-phenylpentadienyl moieties. The stabilization
energy of the latter, SEPhP, is not known but, based on HMO
DEπ ) 1.98â, Figure 5 gives SEPhP ) 18.9 kcal/mol, sensibly
close to the value for the heptatrienyl radical.23c
The predicted enthalpies of activation for the R,ω-diphen-
ylpolyenes, n ) 1-3, are derived as shown in Scheme 1.
Following Doering and co-workers, we use 65.9 ( 0.9 kcal/
mol as the activation enthalpy for the model monoolefin,
neglecting steric efects in the planar ground states and in the
biradicals.23a,36 Applying the stabilization energies for the radical
moieties and for the coplanar ground-state molecules gives ∆Hq
) 47.2, 43.9 and 40.2 kcal/mol as the transition state enthalpies
of stilbene, 1,4-diphenyl-1,3-butadiene, DPB, and central bond
DPH isomerization, respectively. The enthalpy of activation for
terminal bond isomerization in DPH is not shown in Scheme
1. Our estimated value, 41.6 kcal/mol, is a little higher than the
activation enthalpy for central bond isomerization. The value
for stilbene agrees well with experimental measurements of this
quantity that place it at 47.4 ( 1.6 kcal/mol,8,9,37-39 and with a
calculated value of 48.9 kcal/mol based on Benson equivalents.17
No experimental values are available for DPB and DPH, but
the prediction that isomerization activation enthalpies decrease
progressively as one moves from stilbene to the two higher
vinylogues is reasonable.
Figure 6. Ground state and triplet potential energy curves for twisting
about C1C2 (φ) and C3C4 (θ) in DPH.
value for the symmetrical singlet biradical is nearly identical
with that limit, but that for the unsymmetrical biradical is 1.3
kcal/mol higher. In view of the uncertainty in these values, the
question of whether singlet and triplet potential energy surfaces
are separated by a small energy gap, touch, or cross close to
the biradical DPH geometries remains open. However, S0 and
T1 surfaces are more likely to cross upon terminal bond rotation.
Since the 40.3 kcal/mol value is an upper limit, the potential
energy curves in Figure 6 are tentatively shown to cross. Earlier,
one of us had come to the conclusion that S0 and T1 surfaces
cross in the case of the stilbenes.8 Since then, time-resolved
We concluded above that the energies of the triplet biradicals
of DPH can be no higher than 40.3 kcal/mol. The estimated
3
photoacoustic calorimetry measurements have placed p*, the
(35) Streitwieser, A., Jr. Molecular Orbital Theory for Organic Chemists,
Wiley: New York, 1961; pp 46, 393, and 396.
(36) Doering, W. von E.; Roth, W. R.; Bauer, F.; Breuckmann, R.;
Ebrecht, T.; Herbold, M.; Schmidt, R.; Lennartz, H.-W.; Lenoir, D.; Boese,
R. Chem. Ber. 1989, 122, 1263-1275.
stilbene triplet biradical, at 46.5 ( 0.9 kcal/mol,17 somewhat
below, but well within experimental uncertainty of the energy
of the singlet biradical. The categorical nature of the prediction
that S0 - T1 surface crossing is required in stilbene was therefore
rightly questioned.17,40
(37) Kistiakowsky, G. B.; Smith, W. R. J. Am. Chem. Soc. 1934, 56,
638.
(38) Santoro, A. V.; Barrett, E. J.; Hoyer, H. H. J. Am. Chem. Soc. 1967,
89, 4545-4546.
(39) Schmiegel, W. W.; Litt, F. A.; Cowan, D. O. J. Org. Chem. 1968,
33, 3334.
Conclusion
Figure 6 gives a pictorial representation of our results.

902 J. Am. Chem. Soc., Vol. 121, No. 5, 1999
Saltiel et al.
Placement of the global energy minimum of the DPH triplet
state at the all-trans geometry is consistent with early observa-
tions that led Go¨rner14 and Das et al.15 to assign the all-trans
geometry to the DPH triplet. However, the energetic landscape
of Figure 6 allows the presence of significant populations of
planar triplet geometries containing cis double bonds. The
depiction of twisted triplet geometries as torsional transition
states for the interconversion of DPH triplets is consistent with
our calculated triplet biradical energies. Figure 6 reverses the
energetics of twisted vs planar geometries that apply to the
prototypical stilbene triplets, and the 103-fold increase of the
DPH triplet lifetime relative to that of stilbene is a direct
consequence of this maximum/minimum reversal.3,14,15
The relationship of the triplet energy of each of the isomeric
DPH triplets, ExTxt where x is either t or c, to the triplet energy
of ttt-DPH is given by
excitation. The nointerconverting ground-state DPH isomers
become rapidly equilibrating conformers in the triplet state.
Triplet excitation transfer events between DPH isomers are
nonvertical with respect to CC stretching vibrational modes,3
and this is probably the major source of their inefficiency. In
the stilbenes, where the major geometry change on S0 f T1
excitation is along the torsional coordinate, descriptions of
nonvertical triplet excitation transfer have focused naturally on
Franck-Condon (FC) factors involving torsional modes. How-
ever, CC bond length changes are similarly expected in the
stilbenes, and it is likely that unfavorable FC overlap factors
involving CC stretching modes also contribute to the determi-
nation of the overall efficiency of nonvertical triplet excitation
in the prototypical stilbene system.
We conclude that a general requirement for the participation
of quantum chain events in triplet state olefin photoisomerization
is a rather flat triplet potential energy surface with shallow
minima or maxima at twisted geometries. In either case, planar
geometries must be energetically accessible so that sufficiently
large S0 - T1 energy gaps are attained to permit the olefin triplet
to function as a donor. Conjugated alkadienes, for which
quantum chain photoisomerization was first demonstrated,42
having global energy minima at twisted geometries are at one
extreme. Their short triplet lifetimes, in the nanosecond time
scale, require large concentrations for the quantum chain process
to contribute in photoisomerization. The diphenylhexatrienes
and styrylarenes with polybenzenoid aromatic rings, of which
the 2-styrylanthracenes provide the most prominent example,2
are at the other extreme. For such molecules, energy minima at
planar geometries on the triplet potential energy surface ensure
much longer triplet lifetimes and allow efficient participation
of the quantum chain process at much lower concentrations.
Theoretical calculations of the energetics for trans h cis
isomerization in S0 and T1 DPH are not available. Figure 6
should provide a stimulus and an empirical test for such
calculations in the future.
ExTxt ) EtTtt + ∆H/xxt - ∆H
(22)
xxt
With reference to EtTtt ) 34.0 kcal/mol,15,20-22 the triplet
energies of the cis isomers are 34.3 ( 0.3, 34.2 ( 0.2, 34.6 (
0.4 kcal/mol and for ctt-, tct-, and cct-DPH, respectively. The
prediction of nearly identical triplet energies for the isomeric
triplets is nicely consistent with the interpretation of fluorenone-
sensitized photoisomerization quantum yields under degassed
conditions.3 These quantum yields are dominated by quantum
chain processes involving triplet excitation transfer between the
DPH isomers. Rate constants in benzene for excitation transfer
steps in both directions between the ttt, tct, and ctt isomers
cluster in the narrow range of (2.1-3.6) × 108 M-1 s-1 revealing
no energetic advantage for transfer in a specific direction.3 On
the basis of Figure 6, the 25- to 40-fold deviation of these rate
constants from the nearly diffusion controlled value expected
for isoenergetic triplet excitation transfer may seem surprising.3
Energy minima at planar geometries in T1 and S0 surfaces
require that triplet excitation transfer between the DPH isomers
be vertical with respect to torsional coordinates. The seeming
contradiction arises because Figure 6 does not reveal geometry
changes, reflecting the reversal of the order of alternating double/
single bonds in the triene moiety that accompanies S0 f T1
Acknowledgment. This research was supported by NSF,
most recently, by Grant CHE-9612316. J.S. dedicates this paper
to the memory of the late Professor R. B. Turner who showed
the way to Caltech.
JA982551J
3
(40) The maximum triplet energy of p* was erroneously estimated in
(41) Saltiel, J.; Marchand, G. R.; Kirkor-Kaminska, E.; Smothers, W.
K.; Mueller, W. B.; Charlton, J. L. J. Am. Chem. Soc. 1984, 106, 3144-
3151.
(42) Saltiel, J.; Townsend, D. E.; Sykes, A. J. Am. Chem. Soc. 1973,
95, 5968-5973.
ref 8 as ∼44 kcal/mol. Actually, the maximum value given by the sum of
the triplet energy of 9,10-dichloroanthracene, DCA, and the activation
enthalpy for triplet excitation transfer from DCA to trans-stilbene, 45.5 (
0.5 kcal/mol,40 is in good agreement with the calorimetric value.