Temperature-dependent photochemistry of 1,3-diphenylpropenes. The di-π-methane reaction revisited

Article abstract of DOI:10.1021/ja0113652

The temperature-dependent photochemical behavior of 1,3-diphenylpropene and several of its 3-substituted derivatives has been investigated over a wide temperature range. The singlet state is found to decay via two unactivated processes, fluorescence and intersystem crossing, and two activated processes, trans,-cis isomerization and phenyl-vinyl bridging. The latter activated process yields a diradical intermediate which partitions between ground-state reactant and formation of the di-π-methane rearrangement product. Kinetic modeling of temperature-dependent singlet decay times and quantum yields of fluorescence, isomerization, di-π-methane rearrangement, and nonradiative decay provides rate constants and activation parameters for each of the primary and secondary processes. Substituents at the 3-position are found to have little effect on the electronic spectra or unactivated fluorescence and intersystem crossing pathways. However, they do effect the activated primary and secondary processes. Thus, the product ratios are highly temperature dependent.

Full text of DOI:10.1021/ja0113652

J. Am. Chem. Soc. 2001, 123, 11883-11889
11883
Temperature-Dependent Photochemistry of 1,3-Diphenylpropenes. The
Di-π-Methane Reaction Revisited
Frederick D. Lewis,*,† Xiaobing Zuo,† Rajdeep S. Kalgutkar,† Jill M. Wagner-Brennan,†
Miguel A. Miranda,‡ Enrique Font-Sanchis,‡ and Julia Perez-Prieto§
Contribution from the Department of Chemistry, Northwestern UniVersity, EVanston, Illinois 60208-3113,
Departmento de Qu´ımica-Instituto de Tecnologia Quimica UPV-CSIC, UniVersidad Polite´cnica de
Valencia, Valencia, E-46071 Spain, and Departamento de Qu´ımica Organica-Instituto de Ciencia
Molecular, Facultad de Farmacia, UniVersidad de Valencia, Burjassot, E-46100 Spain
ReceiVed June 4, 2001
Abstract: The temperature-dependent photochemical behavior of 1,3-diphenylpropene and several of its
3-substituted derivatives has been investigated over a wide temperature range. The singlet state is found to
decay via two unactivated processes, fluorescence and intersystem crossing, and two activated processes, trans,-
cis isomerization and phenyl-vinyl bridging. The latter activated process yields a diradical intermediate which
partitions between ground-state reactant and formation of the di-π-methane rearrangement product. Kinetic
modeling of temperature-dependent singlet decay times and quantum yields of fluorescence, isomerization,
di-π-methane rearrangement, and nonradiative decay provides rate constants and activation parameters for
each of the primary and secondary processes. Substituents at the 3-position are found to have little effect on
the electronic spectra or unactivated fluorescence and intersystem crossing pathways. However, they do effect
the activated primary and secondary processes. Thus, the product ratios are highly temperature dependent.
Introduction
Scheme 1. Di-π-methane Rearrangement Reaction
Mechanisms for 1,4-Pentadiene: (i) Zimmerman Mechanism
and (ii) Bernardi and Robb Mechanism
The di-π-methane (Zimmerman) rearrangement is among the
most extensively studied unimolecular photochemical reactions.1
The generalized mechanism proposed by Zimmerman and co-
workers for acyclic dienes which react via the singlet state is
outlined in Scheme 1. According to this mechanism, the primary
photoprocess is vinyl-vinyl bridging leading to the formation
of the cyclopropyldicarbinyl diradical Ia which proceeds to the
1,3-diradical Ib, the precursor of the vinylcylopropane product.
It was pointed out by Zimmerman1a that Ia is not necessarily
an energy minimum in singlet di-π-methane rearrangements and
that the excited-state potential energy surface could be dependent
upon the choice of reactant. The potential energy surface
calculated by Bernardi, Robb, and co-workers2 for the rear-
rangement of 1,4-pentadiene leads directly from the singlet state
to the 1,3-diradical Ib via a 1,2-vinyl migration.
Scheme 2. Photochemical Reactions of
1,3-Diphenylpropenes
Di-π-methane rearrangements are also observed for systems
in which one of the π-bonds is part of a phenyl group. The
photochemical rearrangement of trans-1,3-diphenylpropene
(t-1) to trans-1,2-diphenylcyclopropane (Scheme 2) was orig-
inally reported by Griffin et al.3 and its mechanism was
subsequently investigated both by Hixson4 and by Zimmerman
et al.5 On the basis of these studies, Hixson4 proposed that a
cyclopropyldicarbinyl diradical is most likely an intermediate
in this reaction and that its partitioning between product
formation and reversion to the ground state might account in
part for the low quantum yield for rearrangement of t-1.
Calculation of the excited-state potential energy surface for a
molecule the size of t-1 remains a formidable challenge despite
recent advances in computational methods. However, informa-
tion about the potential energy surfaces for complex photo-
chemical reactions can also be obtained from a combination of
experimental measurements and kinetic modeling, as we have
* To whom correspondence should be addressed. E-mail: lewis@
chem.northwestern.edu.
† Northwestern University.
‡ Universidad Polite´cnica de Valencia.
§ Universidad de Valencia.
(1) For reviews see: (a) Zimmerman, H. E. Org. Photochem. 1991, 11,
1-36. (b) Zimmerman, H. E.; Armesto, D. Chem. ReV. 1996, 96, 3065-
3112.
(2) Ruguero, M.; Bernardi, F.; Jones, H.; Olivucci, M.; Ragazos, I. N.;
Robb, M. A. J. Am. Chem. Soc. 1993, 115, 2073-2074.
(3) Griffin, G. W.; Covell, J.; Petterson, R. D.; Dodson, R. M.; Klose,
G. J. Am. Chem. Soc. 1965, 87, 1410-1411.
(4) Hixson, S. S. J. Am. Chem. Soc. 1976, 98, 1271-1273.
(5) Zimmerman, H. E.; Steinmetz, M. G.; Kreil, C. L. J. Am. Chem.
Soc. 1978, 100, 4146-4162.
10.1021/ja0113652 CCC: $20.00 © 2001 American Chemical Society
Published on Web 11/09/2001

11884 J. Am. Chem. Soc., Vol. 123, No. 48, 2001
Lewis et al.
Table 1. Spectroscopic Parameters for the 1,3-Diphenylpropenes at
Room Temperaturea
λ
abs, nm (A)b
λfl, nm
Φfc
τs, nsc,d
10-7 kf, s-1
t-1
t-2
t-3
t-4
254, 284, 293
250, 284, 292
252, 284, 292
254, 284, 294
309
308
307
308
0.28
7.2
1.9
0.63
0.68
3.9
4.2
6.5
6.5
0.080
0.041
0.044
a Data for methylcyclohexane solution. b Shorter wavelength allowed
transition, longer wavelength forbidden transitions. c Deoxygenated
solutions. d Fluorescence decays are single exponentials.
Figure 2. Temperature dependence of the singlet lifetime (O),
fluorescence quantum yield (4), cis,trans isomerization quantum yield
(0), and di-π-methane rearrangement product formation quantum yield
(g) of 1,3,3-triphenyl-propene (t-4) over the temperature range 140-
352 K.
fluorescence with maxima at 308 ( 1 nm. The very weak
emission observed at longer wavelength for t-3 and t-4 is
artificially amplified by the normalization process. The fluo-
rescence emission maxima (λfl), quantum yields (Φf), and singlet
decay times (τs) measured at room temperature in MC solution
are reported in Table 1. Single-exponential fluorescence decays
were obtained in all cases. The values of Φf and τs are dependent
upon the nature of the 3-substituents. The values of τs for t-1
and t-3 are similar to those previously obtained by Hixson in
MC solution (9.7 and 0.65 ns, respectively).4
Values of Φf (140-352 K) and τs (77-352 K) have also
been determined at a number of temperatures. Fluorescence
quantum yields cannot be accurately measured below the glass
transition temperature of MC (ca. 140 K) because of volume
contraction and light scattering by the occurrence of crystal-
lization upon freezing.8 The data obtained for t-4 are shown in
Figure 2 and tabular data for all of the diphenylpropenes
provided as Supporting Information. The low temperature
fluorescence quantum yields have been corrected as described
in the Experimental Section. The fluorescence maxima are not
strongly temperature dependent, however, the vibrational struc-
ture is better resolved at low temperatures. No phosphorescence
is observed even at 77 K, as previously reported for 1-phenyl-
propene.7
Figure 1. Fluorescence spectra of 1,3-diphenylpropenes t-1-t-4 in
methylcyclohexane at room temperature.
recently demonstrated in an investigation of the photochemical
behavior of t-3.6
We report here the results of our collaborative investigation
of the potential energy surfaces for the photochemical reactions
of t-1 and its 3-substituted derivatives t-2, t-3, and t-4 (Scheme
2). The singlet lifetimes and quantum yields of fluorescence
and of formation of the cis isomers c-1-c-4 and the cyclopro-
panes p-1-p-4 have been determined over a wide temperature
range. Kinetic modeling of these data provides conclusive
evidence for the formation of the cis isomers via both singlet
and triplet pathways and for cyclopropane formation and
nonradiative decay via a common intermediate. Modeling further
provides activation parameters for both of the activated primary
photoprocesses and for the partitioning of this intermediate, as
well as for the dependence of these processes upon substituents
at the 3-position.
Results
Photochemical Behavior. The photochemical behavior of
t-1 and t-3 has been the subject of several previous investiga-
tions.3-5 Direct irradiation yields two primary photoproducts,
the cis isomers c-1 and c-3 and the 1,2-diphenylcyclopropanes
p-1 and p-3 (Scheme 2). Analogous products are observed for
t-2 and t-4. Triplet sensitized irradiation results exclusively in
formation of the cis isomers. Quantum yields for trans,cis
Electronic Spectra. The trans-1,3-diphenylpropenes t-1-
t-4 were prepared by standard literature procedures and purified
to >99% by column chromatography. Their electronic absorp-
tion spectra in methylcyclohexane (MC) solution consist of a
weak long-wavelength band which displays vibrational struc-
ture (two resolved maxima) and a stronger, structureless band
at shorter wavelength. The appearance of these bands is similar
to that of 1-phenylpropene and is independent of the nature of
the 3-substituents. The wavelengths (λabs) and intensities of
the longest wavelength absorption maxima are summarized in
Table 1.
isomerization (Φiso) and di-π-methane rearrangement (Φdiπ
)
upon direct irradiation and triplet sensitized trans,cis isomer-
ization (Φsens) at room temperature in MC solution are sum-
marized in Table 2. The value of Φdiπ for t-1 reported in Table
2 is taken from Hixson4 and the value determined for t-3 is the
same as that reported by Hixson.4 The value of Φsens for t-3 is
similar to that reported by Zimmerman et al.5 The temperature
dependence of Φiso and Φdiπ have also been determined over
the range 140-352 K. The data obtained for t-4 are shown in
Figure 2. Tabular data for all of the diphenylpropenes are
The fluorescence spectra of t-1-t-4 are shown in Figure 1
and also resemble that of trans-1-phenylpropene.7 All of the
diphenylpropenes display weakly structured room-temperature
(6) Lewis, F. D.; Zuo, X.; Kalgutkar, R. S.; Miranda, M. A.; Font-Sanchis,
E.; Perez-Prieto, J. J. Am. Chem. Soc. 2000, 122, 8571-8572.
(7) Lewis, F. D.; Bassani, D. M.; Caldwell, R. A.; Unett, D. J. J. Am.
Chem. Soc. 1994, 116, 10477-10485.
(8) Liang, A. C.; Willard, J. E. J. Phys. Chem. 1968, 72, 1018-1023.

Photochemistry of 1,3-Diphenylpropenes
J. Am. Chem. Soc., Vol. 123, No. 48, 2001 11885
Table 2. Quantum Yields for Photoisomerization, Di-π-Methane
Rearrangement, and Nonradiative Decay and the Diradical Partition
Function at Room Temperaturea
fe
b
c
b
d
Φiso
Φsens
Φdiπ
Φnr
t-1
t-2
t-3
t-4
0.30
0.11
0.074
0.059
0.52
0.47
0.45
0.45
0.005f
0.21
0.42
0.30
0.12
0.49
0.39
0.54
0.04
0.30
0.52
0.36
a Data for methylcyclohexane solution. b Direct irradiation of nitrogen-
purged solutions. c Benzophenone-sensitized irradiation of degassed
solutions. d Calculated using eq 6. e Diradical partition function calcu-
lated using eq 12. f Data from ref 4.
Scheme 3. Photoisomerization Pathways
Figure 3. Arrhenius plots of the rate constants of cis,trans isomerization
(0), di-π-methane rearragement (g), and nonradiative decay (3) vs
temperature for t-4.
atures.7,9 As shown in Scheme 3, both pathways lead to twisted
intermediates (1P* or 3P*) which decay to an equal mixture of
ground-state trans and cis isomers. We have confirmed that Φsens
) 0.50 ( 0.05 for t-1-t-4 (Table 2). According to Scheme 3,
the total isomerization quantum yield is described by eq 1 and
eqs 2 and 3 describe the phenomenological and analytical
isomerization rate constants, respectively,
provided as Supporting Information. In the case of t-1 the values
of Φdiπ are too low to permit accurate determination below room
temperature with our apparatus.
Φiso ) 0.5ktwistτs + 0.5kiscτs
kiso ) Φisoτs-1
(1)
(2)
Discussion
-∆Etwist
RT
1
2
kiso
)
kisc + Atwist exp
[
(3)
(
)
]
Electronic Spectra. The absorption and fluorescence spectra
of the diphenylpropenes resemble those of styrene and 1-phe-
nylpropene.7 The long-wavelength absorption and fluorescence
of styrene are assigned to a forbidden 1Lb transition, thus
accounting for the weak absorption and relatively long radiative
lifetime. The presence of 3-alkyl or phenyl substituents in t-2-
t-4 has little effect on the appearance of the absorption or
fluorescence spectra in accord with the SCF-CI calculations
of Zimmerman et al.5 which showed that excitation is localized
on the styryl portion of t-1 in the Franck-Condon excited state.
The fluorescence rate constants for the diphenylpropenes can
be calculated from the measured quantum yields and lifetimes
(kf ) Φfτs). The value reported in Table 1 for t-1 is similar to
that for 1-phenylpropene (kf ) 3.0 × 107 s-1).7 Slightly larger
values are observed for the 3-substituted derivatives t-2-t-4.
These observations suggest that the radiative rate may be
enhanced by weak interactions of the styrene chromophore with
the 3-phenyl substituents, interactions which presumably depend
on the ground-state conformation.
Trans,cis Photoisomerization. In their study of t-3, Zim-
merman et al.5 determined that the quantum yield for trans,cis
isomerization obtained upon direct irradiation was significantly
smaller than that obtained upon triplet sensitized irradiation (Φiso
) 0.065 and Φsens ) 0.51). Based on this observation, they
proposed that isomerization of t-3 occurs predominately via
intersystem crossing. Our subsequent study of the photoisomer-
ization of trans-1-phenylpropene established that isomerization
can occur via both an activated singlet state pathway and an
unactivated triplet pathway, the latter dominating at or below
room temperature and the former dominating at higher temper-
where ktwist is the rate constant for singlet state isomerization
and kisc is the rate constant for intersystem crossing.
An Arrhenius plot (ln(kiso) vs T-1) of the isomerization data
for t-4 is shown in Figure 3. The nonlinear nature of this plot
is similar to that observed previously for the isomerization of
1-phenylpropene and is consistent with the occurrence of both
an activated (singlet) and an unactivated (triplet) mechanism
for isomerization (Scheme 3). Activation parameters for the
singlet state process and the intersystem crossing rate constant
can be estimated from this plot. However, more accurate
parameters can be obtained from nonlinear fitting of the
temperature dependence of kiso according to eq 3 (Figure 4).
Values of the intersystem crossing rate constant, kisc, and
activation parameters for singlet state twisting obtained from
nonlinear fitting of data for all of the diphenylpropenes are
reported in Table 3. The values of kisc are similar to the value
reported for 1-phenylpropene (4.6 × 107 s-1).7
The values of Atwist for all of the diphenylpropenes are larger
than that for 1-phenylpropene (0.63 × 1012 s-1 7
) and are
consistent with a singlet state twisting mechanism. Similar
values of Atwist are obtained for t-1-t-3 whereas a somewhat
lower value is found for t-4. The values of ∆Etwist for the
diphenylpropenes are all smaller than that for 1-phenylpropene
(8.8 kcal/mol in hexane solution). Values of ∆Etwist decrease
with the bulk of the 3-substituent (t-1 > t-2 > t-4); however
(9) For a discussion of the potential energy surfaces for singlet and triplet
isomerization of styrene see: Bearpark, M. J.; Olivucci, M.; Wilsey, S.;
Bernardi, F.; Robb, M. A. J. Am. Chem. Soc. 1995, 117, 6944-6953.

11886 J. Am. Chem. Soc., Vol. 123, No. 48, 2001
Lewis et al.
Table 4. Rate Constants at Room Temperature and Activation
Parameters for Phenyl-Vinyl Bridginga
kpv, s-1
10-10 Apv
∆Epv, kcal/mol
t-1
t-2
t-3
t-4
2.1 × 107
3.5 × 108
1.5 × 109
1.2 × 109
0.94
1.2
4.3
3.6
2.1
2.0
2.1
4.3
a Calculated by fitting the singlet lifetime data to eq 5, as shown for
t-4 in Figure 4.
Scheme 4. Calculated Ground-State Bond Angle θ for
t-1-t-4
Figure 4. Temperature dependence of the singlet lifetime, τ (O), and
rate constant for cis,trans isomerization, kiso (0), for t-4.
1,2-migration (Bernardi-Robb mechanism). A plot of the
temperature-dependent lifetime for t-4 is shown in Figure 4,
and the values of Apv and ∆Epv obtained from nonlinear fitting
are reported in Table 4, along with the room-temperature values
of kpv calculated using these activation parameters.
Table 3. Rate Constants for Intersystem Crossing and Activation
Parameters of Singlet State Cis,trans Photoisomerizationa
10-7 kisc, s-1
10-13 Atwist
∆Etwist, kcal/mol
t-1
t-2
t-3
t-4
5.0
5.1
3.1
3.7
1.3
0.74
1.3
7.6
6.6
6.6
5.6
The room-temperature values of kpv increase upon introduc-
tion of 3-methyl substituents, following the order t-1 < t-2 <
t-3. Hixson4 attributed the large increase in the apparent rate
constant for the di-π-methane rearrangement of t-3 vs t-1 to
the gem-dialkyl effect. According to the classical Thorpe-Ingold
explanation, compression of the internal angle between reactive
groups can account for this effect.10 As shown in Scheme 4,
the calculated ground-state dihedral angles for t-2 and t-3 are
similar and smaller than that for t-1. More modern explanations
for the gem-dialkyl effect attribute rate enhancements to a
decrease in population of ground-state unreactive rotamers11a
or to overall reductions in the enthalpy of reaction resulting
from changes in both ground- and transition-state enthalpies.11b
In most examples of the gem-dialkyl effect, a single alkyl
substituent causes much smaller rate enhancement than dialkyl
substitution.10,11 However, the rate enhancement observed for
t-2 vs t-1 is larger than that observed for t-3 vs t-2 (Table 4).
Furthermore, the values of ∆Epv for the two latter molecules
are essentially the same, the increased rate for t-3 resulting
primarily from the increase in Apv. Thus, the rate enhancement
observed upon 3-alkylation of the diphenylpropenes is a
consequence of complex changes in the entropy and enthalpy
of activation.
When compared to activated (singlet) isomerization (Table
3), the rate determining step for the di-π-methane rearrangement
has significantly lower preexponentials and activation energies
(Table 4). The lower preexponentials are consistent with a
decrease in entropy, as would be expected for either phenyl-
vinyl bridging or 1,2-phenyl-vinyl migration as the rate-
determining step (Scheme 1). As a consequence of the lower
activation energies, values of Φdiπ > Φiso are observed for t-2-
t-4 at temperatures between 180 and 350 K (Figure 2). At
temperatures < 160 K both activated processes become slower
than kisc and kf. Thus, triplet isomerization and fluorescence
become the major excited-state processes. At higher tempera-
tures the ratio Φdiπ/Φiso decreases as a consequence of the larger
A value for singlet isomerization and isomerization is expected
0.20
a Calculated by fitting of the kiso data to eq 3 as shown for t-4 in
Figure 4.
no further decrease is observed for the 3,3-disubstituted t-3.
These changes plausibly reflect the increase in steric energy of
the planar singlet vs twisted singlet, which would result in a
lower barrier for twisting (Scheme 3).
Di-π-methane Rearrangement. Zimmerman et al.5 deter-
mined that the quantum yield for formation of p-3 upon direct
irradiation is significantly larger than that for triplet sensitized
irradiation (Φdiπ ) 0.40 and <0.003, respectively), in accord
with a singlet rearrangement mechanism. The rate constant kdiπ
can be described by a phenomenological rate expression, eq 4,
which is analogous to eq 2.
-1
s
k
diπ ) Φ
τ
(4)
diπ
An Arrhenius plot for the temperature dependence of the data
for t-4 is shown in Figure 3. The linear nature of this plot is
consistent with an activated singlet state rearrangement mech-
anism. Activation parameters for the rearrangement process can
be estimated from this plot. However, if the intermediate Ia
(Scheme 1) undergoes return to the ground state in competition
with product formation, as suggested by Hixson,4 the measured
value of Φdiπ would underestimate the quantum yield for phenyl-
vinyl bridging.
Activation parameters for the rate determining step in the
di-π-methane rearrangement, kpv, and the intersystem crossing
rate constant, kisc, can be obtained from nonlinear fitting of the
temperature dependence of the singlet decay time according to
eq 5, using the previously determined values of kf, Atwist, and
∆Etwist (Tables 1 and 3).
1
τs )
(5)
-∆Epv
-∆Etwist
kf + kisc + Apv exp
+ A
exp
twist
(
)
(
)
(10) Beesley, R. M.; Ingold, C. K.; Thorpe, J. F. J. Chem. Soc. 1915,
1080-1106.
(11) (a) Lightstone, F. C.; Bruice, T. C. J. J. Am. Chem. Soc. 1994, 116,
10789-10790. (b) Parrill, A. L.; Dolata, D. P. J. Tetrahedron Lett. 1994,
35, 7319-7322.
RT
RT
This expression is valid for both rate determining phenyl-vinyl
bridging (Scheme 1, Zimmerman mechanism) and phenyl-vinyl

Photochemistry of 1,3-Diphenylpropenes
J. Am. Chem. Soc., Vol. 123, No. 48, 2001 11887
Scheme 5. Schematic Potential Energy Surface for
Di-π-methane Rearrangement of t-4
Figure 5. Simultaneous kinetic fitting of the di-π-methane rearrange-
ment product formation quantum yield (g) and nonradiative decay
quantum yield (3) for t-4.
Table 5. Activation Parameters for Nonradiative Decay and
Formation of Diradical Iba
10-10 Anr
∆Enr, kcal/mol
10-10 AIb
∆EIb, kcal/mol
to be the major process at very high temperatures (>440 K). In
the case of t-1, intersystem crossing and fluorescence are more
rapid than either activated process for the entire temperature
range.
t-2
t-3
t-4
0.07
0.69
4.4
0.28
0.44
0.85
6.3
8.0
7.0
3.0
1.9
1.5
Nonradiative Decay. Hixson4 suggested that the much lower
quantum yield for rearrangement of t-1 vs t-3 (Table 2) might
arise in part from reversion of the bridged intermediate Ia to
the starting olefin in competition with ring-opening to form the
diradical Ib, the precursor of the cyclopropane product (Scheme
1). A nonradiative decay pathway is necessary to account for
the inefficiencies in radiative and product forming reactions.
The quantum yield for nonradiative decay, Φnr, can be calculated
using eq 6,
a Calculated by simultaneous fitting of the quantum yields of di-π-
methane product formation and nonradiative decay as shown for t-4 in
Figure 5.
According to the Zimmerman mechanism1 the intermediate
Ia proceeds to the rearranged product via a second intermediate
Ib with a rate constant kIb in competition with nonradiative
decay (Scheme 5). This scheme provides the expressions shown
in eqs 8 and 9 for the quantum yields of these two competing
processes in terms of the probabilities of forming Ia from the
singlet state (P1) and of forming the rearrangement product from
Ia (P2) (eqs 10 and 11).
Φnr ) 1 - (Φf + 2Φiso + Φdiπ
)
(6)
where it assumed that both the singlet and triplet pathways for
photoisomerization involve twisted intermediates which decay
with equal probability to the trans starting material and its cis
isomer (Scheme 3), as is the case for 1-phenylpropene.7,12
Calculated room-temperature values of Φnr are reported in Table
2 and are seen to account for a significant fraction of the singlet
state decay for t-2-t-4 and a smaller fraction for t-1.
The temperature dependence of Φnr can also be calculated
from the temperature-dependent quantum yield data using eq
6. The resulting values for t-4 are shown in Figure 5 along with
the data for Φdiπ. The values of Φnr display a maximum at ca.
250 K, decreasing at both higher and lower temperatures. By
analogy to eqs 2 and 4, the phenomenological rate constants
for nonradiative decay can be described by eq 7.
ΦIb ) P1 × P2
Φnr ) P1 × (1 - P2)
kpv
(8)
(9)
P1 )
(10)
(11)
kf + kisc + kpv + ktwist
kIb
P2 )
knr + kIb
Assuming that Ib is formed irreversibly, ΦIb ) Φdiπ. The
temperature-dependent quantum yields Φnr and ΦIb obtained
for t-4 are shown in Figure 5 along with the results of
simultaneous kinetic fitting of these data (Experimental Section)
which provides activation parameters for both processes.
Activation parameters determined by this procedure for t-2-
t-4 are reported in Table 5. In the case of t-1 the values of Φdiπ
are too low to permit accurate measurement at low temperatures.
Values of ∆EIb for conversion of Ia to Ib are seen to decrease
for the series t-2 > t-3 > t-4, whereas values of ∆Enr increase.
This result is consistent with the anticipated changes in the
cyclopropane exocyclic dihedral angles upon ring opening
(Scheme 1). Opening of bond b results in an increase in these
bond angles and is thus subject to steric acceleration. In contrast,
opening of bond a results in a decrease in these bond angles
and thus should be subject to steric deceleration. Alkyl or phenyl
substituents can also stabilize the incipient radical center in
knr ) Φnrτs-1
(7)
An Arrhenius plot of the temperature dependence of knr for t-4
(Figure 3) is linear over the entire temperature range 140-352
K and provides activation parameters (Anr ) 1.5 × 1010 and
∆Enr ) 1.8 kcal/mol) that are similar to those obtained from
the kpv data for t-4 (Table 4). This is consistent with the
Zimmerman1 mechanism (Scheme 1) in which nonradiative
decay and the di-π-methane rearrangement occur via a common
intermediate Ia. However, it is apparently inconsistent with the
Bernardi-Robb2 mechanism since the intermediate Ib is unlikely
to revert to the starting olefin.
(12) Ni, T.; Caldwell, R. A.; Melton, L. A. J. Am. Chem. Soc. 1989,
111, 457-464.

11888 J. Am. Chem. Soc., Vol. 123, No. 48, 2001
Lewis et al.
intermediate Ib, thus favoring path b. This is consistent with
the smaller value of ∆EIb for t-4 than for t-2.
This analysis of the di-π-methane rearrangement serves to
further illustrate the power of kinetic modeling of temperature-
dependent data sets to elucidate photochemical reaction mech-
anisms which are too complex for simple kinetic analysis.13
Applications of these methods to other photochemical processes
are in progress in our laboratories.
As noted previously, Hixson4 suggested that the larger value
of Φdiπ for t-3 than for t-1 might result from differences in the
partitioning of intermediate Ia between rearrangement via Ib
vs starting material (Scheme 5). The efficiency of product
formation from Ia, f, can be quantified using eq 12.
Experimental Section
f ) Φdiπ/(Φdiπ + Φnr)
(12)
Materials. trans-1,3-Diphenylpropene (t-1) was prepared by heating
phenylacetaldehyde and potassium in ethanol using the method of
Stoermer et al.14,15 and was purified by recrystallization at -77 °C from
ethanol. trans-1,3-Diphenyl-1-butene (t-2) was prepared by the method
of Higashimura et al.16 via acetyl perchlorate catalyzed dimerization
of styrene and purified by column chromatography. trans-1,3-Diphenyl-
3-methyl-1-butene (t-3) was prepared by a Grignard reaction of
neophylmagnesium chloride and benzaldehyde, followed by dehydration
of the resulting alcohol catalyzed by p-toluenesulfonic acid in benzene,
and then finally purified by column chromatography, as described by
Zimmerman et al.5,17 trans-1,3,3-Triphenylpropene (t-4) was prepared
by the method of Ahlberg et al.18 via the reaction of benzylideneac-
etophenone and phenylmagnesium bromide, reduction of the resulting
ketone with NaBH4, then dehydration of the resulting alcohol.
Compounds t-1-t-3 are colorless oils and t-4 is a colorless crystalline
solid mp ) 94-95 °C (lit.18 mp ) 98-99 °C). All compounds were
found to have greater than 99.9% purity as estimated by GC analysis.
The cis olefins c-1,15 c-2,19 and c-35 were obtained by acetone-sensitized
photoisomerization of the corresponding trans-isomers and purified by
HPLC. The phenylcyclopropanes p-220 and p-35 were obtained from
the corresponding trans-alkenes by irradiation (medium-pressure
mercury lamp, Pyrex filter) in cyclohexane solution. 1H NMR and GC/
MS were used to establish the identity and purity of all compounds.
Spectral data for the cis isomers and phenylcyclopropanes were identical
to those published in the literature. All solvents used for spectroscopy
and photolyses were either spectrophotometric or HPLC grade and were
used as received.
Experimental Methods. GC analysis was performed on a Hewlett-
Packard HP 5890 instrument equipped with a HP1 poly(dimethylsi-
loxane) capillary column. UV-vis spectra were measured on a Hewlett-
Packard 8452A diode array spectrometer with a 1-cm path length quartz
cell. Fluorescence spectra were measured on a SPEX Fluoromax
spectrometer and are uncorrected. Fluorescence quantum yields for
deoxygenated solutions were measured by comparing the integrated
area under the fluorescence curve to that for trans-1-phenylpropene
(Φf ) 0.35, in hexanes7) at equal absorbance at the same excitation
wavelength. The fluorescence quantum yields are corrected for the
refractive index of the solvent. The estimated error is (10%.
Fluorescence decays were measured on a Photon Technologies
International (PTI) LS-1 stroboscopic detection instrument with a gated
hydrogen arc lamp using a scatter solution to profile the instrument
response function. Nonlinear least-squares fitting of the decay curves
was performed with the Levenburg-Marquardt algorithm described by
James et al.21 as implemented by the PTI Timemaster (version 1.2)
Values of f are summarized along with the room-temperature
quantum yield data in Table 2. The values of f for t-1 and t-3
are similar to those calculated by Hixson. Introduction of a single
methyl substituent in t-2 results in a value of f intermediate
between those of t-1 and t-3. The phenyl substituent in t-4 has
a value of f only slightly larger than that of the methyl
substituent in t-2. This plausibly reflects an early transition state
for bond breaking in Ia. The values of f are also temperature
dependent as a consequence of the different activation param-
eters for kIb and knr. The former process has the larger activation
energy and larger preexponential and thus is favored at higher
temperatures, whereas the latter process is favored at lower
temperatures (Figure 5).
Concluding Remarks. The results of this investigation
provide a complete description of the competing photochemical
reactions which occur via the singlet state of several 1,3-
diphenylpropenes. These include isomerization via both the
singlet and triplet states (Scheme 3) and singlet phenyl-vinyl
bridging to yield a diradical intermediate which can either
proceed to the di-π-methane product or revert to starting material
(Scheme 5). Activation parameters have been determined for
both the primary processes (singlet isomerization and phenyl-
vinyl bridging) and diradical processes (nonradiative decay and
product formation). The results of this analysis are consistent
with the stepwise Zimmerman mechanism (Scheme 1, path i)
rather than the Bernardi-Robb concerted migration (Scheme 1,
path ii). The Bernardi-Robb energy surface for 1,4-pentadiene
evidently is not applicable to more complex molecules such as
the 1,3-diphenylpropenes. This illustrates the potential hazard
of using truncated models to calculate potential energy surfaces
for more complex molecules.
Substituents at the 3-position are found to have little effect
on either the absorption and fluorescence spectra or the
temperature-independent rate constants for fluorescence and
intersystem crossing (Tables 1, 3). They do, however, affect
the activation parameters for the competing activated singlet
state processes, isomerization and phenyl-vinyl bridging (Tables
3, 4). Activation energies for both processes decrease with
increasing 3-substitution. Phenyl-vinyl bridging has both a lower
activation energy and a lower preexponential than isomerization,
and is the dominant reaction pathway for t-2-t-4 at temperatures
between 160 and 350 K. At temperatures below 160 K triplet
isomerization and fluorescence are the major processes, whereas
above 440 K singlet isomerization is expected to be the major
pathway.
Substituents at the 3-position also affect the partitioning of
the diradical intermediate Ia (Scheme 5). Ring opening leading
to the product has larger preexponentials and larger activation
energies than ring opening to regenerate the ground-state reactant
(Table 5), resulting in complex temperature dependence for the
quantum yield ratios (Figure 5). Activation energies for the ring
opening leading to product decrease with increasing 3-substitu-
tion. This could result from either relief of angle strain or
stabilization of the diradical Ib.
(13) For examples see: (a) Saltiel, J. A.; Zhang, Y.; Sears, D. F., Jr. J.
Am. Chem. Soc. 1997, 119, 11202-11210. (b) Catala´n, J.; Zima´nyi, L.;
Saltiel, J. J. Am. Chem. Soc. 2000, 122, 2377-2378. (c) Lewis, F. D.; Li,
L.-S.; Kurth, T. L.; Kalgutkar, R. S. J. Am. Chem. Soc. 2000, 122, 8573-
8574.
(14) Stoermer, R.; Their, C.; Laage, E. Chem. Ber. 1925, B85, 2607-
2615.
(15) Raunio, E. K.; Bonner, W. A. J. Org. Chem. 1966, 31, 396-399.
(16) (a) Sawamoto M.; Masuda T.; Nishii H.; Higashimura T. J. Polym.
Sci. Polym. Lett. Ed. 1975, 13, 279-282. (b) Higashimura T.; Nishii H. J.
Polym. Sci. Polym. Chem. Ed. 1977, 15, 329-339.
(17) Calcott, W. S.; Tinker, J. M.; Weinmayr, V. J. Am. Chem. Soc.
1939, 61, 1010-1015.
(18) Ahlberg P.; Janne K.; Lofas S.; Nettelblad F.; Swahn L. J. Phys.
Org. Chem. 1989, 2, 429-447.
(19) Ella, S. W.; Cram, D. J. J. Am. Chem. Soc. 1966, 88, 5777-5791.
(20) Fox, M. A.; Chen, C. C.; Campbell, K. A. J. Org. Chem. 1983, 48,
321-326.
(21) James, D. R.; Siemiarczuk, A.; Ware, W. R. ReV. Sci. Instrum. 1992,
63, 1710-1716.

Photochemistry of 1,3-Diphenylpropenes
J. Am. Chem. Soc., Vol. 123, No. 48, 2001 11889
software. Goodness of fit was determined by judging the ø2 (0.8 < ø2
<1.3 in all cases), the residuals, and the Durbin-Watson parameter
(>1.6 in all cases).
dependent fluorescence quantum yield data to eqs i-iii were similar
to those obtained by fitting temperature-dependent singlet lifetime data
(e.g. Figure 4: Apv ) 5.6 × 1010, ∆Epv ) 2.0 kcal/mol). The corrected
fluorescence quantum yields can be calculated using eq iii.
Measurements of quantum yields for direct photoisomerization and
di-π-methane rearrangement product formation for t-1-t-4 were
performed on optically dense deoxygenated solutions (∼10-3 M) excited
at 270 nm. Solutions were deoxygenated by purging with dry N2 for
20-25 min. The extent of photochemical conversion (<5%) was
quantified by GC. Excitation at 270 or 366 nm was achieved with a
200 W high-pressure Hg(Xe) arc lamp and a 0.25 M monochromator.
trans-Stilbene isomerization (Φiso ) 0.52, in hexanes22) was used as
an external standard for the measurement of quantum yields. For
temperatures below ambient, a nitrogen-cooled Oxford Instruments
optical cryostat (DN 1704) and ITC temperature controller were used
to maintain the sample temperature within (0.1 K of the desired value.
Quantum yields for triplet-sensitized irradiation were determined on
freeze-pump-thaw degassed benzene solutions containing 0.05 M
benzophenone and 0.025 M t-1-t-4. Solutions were irradiated at 366
nm to low conversions (<5%) and the yield of cis isomer compared to
that for 1-phenylpropene (Φiso ) 0.51).7
Data Fitting. All data fitting procedures were carried out by using
either Origin (version 6)23 or Mathematica (version 4.0).24 The fitting
strategy involved the use of as many experimental data points as
possible. In all cases 15 or more data points were used to model two
to four parameters. For example, four parameters, values of kf (from
Φf data), kisc, Atwist, and ∆Etwist (from Φiso data), were employed for
modeling the lifetime data, providing two parameters, Apv and ∆Epv
(eq 5). For the final modeling, two independent data sets were analyzed
using a global optimization strategy with a Multi-Start algorithm that
examines literally hundreds of staring points. To simultaneously fit two
sets of data, a penalty function f is constructed,
f(A ,∆E ) )
[R(Φ(T )Exp - Φ(Ti)nFrit)2 +
∑
j
j
i nr
Ti
(Φ(Ti)dEixπp - Φ(Ti)dFiiπt )2]
Correction of Low-Temperature Fluorescence Quantum Yields.
Fluorescence quantum yields will be influenced while lowering
temperature owing to the change of solvent viscosity, refractive index,
and volume. The application of a linear correction (eq i) was found to
give corrected quantum yields consistent with fitting of our other
temperature-dependent data.
where superscript “Exp” indicates experimental data and “Fit” indicates
calculated data. R is a scaling factor used to adjust relative error. If a
large error exists in the first set of data, R will be set less than 1.0 to
improve fitting for the second set of data. In our data analysis, R ) 1
and parameters Aj,∆Ej are obtained by minimizing function f(Aj,∆Ej).
Molecular bond angles were measured based on SCF/AM1 optimized
ground-state geometries by using the HyperChem (standard version,
Release 5).25
Φf ) Φf0 × (A + BT)
A + BTRT ) 1
(i)
Acknowledgment. Funding for this project was provided
by NSF grants CHE-9734941 and CHE-0100596 and by Spanish
DGES Grant PB97-0339. The authors thank Igor Alabugin for
fruitful discussions. This work is dedicated to Howard E.
Zimmerman on the occasion of his 75th birthday.
(ii)
kf
Φf0 )
-∆Etwist
-∆Epv
kf + kisc + Atwist exp
+ A exp
pv
(
)
(
)
Supporting Information Available: Temperature-dependent
singlet lifetimes and quantum yields of fluorescence, trans,cis
isomerization, and di-π-methane rearrangement product forma-
tion for t-1-t-4 (PDF). This material is available free of charge
via the Internet at http://pubs.acs.org.
RT
RT
(iii)
In this approach, no correction is made for room-temperature measure-
ments and the magnitude of the correction factor increases as the
temperature decreases. Observed fluorescence quantum yields, Φf, were
fit over temperature based on the above equations (i-iii), and phenyl-
vinyl bridging activation parameters were obtained that are comparable
to those obtained from singlet lifetime fitting. For t-4, phenyl-vinyl
bridging activation parameters obtained by fitting the temperature-
JA0113652
(23) Microcal Software, Inc., Northampton, MA 01060; (413) 586-2013;
http://www.microcal.com.
(24) Wolfram Research, Inc., Champaign, IL 61820; (217) 398-0700;
http://www.wolfram.com.
(22) Saltiel, J.; Margianari, A.; Chang, D.; Mitchener, J. C.; Megarity,
E. D. J. Am. Chem. Soc. 1979, 101, 2982-2996.
(25) Hypercube, Inc., Gainesville, FL 32601; (352) 371-7744; http://
www.hyper.com.