Structural volume changes upon photoisomerization: A laser-induced optoacoustic study with a water-soluble nitrostilbene

Article abstract of DOI:10.1021/jp004334m

The trans to cis photoisomerization of 4,4′-dinitro-2,2′-disulfonylstilbene (DS) was studied by laser-induced optoacoustic spectroscopy (LIOAS) in aereated neat water and in aereated aqueous solutions of various monovalent cations (NH₄⁺, N(CH₃)₄⁺, Na⁺, K⁺, and Cs⁺) and the respective cis to trans photoisomerization only in the presence of NH₄⁺. In every case, two single-exponential components were required to fit the data, one with an unresolved lifetime (<20 ns) for the appearance of the triplet state mixture T (the perpendicular triplet state ³p* in equilibrium with the lowest trans triplet state ³t*) and one with a longer lifetime of (75 ± 20) ns at 5.5 °C for the decay of the T mixture. The temperature dependence of the LIOAS amplitudes in combination with the determined isomerization quantum yields afforded a contraction of -(1.4 ± 0.15) ml/mol for the trans to T transition, whereas a smaller contraction of -(0.15 ± 0.15) ml/mol was obtained for the cis to T transition. The different values of the contraction indicate a greater similarity between the average structures of the T components with the cis ground singlet state than with the trans ground singlet. The total structural volume change for the trans to cis transition is in average ΔV_tc = - (1.2 ± 0.1) ml/mol. The calculated contribution of electrostriction is at most 50% of this value. However, the nature of the countercation had no influence on the data as would be expected for changes in the specific interaction with the H-bond network in water upon photoisomerization. Thus, ca. 50% of the total contraction is attributed to intrinsic effects, related to a shorter C=C bond and a smaller accessible volume in the cis isomer. The LIOAS data show that cis-DS lies (28 ± 35) kJ/mol above trans-DS in agreement with the calculated value of 37 kJ/mol.

Full text of DOI:10.1021/jp004334m

4814
J. Phys. Chem. A 2001, 105, 4814-4821
Structural Volume Changes upon Photoisomerization: A Laser-Induced Optoacoustic Study
with a Water-Soluble Nitrostilbene
Ingolf Michler, Alessandro Feis,† Miguel A. Rodr´ıguez,‡ and Silvia E. Braslavsky*
Max-Planck-Institut fu¨r Strahlenchemie, Postfach 10 13 65, D-45413 Mu¨lheim an der Ruhr, Germany
ReceiVed: NoVember 30, 2000; In Final Form: February 22, 2001
The trans to cis photoisomerization of 4,4′-dinitro-2,2′-disulfonylstilbene (DS) was studied by laser-induced
optoacoustic spectroscopy (LIOAS) in aereated neat water and in aereated aqueous solutions of various
+
+
monovalent cations (NH4 , N(CH3)4 , Na+, K+, and Cs+) and the respective cis to trans photoisomerization
+
only in the presence of NH4 . In every case, two single-exponential components were required to fit the data,
one with an unresolved lifetime (<20 ns) for the appearance of the triplet state mixture T (the perpendicular
triplet state 3p* in equilibrium with the lowest trans triplet state 3t*) and one with a longer lifetime of (75 (
20) ns at 5.5 °C for the decay of the T mixture. The temperature dependence of the LIOAS amplitudes in
combination with the determined isomerization quantum yields afforded a contraction of -(1.4 ( 0.15) ml/
mol for the trans to T transition, whereas a smaller contraction of -(0.15 ( 0.15) ml/mol was obtained for
the cis to T transition. The different values of the contraction indicate a greater similarity between the average
structures of the T components with the cis ground singlet state than with the trans ground singlet. The total
structural volume change for the trans to cis transition is in average ∆Vtc ) - (1.2 ( 0.1) ml/mol. The
calculated contribution of electrostriction is at most 50% of this value. However, the nature of the countercation
had no influence on the data as would be expected for changes in the specific interaction with the H-bond
network in water upon photoisomerization. Thus, ca. 50% of the total contraction is attributed to intrinsic
effects, related to a shorter CdC bond and a smaller accessible volume in the cis isomer. The LIOAS data
show that cis-DS lies (28 ( 35) kJ/mol above trans-DS in agreement with the calculated value of 37 kJ/mol.
Introduction
The contractions determined by LIOAS for the trans f cis
photoisomerization of the three isomers (para, meta, and ortho)
of potassium azobenzenecarboxylates were also rationalized in
terms of the difference in the chromophore-water hydrogen
bonds strength between the photoisomer and the parent com-
pound. Due to a reduced conjugation, a stronger interaction of
the nitrogens’ lone pairs and water is expected in the cis isomers,
leading to the contraction upon photoisomerization.6
Measurements of reaction volume changes during isomer-
ization reactions by conventional techniques (i.e., by analyzing
the pressure dependence of the equilibrium constant) are
infrequent.1 One of the reasons is probably the small expected
value of ∆VR. Another reason is that in order to obtain ∆VR
from steady-state measurements, relatively large pressure varia-
tions are needed, which poses special technical problems for
photoreactions. Laser-induced optoacoustic spectroscopy
(LIOAS)2 is thus the method of choice for the determination of
those volume changes.
During our LIOAS study with 3,3′-diethyloxadicarbocyanine
iodide (DODCI), we concluded that the photoinduced structural
volume changes in aqueous solutions are mainly due to changes
in the specific interactions of the solvent molecules with the
isomerized DODCI.3 The contraction of ∆VR ) -29 mL/mol
upon trans f cis isomerization cannot be explained with the
continuum model for electrostriction, originally used by Drude
and Nernst4 to relate the reorganization of solvent around
solvated ions. The calculated5 electrostrictive contraction of ca.
0.1 ml/mol is negligible in comparison to the effect observed
which, therefore, should be attributed to changes in the hydrogen
bond strength between the solvent molecules and the photo-
isomer versus the parent compound. Most probably, the lone
pair of one of the heterocyclic nitrogens is involved in these
hydrogen bonds.3
On the contrary, the values of ∆VR observed for intra-
molecular electron-transfer reactions of large donor-bridge-
acceptor molecules in nonpolar organic solvents can be indeed
explained by using the concept of a solvent continuum, in
addition to intrinsic photoinduced changes, such as intramo-
lecular exciplex formation (a transient isomerization) in flexible
donor-bridge-acceptor molecules.7,8 Intrinsic volume changes
explain also the contraction measured upon photoexcitation of
2+
Ru(bpy)3 (unable to form hydrogen bonds) in water in view
of the shortening of the Ru-N bond in the produced metal-to-
ligand charge transfer state.9
Thus, a picture emerges which relates the photoinduced
structural volume changes to the particular type of chromophore-
medium interactions. We are interested in finding a general
picture relating the structural volume changes to molecular
properties that would help us understanding the changes
observed upon photoexcitation of biological photosensors.10-12
To this aim, we performed LIOAS studies of three retinal
isomers in a series of n-alkanes. These studies helped us to
understand the different photochemistry of the isomers but little
could be learned about the time-resolved ∆VR values.13 The low
photoisomerization quantum yield for all-trans-retinal and a
* To whom correspondence should be addressed. E-mail: braslavskys@
mpi-muelheim.mpg.de. Fax: *49 (208) 306 3951.
† Present address: Dipartimento di Chimica, Universita´ di Firenze, Via
Gino Capponi 9, I-50121 Firenze, Italy.
‡ On leave from the Departamento de Qu´ımica, Universidad de La Rioja,
E-26071 Logron˜o, Spain.
10.1021/jp004334m CCC: $20.00 © 2001 American Chemical Society
Published on Web 04/25/2001

Structural Volume Changes upon Photoisomerization
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4815
dependence of the isomerization quantum yield on the solvent
for 13-cis-retinal difficulted the quantitative evaluations.
We thus decided to determine by LIOAS the ∆VR values for
the photoisomerization of a water-soluble stilbene derivative,
4,4′-dinitro-2,2′-disulfonylstilbene (DS) because the cis f trans
transformation of stilbene and its derivatives is one of the most
investigated photoisomerizations, the energetics and dynamics
of these systems have been extensively characterized, and the
isomerization quantum yields are in general large.14,15
An advantage of DS is that the cis and trans isomers are
separable and stable in their ground states. Thus, a reaction
volume change determination is possible for the photoisomer-
ization in both directions.
In the present paper, we concentrate on the structural volume
changes derived from LIOAS studies for the trans f cis and
cis f trans photoisomerization of DS in neat water and in
aqueous solutions of various monovalent cations.
An adequate knowledge of the photochemical properties is a
prerequisite for the determination of ∆VR by LIOAS. To this
aim, we measured the photoisomerization and fluorescence
quantum yields of both DS isomers and checked for the presence
of long-lived energy-storing species upon photoexcitation of
both isomers. To estimate the electrostriction volume change
we also calculated the variation in dipole moment upon
photoisomerization and the size of each isomer.
LIOAS. LIOAS was performed as already described using
the 3rd harmonic (λexc ) 354.7 nm) of a Nd:YAG laser,
operating at a frequency of 1 Hz.16 To accomplish an homo-
geneous isomer distribution in the DS measurements by stirring,
only one in every three shots was let through the shutter. A
homemade variable delay box controlled the measurements. The
excitation beam was shaped by a slit (w × h ) 0.8 × 6 mm),
resulting in an acoustic transit time of about 500 ns, allowing
a time resolution down to ∼50 ns, employing deconvolution
algorithms.17 All samples were measured in a brass cuvette
holder ensuring heat exchange through all four vertical walls,
thus minimizing the temperature gradient in the cuvette to a
maximum of ( 0.1 degrees. 100 shots (<10 µJ per shot) were
averaged per signal trace and 2-8 traces were measured for
each solution and temperature. Each DS sample received only
200 shots, corresponding to a total conversion < 1% in each
isomerization direction, and was then replaced by another aliquot
of the standard solution for further measurements.
Three series of LIOAS experiments were carried out. The
first series performed in a temperature range 4-35 °C was
restricted to NH4+ as the countercation, in view of the fact that
the HPLC separation of the cis isomer was performed with an
NH4 CH3COO aqueous solution as part of the mobile phase
(vide supra). The second and third series included the different
cations mentioned above for the trans to cis isomerization. The
data obtained at only two close temperatures (the two-temper-
atures method, TT method, vide infra) were used in the two
latter sets. The third series also included neat water (again only
for the trans to cis isomerization), and the data were evaluated
using deconvolution. In all three series, the isomerization
quantum yield for both isomerization directions was determined.
Materials and Methods
Protonated 4,4′-dinitro-2,2′-disulfonylstilbene (DS) in its
trans-isomeric form (Bayer) was recrystallized twice from
methanol-water.
To obtain cis-DS a 0.17 M solution of trans-DS in the HPLC
mobile phase (vide infra) was irradiated for 10 min with a
250-W tungsten halogen lamp. The photoisomer mixture of
trans- and cis-DS was separated on a preparative reversed phase
HPLC column (Nucleosil-C18-120-3) with a 0.07 M NH4-
CH3COO in 20% CH3CN/H2O solution. After separation, CH3-
CN was evaporated.
All measurements with the cis-DS were performed in aqueous
90 mM NH4CH3COO solutions. The trans-DS was investigated
in aqueous solutions containing 90 mM acetate salts of one of
the monovalent cations NH4+, N(CH3)4+, Na+, K+, and Cs+,
as well as in neat water. Water was tri-distilled. K2Cr2O7
(Merck) and indigocarmin (EGA-Chemie, Steinheim/Albuch,
Germany) were the calorimetric reference substances, the former
for the monovalent salt solutions and the latter for neat water.
K2Cr2O7 was not stable in neat water. 5,10,15,20-Tetrakis-(4-
sulfonatophenyl)-porphyrin (TSPP, Porphyrin Products Inc.) in
tris buffer (pH ) 7.8) was used as a standard photosensitizer
for the generation of molecular singlet oxygen, O2(1∆g). K2-
Cr2O7, indigocarmin, and TSPP were used without further
purification.
The use of two close lying temperatures (TT method)16,18 was
favored in this case over the several temperatures method, in
view of the fact that the results with the latter method showed
deviations from linearity.
O2(1∆g) Quantum Yield, Φ∆. The O2(1∆g) quantum yield,
Φ∆, was determined for the third series of experiments by
monitoring the photoinduced luminescence at 1270 nm as
already described,19-21 with the same laser as described above.
The beam was shaped by a 3 mm diameter pinhole and the
repetition rate was 1 Hz. A liquid-nitrogen cooled germanium
diode (EO-817P, North Coast) in combination with a silicon
and an interference filter was used for detection.21 Laser energies
were 0.5 mJ per pulse for trans-DS and TSPP and 1 mJ for
cis-DS. Data were recorded as in LIOAS, again averaging 100
shots per trace. A total of 6 traces was acquired per sample and
reference, respectively. The DS samples were replaced after 100
shots.
Isomerization Quantum Yields. Isomerization quantum
yields were determined at 6 °C, using the same optical
conditions as for LIOAS. The total fluence absorbed by the
sample was also measured as in LIOAS (vide supra). Excitation
was at 1 Hz. After application of a defined total energy a UV-
vis spectrum was taken. Thereafter, the sample was submitted
to further irradiation. In these experiments the total conversion
was always < 10%.
In every case, the samples as well as the reference solutions
were stirred in order to minimize the build up of the respective
other isomer in the excited volume.
Absorption Measurements. Absorption measurements were
carried out with a Shimadzu UV-2102PC spectrophotometer.
The sample and reference solutions were matched in absorbance
within 5% at the excitation wavelength for the LIOAS experi-
ments. In the first measurements series, absorbances in the range
of A355 ) 0.1-0.3 were used (2 ml sample volume), whereas
an (initial) absorbance of A355 ) 0.3 (3 ml sample volume) was
kept for all experiments throughout the second and third series.
Absorption spectra were recorded between 200 and 500 nm for
the determination of the isomerization quantum yields.
Fluorescence Quantum Yield. The fluorescence quantum
yield was determined by comparison of the integrated emission
spectra with that of a standard solution of quinine sulfate in
0.1 N sulfuric acid.22
Data Processing and Handling. Data processing was carried
out with commercial PC software. LIOAS data were deconvo-
luted using Sound Analysis, Version 1.50D (Quantum Northwest
Inc., Spokane, WA). All fittings were performed with Microcal

4816 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Michler et al.
Origin Professional, Version 5.0 SR2 (Microcal Software, Inc.,
Northampton, MA). PM3 calculations were performed using
Spartan, Version 4.0.4; Wave function: Irvine, 1995 (Hehre,
W. J.; Huang, W. W.; Burke, L. D.; Shusterman, A. J.)
The amplitudes, æi, recovered from the deconvolution depend
on cpF/â, calculated for water from the values in tables.23
Plotting æi vs cpF/â reveals a linear behavior with Ri, released
in the step i, as intercept and the corresponding structural molar
volume change, ∆VR,i, times the quantum yield, Φi, as slope16,24,25
determined with solutions containing weighted amounts of the
compound resulted to be ꢀt ) (26400 ( 1800) M-1cm-1 at 355
nm. The normalization of the cis spectrum was done with the
absorption coefficient of the trans spectrum at the isosbestic
point, λisosb ) (311.2 ( 0.2) nm. The calculated value for the
cis isomer at 355 nm was ꢀc ) (5900 ( 600) M-1cm-1
.
The trans- and cis-DS samples were irradiated stepwise for
the determination of the isomerization quantum yields, Φtfc
and Φcft. After the application of defined photon fluxes, the
induced changes in the absorption spectra were recorded and
fitted with the spectra of the pure isomers. The inset in Figure
2 shows such a mixed spectrum as well as the contributing
isomer spectra. From the fits the concentrations of the individual
isomers were determined and inserted into eq 327
cpF Φi∆VR,i
(
æ ) R +
(1)
)
i
i
â
T
Eλ
The introduction of a salt results in an alteration of cpF/â. To
determine this ratio, comparative measurements of the calori-
metric references in the various cation solutions and in neat
water were performed. The plot of the laser-energy normalized
LIOAS amplitudes for the reference vs temperature (plots not
shown) reflects the behavior of â/(cpF).25,26 The main feature
is obviously a far reaching parallelism between all curves,
especially in the range 2.8-6.0 °C, i.e., in the temperature range
in which the quantitative LIOAS experiments were carried out.
Thus, in this relatively small range the salt addition only changes
the transition temperatures (ϑâ)0, at which the thermal signal
A′ A′2
3 + A′
[trans]0
Ψ ) 1 +
+
ln
+
(ꢀ′t - ꢀ′c)[cis]d +
(
) (
)
2
12
1
6
[trans]
... + (ꢀ′t - ꢀ′c)2 d2(2[trans]0[cis] - [cis]2) (3)
24
Φ
tfcdꢀ′t
)
nphot
V
A′ ) ꢀ′c d[trans]0, ꢀ′ ) 2.3ꢀ355
component vanishes), which were ϑâ)0 ) 3.9 °C for neat water
This equation (eq 3) is written for the photoisomerization
direction trans f cis and takes into account absorption changes
upon irradiation. d is the optical path length, [trans]0 is the initial
concentration, V is the solution volume, and nphot is the incident
photon amount.
The slope of the plot of Ψ vs nphot for both isomerization
directions (Figure 2) yields the respective quantum yield, Φcft
) 0.27 ( 0.08 and Φtfc ) 0.47 ( 0.08. Φtfc is the average of
a series in 90 mM aqueous NH4CH3COO solution and another
one in neat water. Both series afforded the same result within
the error limits.
Φtfc was not altered by the various cations as verified by
comparing the spectra before and after the application of a
defined photon flux. Because the shape of the corresponding
spectra was always the same it was enough to monitor the
absorbance changes at one particular wavelength (350 nm). The
initial absorbance at 350 nm was always A350 ) 0.300 ( 0.005.
The absorption changes plotted vs the incident photon quantity
are depicted in Figure 3. For all solutions the points for similar
photon fluxes are found within small “clouds” representing the
error distribution. Thus, Φtfc is the same within the error limits
for all solutions.
and 3.2, 2.9, 3.1, 2.9, and 3.0 °C for N(CH3)4+, Cs+, NH4
,
+
K+, and Na+ acetate aqueous solutions, respectively (all salts
were 0.09 M).
Results
LIOAS. The data for the series including the various
countercations and neat water for the trans to cis photoisomer-
ization were analyzed with eq 2 using data at ϑâ)0 and at a
18,16
second temperature, ϑâ*0, not far apart from ϑâ)0
Ri ) æi(ϑâ*0) - æi(ϑâ)0
)
â
cpF
Φi∆VR,i ) æi(ϑâ)0
)
Eλ
(2)
[
]
ϑâ*0
The individual points for the two-temperatures (TT) analysis
were obtained by performing up to four times more averages
(ca. 800 traces were averaged) than for the several-temperatures
(ST) analysis. In every case, the deconvolution of these data
revealed a two-components kinetics. In addition to the prompt
component (i ) 1, τ1 < 20 ns), a second one could be detected
(i ) 2) with a lifetime of ca. 75 ns (the exact value depending
of the particular measurement) in the air-saturated solutions.
Figure 1 shows the LIOAS data for trans- and cis-DS in NH4-
CH3COO solution (at ϑâ*0 ) 5.5 °C) together with that for the
respective reference, the simulated curve, and the residuals. The
curves for the stilbenes at ϑâ)0 are also included. The decon-
volution results for all samples are summarized in Table 1.
In the first and second series with trans- and cis-DS there
was no indication of any resolvable kinetics. In this special case,
no deconvolution is necessary, and it is sufficient to use the
energy-normalized signal amplitude, Hn. Under these circum-
stances, æi in eqs 1 and 2 is simply replaced by the quotient
Fluorescence Quantum Yields. The fluorescence quantum
yields resulted to be < 10-2 for both DS isomers.
Determination of Φ∆. The determination of Φ∆ was
performed by comparing the near-IR emission upon photoex-
citation of aerated solutons of trans- and cis-DS with that of an
aerated solution of TSPP in tris buffer (pH ) 7.8) with Φ∆ )
0.62 ( 0.05.28
No near-IR luminescence signals were observed for trans-
and cis-DS in NH4CH3COO, although rather high energies were
applied (about 26 photons per trans-molecule and 12 photons
per cis-molecule initially present). From the amplitude of the
TSPP signal it is concluded that Φ∆ e 0.05 for both isomers.
The small Φ∆ e 0.05 is mainly due to kinetic reasons,
considering that DS triplet state is simply too short-lived to
generate O2(1∆g) by quenching in aqueous solutions. Assuming
a diffusion-controlled quenching obeying spin statistics, a
maximum O2(1∆g) generation rate of R∆ ) 1/9 k0 [O2] is
expected.29 With k0 ) 1.2 × 1010 M-1s-1 estimated with the
Hnsam/Hnref 2,3,26 For the data analysis ϑâ)0 and 5 °C were used.
.
The results were ∆Htc ) (35 ( 35) kJ/mol and ∆Vtc ) -(1.1
( 0.15) ml/mol.
Isomerization Quantum Yields. The isomerization quantum
yields were determined from absorption changes following
irradiation. The molar absorption coefficient for trans-DS

Structural Volume Changes upon Photoisomerization
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4817
TABLE 1: Data Derived from the Deconvolution of the LIOAS Signals (e.g., Figure 2) for the Triplet State Production
(Subindex 1, eq 2) and Decay (Subindex 2, eq 2) of DS in Aqueous Solutions of Various Cations and in Neat Watera
trans f cis
cis f trans
H2O
N(CH3)4
Cs+
fast component (triplet production)
-1.28 (( 0.05) -0.81 (( 0.05) -0.90 (( 0.05) -1.03 (( 0.10) -1.02 (( 0.10) -1.04 (( 0.05) -0.19 (( 0.10)
NH4
K+
Na+
NH4
+
+
+
Φ1∆VR,1 (ml/mol)
(τ1<20ns)
R1
0.65 (( 0.10)
0.53 (( 0.10)
0.52 (( 0.10)
0.54 (( 0.10)
0.61 (( 0.10)
0.56 (( 0.10)
0.42 (( 0.15)
slow component (triplet decay)
Φ2∆VR,2
0.52 (( 0.05)
0.37 (( 0.10)
0.17 (( 0.05)
0.45 (( 0.10)
0.34 (( 0.05)
0.38 (( 0.10)
0.44 (( 0.10)
0.42 (( 0.10)
0.45 (( 0.10)
0.38 (( 0.10)
0.35 (( 0.05)
0.44 (( 0.10)
0.54 (( 0.10)
0.63 (( 0.15)
(τ2 ) 75 ns ( 20 ns)
R2
a The two temperature analysis was applied.
Figure 2. Ψ vs nphot for both isomerization directions at 5 °C. The
slopes yield the respective quantum yields, Φtfc and Φcft, according
to eq 3. The inset shows a mixture spectrum as well as the contributing
isomer spectra.
Figure 3. Absorption changes at 350 nm, ∆A,350 of trans-DS in the
various aqueous solutions of monovalent salts, vs the incident photon
quantity. The initial absorbance was always A350 ) 0.300 ( 0.005.
Figure 1. LIOAS signals at 5.5 °C in aerated aqueous 90 mM NH4-
CH3COO solution (dotted lines) for (A) trans-DS, τ1 < 20 ns, æ1 )
0.15 ( 0.11; τ2 ) (75 ( 20) ns, æ2 ) 0.59 ( 0.11, and (B) cis-DS, τ1
< 20 ns, æ1 ) 0.35 ( 0.15; τ2 ) (75 ( 20) ns, æ2 ) 0.84 ( 0.15,
together with the respective reference (thick solid line), the simulated
curve (fine solid line), and the residuals of the fitting. In both panels,
the smallest signals (dashed line) are for the corresponding DS isomer
of Φ∆ e 0.05 in aerated aqueous DS solutions. Similar to the
present case, relatively low Φ∆ values have been reported for
trans-4,4′-dinitrostilbene in organic solvents, despite the high
intersystem crossing quantum yield.31
Discussion
at ϑâ)0 ) 3.1 °C. The reference solution shows a zero signal at ϑâ)0
.
The data obtained during the third series of experiments for
the two components of the LIOAS signal deconvolution after
excitation of trans- and cis-DS are collected in Table 1. The
quantum yields are necessary to determine ∆Vi and ∆Hi from
these data. Go¨rner and Kuhn14 discussed the photoisomerization
mechanism for nitrostilbenes, depicted in Figure 4. The intro-
Smoluchowski equation and [O2] in aerated water,30 a maximum
R∆ value of ca. 3.3 × 106 s-1 is calculated. Compared to the
decay rate of kT ) 1/(75 ns) ) 1.3 × 107 s-1, triplet quenching
by O2 can only contribute to T decay with ca. 3%, that is, the
expected value is in good agreement with the experimental value

4818 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Michler et al.
holds of course also for the ratio of the corresponding released
heat, R2
ΦtfT (Φ2∆VR,2 t
)
(R2)t
(R2)c
)
)
(6)
ΦcfT
(Φ2∆VR,2 c
)
Combination of eqs 4, 5, and 6 gives access to the efficiencies
of T decay (ηTfc and ηTft) and, thus, to the triplet formation
quantum yields because Φtfc ) ΦtfT ηTfc and Φcft ) ΦcfT
η
Tft. This calculation was possible because the isomerization
of DS could be measured in both directions (albeit under
restricted conditions for the cis isomer).
A prerequisite for the calculation is that there is no other
pathway of triplet deactivation, i.e., O2(1∆g) is not generated,
as was effectively shown.
A similar situation as for the structural volume change exists
for the energy release. The enthalpy difference between the two
isomers (∆Htc) and between these isomers and the triplet state
(∆HtT and ∆HcT) are derived using energy balance consider-
ations from the values Ri and the quantum yields according to
eq 7 again written for the trans f cis direction
Figure 4. Isomerization mechanism for nitrostilbenes.14,31-33
A
thermally equilibrated mixture (T) of the lowest trans triplet state, 3t*,
3
and the lowest perpendicular triplet state, p*, is formed. This figure
was adapted from Go¨rner and Kuhn (Scheme 3).14
duction of nitro groups strongly enhances intersystem crossing
and isomerization upon excitation of trans-4,4′-dinitrostilbene
occurs 100% from the triplet state.32 For DS in aqueous solution,
we have assumed that also from the cis isomer the photoi-
somerization involves mostly the triplet state. Thus, photoi-
somerization in both directions implies the triplet state mixture,
T, i.e., a thermal equilibrium is established between the lowest
trans triplet, 3t*, and the triplet of the perpendicular state,
3p*.32,33 According to Go¨rner and Kuhn14 the rate constant for
the step 3p*f1p is (1-3)×107s-1 (in organic solvents at room
temperature). Hence, the quantum yields for the first step
(establishment of the triplet equilibrium) and for the total process
(including the decay to the ground state of either the cis- or the
trans-isomer) are different. Using the decay efficiency from T
to cis (ηTfc) and T to trans (ηTft) with ηTfc + ηTft ) 1, the
products of quantum yields and structural volume changes for
the individual steps can be written as in eq 4. The subscripts, t
and c, indicate which isomer was excited
1
∆HtT )
(1 - (R1)t) Eλ
ΦtfT
1
∆Htc )
(1 - [(R1)t + (R2)t]) Eλ
(7)
Φtfc
The set of eqs 4-7 allows to transform the data in Table 1 to
the molar quantities summarized in Table 2.
The plot of the energy differences between the individual
isomers and the triplet state vs the structural molecular volume
change is shown in Figure 5A. The squares are for the trans f
cis direction (first six columns in Table 2) and the circles for
cis f trans (Table 2, last column). The filled symbols represent
the step from the initial isomer toward the triplet state (Table
2, upper panel) and the open symbols indicate the step from
the triplet state toward the respective opposite isomer (Table 2,
middle panel). For this reason, a central symmetry with respect
to the origin of the plot is found between points for the two
directions.
The energy of both isomers lies about 200 kJ/mol below the
triplet state [∆HcT ) (199 ( 50) kJ/mol and ∆HtT ) (215 (
38) kJ/mol], in good agreement with the values obtained from
the PM3 calculation (∆HcT ) 133 kJ/mol and ∆HtT ) 170 kJ/
mol, vide infra).
The most significant difference between the trans and cis
isomers is the change in molecular volume upon going to the
triplet state. The transition trans f T is associated with a
contraction of ∆VtT ) -(1.4 ( 0.15) ml/mol. A smaller
contraction of ∆VcT ) -(0.15 ( 0.15) ml/mol is found for the
cis f T step. The values for both the enthalpy differences and
the structural volume changes are averages of all available
values, i.e., ∆HcT and -∆HTc as well as ∆VcT and -∆VTc, and
the corresponding values involving the trans isomer, in Table
2 for all solutions and both isomerization directions.
The corresponding plot for the overall process is shown in
Figure 5B (Table 2, lower panel). The average values for the
total process including all series are ∆Vtc ) -(1.2 ( 0.1) ml/
mol and ∆Htc ) (28 ( 35) kJ.
(Φ1∆VR,1)t ) ΦtfT∆VtT
(Φ2∆VR,2)t ) ΦtfT(ηTfc∆VTc + ηTft∆VTt)
(4)
ΦtfT and ΦcfT are the quantum yields for the formation of T
coming from the trans and the cis side, respectively. The first
component (τ1 < 20 ns) is the production of T, whereas the
second component (with a lifetime τ2 and associated with Φ2
∆V2) comprises the changes upon T decay to trans and to
cis ground-state DS, with efficiencies ηTfc and ηTft, respec-
tively.
In general terms, ∆VAB is the structural volume change on
going from state A to state B (the same notation is used for the
enthalpies) and ∆VAB ) -∆VBA
.
On the other hand, eq 5 holds for the overall quantum yield
Φtfc∆Vtc ) (Φ1∆VR,1)t + (Φ2∆VR,2 t
)
(5)
The eqs 4 and 5 are written for the trans to cis direction. They
can readily be changed for the opposite direction by interchang-
ing the indices t and c.
According to eq 4, Φ2∆VR,2 obtained by excitation of trans-
and cis-DS, respectively, contains information on the formation
quantum yields of T in a manner that the ratio of these two
terms gives the ratio of the respective quantum yields. The same
Neither for the individual resolvable steps nor for the total
process, a systematic correlation between structural changes,
enthalpy difference, and the cation present could be found. This
finding was supported by the data from the series of measure-
ments in which only the LIOAS amplitudes were used for the

Structural Volume Changes upon Photoisomerization
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4819
TABLE 2: Molar Volume and Enthalpy Changes for the Triplet Production (Upper Panel), the Triplet Decay (Middle Panel),
and the Total Processa
trans f cis
cis f trans
Cs+
NH4
K+
Na+
NH4
+
+
+
H2O
N(CH3)4
ηTfc ) 0.70 ( 0.20
ΦtfT ) 0.70 ( 0.20
ηTft ) 0.30 ( 0.20
ΦcfT ) 0.85 ( 0.50
∆VtT (ml/mol)
∆VcT (ml/mol)
-0.20 (( 0.20)
-1.85 (( 0.55)
170 (( 105)
-1.15 (( 0.35)
230 (( 90)
-1.30 (( 0.40)
-1.50 (( 0.45)
225 (( 95)
-1.50 (( 0.45)
190 (( 105)
0.25 (( 0.45)
-185 (( 140)
-1.20 (( 0.15)
5 (( 95)
-1.50 (( 0.45)
215 (( 95)
∆HtT (kJ/mol)
∆HcT (kJ/mol)
230 (( 120)
235 (( 90)
∆VTc (ml/mol)
∆VTt (ml/mol)
1.50 (( 0.35)
0.25 (( 0.55)
-185 (( 140)
-1.60 (( 0.20)
-15 (( 95)
-0.20 (( 0.40)
-215 (( 130)
-1.35 (( 0.15)
15 (( 95)
0.10 (( 0.40)
0.25 (( 0.50)
-195 (( 130)
0.05 (( 0.50)
-215 (( 135)
-1.45 (( 0.20)
0 (( 95)
∆HTc (kJ/mol)
-165 (( 125)
∆HTt (kJ/mol)
-260 (( 290)
∆Vtc (ml/mol)
∆Vct (ml/mol)
1.30 (( 0.30)
-1.20 (( 0.15)
-1.25 (( 0.15)
∆Htc (kJ/mol)
∆Hct (kJ/mol)
-30 (( 265)
70 (( 90)
30 (( 95)
a The data from Table 1 were processed using the quantum yields Φtfc and Φcft (eq 3) and the efficiencies ηΤfc and ηΤft (eqs 4 and 5).
isomerization. Also, in this case, all points were in the “cloud”
formed by the overlapping error bars. In addition, attempts to
correlate enthalpy and volume changes (see ref 9) determined
in the two series in which measurements were carried out with
various cations, led to similar but unrealistic fit results. We
attribute the false apparent correlation to error compensations.34
These arguments strongly indicate that in this case no compen-
sation effect between ∆H and ∆V is observed, in contrast to
previous findings for other systems.9
The most important feature of the isomerization process for
both cis- and trans-DS is that the triplet production is always
linked to a contraction (cf. the values quoted above), whereas
the triplet decay always results in an expansion.
To understand the origin of this behavior the electrostatic
interaction resulting in electrostriction between DS and the
solvent molecules was calculated.1,4,7,35,36 Within the frame of
the electrostriction theory, the molecule is regarded as a hard
sphere interacting with the solvent assumed to be a continuum
of dielectric constant ꢀ. This treatment leads to the Drude-
Nernst equation originally developed for purely Coulombic
(monopole) interactions4
(ze)2 ∂(ꢀ-1)
1
2
z2
r
∆Velect
)
) -B
(8)
r
∂p
z is the charge, r is the molecule radius, and p is the pressure.
This equation can easily be converted into eq 9 for the case of
dipole interactions37
Figure 5. (A) Enthalpy difference, ∆HAB between the individual
isomers and the triplet state vs the structural molecular volume change,
∆VAB. (9) ∆HtT vs ∆VtT, for the trans f T transition, (0) ∆HTc vs
∆VTc, for the T f cis transition, derived from the analysis of the 1st
and 2nd component, respectively, of the LIOAS signal upon trans-DS
excitation. (b) ∆HcT vs ∆VcT, for the cis f T transition, (O) ∆HTt vs
∆VTt, for the T f trans, from the LIOAS signal upon cis-DS excitation.
(B) Enthalpy differences between the isomers vs. their molecular
volume differences: (9) ∆Htc vs ∆Vtc, for the isomerization trans f
cis, (b) ∆Hct vs ∆Vct, for the isomerization cis f trans.
2 ∂(ꢀ-1)
3 µ
∆Vµelect
)
(9)
3
4
∂p
r
with µ the dipole moment. The Drude-Nernst equation can be
transformed using the Clausius-Mossotti equation to circumvent
the use of ∂(ꢀ-1)/∂p for which not many reliable values can be
found in the literature.5,7 However, the Clausius-Mossotti
equation is only valid for non polar solvents. For polar solvents
the underlying model does not hold inasmuch as compression
of the regarded molecule also plays a role. Taking this into
account, eq 10 is obtained upon expanding the electrostriction
evaluation. In the corresponding figure (equivalent to Fig 5B,
not shown) a randomly different distribution of the data points
for the various cations was found for the trans f cis photo-

4820 J. Phys. Chem. A, Vol. 105, No. 20, 2001
Michler et al.
TABLE 3: Total Binding Energy, H0, Dipole Moment, µ,
and C7-C8 Bond Length, l, Calculated Using the PM3
Semiempirical Method
DS in
perpendicular
trans-DS
triplet state
cis-DS
H0 (kJ/mol)
µ (D)
l (Å)
-1065
0.05
1.343
-895
4.08
-1028
4.11
1.335
1.434a
a The bond length, l, for the perpendicular state is not comparable
in the sense that there is no double bond in this case.
considerations to the dipole interaction37
∂(ꢀ-1) ∂(ln r)
1 z2e2
2 r
∆Velect
)
+
+
(
)
∂p
∂p
∂(ꢀ-1) ∂(ln r)
2
3 µ 1
2
+
(10)
(
)
3
2
∂p
∂p
r
The first term in parentheses of the sum in eq 10 reflects
Coulombic interactions, the second is due to dipole interactions.
Terms of higher order are neglected here. ∂(ꢀ-1)/∂p refers to
the solvent effects and ∂(ln r)/∂p describes changes in molecular
size due to the force exerted on the molecule by the solvent.
The complex structure of eq 10 is reflected in the fact that
the value calculated in water with eq 8 (B ) 4.175 Å ml/mol)
must be replaced by a significantly higher semiempirical value,
Bemp ) (9.6 ( 1.5) Å ml/mol,35,36 that is, the measured volumes
are due not only to solvent reorganization without a volume
change of the molecule itself (very first term in eq 10).
Notwithstanding the above problems, a rough estimation of
the electrostriction was made by assuming Bemp to be valid for
our system in order to calculate ∂(ln r)/∂p with eq 10. The dipole
term in eq 10 is the appropriate term to describe the electro-
striction volume changes upon a change in the dipole moment.
This term is very sensitive to the molecular radius, r. A spherical
molecule was assumed which is justified for cis-DS (r ≈ 6 Å)
but not for trans-DS where a cylindrical shape (14 Å × 10 Å)
is found. Thus, ∆Vµ
was calculated not only with r ) 6 Å,
elect
Figure 6. PM3 optimized geometries for (A) trans-DS, (B) DS in its
perpendicular triplet state, and (C) cis-DS.
but also with 3 Å. Using the calculated value µ ) 4 D (cf.
Table 3) as well as the approximation r ≈ 6 Å, a volume change
due to electrostriction of ca.-0.1 mL/mol is obtained for the trans
f cis transformation. With the extreme value of r ) 3 Å (as a
minimum value in view of the flat form of the trans cylinder)
and the upper error limit of Bemp, however, an upper limit of
|∆Vµelect| e 0.7 ml/mol is obtained. It is clear that the empirical
value Bemp should also contain specific interactions between the
molecule and its solvent environment, e.g., H-bridges. However,
the volume changes calculated with Bemp, are not big enough
to explain the molar values of ∆VAB for DS even if Bemp reflects
such interactions.
Whatever the quantitative explanation for the value of the
structural volume change is, should specific stilbene-water
interactions be responsible for the observed effects, changes in
the water structure would affect the results.9,38 However, the
experiments in the presence of monovalent cations (of organiz-
ing and unorganizing nature) yield all, within the error limits,
the same results as those of the experiment with trans-DS in
neat water (Figure 5). Although in the solutions with added salt
the DS anions (always at ca. 10-5 M) should be mostly
surrounded by the countercations, no influence of the nature of
the cation upon photoisomerization was detected. These results
indicate that the contraction observed should be mainly attributed
to intrinsic effects, as it was the case with the Ru(bpy)3+2 cation
in water.9
Contrary to the large expected shortening of the Ru-N bonds
in Ru(bpy)3+2 upon photoexcitation, only a small shortening of
the CdC bond was calculated for the trans f cis DS
photoisomerization (Table 3). However, a rough calculation
using the dimensions of both DS isomers, i.e., a cylinder for
the trans and a sphere for the cis isomer, affords molecular
volumes of 662 and 544 Å3, respectively, pointing to a large
contraction from trans to cis, although this is a very crude
estimation which does not consider the accessibility of the water
molecules. Therefore, we attribute at most 50% of the total
structural volume change to electrostriction and the rest to an
intrinsic volume change. Although very approximate, this picture
explains the lack of effect of the salt variation as well as the
sign of the observed effects.
Thus, the values obtained for the stepwise structural volume
changes may be accounted for by analyzing the structure of
the isomers and that of the intermediate state. The trans molecule
possesses the largest intrinsic volume (and the highest conjuga-
tion). Hence, in this case, a loss in conjugation (as indicated by
the somehow shorter CdC double bond in the cis isomer, Table
3) is concomitant with a decrease in volume leading to a
contraction. A gain in conjugation, on the contrary, leads to an
expansion. According to this line of arguments we should have
observed much larger volume changes. The water accessibility,

Structural Volume Changes upon Photoisomerization
J. Phys. Chem. A, Vol. 105, No. 20, 2001 4821
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larger for the trans than for the cis isomer, however, might
compensate the effect to a certain degree.
The above arguments indicate that the states in equilibrium
forming the intermediate T (the triplet perpendicular state 3p*,
devoid of conjugation of the C7-C8 bond, in equilibrium with
3
the lowest trans triplet state t*) have in average a structure
more similar to the cis isomer than to the trans one because
the contraction for the step trans f T is larger than that for the
cis f T.
The only other determination of a structural volume change
upon a stilbene isomerization known to us is that of the water
insoluble trans-stilbene in mixtures of nonpolar solvents. The
contribution of ∆VR to the LIOAS signal could not be separated
in these mixtures. An expansion of 5.6 mL/mol was reported
for the trans f cis photoreaction in micellar solutions.39 No
results were reported for the cis f trans photoisomerization in
this molecule. In view of the differences in photochemical
mechanisms (the trans-cis photoisomerization in stilbene occurs
through a singlet mechanism vs the triplet mechanism in the
nitrostilbenes14), and the differences in media it makes no sense
comparing our present data with those by Herman and Good-
man.39
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Regarding the enthalpy difference between both DS isomers,
geometry optimization performed by PM3 calculations (cf. Table
3, and Figure 6)40 indicate that the energy of trans-DS in the
gas-phase lies 37 kJ/mol below that of cis-DS. This is in
agreement with the experimental data, notwithstanding the large
error, ∆Hct ) -(28 ( 35) kJ/mol, vide supra. The comparison
between the experimental and the calculated value is justified
because the calculated change in dipole moment upon photo-
excitation is very small and no big changes in the electrostatic
interactions with the medium upon photoisomerization are
expected (as shown by the calculations presented above).
Acknowledgment. We are indebted to Dr. Helmut Go¨rner
for many fruitful discussions, to Dr. Paul Verhoeven for
preliminary molecular mechanics calculations, and to Professor
Kurt Schaffner for his continuous support of this project. We
are very grateful to Gul KoH-Weier for the separation of the
DS isomers by HPLC and acknowledge the able technical
assistance of Gudrun Klihm, Dagmar Lenk, and Sigrid Russell.
Miguel Angel Rodr´ıguez was a fellow of the Alexander von
Humboldt Foundation (1998 and 2000) and Alessandro Feis was
recipient of an EU fellowship (1995).
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