Physical chemistry of the lowest excited singlet state of trans-stilbene in solution as studied by time-resolved Raman spectroscopy

c. Jpn.

Bull. Chem. Soc. Jpn., 75, 883–897 (2002)

883

e Chemical

ciety of Ja-

n

e Chemical

ciety of Ja-

n

Accounts

Physical Chemistry of the Lowest Excited Singlet State of trans-Stilbene

in Solution as Studied by Time-Resolved Raman Spectroscopy

02

3

7

SJA8

09-2673

325

H. Hamaguchi et al.

Hiro-o Hamaguchi* and Koichi Iwata

Department of Chemistry and Research Centre for Spectrochemistry, School of Science, The University of Tokyo,

7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033

01

02

(Received November 20, 2001)

Structure and dynamics of the lowest excited singlet state of trans-stilbene (the S₁state of tSB) in solution are dis-

cussed with an emphasis placed on the elucidation of the mechanism of the trans–cis photoisomerization. Structure of S₁

tSB in solution is ﬁrst discussed based on the time-resolved Raman spectral data and their isotope substitution effects.

Original data for an asymmetrically deuteriated tSB, tSB-d₅, are presented to conﬁrm the ethylene-like structure of the

central C–C linkage of S₁tSB. Next, the time-, temperature-, and solvent-dependent band shape changes of the oleﬁnic

CwC stretch band are discussed in terms of the solvent induced dynamic polarization. It is shown that the dynamic polar-

ization model accounts very well, not only for the observed band shape changes, but also for their relevance to the

isomerization mechanism. A new microscopic view on the photoisomerization of tSB is thus presented. Picosecond en-

ergy dissipation process of S₁tSB is then discussed in relation to the microscopic solvation structure in chloroform. Fi-

nally, the mechanism of a new bimolecular reaction between S₁tSB and carbon tetrachloride is discussed on the basis of

the diffusion-controlled reaction model.

.3

.9

The cis–trans photoisomerization of oleﬁns is one of the

simplest chemical reactions that can be initiated by light. Us-

ing ultrashort laser pulses for photoexcitation and probing, we

are now able to trace the whole process of photoisomerization

by various time-resolved spectroscopies. Unprecedented op-

portunities of looking at a reaction in its real time-course are

now open to us. trans-Stilbene is a prototype oleﬁn that exhib-

its photoisomerization. Both the trans and the cis isomers of

stilbene (tSB and cSB) are stable in the ground state and no in-

terconversion takes place at room temperature. Photoexcita-

tion of tSB with near-ultraviolet light results in the formation

of cSB with a quantum yield of about 0.5. This photoisomer-

ization of tSB is known to proceed via the lowest excited sin-

glet (S₁) state.¹Being the key intermediate of photoisomeriza-

tion, S₁tSB has been stimulating the ﬁeld of time-resolved

spectroscopy continuously for both the electronic and the vi-

brational degrees of freedom. The isomerization kinetics of S₁

tSB can be studied directly by time-resolved ﬂuorescence

spectroscopy. Since the isomerization rate in the S₁state is

much larger than the radiative decay rate and the rates of the

other non-radiative decay processes, the observed ﬂuorescence

decay rate is approximately equal to the rate of isomerization.

Numerous time-resolved ﬂuorescence studies were thus per-

formed in the last two decades for S₁tSB in a wide range of

environments, from the isolated molecule in a supersonic jet to

the solvated molecules in polar and non-polar solvents. These

studies were already collected in two comprehensive re-

views.^2,3Brieﬂy summarizing, the observed temperature-de-

pendent rates of isomerization were ﬁt to the Arrhenius-type

formula to give the frequency factors (pre-exponential factors),

which then, were interpreted in terms of various statistical

models. The RRKM model was most often used for the isolat-

ed molecule and the Kramers model and its modiﬁcations were

the choice for the solvated molecules.³The results indicate

that the agreement between the experiment and theory is not

global. In particular, the marked solvent dependence of the S₁

tSB isomerization is yet to be elucidated on new experimental

and theoretical bases. Meanwhile, the present authors concen-

trated on Raman spectroscopy of S₁tSB in solution in order to

look at the photoisomerization process from the viewpoint of

structural chemistry. As is well established, Raman spectros-

copy is the most sensitive structural probe of short-lived inter-

mediate species in solution.^4–6Any correlation between the

isomerization dynamics and the molecular structure is likely to

be manifested in the Raman spectrum. In the present Account,

we focus on our time-resolved Raman spectroscopic investiga-

tions of S₁tSB in solution. The primary objective is to intro-

duce a structural perspective of the S₁tSB photoisomerization.

Two other topics related to S₁tSB, the solvent/solute interac-

tion and the new photochemistry with carbon tetrachloride are

also included.

Raman spectroscopy of S₁tSB started in the year 1983,

884 Bull. Chem. Soc. Jpn., 75, No. 5 (2002)

ACCOUNTS

when two independent papers were published simultaneously.

The Standard Oil group in the US (Gustafson et al.) used a

high repetition-rate ampliﬁed dye laser system to obtain a pi-

cosecond transient Raman spectrum of S₁tSB in hexane.⁷The

Tokyo group (Hamaguchi et al.) used low repetition-rate (10

Hz) nanosecond lasers and observed the same S₁Raman spec-

trum of tSB in hexane.⁸The latter work demonstrated that

Raman spectroscopy of a picosecond-lived excited state was

still possible using nanosecond lasers, provided that the pump

peak power was sufﬁciently high to ensure a detectable popu-

lation of the excited state. After these papers were published,

S₁tSB has been repeatedly studied by many groups using tran-

sient and time-resolved (spontaneous and coherent) Raman

spectroscopy.^9–49There is a good reason why S₁tSB is chosen.

The strong S₁← S₀absorption of tSB is located in the near ul-

traviolet region and an even stronger S_n← S₁absorption band

lies around 600 nm. These locations of absorptions facilitate a

convenient experimental set-up in which the second harmonic

(~300 nm) of a picosecond dye laser is used for photoexcita-

tion, while the fundamental (~600 nm) is used for probing res-

onance Raman scattering from the S₁state. Furthermore, S₁

tSB is not too strongly ﬂuorescent in the wavelength region

near 600 nm, where Raman scattering is to be detected. The

early transient Raman works were devoted to establishing the

vibrational assignments of S₁tSB through the use of the isoto-

pic substitution technique. Structure of S₁tSB was thus char-

acterized on the basis of these vibrational assignments.⁵Then,

the focus moved to the ultrafast time-dependent spectral

changes which had been predicted from the probe-laser power

dependence of the nanosecond transient Raman spectrum.¹⁴It

was only in 1992, ten years after the ﬁrst demonstration of the

S₁tSB transient Raman spectrum, that the predicted time de-

pendence was actually observed by real picosecond time-re-

solved experiments.^21,22The discovery of this ultrafast phe-

nomenon led many researchers to go further into the Raman

spectroscopy of S₁tSB. More recent studies measure the time-

resolved Raman spectra in the anti-Stokes region to obtain in-

formation on the vibrational relaxation dynamics. The analy-

sis of the Raman excitation proﬁles by Nakabayashi, Okamoto,

and Tasumi has shown that the vibrational relaxation of S₁tSB

is very fast so that the v = 1 state of the oleﬁnic CwC stretch

vibration is formed within a few picoseconds after the photo-

excitation.⁴²Transient and time-resolved Raman studies have

also been extended to trans-stilbene in the lowest-excited trip-

let state.^50,51

Fig. 1. Schematic diagram of the adiabatic potential curves

accounting for the stilbene photoisomerization.

then thermally activated to go over the barrier in 30–100 ps

time scale to generate a perpendicular singlet state, which is

internally converted very rapidly (< 1 ps) to the ground-state

with the same perpendicular conﬁguration. Thus, the trans to

perpendicular isomerization serves as the simplest model for

the thermally activated reaction process. On the ground-state

potential curve, the perpendicular conﬁguration relaxes to the

trans and cis conﬁgurations with nearly a 50/50 ratio. This

scheme explains the observed photoisomerization quantum

yield close to 0.5. The barrier to the trans-perpendicular rota-

tion was ﬁrst explained theoretically in terms of an avoided

crossing between the π–π* S₁state, which has a potential min-

imum at the trans conﬁguration, and a higher-lying singlet

state, called here the Z state, which has a potential minimum at

the perpendicular conﬁguration.⁵³Since then, the electronic

structure of tSB in the lowest excited singlet manifold and its

relevance to the isomerization mechanism has been an issue in

quantum chemistry.⁵⁴Here, we do not go into the details of

these quantum chemical studies but note that the Z state is like-

ly to be a highly polar zwitterionic state.^55,56The cis to trans

isomerization is thought to proceed in a similar way via the

perpendicular singlet state. In this cis case, the isomerization

rate is much larger than that of the trans, because of a much

lower barrier to the internal rotation.

Raman Spectra and Structure of S₁tSB in Solution

The presently accepted view on the stilbene photoisomer-

ization is based on the adiabatic potential curves schematically

shown in Fig. 1.⁵²In the ground electronic state (S₀), there is a

large potential barrier separating tSB and cSB. The two

ground-state isomers are therefore stable and are not inter-

changeable with each other at room temperature. The excited

singlet potential curve has a deep minimum at the (90 degree

twisted) perpendicular conﬁguration and shallow minima at

the trans and cis conﬁgurations. The barrier to the trans-per-

pendicular rotation is reported to be 2–4 kcal mol⁻¹depending

on the solvent and is signiﬁcantly higher than that to the cis-

perpendicular rotation (at most 1 kcal mol⁻¹). If S₀tSB is

photoexcited in solution, vibrationally-relaxed S₁tSB is

formed in 10–20 picoseconds (see the discussion below). It is

The ﬁrst step for elucidating the tSB photoisomerization is

to establish the structure of the key intermediate, S₁tSB. Ra-

man spectrum has so far been the only source of information

on the structure of S₁tSB in solution. A representative Raman

spectrum of S₁tSB in heptane is shown in Fig. 2. More than

ﬁfteen Raman bands are observed with high S/N ratios. The

vibrational assignments of these bands were carried out

through the use of isotopic frequency shifts.⁵The results are

listed in Table 1, together with the ¹³C shift values reported by

Gustafson et al.¹⁵The primary concern here is the vibrational

assignments of the oleﬁnic vibrations and the structural infor-

mation coming therefrom. There are three Raman-active ole-

ﬁnic vibrations to be considered; the central CwC stretch vibra-

H. Hamaguchi et al.

Bull. Chem. Soc. Jpn., 75, No. 5 (2002) 885

Fig. 2. Transient Raman spectrum of S₁trans-stilbene measured at 50 ps after the photoexcitation in heptane. Pump and probe

wavelengths are 294 nm and 588 nm.

Table 1. Observed Raman Shifts of S₁trans-Stilbene and S₁trans-Stilbene-¹³C, and Their

Mode Assignments

Raman shift/ cm⁻¹

S₁α,αꢀ-¹³C-trans-stilbene^b)

Assignment^a),c)

oleﬁnic CwC str

ring str

S₁trans-stilbene^a)

1570

1534

1470

1457

1424

1333

1242

1182

1150

1079

980

1521

1545

ring str

1418

1331

1236

1144

1169

1075

976

ring str + CH def

oleﬁnic CH def

C-Ph str

ring CH def + C–Ph str

ring CH def

trigonal + breath

ring def + CwC–C def

ring def

845

619

834

620

285

287

C–C₀def

198

194

CwC–C def

a) Present study in heptane. b) Ref. 15. c) Ref. 57.

tion, the symmetric C–Cph stretch vibration, and the symmet-

ric C–H in-plane bend vibration. They are all characterized by

their sensitivity to the ¹³C substitution of the oleﬁnic carbons.

In the Raman spectrum displayed in Fig. 2, a strong band is ob-

served at 1570 cm⁻¹. As is shown later, this band shows sig-

niﬁcant shifts of the peak position depending on time, solvent,

and temperature and is therefore called the “~1570 cm⁻¹

band” in the following. The ~1570 cm⁻¹band shows a large

¹³C shift of 45 cm⁻¹, which is 74% of the theoretical ¹³C shift

for the pure CwC stretch. It is therefore assigned to the oleﬁnic

CwC stretch vibration. The bands at 1242, 1182, 1150, and

ent groups using empirical⁵⁷as well as quantum-chemical

force ﬁelds.^58,59They all show that the three oleﬁnic vibrations

mix signiﬁcantly with one another and that the magnitude of

mixing depends strongly on the force ﬁeld. Due to the lack of

a reliable force ﬁeld, however, the details of these mode mix-

ings still remain unclear and the experimental vibrational as-

signments in Table 1 have not been fully supported by normal

coordinate analysis. In fact, a recent quantum chemical calcu-

lation by Negri et al.⁵⁹has suggested a drastic change of the

structure of tSB on going from the S₀to the S₁state. Accord-

ing to their calculation, the central part of S₁tSB is not ethyl-

ene-like but somewhat butadiene-like rather; the calculated C–

Cph bond length (1.403 Å) is shorter than the CwC length

(1.493) in the S₁state. Such calculated structural changes have

led Negri et al. to assign the ~1570 cm⁻¹band to the C–Cph

stretch vibration which is supposed to be a double bond ac-

cording to their calculation. This assignment, however, is not

845 cm⁻¹show small but signiﬁcant ¹³C shifts (5–10 cm⁻¹

)

and are assigned to the vibrational modes that have contribu-

tions from the three oleﬁnic vibrations. All the other bands

showing no or much less ¹³C shifts are safely assigned to the

ring vibrations.

Normal coordinate analyses have been carried out by differ-

886 Bull. Chem. Soc. Jpn., 75, No. 5 (2002)

ACCOUNTS

Fig. 3. Transient Raman spectrum of S₁trans-stilbene (upper

trace) and S₁trans-stilbene-d₅(lower trace) measured at 50

ps after the photoexcitation in heptane.

Fig. 4. Time dependence of the ~1570 cm⁻¹band of S₁

trans-stilbene measured in chloroform. Delay time for

each trace is shown in the ﬁgure.

compatible with our new Raman data on an asymmetrically

substituted tSB, tSB-d₅, in which one of the two phenyl rings is

deuteriated. In tSB-d₅, there are two different C–Cph bonds,

C–Cph-d₀and C–Cph-d₅and hence two different C–Cph

stretch frequencies. A Raman band contributed signiﬁcantly

by the C–Cph stretch vibration should show a splitting or, at

least, a broadening on going from tSB to tSB-d₅. As shown in

Fig. 3, the ~1570 cm⁻¹band of S₁tSB does not show either a

splitting or a broadening. In stead, the three Raman bands near

1200 cm⁻¹change markedly on going from the normal tSB to

tSB-d₅. From these observations we conclude that the C–Cph

stretch mode does not contribute signiﬁcantly to the ~1570

cm⁻¹band and that its contribution is distributed among the

three vibrations located around 1200 cm⁻¹. The assignment of

the ~1570 cm⁻¹band to the CwC stretch vibration is thus

strongly supported. Considering the fact that the frequency

~1570 cm⁻¹falls in the frequency region of a CwC double

bond, we conclude that S₁tSB has an ethylene-like structure

with a slightly reduced CwC bond order. Note that the CwC

stretch frequency in the S₀state is 1639 cm⁻¹. The frequency

decrease of 70 cm⁻¹on going from S₀to S₁is signiﬁcant but

not large enough to rationalize the rotation around the CwC

bond in the S₁state.

ments by Hester et al.²⁵and Qian et al.²⁶have conﬁrmed that

the spectral changes are in fact due to the vibrational cooling

of photogenerated “hot” S₁tSB. Figure 5 compares the delay-

time dependence of the peak position of the ~1570 cm⁻¹band

and the observed anti-Stokes/Stokes intensity ratio of the 285

cm⁻¹band, which is proportional to the temperature.³⁸The

time dependence of the peak position agrees very well with

that of the temperature, indicating that the peak position

changes linearly with temperature.

Why does the ~1570 cm⁻¹(CwC stretch) band of S₁tSB

change with temperature? A naive answer to this question

would be to assume the contributions from the hot transitions

(inhomogeneous broadening). At higher temperatures, many

low-frequency modes of S₁tSB are thermally excited and, if

the CwC stretch vibration is anharmonically coupled with

Analysis of the Time- and Solvent-Dependent Raman Spec-

tral Changes of S₁tSB

Time-Dependent Raman Spectral Changes and Vibra-

tional Cooling. The time-dependent Raman spectral chang-

es of S₁tSB in chloroform are shown in Fig. 4. As the delay

time between the pump and probe pulses increases, the peak

position of the ~1570 cm⁻¹band shifts to higher frequency

and, concomitantly, the bandwidth decreases. A similar

change is found also for the 1180 cm⁻¹band, though in a much

less magnitude (not shown in Fig. 4). These time-dependent

spectral changes were ﬁrst predicted from the probe-power de-

pendence of the nanosecond transient Raman spectra (optical

depletion timing) and were ascribed to the formation of “hot”

S₁tSB by photoexcitation.¹⁴Time-resolved Raman measure-

Fig. 5. Time dependence of the peak position of the ~1570

cm⁻¹band (ﬁlled triangles, left axis) and the anti-Stokes/

Stokes intensity ratio of the 285 cm⁻¹band (open circles,

right axis) of S₁trans-stilbene in chloroform.

H. Hamaguchi et al.

Bull. Chem. Soc. Jpn., 75, No. 5 (2002) 887

Fig. 6. Relationship between the peak position (Ω) and the

bandwidth (Γ ) of the ~1570 cm⁻¹band of S₁trans-stil-

bene measured in heptane at various delay times. Delay

time for each point is indicated in the ﬁgure. Data points

marked with crosses are those used for least squares ﬁtting

analysis. The result of the ﬁtting is shown with a solid line.

Fig. 7. Solvent dependence of the ~1570 cm⁻¹band of S₁

trans-stilbene measured at 50 ps. Used solvent for each

trace is indicated in the ﬁgure.

these low-frequency modes, the ~1570 cm⁻¹band shape may

well change with temperature, reﬂecting the distributed fre-

quencies of the hot transitions. A detailed band-shape analy-

sis, however, has indicated that the shape of the CwC stretch

band of S₁tSB is always a Lorentzian, regardless of the delay

time and therefore regardless of temperature. It is unlikely that

the frequency distribution of the hot transitions is always acci-

dentally a Lorentzian. The Lorentzian band shapes are more in

shape in seven different alkanes. A monotonic up-shift of the

peak position and a less clear but meaningful band narrowing

are concomitantly observed on going from hexane to hexade-

cane. These spectral changes are found to be very similar to

the temperature-dependent changes described above in the

sense that the band shape is always a Lorentzian and that a Ω–

Γ linear relationship holds. It seems that the time- and solvent-

dependent CwC band shape changes of S₁tSB originate from

the same molecular mechanism.

harmony with a homogeneous broadening mechanism.

A

least-squares ﬁtting analysis using a Lorentzian function gives

precise values of the peak position Ω and the bandwidth Γ of

the CwC stretch Raman band at a certain delay time. The Ω

and Γ values thus determined for 14 delay times are plotted in

Fig. 6. The plot shows that a linear relationship holds between

these two quantities. It is likely that the deviation from the lin-

ear relationship, observed between 0 ps and 5 ps, is caused by

the temporally overlapping pump electromagnetic ﬁeld, which

affects both the position and width of the S₁tSB Raman bands

including the ~1570 cm⁻¹band.⁴⁹Such a linear relationship

between Ω and Γ is also obtained in a wider temperature range

from the results reported by Hester et al.²⁵This unexpected

linear relationship between Ω and Γ led the present authors to

set up a new model to account for the observed temperature

dependence of the S₁tSB Raman spectrum.

It has also been found that the observed solvent-dependent

spectral changes are correlated very closely with the isomer-

ization dynamics. Figure 8 shows a plot of the observed peak

Solvent-Dependent Raman Spectral Changes and the

trans-perpendicular Isomerization. As mentioned earlier,

the rate of trans-perpendicular isomerization of S₁tSB de-

pends strongly on the solvent. If there is any manifestation of

the isomerization dynamics in the observed Raman spectrum

of S₁tSB, it should be solvent-dependent. We therefore exam-

ined the solvent dependence of the S₁Raman spectra in detail

both in alkane solutions²⁴and in alcohol solutions.⁶⁰In both

classes of solvents, marked changes were found for the CwC

stretch band. Figure 7 shows the change of the CwC band

Fig. 8. Relationship between the peak position (Ω) of the

~1570 cm⁻¹band and trans-perpendicular isomerization

rate constant (k_iso) of S₁trans-stilbene measured in various

normal alkane solvents. Number of carbon atoms in al-

kane molecules for each data point is shown in the ﬁgure.

888 Bull. Chem. Soc. Jpn., 75, No. 5 (2002)

ACCOUNTS

position Ω against the rate of isomerization k_isowhich was de-

termined separately by picosecond time-resolved ﬂuorescence

spectroscopy. We see a clear linear relationship between Ω

and k_iso. A similar linear relationship should hold between Γ

and k_isobecause Ω is linearly correlated with Γ. This Ω–k_iso(or

Γ–k_iso) linear relationship is totally unexpected; there is no ob-

vious reason why the peak position (= vibrational frequency)

Ω or the bandwidth Γ should be linearly correlated with the

rate of isomerization k_iso. If we extrapolate the Ω–k_iso(or Γ–

k_iso) linear relationship to k_iso= 0, we obtain the intrinsic val-

ues of Ω (or Γ ) which should be regarded as the peak position

(or bandwidth) that is not affected by the isomerization dy-

namics. By using these intrinsic values of the peak position

and the bandwidth, we can convert the observed Ω and Γ val-

ues to the change of the peak position ∆Ω and the increase in

the bandwidth ∆Γ. The ∆Ω and ∆Γ values then represent the

“net” effect of the isomerization dynamics on the shape of the

CwC Raman band. Note that the linear relationship between Ω

and Γ is transferred to that between ∆Ω and ∆Γ. The Ω–k_iso(or

Γ–k_iso) relationship is transferred to the ∆Ω–k_iso(or ∆Γ–k_iso) re-

lationship as well.

Fig. 9. Schematic diagram for the exchange between the C–

C stretching frequency (ω₁) and the C–C stretching fre-

quency (ω₂) caused by solvent induced dynamic polariza-

tion between the S₁state and the Z state.

this asymmetric exchange limit, which we believe is the case

with S₁tSB in solution, the CwC angular frequency stays at ω₁

for most of the time and it occasionally hops to ω₂but comes

back very quickly to ω₁(Fig. 9). In other words, the tSB mol-

ecule is in the S₁state for most of the time and it occasionally

hops to the Z state but it returns to the S₁state very quickly be-

cause of the very short duration of the collision. The second

condition, W₁<< |δω| or |δω| /W₁>> 1, means that the hop

from ω₁to ω₂occurs only occasionally so that there is no rela-

tion between any two consecutive hops. The band shape in this

limit is given by a Lorentzian with a shift of the peak position

Ω and an increase in the bandwidth Γ from the unperturbed

CwC stretch band shape;⁶³

Solvent-Induced Dynamic Polarization, Vibrational

Dephasing, and the CwC Stretch Band Shape.

We now

consider theoretically the two newly observed features of the

CwC Raman band shape changes of S₁tSB in solution. 1) The

change of the peak position ∆Ω and the increase in the band-

width ∆Γ are correlated with each other making a linear ∆Ω–

∆Γ relationship. This is true for both the temperature- and sol-

vent-dependent changes. 2) The band shape changes are corre-

lated with the isomerization dynamics. A linear ∆Ω–k_iso(or

∆Γ–k_iso) relationship has been obtained.

The isomerization dynamics is most likely to be related to

the interaction of the S₁state with the nearby Z state (see Fig. 1).

How can the CwC stretch frequency of S₁tSB be correlated

with the interaction with the Z state? Or how can the vibra-

tional dephasing (band width) of the CwC stretch mode be cor-

related with the interaction with the Z state? We have pro-

posed a model based on the idea that the CwC stretch frequen-

cy is stochastically modulated by the time-dependent polariza-

tion of the S₁state (termed dynamic polarization). According

to this model, the ﬂuctuation of the solvent ﬁeld affects the en-

ergy gap between the S₁and Z states and hence the Z state is

occasionally mixed into the S₁state by time-dependent pertur-

bation. The CwC stretch angular frequency then changes sto-

chastically between the two limiting values, the CwC double-

bond angular frequency ω₁in the S₁state and the C–C single-

bond angular frequency ω₂in the Z state (ω₁> ω₂). Both the

short-range Lennard-Jones type interaction and the long-range

Coulombic interaction are likely to cause the dynamic polar-

ization.

∆Ω = W₁τ/(1 + τ²),

∆Γ = W₁τ²/(1 + τ²),

(1)

(2)

where τ = δω/W₂represents the mean phase shift for one hop.

Note that 1/W₂is the mean time that tSB stays in the Z state

and the product of this mean time with the angular frequency

difference δω makes the mean phase shift for a hop. A large τ

value (|τ|>> 1) means that there is no phase memory after a

hop. For this case, Eqs. 1 and 2 give ∆Ω = 0, ∆Γ = W₁, in

agreement with the ordinary collision-broadened band shape

theory. Note that W₁corresponds to the collision frequency in

the gas phase experiment. For τ = 0, we have no effect of the

hop as expected. For |τ| < ~1, ∆Ω and ∆Γ are the functions

of two quantities W₁and τ and they satisfy the relation ∆Γ =

τ∆Ω. This relation indicates that, under a condition where the

mean phase shift τ is regarded as constant, a linear relationship

holds between the change of the peak position ∆Ω and the in-

crease in the bandwidth ∆Γ.

Inversely, the observed linear relationship between ∆Ω and

∆Γ of S₁trans-stilbene can be considered to be a consequence

of the constant mean phase shift τ for both the temperature-

and solvent-dependent changes under our experimental condi-

tions. It is likely that, in a small temperature range, the charac-

teristics of the solute–solvent interaction do not change much

except for the frequency of solvent ﬂuctuation that corresponds

to W₁. We can assume that the mean phase shift τ stays con-

stant, while the forward hopping rate W₁increases with in-

creasing temperature. Equations 1 and 2 then account for the

In the following, we ﬁrst adopt the simplest model in which

the CwC angular frequency hops to and fro between ω₁and ω₂.

The Raman band shape corresponding to this two-frequency

exchange dynamics was formulated ﬁrst by Anderson⁶¹and

later by Shelby et al.⁶²and Hamaguchi⁶³using different ap-

proaches. We assume that the forward (ω₁to ω₂) hopping rate

W₁is much smaller than the backward (ω₂to ω₁) hopping rate

W₂and, at the same time, W₁is much smaller than the absolute

value of the angular frequency difference |δω| = |ω₂− ω₁|. In

H. Hamaguchi et al.

Bull. Chem. Soc. Jpn., 75, No. 5 (2002) 889

the band shape analysis. The unperturbed CwC stretch fre-

quency, ω₁, is determined by the extrapolation of the observed

Ω values to k_iso= 0. In the case of S₁tSB-d₁₀in alkanes, ω₁=

1568 cm⁻¹is obtained.³⁷By taking the difference, we can con-

vert Ω to ∆Ω = Ω−ω₁. By introducing the ∆Ω and τ (−0.36)

values into Eq. 1, we obtain the forward hopping rate W₁for

each solvent. The W₁value thus determined is 2.7×10¹²s⁻¹

((370 fs)⁻¹) in hexane and 1.5×10¹²s⁻¹((670 fs)⁻¹) in dode-

cane. These values seem to be physically reasonable, since our

recent molecular dynamics/quantum chemical approach⁶⁵has

shown that the solvent ﬂuctuation causing the dynamic polar-

ization of acetone in acetonitrile occurs with a frequency of a

few hundred fs⁻¹. By using these W₁and τ values, we can re-

produce the observed band shapes of the CwC stretch Raman

bands in hexane and dodecane as shown in Fig. 10. The sol-

vent dependent Raman spectral changes of S₁tSB are thus

very well interpreted in terms of Eqs. 1 and 2. The tempera-

ture-dependent band shape changes of the ~1570 cm⁻¹band

are also interpreted very well in the same way.

Solvent-Induced Dynamic Polarization and the trans to

Perpendicular Isomerization Dynamics

By using Eq. 1, the observed Ω–k_isolinear relationship can

be converted to the more “foreseeable” k_iso–W₁linear relation-

ship,

Fig. 10. The ~1570 cm⁻¹band of S₁trans-stilbene-d₁₀in

hexane (upper trace) and in dodecane (lower trace). Ob-

served bands are shown with solid traces while bands sim-

ulated by the dynamic polarization model are shown with

dotted traces.

k_iso= W₁P(T),

(3)

where P(T) is the temperature dependent coefﬁcient and T is

temperature. For S₁tSB in seven alkanes at 300 K, P(300) =

(3.2 1.2)×10²has been obtained.²⁴Recent temperature de-

pendent experiments in three alkanes have given P(T) values

ranging from 2.8×10²(283 K) to 3.8×10²(313 K).⁶⁴These

P(T) values mean that one in about three hundred solvent ﬂuc-

tuations is effective in rotating the C–C bond, resulting in the

trans to perpendicular isomerization.

observed down shift of the peak position (∆Ω < 0) and the in-

crease in the bandwidth (∆Γ > 0) of the CwC stretch Raman

band of S₁tSB with increasing temperature. It is also expected

that, in a class of like solvents, the frequency of solvent ﬂuctu-

ation is the primary quantity that changes and the other charac-

teristics of the interaction remain the same. The ﬂuctuation

frequency is expected to increase with decreasing viscosity or

on going from a small solvent to a large one. Then, on going

from a short alkane to a long alkane, W₁is expected to de-

crease. Equations 1 and 2 again account well for the observed

down shift (∆Ω < 0) and the band width increase (∆Γ > 0)

with increasing the chain length of the alkane solvent. The ex-

perimentally determined value of τ is slightly different for al-

kanes and for alcohols. For alkanes, τ = −0.31²⁴and −0.36³⁷

were obtained for S₁tSB and S₁tSB-d₁₀, respectively. More

recent experiments for three alkanes, hexane, octane, and de-

cane, at ﬁve different temperatures gave τ = −0.35.⁶⁴A larger

value, τ = −0.45, was obtained for S₁tSB in alcohols.⁶⁰It

seems reasonable that the τ value is larger in polar solvents

than in nonpolar solvents, because the polar environments are

likely to stabilize the Z state and lengthen the duration of one

hop (a smaller value of W₂), leading to a larger value of the

mean phase shift for a hop.

Equation 3 has a formulaic resemblance with the Arrhenius

formula,

k_iso= Aexp(−∆E/RT),

(4)

where A is the frequency factor and ∆E is the activation energy

and R is the gas constant. The activation energy for the

isomerization in shorter normal alkanes has been determined

from the isoviscocity plot of k_isovs temperature as 3.5 kcal

mol^{−1 66,67}If we convert P(300) = (3.2 1.2)×10²to an ex-

.

ponential factor, exp(−∆Eꢀ/RT), with T = 300 K, we obtain

∆Eꢀ = 3.4 0.3 kcal mol⁻¹. Thus, there is a numerical agree-

ment between Eq. 3 and the Arrhenius formula. In other

words, information on the frequency factor A for the trans to

perpendicular isomerization of S₁tSB is obtained from the

analysis of the dephasing kinetics of the oleﬁnic CwC stretch

mode. Generally speaking, we can think of a vibration, reac-

tion mode, which is involved directly in the course of a reac-

tion and without whose dephasing the reaction can never pro-

ceed. The reaction mode may well be a vibration that has a

signiﬁcant amplitude along the reaction coordinate so that the

coherence of the vibration must be lost when the reaction is

initiated. It is then not surprising if there is a correlation be-

By using the dynamic polarization model, we can interpret

the solvent dependent change of the ~1570 cm⁻¹Raman

bands very well. In this analysis, we use tSB-d₁₀rather than

tSB-h₁₀. A ring mode is observed at 1534 cm⁻¹in the Raman

spectrum of S₁tSB-h₁₀as a shoulder of the ~1570 cm⁻¹band

(see Figs. 2 and 3). This band is downshifted in S₁tSB-d₁₀

leaving the ~1570 cm⁻¹band isolated and more suitable for

890 Bull. Chem. Soc. Jpn., 75, No. 5 (2002)

ACCOUNTS

tween the reaction rate and the rate of dephasing of such a

mode. The CwC stretch mode of S₁tSB provides the most ob-

vious and the most illuminating example of the reaction mode.

Recently, we extended the treatment of dynamic polarization

from the two-frequency exchange model to the more general

case of the continuous frequency modulation.⁶⁴We showed

that the key results of the two-frequency exchange model can

also be obtained for the continuous frequency modulation

model.

The formulaic resemblance and the numerical agreement

between Eqs. 3 and 4 indicate that (3) is as meaningful as (4)

in describing the chemical reaction kinetics. The Arrhenius

formula (4) does not tell much about the microscopic details of

the reaction. On the other hand, Eq. 3 shows us that the

isomerization reaction of S₁trans-stilbene is triggered by the

solvent induced dynamic polarization of the CwC bond and

that such a polarization occurs once in a few to ten hundred

femtoseconds on an average in alkane solvents at room tem-

perature, with one in about 300 of those polarizations eventual-

ly leading to the isomerization. Equation 3 is complementary

to the Arrhenius formula (4) in the sense that it provides a de-

tailed molecular-level view on the process of chemical reac-

tions in solution.

which shows that the linear relationship holds between 265

and 308 K. The same linear relationship has been reported by

Hester et al.,²⁵although there is quantitative difference be-

tween the two results. Linear relationships have also been ob-

tained for hexane between 271 and 318 K, for octane between

268 and 332 K, for decane between 269 and 348 K,⁶⁴and for

SDS micellar solution between 294 and 328 K.⁴³On the basis

of this linear relationship, we can determine the temperature of

S₁tSB by measuring the peak position of the ~1570 cm⁻¹

band. Note that it is much easier and more reliable to measure

the peak position than to measure the anti-Stokes/Stokes inten-

sity ratio. Since we can determine the temperature with pico-

second time resolution, we now have a “picosecond Raman

thermometer”.

When a molecule is photoexcited with more energy than

needed for the 0–0 excitation, the excess energy is deposited to

the vibrational degrees of freedom. As the excess energy is

dissipated into the surroundings, the molecule cools down. If

the molecule is solved in solution, the dissipated excess energy

has to be transferred to the nearby solvent molecules. It is

known that the excess energy generated in the course of a

chemical reaction is removed by the surrounding molecules

quite effectively in solution. This quenching process plays an

important role in controlling the reaction, by stabilizing the re-

action products and preventing the back reaction and/or further

undesired reactions from occurring. The situation is quite dif-

ferent in chemical reactions in the gas phase where the excess

energy is preserved in the hot product molecules unless they

collide with other molecules. It is therefore important to clari-

fy the mechanism of intermolecular energy transfer in solution

so as to fully understand and control the chemical reaction pro-

cess in solution. By measuring the cooling kinetics of a solute

molecule by the “picosecond Raman thermometer”, we can

monitor the solute-solvent energy transfer process.

The dynamic polarization model of photoisomerization is a

working hypothesis to account for the newly observed relation-

ship between the isomerization rate and the Raman spectral

changes of S₁tSB in solution. It needs more experimental sup-

port as well as theoretical sophistication before it is accepted

as a general model.

Solvent/Solute Interaction as Revealed by Energy Dissipa-

tion Kinetics

As shown in Fig. 5, the peak position of the ~1570 cm⁻¹

Raman band of S₁tSB changes linearly with temperature. This

correlation is further conﬁrmed by plotting the peak position

observed at the delay time of 50 ps, when the time dependent

spectral change is over, against the temperature of the bulk so-

lution. The plot for the chloroform solution is given in Fig. 11,

From the observed time dependence of the peak position of

the ~1570 cm⁻¹band (Fig. 5), it is concluded that S₁tSB

cools down in approximately 10 ps in chloroform. In this ex-

periment, the amount of excess energy given to S₁tSB upon

the photoexcitation is 2800 cm⁻¹. What does this cooling time

of 10 ps mean? We have measured the cooling curves of S₁

tSB in a number of solvents and found that the cooling kinetics

has a strong correlation with the temperature diffusivity of the

solvent. For example, the temperature diffusivity of ethylene

glycol is 9.75×10⁻⁸m²s⁻¹while that of chloroform is

8.22×10⁻⁸m²s^{−1 68}

The time dependent changes of the peak

.

position of the ~1570 cm⁻¹band in these two solvents clearly

show that the cooling rate in ethylene glycol is larger than that

in chloroform (Fig. 12). By ﬁtting these curves with single ex-

ponential functions, we obtain the cooling time constants of S₁

tSB as 6.7 ps for ethylene glycol and 13 ps for chloroform.

The cooling rates of S₁tSB obtained in this way are plotted

against the temperature diffusivity for 10 solvents in Fig. 13.³⁸

Strong correlation between the cooling rate and temperature

diffusivity is obvious in this ﬁgure. However, temperature dif-

fusivity is a bulk property of the solvent while the cooling rate

reﬂects the rate of population decay of vibrationally excited

states. Why are these two quantities correlated with each oth-

er? In order to answer this question, we assume the following

mechanism for the excess energy dissipation process. When

Fig. 11. Temperature dependence of the peak position of the

~1570 cm⁻¹band of S₁trans-stilbene measured at 50 ps in

chloroform.

H. Hamaguchi et al.

Bull. Chem. Soc. Jpn., 75, No. 5 (2002) 891

transfer determines the rate of excess energy dissipation from

the solute, we have tried to explain the observed cooling kinet-

ics by using the diffusion equation of heat (5).³⁸The equation

can be solved if the initial condition and the boundary condi-

tion are given appropriately. As the initial condition, we as-

sume that, immediately after the photoexcitation (or within the

3 ps duration of the light pulse used in the experiment), the ex-

cess energy is equally distributed in a box that corresponds to

the solute and nearby surrounding solvent molecules. Heat lo-

calized in this box then starts to be dissipated, following the

diffusion equation (5) with the temperature diffusivity of the

room temperature bulk solvent. The box is assumed to have

dimensions of (1.3 + α) nm×(0.7 + α) nm×(0.2 + α) nm.

The volume of 1.3 nm×0.7 nm×0.2 nm corresponds to the

molecular volume of S₁tSB and the parameter α represents ad-

ditional volume for the surrounding solvent molecules that

share the energy immediately after the photoexcitation. The

value of α is used as a ﬁtting parameter. For temperature diffu-

sivity, the value reported in the literature is used throughout the

analysis. As shown in Fig. 14, this model reproduces the ob-

served cooling curve in hexane very well with the use of the

temperature diffusivity value given in the literature.⁶⁸The best

ﬁt is obtained when the parameter α is equal to 1.25 nm (Fig.

14(a)). If, however, it is assumed that the excess energy is ini-

tially localized at the coordinate origin, the model function

does not reproduce the observed kinetics (Fig. 14(b)). The α

value of 1.25 nm matches, at least semi-quantitatively, the

thickness of the ﬁrst solvation shell. This result supports our

assumption that the solute–solvent energy transfer is much

faster resulting in the immediate energy transfer from the sol-

ute to the nearby solvent molecules just after the photoexcita-

tion. The apparent cooling rate of the solute is determined by

Fig. 12. Cooling kinetics of S₁trans-stilbene, as indicated by

the observed time dependence of the peak position of the

~1570 cm⁻¹band, in chloroform (ﬁlled circles, left axis)

and in ethylene glycol (open circles, right axis). Best ﬁtted

single exponential functions are also shown. Steeper in-

crease in ethylene glycol means faster cooling of S₁trans-

stilbene in this solvent than in chloroform.

Fig. 13. Relationship between the vibrational cooling rate of

S₁trans-stilbene and the temperature diffusivity of the

used solvent.

the excess energy is dissipated from the solute molecule into

the bulk solvent, the energy should move over two types of

molecular interfaces, the solute-solvent interface and the sol-

vent-solvent interface. If the energy transfer through the sol-

ute-solvent interface is much faster than through the solvent-

solvent interface, the whole transfer rate is determined by the

slower solvent-solvent energy transfer rate. The rate of the sol-

vent-solvent energy transfer process should be described well

by the heat conduction in the bulk solvent, which follows the

diffusion equation of heat,

Fig. 14. Cooling kinetics of S₁trans-stilbene in hexane, as

indicated by measured time dependence of the peak posi-

tion of the ~1570 cm⁻¹band (ﬁlled circles). The observed

kinetics is interpreted by an excess energy dissipation

mechanism based on the diffusion equation of heat. Simu-

lated curves are also shown for two initial conditions, (a)

the energy is initially distributed in a box with dimensions

of (1.3 + α) nm× (0.7 + α) nm × (0.2 + α) nm, and (b)

at the coordinate origin. The best ﬁt for (a) is obtained

when α = 1.25 nm.

∂U

= κ∇²U

(5)

∂T

where U is temperature and κ is temperature diffusivity.

Based on the assumption that the solvent–solvent energy

892 Bull. Chem. Soc. Jpn., 75, No. 5 (2002)

ACCOUNTS

the solvent–solvent energy transfer and hence by the heat con-

duction capability of the bulk solvent.

tSB (1140 cm⁻¹). Because the only other degrees of freedom

that can share the excess energy are those from the solvent, it is

concluded that a portion (1660 cm⁻¹) of the initial excess ener-

gy is shared among the nearby solvent molecules instanta-

neously within the time resolution of the experiment. This re-

sult is fully consistent with our previous conclusion that the

solute-solvent energy transfer is quite effective and that it is

complete within the duration of the laser pulse (3 ps).

It is possible to estimate the number of solvent chloroform

molecules in the ﬁrst solvation shell which accept energy efﬁ-

ciently from S₁tSB. The initial temperature rise upon the pho-

toexcitation in the chloroform solution is determined to be 65

K with the use of the “picosecond Raman thermometer”. Be-

cause we know that the excess energy is 2800 cm⁻¹in the

present system, we can calculate the expected temperature rise

of S₁tSB just after the photoexcitation. If we assume that all

the normal vibrations of S₁tSB are harmonic oscillators, the

energy E(∆T) needed for a temperature rise from T to T + ∆T

is given by,

If we assume that the temperature rise of the solvent mole-

cules that share the excess energy is the same as that of S₁tSB,

we can estimate the number of the solvent molecules that ac-

cept the energy of 1660 cm⁻¹. For this calculation, we need

the heat capacity of the solvent chloroform. Heat capacity of

chloroform, however, is available only under the equilibrium

conditions. In other words, there are no experimental data that

show which of the vibrational, rotational, and translational de-

grees of freedom becomes or does not become statistical in a

few picoseconds during the course of intermolecular energy

transfer. Therefore, we calculate for the two extreme but pos-

sible cases. If all the three degrees of freedom become statisti-

cal in a few picoseconds, the number of the solvent molecules

that initially share the excess energy is 4.8, because the energy

acceptable by one chloroform molecule is 68 cm⁻¹for the vi-

brational, 68 cm⁻¹for the rotational, and 208 cm⁻¹for the ro-

tational degrees of freedom. If, however, the energy is shared

only among the translational and rotational degrees of free-

dom, the number should be 12. Since chloroform can move

only 0.2 nm in 3 ps by normal diffusion, molecules that share

the initial excess energy are most probably those contained in

the ﬁrst solvation shell. Thus, we estimate that, in chloroform

solution of S₁tSB, the number of solvent molecules in the ﬁrst

solvation shell is between 5 and 12.

In the excess energy dissipation process, there are two types

of solvent molecules playing different roles: the solvent mole-

cules in the ﬁrst solvation shell and those in the bulk. All the

solvent molecules, however, are the same chemical species and

they are not distinguished with usual spectroscopic techniques.

In order to chemically separate the role of the solvent in the

ﬁrst solvation shell and that in the bulk, we use micellar solu-

tions. In the micelle of sodium dodecyl sulfate (SDS) aqueous

solution, tSB is expected to be solvated in the hydrophobic

part. In this system, the nearest species surrounding the solute

is the dodecyl groups. Therefore, the ﬁrst salvation shell con-

sists of the dodecyl groups, whereas the bulk solvent is water.

It is interesting to compare the excess energy dissipation pro-

cess in this SDS micellar solution with that in dodecane, in

which both the solvating and bulk species are dodecane. Pico-

second ﬂuorescence spectroscopy has revealed that the ﬂuores-

cence lifetime of tSB in the SDS micellar solution is the same

as that in the dodecane solution_.⁴³Since the ﬂuorescence life-

time is a sensitive probe of the microscopic environment of S₁

tSB, as mentioned above, intermolecular interaction between

S₁tSB and the ﬁrst solvation shell should be similar between

the two solutions. However, the observed cooling curves in the

SDS micellar solution and that in the dodecane solution are

different from each other (Fig. 16).⁴³Faster cooling in the mi-

cellar solution, as shown in the ﬁgure, is explained well by

considering the difference between the temperature diffusivity

of water (1.5×10⁻⁷m²s^{−1 68}) and that of dodecane. Although





72





3

1

E(T, ∆T) = k∆T + k∆T +

hv_i

−

∑





hv_i

kT

hv_i

k(T + ∆T)

2





















i = 1

exp









exp

(6)

where ν_iis the frequency of the i-th normal mode and k is the

Boltzmann constant. The ﬁrst, second, and third terms in the

equation represent contributions from the translational, rota-

tional, and vibrational degrees of freedom. We have used the

frequencies of the 72 normal modes of tSB in the ground

state,⁶⁹since reliable vibrational frequencies, especially those

for low frequency modes, are not available for S₁tSB. In

Fig. 15, the calculated energy is plotted against the tempera-

ture rise from 294 K, at which temperature the experiments

were performed. If the given excess energy of 2800 cm⁻¹is

distributed solely among the vibrational, rotational, and trans-

lational degrees of freedom of S₁tSB, temperature should in-

crease by 140 K. In reality, however, the observed temperature

rise is 65 K. Energy of only 1140 cm⁻¹is needed for increas-

ing the temperature of tSB by 65 K. There is a difference of

1660 cm⁻¹between the given excess energy (2800 cm⁻¹) and

the energy consumed for the observed temperature rise of S₁

Fig. 15. Relationship between the energy (E(294 K, ∆T))

needed for increasing temperature of trans-stilbene by ∆T

from 294 K, and ∆T.

H. Hamaguchi et al.

Bull. Chem. Soc. Jpn., 75, No. 5 (2002) 893

Fig. 16. Cooling kinetics of S₁trans-stilbene, as indicated by

the observed time dependence of the peak position of the

~1570 cm⁻¹band, in SDS micellar solution (open circles,

left axis) and in dodecane (ﬁlled circles, right axis). Best

ﬁtted single exponential functions are also shown. Steeper

increase in SDS micellar solution means faster cooling in

this solution than in dodecane.

Fig. 17. Time-resolved Raman spectra of S₁trans-stilbene in

carbon tetrachloride measured at 0 ps (a), 1 ps (b), 3 ps (c),

5 ps (d), 7 ps (e), 10 ps (f), and 15 ps (g) after the photoex-

citation.

isomerization rate is accelerated by ten times or more in car-

bon tetrachloride. The answer for this question has been ob-

tained by a steady-state photoirradiation experiment. When

tSB is irradiated with near-UV light in ordinary solvents, its

concentration gradually decreases while the concentration of

the cis-isomer increases. When this process is monitored with

UV absorption spectroscopy, an isosbestic point is observed at

265 nm (Fig. 18). If the same experiment is performed in car-

the temperature diffusivity of dodecane is not known, it should

be similar with the values for other alkanes. The temperature

diffusivity of hexane, heptane, octane, nonane, and decane are

8.2×10⁻⁸, 8.0×10⁻⁸, 8.5×10⁻⁸, 8.6×10⁻⁸, and 8.6×10⁻⁸m²

s⁻¹, in this order. Because the temperature diffusivity of water

should be much larger than that of dodecane, and because the

entire energy dissipation rate is controlled by the heat transfer

capability of the bulk solution, it is natural to have a faster

cooling rate in the micellar solution than in dodecane, even if

the microscopic solvation environments are similar between

the two.

Thus far, we have obtained no experimental result that

shows the origin of the fast solute–solvent energy transfer. Al-

though vibration to vibration (V–V) resonance energy transfer

could be an important energy transfer mechanism, there was

no difference observed between the cooling kinetics in CHCl₃

and that in CDCl₃.⁴⁷

Chlorine Abstraction of S₁trans-Stilbene

In the course of our systematic study of the solvent effect on

the Raman spectrum, we have found that the S₁lifetime of tSB

is drastically shortened in carbon tetrachloride. Time-resolved

Raman spectra of tSB measured in carbon tetrachloride are

shown in Fig. 17. Since all the Raman bands observed in the

ﬁgure are assigned to S₁tSB, it is obvious that the S₁state is

formed and quenched within 10 ps after the photoexcitation.

Picosecond time-resolved ﬂuorescence spectroscopy has re-

vealed that the ﬂuorescence lifetime of tSB in carbon tetra-

chloride is about 3 ps.⁴¹Although the ﬂuorescence lifetime of

tSB was measured in a number of solvents, the shortest life-

time ever reported was 30 ps, that in methanol and in acetoni-

trile. The newly found ﬂuorescence quenching rate in carbon

tetrachloride is larger than that in ordinary solvents by ten

times or more.

Fig. 18. UV absorption spectra of trans-stilbene in heptane

(A) and in carbon tetrachloride (B) measured before (a)

and after 5 min (b), 10 min (c), 15 min (d), 20 min (e), 25

min (f), and 30 min (g) of steady-state photoirradiation in

the near-UV.

An obvious question on this anomalous ﬂuorescence life-

time shortening is whether or not the trans–perpendicular

894 Bull. Chem. Soc. Jpn., 75, No. 5 (2002)

ACCOUNTS

bon tetrachloride, however, there is no formation of the cis-iso-

mer observed. The absorption signal for tSB decreases mono-

tonically, indicating that it decomposes as a result of some un-

known photochemical reactions.

Figure 18 shows that there is no distinct electronic absorp-

tion signature that is assignable to the product of the photo-

chemical reaction of tSB in carbon tetrachloride. Thus, time-

resolved infrared absorption spectroscopy has been used, in

which a carbon tetrachloride solution of tSB was irradiated

with the 262 nm light pulse and the induced infrared spectral

changes were recorded by a highly sensitive nanosecond time-

resolved infrared spectrometer.^70,71The result is shown in Fig.

19.⁴¹In the ﬁgure, transient infrared absorption from newly

generated species is represented by upward peaks while the de-

pletion of the ground-state absorption is represented by down-

ward peaks. The prominent upward peak at 896 cm⁻¹has been

identiﬁed as due to the trichloromethyl (CCl₃) radical. The

downward peak at 960 cm⁻¹is ascribed to the loss of the CH

out-of-plane bend mode of the oleﬁnic part of tSB. These re-

sults indicate that a chlorine atom is transferred from carbon

tetrachloride to tSB upon photoexcitation, forming the tSB–Cl

adduct and the CCl₃radical. Time dependence of the 896 cm⁻¹

band has revealed that the CCl₃radical decays in approximate-

ly 100 µs, following the second-order decay kinetics.⁴¹Be-

cause the CCl₃radical and the tSB–Cl adduct are formed in a

single photochemical reaction and because their initial concen-

trations are the same, the recombination reaction should follow

the second-order kinetics if it occurs after complete dissocia-

tion of the geminate pair. Recently, similar photochemical re-

actions with carbon tetrachloride have been shown for

anthracene⁷²and biphenyl,⁷³based on the experimental results

from nanosecond time-resolved infrared spectroscopy and pi-

cosecond time-resolved ﬂuorescence spectroscopy. It seems

general for aromatic molecules to react with carbon tetrachlo-

ride when photoexcited to the electronically excited singlet

state.

Fig. 20. Time-resolved visible absorption spectra of trans-

stilbene in carton tetrachloride. Time dependence of the

S_n–S₁absorption is shown. Vertical line with an arrow in-

dicates the spectral position where the absorption band

from the cation radical of trans-stilbene is expected.

The bimolecular reaction between S₁tSB and carbon tetra-

chloride in the picosecond time region has been traced by fem-

tosecond time-resolved visible absorption spectroscopy.⁷⁴In

this experiment, tSB is photoexcited with the 266 nm light

pulse and the induced absorption change in the visible region

is monitored with the white light continuum generated by the

self-phase modulation of the 800 nm light in water.⁷⁵The ob-

tained time-resolved spectra are shown in Fig. 20. Transient

absorption band at 580 nm is due to the S_n–S₁absorption of

tSB. The characteristic absorption band of the tSB cation radi-

cal at 480 nm⁷⁶is not observed in the spectra in Fig. 20.

Therefore, the cation radical is not a reaction intermediate in

the photochemical reaction between tSB and carbon tetrachlo-

ride. It is highly likely that the chlorine atom is directly trans-

ferred from carbon tetrachloride to S₁tSB.

Exact kinetic behavior of the bimolecular reaction can be

obtained by plotting the intensity of the S_n–S₁absorption at

580 nm against time. The observed kinetics (Fig. 21) is ex-

plained well by the Smoluchowski theory of diffusion-con-

trolled reactions.^77,78According to this theory, the bimolecular

reaction constant k(t) can be expressed as,

R







k(t) = 4πRN_AD 1 +



(7)

πDt

where D is the relative diffusion coefﬁcient, N_Ais the

Avogadro number, and R is the distance between the two reac-

tants where the reaction occurs with unit probability. The best

ﬁt to the observed reaction kinetics is obtained when R is 0.42

nm (Fig. 21). The R value calculated from the molecular vol-

ume with the ﬁlling factor of 0.740 (corresponding to the clos-

est packing crystals) is 0.67 nm. The Collins–Kimball theo-

ry,^78,79which assumes a ﬁnite reaction probability at the dis-

tance R, also reproduces the observed bimolecular kinetics

successfully when R is 0.50 nm and the intrinsic bimolecular

Fig. 19. Time-resolved infrared difference spectra of trans-

stilbene in carton tetrachloride measured at 0–50 µs (a),

50–100 µs (b), 100–150 µs (c), 150–200 µs (d), and 200–

250 µs (e) after the photoexcitation at 262 nm.

H. Hamaguchi et al.

Bull. Chem. Soc. Jpn., 75, No. 5 (2002) 895

vent-solute interaction to a new photochemical reaction in car-

bon tetrachloride. We owe this wealth of new molecular infor-

mation to S₁tSB and time-resolved Raman spectroscopy.

It is a great pleasure and honor for the present authors to

compile their decadal Raman spectroscopic investigations of

S₁trans-stilbene as an Account of the Bulletin of the Chemical

Society of Japan. They are grateful to Professor Renji

Okazaki, the Editor of the Bulletin, for this opportunity. They

also express their sincere gratitude to all the collaborators of

the work described in this Account.

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Hiro-o Hamaguchi, Professor at the Department of Chemistry, School of Science, the Uni-

versity of Tokyo, was born on September 21, 1947. He graduated from The University of

Tokyo in 1970 and obtained the degree of Doctor of Science in 1975 under the supervision

of Professor Takahiko Shimanouchi. Since then he worked as a faculty (Research Associate,

Lecturer, Associate Professor) of the Department of Chemistry until 1990 when he moved to

the Kanagawa Academy of Science and Technology. During 1977–1979 he was a Ramsay

Fellow working with Professor A. D. Buckingham at the Department of Theoretical Chemis-

try, Cambridge University, UK. Since 1995, he has been Professor at The University of

Tokyo (1995–1997, Graduate School of Arts and Sciences; 1997–, School of Science). He is

interested in looking into the wonder world of molecules by spectroscopy, particularly by vi-

brational spectroscopy. His recent research activities include development of new spectro-

scopic methods, ultrafast molecular processes in solution, properties of ionic liquids and

physical chemistry of living cells.

Koichi Iwata, Associate Professor, Research Centre for Spectrochemistry, School of Science,

The University of Tokyo, was born in 1961. He graduated from Department of Chemistry,

School of Science, The University of Tokyo in 1984. He joined Prof. Tasumi’s group as a

graduate student and received his Dr. Sci. degree from The University of Tokyo in 1989. He

then joined Prof. Gustafson’s group at Department of Chemistry, The Ohio State University,

USA, as a postdoctoral fellow. In 1991, he joined Prof. Hamaguchi’s group at Kanagawa

Academy of Science and Technology (KAST) as a research associate. After serving as Vis-

iting Research Associate Professor, Advanced Research Institute for Science and Engineer-

ing, Waseda University, he joined Department of Chemistry, School of Science, The Univer-

sity of Tokyo as an associate professor in 1997. He moved to the present institute at 2001.

He is Visiting Associate Professor of Institute for Molecular Science. His research interests

include development of molecular spectroscopic methods as well as studying time-depen-

dent phenomena, in particular dynamic processes accompanying chemical reactions in con-

densed phases.

Article Doi

Physical chemistry of the lowest excited singlet state of trans-stilbene in solution as studied by time-resolved Raman spectroscopy

DOI: 10.1246/bcsj.75.883

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Article abstract of DOI:10.1246/bcsj.75.883

Full text of DOI:10.1246/bcsj.75.883

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