Vibrational cooling after ultrafast photoisomerization of azobenzene measured by femtosecond infrared spectroscopy

Article abstract of DOI:10.1063/1.473392

The vibrational cooling of azobenzene after photoisomerization is investigated by time resolved IR spectroscopy with femtosecond time resolution. Transient difference spectra were obtained in a frequency range where phenyl ring modes and the central N=N-s

Full text of DOI:10.1063/1.473392

Vibrational cooling after ultrafast photoisomerization of azobenzene
measured by femtosecond infrared spectroscopy
P. Hamm, S. M. Ohline, and W. Zinth
Citation: J. Chem. Phys. 106, 519 (1997); doi: 10.1063/1.473392
View online: http://dx.doi.org/10.1063/1.473392
View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v106/i2
Published by the American Institute of Physics.
Additional information on J. Chem. Phys.
Journal Homepage: http://jcp.aip.org/
Journal Information: http://jcp.aip.org/about/about_the_journal
Top downloads: http://jcp.aip.org/features/most_downloaded
Information for Authors: http://jcp.aip.org/authors
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

Vibrational cooling after ultrafast photoisomerization of azobenzene
measured by femtosecond infrared spectroscopy
P. Hamm, S. M. Ohline,a) and W. Zinth
¨
¨
¨
Institut fur Medizinische Optik, Ludwig Maximilians Universitat Munchen, Barbarastr. 16,
¨
80797 Munchen, Germany
͑Received 22 July 1996; accepted 1 October 1996͒
The vibrational cooling of azobenzene after photoisomerization is investigated by time resolved IR
spectroscopy with femtosecond time resolution. Transient difference spectra were obtained in a
frequency range where phenyl ring modes and the central NvN-stretching mode absorbs. The
experimental data are discussed in terms of a simple theoretical model which was derived in order
to account for the off-diagonal anharmonicity between the investigated high-frequency modes and
the bath of the remaining low-frequency modes in a polyatomic molecule. It is shown that these
off-diagonal anharmonic constants dominate the observed transient absorbance changes while the
anharmonicity of the high-frequency modes themselves ͑diagonal anharmonicity͒ causes only minor
effects. Based on the transient IR spectra, the energy flow in the azobenzene molecule can be
described as follows: After an initial ultrafast intramolecular energy redistribution process, the
decay of the related intramolecular temperature occurs via intermolecular energy transfer to the
solvent on a time scale of ca. 20 ps. © 1997 American Institute of Physics.
͓S0021-9606͑97͒00502-3͔
I. INTRODUCTION
one can roughly estimate the energy distribution and/or the
time dependent intramolecular temperature of the system.
With the help of this kind of experiments it was proposed
that IVR is not necessarily ultrafast ͑i.e., in the range of 10
ps͒, even in the case of rather big molecules like stilbene6 or
TINUVIN.7 However, the interesting questions concerning
the initial energy distribution and the detailed pathway to a
thermal distribution is difficult to address with this kind of
experiments since the vibronic structure of the electronic
transition is usually not spectrally resolved in solution.
So far, only very few experiments with sufficiently high
time resolution in connection with real mode selectivity have
been published. Basically two experimental techniques are
conceivable: ͑i͒ Time resolved ͑transient͒ Raman spectros-
copy ͑see, for example, Refs. 1,8–14͒ and ͑ii͒ time resolved
infrared spectroscopy ͑see, for example, Refs. 15–20͒. Tran-
sient anti-Stokes Raman spectroscopy is selective for vibra-
tionally excited modes and therefore is favorable for measur-
ing IVR. However, due to the small Raman cross section,
Raman spectroscopy often fails for fluorescing molecules. In
addition, subpicosecond time resolution simultaneously im-
plies the loss of frequency resolution since frequency and
time resolution are achieved during the same interaction be-
tween the short light pulse and the molecule.
With the recent technical progress in ultrafast IR spec-
troscopy with time resolution in the range of several hundred
femtoseconds ͑see, for example, Refs. 19–25͒, transient IR
experiments with subpicosecond time resolution have now
become feasible. Due to the high repetition rate of modern
Ti:sapphire systems, a sufficiently high signal-to-noise level
can be obtained allowing to apply transient fs-IR experi-
ments to a broad variety of different molecules. In addition,
since frequency resolution can be incorporated after the mea-
surement process ͑frequency selection in a spectrometer be-
The energy relaxation following a photochemical reac-
tion of a molecule in solution is an interesting and not fully
understood problem ͑for some review articles see Refs. 1–5͒.
In an oversimplified picture, the process may be separated
into two steps: ͑i͒ Intramolecular vibrational redistribution
͑IVR͒ which dissipates the energy from an initial, nonther-
mal energy distribution to a fully thermalized state where all
vibrational modes are excited according to a thermal Boltz-
mann factor and an initial temperature of the molecule can
be defined. ͑ii͒ Intermolecular energy transfer from the mol-
ecule to the solvent. The kinetics of both processes strongly
depend on the mode density of both the molecule and the
solvent and in particular on the spectral overlap between mo-
lecular and bath modes, and on the polarity of the system.5
Especially in medium sized molecules, the time scales of
both processes are not clear. The assumption that intramo-
lecular vibrational redistribution is much faster than intermo-
lecular energy transfer, i.e., the assumption that both pro-
cesses are well separated, needs further experimental
verification.
Most experiments published so far investigated large dye
molecules and used the slope of the low energy edge of an
electronic transition as an intrinsic molecular thermometer
͑see, for example, Ref. 3͒. In this way, it was possible to
measure the energy flow from the molecule to the solvent.
Another, more sophisticated estimate of the energy distribu-
tion can be given by modeling the temperature dependent
absorption spectrum of the S0 –S1-transition6,7 where the
Franck–Condon factors of the active modes are obtained
from their resonance Raman intensities. Using this method,
a͒
Present address: Department of Chemistry, Wellesley College, Wellesley,
MA 02181.
J. Chem. Phys. 106 (2), 8 January 1997
0021-9606/97/106(2)/519/11/$10.00
© 1997 American Institute of Physics
519
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

520
Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
II. EXPERIMENT
hind the sample͒, high frequency and high time resolution
can be obtained simultaneously when carefully considering
the coherent interaction between the ultrashort probing pulse
and the sample.26,27 The limiting factor now is the dephasing
time T2 of the investigated vibrational mode. In other words,
the sample itself finds the best compromise between fre-
quency and time resolution.
A. Background: Spectroscopic properties of
azobenzene
First, the spectral properties of azobenzene shall be
briefly summarized ͑for a review article, see for example
Ref. 33͒.
Electronic spectra. The two lowest electronic transi-
While extensive theoretical work treated IVR process on
one single electronic potential surface ͑for a review see, for
example, Ref. 28͒, there are only few theoretical investiga-
tions that consider vibrational relaxation processes initiated
by an ultrafast internal conversion process.29–31 Multi-
dimensional quantum mechanical simulations of a nonadia-
batic cis-trans photoisomerisation process indicate that the
energy redistribution of high-frequency modes coupled
strongly to the electronic transition occurs on a time scale of
several hundred femtoseconds30 and therefore is too fast to
be addressed with the present IR technology. Semiclassical
simulations have shown, however, that the subsequent pro-
cess of redistribution of these initially nonthermally excited
vibrational modes into weakly coupled intra- and intermo-
lecular modes occurs on a picosecond time scale31 and
should be observable experimentally. Consequently, tran-
sient femtosecond vibrational spectroscopy might give de-
tailed information on modes coupled strongly to the internal
conversion process. These technique might supplement the
information obtained from stationary resonance Raman ex-
periments which determine the dominant modes at the begin-
ning of the reaction, i.e., during the electronic dephasing
time ͑10–30 fs͒.
It is the aim of the present paper to study the ability of
mode selective subpicosecond IR spectroscopy to measure
the initial vibrational energy distribution, the subsequent in-
tramolecular energy redistribution process, and the final in-
termolecular cooling process after photoisomerisation of cis-
azobenzene. This molecule was chosen for several reasons:
͑i͒ An electronically excited cis-azobenzene molecule
reaches the electronic ground state after a very short time
͑Ͻ200 fs, see below͒, transferring most of the electronic en-
ergy into the vibrational degrees of freedom. ͑ii͒ The wave-
length position of the lowest electronic transition of cis-
azobenzene fits well to the second harmonic of a Ti:sapphire-
system. ͑iii͒ Cis- and trans-azobenzene have spectrally
separated electronic transitions. Therefore, the molecule may
be reversibly switched from one configuration into the other
by exciting it with light of the proper wavelength. Because of
this properties, azobenzene was proposed as an ultrafast mo-
lecular switch or as an image storage device ͑see, for ex-
ample, Ref. 32͒. In order to simulate the experimental data, a
simple theoretical model is derived in the second part of the
paper which is applied to describe the shape of a vibrational
transition in a vibrationally excited molecule under distinct
model assumptions. A direct comparison of the experimental
data and the model will demonstrate the capability of the
model description.
*
tions of trans-azobenzene are the ␲–␲ transition centered
*
at 320 nm and the n–␲ transition centered at 440 nm.
While the ␲–␲ transition is strong ͑⑀ϭ21 000 MϪ1 cmϪ1
͒
*
*
the n–␲ transition is formally symmetry forbidden ͑⑀ϭ405
M
Ϫ1 cmϪ1͒. The corresponding transitions of cis-azobenzene
are found at 260 nm ͑␲–␲ , ⑀ϭ10 000 MϪ1 cmϪ1͒ and at
*
440 nm ͑n–␲ , ⑀ϭ1250 MϪ1 cmϪ1͒.
*
Photoreaction. Cis-azobenzene isomerizes into the
trans-configuration with a quantum yield of Ϸ40% when
exciting the ␲–␲ transition and with a quantum yield of
*
*
Ϸ55%, when exciting the n–␲ transition, respectively. The
quantum yield depends slightly on the polarity of the
solvent.33,34 One open question is whether the isomerisation
pathway is through rotation or inversion.33,35,36 Extended
femtosecond VIS-pump-near-UV-probe experiments ͑pump:
435 nm, probe 350–435 nm, cross correlation time 250 fs͒
have been performed which will be described in detail
elsewhere.37 The basic results of these experiments are as
follows: Around delay zero, a strong induced excited state
absorption occurs which decays with a time constant on the
order Ͻ200 fs. Afterward, absorption changes are observed
on a time scale of 10 ps which may be related to a vibrational
cooling process of the initially hot ͑or vibrationally excited͒
cis- and trans-azobenzene. Thus, the transition from the elec-
tronically excited state to the ground state is completed after
several hundred femtoseconds yielding a mixture of vibra-
tionally excited cis- and the trans-azobenzene in the elec-
tronic ground state. Since we treat here only delay times after
the electronic decay, the stationary vibrational absorption
spectra of both species can be used as a starting point for the
discussion of the IR spectra of the vibrationally excited mol-
ecules.
Vibrational spectra.
Stationary mid-IR-absorption
spectra of trans- and cis-azobenzene are shown in Fig. 1͑a͒
and ͑b͒ ͑dissolved in DMSO-d6 , the contribution of the sol-
vent is small in the investigated spectral range and has been
subtracted͒. The time resolved experiments presented in this
paper were performed between 1400 and 1550 cmϪ1 where
the strongest IR transitions of azobenzene are found. Five
IR-active vibrational transitions are observed in this spectral
range in which a trustworthy assignment can be given:38,39 In
cis-azobenzene, the NvN-stretch mode is observed at 1512
cmϪ1 ͑␯
͒ while the corresponding transition in trans-
NvN
azobenzene is IR forbidden due to its inversion symmetry. In
a Raman spectrum, the NvN-stretch mode of trans-
azobenzene shows up at 1440 cmϪ1. In addition, two in-
plane phenyl ring modes are observed at 1454 cmϪ1 (␯
)
19b
and 1484 cmϪ1 (␯19a) in the trans-configuration and at 1446
cmϪ1 (␯19b) and 1480 cmϪ1 (␯19a) in the cis-configuration,
respectively. These modes are assigned to the antisymmetric
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
521
one single data point. A signal to noise level sufficient to
detect absorbance changes as small as ⌬Aϭ5ϫ10Ϫ5 was
achieved.
Trans-azobenzene ͑Sigma͒ was dissolved in deuterated
DMSO ͑99 atom % deuterium͒ at a concentration of 50 mM.
No concentration dependent changes in the electronic and in
the vibrational spectra were observed even at much higher
concentrations of up to 200 mM. Therefore, we can exclude
disturbing effects by aggregation at a concentration of 50
mM. The solvent is transparent in the investigated spectral
range between 1400 and 1550 cmϪ1. The sample was held in
a CaF2 cuvette ͑path length: Ϸ50 ␮m͒ which was rotated in
order to exchange the sample between two successive laser
shots. In addition, the cuvette holder was translated perpen-
dicular to the beam axis. In total, a ring with Ϸ20 mm in
diameter and Ϸ3 mm broad was sampled by the excitation
pulses. In the fs experiment, the cis→trans isomerization of
*
azobenzene was investigated by exciting the n–␲ transi-
FIG. 1. Absolute mid-IR-absorption spectrum of ͑a͒ trans-azobenzene and
of ͑b͒ cis-azobenzene in DMSO-d6 . The small contribution of the solvent in
this spectral range is subtracted. For a assignment of the absorption lines,
see text.
tion of cis-azobenzene. In order to regenerate the sample
during the measurement, the sample was illuminated by a
filtered broadband cw-light source which selectively excited
*
the ␲–␲ transition of trans-azobenzene and thus shifted the
cis-trans-photostationary equilibrium strongly to the cis-
configuration. This was done by a filtered Hg͑Xe͒ lamp
͑Oriel, Stanford, with glas filters UG11, WG305, Schott,
Mainz, combined transmission range: 300 nm–380 nm͒
transmitted through a fused silica fiber bundle ͑diameter: 3
mm͒ which was used to illuminate the same ring of the
sample as the excitation light ͑total power of the cw light at
the sample: Ϸ100 mW͒. The photostationary equilibrium
was essentially unchanged when the femtosecond excitation
pulses at 408 nm illuminated the sample ͑which switched the
molecules from the cis- to the trans-configuration͒ since the
average power of the Hg͑Xe͒ lamp was much higher than the
average power of the pumping light. A steady-state IR ex-
periment was used to measure the photostationary cis-trans-
distribution. By using two well separated IR transitions at
1454 cmϪ1 ͑trans͒ and at 1446 cmϪ1 ͑cis͒ as marker modes
͑see Fig. 1͒, one could estimate that more than 70% of the
molecules are in the cis-configuration under these illumina-
tion conditions. Taking into account that the cross section of
linear combination of a fundamental ring mode of both ben-
zene rings,40 namely the ␯19 mode ͑1482 cmϪ1, Wilson num-
bering used throughout the paper͒ which is twofold degener-
ate in benzene and which splits into two transitions due to
the perturbed symmetry in azobenzene. The ␯19b-mode shifts
significantly from 1446 cmϪ1 to 1454 cmϪ1 when switching
from the cis- to the trans-configuration allowing one to esti-
mate the proportions of the cis- to trans-configuration in a
mixture.
B. Materials and methods
A standard excite and probe scheme was used. Excita-
tion was performed by femtosecond pulses ͑pulse duration:
␶ϭ150 fs FWHM; center wavelength: ␭ϭ408 nm͒ generated
by frequency doubling the output of a 1 kHz Ti:sapphire-
regenerative amplifier. The generation of the IR-probing
pulses and the detection scheme was described in detail in
Refs. 22 and 23. Briefly, the absorbance changes of the
sample were recorded by tunable probing pulses generated
by difference frequency mixing between the output of the
regenerative Ti:sapphire amplifier and the output of a tunable
traveling wave dye laser in an AgGaS2 crystal. Pulses with a
pulse duration of Ϸ300 fs and a spectral bandwidth of Ϸ60
cmϪ1 were obtained. The probing pulses were dispersed in a
grating spectrometer ͑spectral resolution: 5 cmϪ1͒ after pass-
ing the sample. A 10-element MCT-detector array was used
to cover the complete spectral bandwidth of the probing
pulses simultaneously. The time resolved spectra shown be-
low are a superposition of several 10-point spectra which
overlap by several elements. The noise of two different
points of one single 10-element spectrum is strongly corre-
lated, yielding time resolved difference spectra with a rela-
tive accuracy which is better than the absolute accuracy of
*
the n–␲ transition of cis-azobenzene is three times larger
than that of trans-azobenzene, one concludes that more than
90% of the excited molecules started from the cis-state while
a small fraction of below 10% started from in the trans-state.
Two effects disturb the time resolved results around the
experimental delay zero position: ͑i͒ The coherent perturbed
free induction ͑PFID͒ decay effect26,27 which is of impor-
tance when the inhomogeneous dephasing time of a vibra-
tional transition is longer than the pulse duration of the prob-
ing pulses. However, it should be kept in mind that the PFID
effect contributes only at negative delay times and during the
overlap of excitation and probing pulse but not at larger posi-
tive delay times.26 ͑ii͒ Due to the short wavelength and the
high energy of the excitation pulses, an optical Kerr effect
originating mainly from the cuvette windows was observed
which causes a transient frequency shift of the probing
pulses around delay zero.41 The Kerr effect mimics absor-
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

522
Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
neighboring solvent bands ͑observed at 1050 cmϪ1 and at
2100 cmϪ1͒ which are orders of magnitudes stronger ͑AϷ2
OD͒ than the transient azobenzene absorption lines ͑⌬A
Ϸ0.1 mOD͒. A similar baseline shift is also observed in a
static absorption spectrum of pure DMSO upon heating. In
any case, the baseline shift is a small broadband effect and
we discuss here only the narrow band features originating
from the sample molecules.
In detail, the following spectral features are observed in
the 70 ps spectrum: The NvN-stretching mode ͑1512 cmϪ1
͒
which is IR active only in the cis-configuration bleaches
upon switching from the cis- into the trans-configuration. In
addition, both phenyl ring modes ␯ and ␯ are frequency
19b
19a
shifted when photoisomerizing from the cis-state ͑1446 cmϪ1
and 1480 cmϪ1͒ to the trans-state ͑1454 cmϪ1 and 1484
cmϪ1͒.
More interesting are the transient difference spectra at
earlier delay times: In Fig. 2͑a͒, time resolved difference
spectra measured 1 ps ͑open circles͒ and 10 ps ͑gray squares͒
after electronic excitation are shown together with the 70 ps
spectrum ͑triangles͒. The transient difference spectra are a
superposition of negative and positive contributions. While
the negative contributions are due to bleaching cis-
azobenzene bands ͑and eventually due to a stimulated emis-
sion of a vibrationally excited state, see discussion͒, the posi-
tive contributions are due to transient photoproducts. Both
contributions will be discussed separately:
͑i͒ In all transient difference spectra, three negative ab-
sorption lines are found close to the spectral positions of
cis-azobenzene bands ͑1446 cmϪ1, 1481 cmϪ1, and 1515
cmϪ1͒. The spectral positions of these negative bands do not
change with time, as expected for bands of the disappearing
cis-azobenzene molecules. However, the amount of the
bleach changes with time. For two bands ͑1481 cmϪ1 and
1515 cmϪ1͒, a partial refill of the initial bleach can be rec-
ognized, while the third band ͑1446 cmϪ1͒ shows a further
absorption decrease between 1 ps and 70 ps.
FIG. 2. ͑a͒ Transient difference spectra after photoisomerisation of cis-
azobenzene measured 1 ps ͑open circles͒, 10 ps ͑gray squares͒, and 70 ps
͑filled triangles͒ after electronic excitation. ͑b͒ 70 ps difference spectrum
͑triangles͒ compared with a difference spectrum obtained in a FTIR spec-
trometer under steady-state illumination by light at ␭ϭ300–380 nm.
bance changes which are about three times larger than the
absorbance changes caused by the photoisomerisation of
azobenzene. All experiments presented below are done with
the polarization of the probe perpendicular to that of the
pump since this considerably reduces this effect. Both effects
͑i.e., the PFID effect and the Kerr effect͒ overlap around
delay zero. As a consequence, the experimental data were
analyzed for delay times Ͼ0.7 ps only, when both disturbing
effects have vanished.
C. Results
Figure 2 shows the experimental results obtained be-
tween 1420 and 1540 cmϪ1. In Fig. 2͑b͒, a time resolved
difference spectrum measured 70 ps after electronic excita-
tion ͑triangles͒ is compared with a stationary difference spec-
trum ͑solid line͒. The stationary spectrum was obtained in a
FTIR spectrometer by switching trans-azobenzene into the
cis-configuration with the filtered Hg͑Xe͒ lamp ͑␭ϭ300–380
nm͒. In order to fit the 70 ps spectrum to the stationary
spectrum, the stationary spectrum was inverted ͑since the
cis→trans-transition is observed in the time resolved experi-
ment͒ and linearly scaled. In addition, a small baseline cor-
rection ͑ϩ0.05 mOD͒ is necessary to match the 70 ps and the
stationary spectrum. ͓The corrected baseline is depicted in
Figs. 2͑a͒ and 2͑b͒. The baseline shift is also observed for
later delay times up to 300 ps.͔ A perfect agreement between
the transient 70 ps spectrum and the stationary difference
spectrum is obtained demonstrating the precision of the time
resolved experiments and indicating that both the photoreac-
tion and the cooling process are completed after 70 ps as
expected from the UV experiments.37 The base line shift may
be explained by a temperature dependent broadening of
͑ii͒ Two trans-azobenzene bands are clearly observed in
the late ͑70 ps͒ spectrum ͑␯19b, 1454 cmϪ1 and ␯19a, 1484
cmϪ1͒. However, these bands are absent in the earlier differ-
ence spectra. Instead of them, three pronounced new bands
peaked at 1431 cmϪ1, 1466 cmϪ1, and 1491 cmϪ1 are ob-
served. They exhibit large bandwidths in the order of 10–20
cmϪ1. These new bands ͑which will be called ‘‘hot-bands’’
throughout the paper͒ are most pronounced in the 1 ps spec-
trum and start to decay in the 10 ps spectrum. In combination
with a decay of intensity of these bands, a shift to higher
frequencies can be recognized in particular for the band at
1466 cmϪ1 between 1 ps and 10 ps.
Kinetic absorption data are shown in Fig. 3 for several
selected frequency positions ͑marked by arrows in Fig. 2͒:
In Fig. 3͑a͒, a measurement close to the peak position of
an absorption line of the reactant cis-azobenzene ͑␯19a, 1481
cmϪ1͒ is shown. Immediately after electronic excitation, a
strong bleach of this band due to the disappearance of cis-
azobenzene is observed. At later delay times, the bleach re-
covers ͓see also the transient difference spectra in Fig. 2͑a͔͒.
However, two temporal phases may be identified for this
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
523
the data with a sum of two exponential functions. However,
it shall be noted that these fit curves should be understood
only as a smoothed representation of the experimental data
since the values obtained from the fit algorithm certainly are
unphysical, in particular for the data shown in Fig. 3͑a͒ and
͑b͒. The fit algorithm yields two almost identical time con-
stants ͑4 ps and 6 ps͒ with unphysical large fit amplitudes
with opposite signs, indicating that modeling the experimen-
tal data with the help of exponential functions is not ad-
equate. An explanation of this phenomenon will be given in
the next section.
III. THEORY
As long as the vibrational spectrum of a molecule is
described in the harmonic approximation, no absorption
changes are expected in a transient vibrational spectrum
when exciting a vibrational mode from the ground state to a
vibrationally excited state. This is a consequence of the prop-
erties of the quantum mechanical harmonic oscillator: ͑i͒ The
energy spectrum is equidistant, i.e., the frequency of the
ground state transition nϭ0→nϭ1 and that of a higher tran-
sition n→nϩ1 are identical. ͑ii͒ The absorption cross sec-
tion A(n→nϩ1) of a vibrationally excited mode increases
linearly with (nϩ1).40 However, on the other side, stimu-
lated emission gives rise to a negative contribution
ϪA(n→nϪ1) which increases linearly with n, i.e., the sum
of both contributions is independent on n and does not
change with the level of excitation.
FIG. 3. The temporal evolution of the absorption changes at three selected
spectral positions ͓marked by arrows in Fig. 2͑a͔͒: ͑a͒ 1481 cmϪ1: refill of
the bleach of a cold cis-azobenzene absorption line; ͑b͒ 1456 cmϪ1: forma-
tion of a cold trans-azobenzene absorption line; ͑c͒ 1466 cmϪ1: decrease of
a hot-band of both cis- and trans-azobenzene.
The anharmonicity of the molecule gives rise to anhar-
monic frequency shifts and consequently is responsible for
detectable difference bands. Therefore, the anharmonicity is
essential to understand the IR spectrum of a vibrationally
excited molecule. Therefore, the formalism of the anhar-
monic constants shall be briefly reviewed in the following
͑for more details, see, for example, Refs. 42–46͒: The energy
states of a molecule ͑without degenerate modes47͒ including
the anharmonic corrections can be expressed as42,46
process: While between 1 ps and 10 ps, a small additional
absorption decrease is observed, the refill of the bleach pro-
ceeds only between 10 ps and 70 ps.
In Fig. 3͑b͒, data measured at the peak position of an
absorption band of the photoproduct trans-azobenzene ͑␯
,
19b
1456 cmϪ1͒ are presented showing the formation of this
band. Again, two temporal phases may be found: Starting
from a small instantaneous absorption increase, a small ab-
sorption decrease between 1 ps and 10 ps is observed fol-
lowed by a subsequent absorption increase which is finished
after ca. 70 ps.
E/បϭ
␻ n ϩ1/2͒ϩ
x
n ϩ1/2͒ n ϩ1/2͒. ͑1͒
͑ ͑
ij i j
͑
͚
͚
i
i
i
iрj
In Fig. 3͑c͒, data at the peak position of the strongest
positive absorption line of the 1 ps difference spectrum are
presented ͑1466 cmϪ1͒. At this frequency, neither cold cis-
nor the cold trans-azobenzene absorbs. A relatively large
instantaneous absorption rise is observed here which van-
ishes in about 70 ps. For this curve, a monotone decay is
obtained which, however, cannot be fit satisfactorily by us-
ing one single exponential function. The best biexponential
fit yields 1 ps and 20 ps as decay time constants ͑solid line͒.
At 1471 cmϪ1, only 5 cmϪ1 at higher frequencies and still
within the hot-band, a biphasic behavior is evident again
͑data not shown͒: Here, the absorption increase stays almost
constant between 1 and 10 ps, but most of the decrease of the
signal is observed between 10 ps and 70 ps ͓see also Fig.
2͑a͔͒.
␻ is the harmonic frequency of the ith mode, ni the level of
i
excitation of this mode, and xij are the anharmonic constants
which can be expressed in terms of the cubic and quartic
force constant in a normal coordinate basis. Equation ͑1͒
describes the system in the harmonic approximation ͑i.e., in
the formalism of eigenfrequencies and eigenmodes͒, while
the anharmonicity is treated by perturbation theory. One can
derive the transition frequency of a selected mode k coupled
to the bath of the remaining modes iÞk:
␯ n →n ϩ1͒ϭ␯ ϩ2x n ϩ
x n ,
ik i
͑2a͒
͑
͚
k
k
k
kk
k
iÞk
where the first term
␯ ϭ␻ ϩ2x ϩ
x /2
ik
͑2b͒
͚
k
k
kk
The solid curves shown in Fig. 3 were obtained by fitting
iÞk
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

524
Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
is the anharmonic correction of the nkϭ0→nkϭ1 transition
in the vibrational ground state, i.e., in the cold molecule. The
second ͑diagonal͒ term of Eq. ͑2a͒ describes the anharmonic
shifts of an excited vibrational mode k, and the third term
describes the frequency shifts due to the off-diagonal anhar-
monicity between the selected mode k and the remaining
bath modes.
on the so-called exchange theory modeling the temperature
dependent shape of an absorption line was reported in Refs.
48–50.
When the frequencies ␯ and the anharmonic constants
k
xik are all known, the shape of a vibrational transition can be
evaluated for given population distributions of the observed
mode k (␣(nk)) and the bath modes iÞk (␣(ni)). While the
In the following, an expression describing the shape of
an absorption line Ak(␻) of one selected vibrational mode k
is derived. In a first step, the off-diagonal constants terms in
Eq. ͑2a͒ are neglected. The cross section for absorption and
stimulated emission are modeled in the harmonic approxima-
tion ͑see above͒. According to the ‘‘Golden Rule,’’ one ob-
tains:
␯ are measurable and can be computed with reasonable pre-
k
cision, the determination of the anharmonic constants still is
a real challenge, from an experimental as well as from a
theoretical point of view. They are, at least in principle, mea-
surable when a complete set of overtone and combination
bands is known. However, in a molecule as large as azoben-
zene, this will be an impossible task since the assignment of
the enormous number of very weak combination modes cer-
tainly would fail. In order to calculate the anharmonic con-
stants xik , it is necessary to derive the Taylor expansion of
the ground state potential surface to fourth order with high
precision.42–45 Consequently, no anharmonic constants have
been determined for azobenzene. Therefore, a different ap-
proach has to be adopted here: In a first step, the effects of
the anharmonicity are analyzed by using realistic anharmonic
constants of a large molecule. A complete set of anharmonic
constants exists for benzene,44 which was calculated on an
ab initio MP2 level. Since two of the experimentally ob-
served vibrational modes are the phenyl ring modes of
azobenzene, it is justified to use the anharmonic constants of
benzene for an first order estimate of the anharmonic effects
in azobenzene. In a second step, a direct comparison between
the model calculation and the experimental data will be dis-
cussed using estimated anharmonic constants.
ϱ
A ␻͒ϰ
␣ n ͒Ϫ␣ n ϩ1͒͒ n ϩ1͒
͑ ͑
͑
͑
͑
͚
k
k
k
k
n ϭ0
k
ϫ␦ ␻Ϫ␯ Ϫ2x n ͒.
͑3a͒
͑
k
kk k
␣(nk) is a given population distribution of the mode k with
normalization ͚ ␣(nk) ϭ 1. ␦ is the delta function which
n
k
later will be replaced by a line shape function with finite
bandwidth. The first term ϩ␣(nk) in Eq. ͑3a͒ describes the
absorption between the states nk→nkϩ1 ͑depending linearly
on nkϩ1͒, while the second term Ϫ␣(nkϩ1) is responsible
for the stimulated emission between the states nkϩ1→nk
͑again depending linearly on nkϩ1͒.
When taking into account vibrational excitation of the
bath modes, the energy spectrum Ak(␻) is further shifted
according to the off-diagonal constants in Eq. ͑2a͒:
A. Model calculations
A ␻͒ϰ
␣ n ͒Ϫ␣ n ϩ1͒͒ n ϩ1͒
͑
͑ ͑
͑
͑
͚
k
k
k
k
ͫ
n
k
In the following, two simulations of the transient IR
spectrum will be discussed assuming two limiting cases: ͑i͒
ultrafast IVR and ͑ii͒ slow ͑compared to our time resolution͒
IVR. The calculations address the question whether ultrafast
vibrational spectroscopy is able to distinguish between IVR
͑i.e., thermalization within the molecule itself͒ and the inter-
molecular energy relaxation ͑i.e., the energy transfer from
the molecule to the solvent͒.
ϫ
␣ n ͒
͑
i
͚
͟
ͫ
ͩ
ͪ
n
,..n ,..n
jÞk
iÞk
1
j
m
ϫ␦ ␻Ϫ␯ Ϫ2x n Ϫ
x n
ik
.
͑3b͒
͚
k
kk
k
i
ͩ
ͪ
ͬͬ
iÞk
m is the number of vibrational modes and the ␣(ni) the
population distribution functions for all bath modes iÞk,
1. Ultrafast IVR
In the first limiting case, it is assumed that the excess
energy is redistributed over the molecule in a very short time
͑Ͻ1 ps͒ while intermolecular energy transfer, i.e., cooling, is
considerably slower. In this case, the molecule may be
viewed initially as an isolated system and an internal tem-
perature of the molecule can be determined after the IVR
process. At later delay times, intermolecular energy transfer
between the solute and the solvent leads to a decrease of the
temperature of the molecule. An upper limit of the initial
temperature can be estimated: When taking into account a
thermal Bolzmann distribution, the initial temperature of the
molecule is determined according to
again with normalization ͚n ␣(ni) ϭ 1. This expression mod-
i
els the absorption band by taking into account all possible
transition frequencies of Eq. ͑2a͒ and weighting each indi-
vidual line by its probability ⌸iÞk␣(ni).
Equation ͑3b͒ models the line shape in a static picture,
i.e., it describes a cw-absorption spectrum of the sample. It
will be seen later that the shape of the absorption line
changes on a time scale of several picoseconds due to the
cooling process. A dynamic picture considering the polariza-
tion of the vibrational transition would be required ͑in anal-
ogy to Refs. 26 and 27͒ when faster processes would be
investigated. However, for the time scales discussed here, the
static description should be a reasonable approximation. Fi-
nally, it shall be noted that an alternative description based
ប␻
i
E ϭ
ph
ϪE T ͒.
͑4͒
͑
͚
0
1Ϫexp Ϫប␻ /kT͒
͑
i
i
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
525
essentially carrying the same information͒ since they are di-
rectly related to the situation in the experiment where ab-
sorption lines of trans-azobenzene ͑formation of a photo-
product͒ and cis-azobenzene ͑vibrational cooling of the
reactant͒ are involved. At 300 K, only a minor frequency
shift ͑ϷϪ0.05 cmϪ1͒ compared to the zero-temperature po-
sition ͑origin of the x axis͒ is observed. However, at 400 K a
larger frequency shift in the order of Ϫ0.15 cmϪ1 is found
which increases considerably at higher temperatures and
reaches a value of Ϫ5 cmϪ1 at 1150 K. In addition, a strong
asymmetric broadening of the band is observed for higher
temperatures. Since almost all of the anharmonic constants
xi,19 are negative, the peak position of the line is shifted to
smaller frequencies. It is important to note that the main
contribution to the anharmonic effects is due to the off-
diagonal anharmonic constants xik , iÞk, in particular to
those to the low-frequency modes, and not due to the diag-
onal term 2xkk . This becomes evident when one considers ͑i͒
that even at the highest temperature used in this simulation,
the excitation probability of the ␯19 mode is only Ϸ15%, ͑ii͒
that the diagonal harmonic constant ͑2x19,19ϭϪ1.8 cmϪ1͒ is
comparably small, and ͑iii͒ that the sum of the off-diagonal
elements of all low-frequency modes ͑which are excited con-
siderably at this temperature and therefore, are responsible
for the anharmonic effect͒ is much larger than the diagonal
term ͑a value of ⌺xi,19ϭϪ21 cmϪ1 is obtained when taking
into account all modes with frequencies smaller than that of
FIG. 4. Simulated shape of the ␯ mode of benzene at different tempera-
19
tures according to the anharmonic constants reported in Ref. 44. Frequency
shift is plotted relative to the frequency of ␯19 in the cold molecule ͑0 K͒. ͑a͒
Absorption spectrum A(T); ͑b͒ difference spectrum ⌬A(T)ϭA(T)ϪA͑300
K͒.
Eph is the energy of the exciting photon, E(T0) the en-
ergy content of the molecule at room temperature, and i
numbers all vibrational modes of the molecule with fre-
quency ␻i . Assuming a thermal Bolzmann distribution for
the population distribution functions ␣(nk) for a selected
mode k and ␣(ni) for the intramolecular bath modes, a tem-
perature dependent shape of the absorption line of this mode
␯ ͒. The monotone behavior of the frequency shift and line
19
broadening with temperature allows an interesting applica-
tion of this phenomenon: The measurements of the absorp-
tion spectra can be used as a molecular thermometer for the
intrinsic temperature of the solute molecule ͑see also below͒.
Model calculations simulating a kinetic experiment at
several distinct frequency positions ͑marked by arrows in
Fig. 4͒ are shown in Fig. 5, again for both situations of Fig.
4 ͓Fig. 5͑a͒: A(T(t)), Fig. 5͑b͒: ⌬A(T(t))ϭA(T(t))
ϪA͑300 K͔͒. In the modeling it was assumed that the tem-
perature T(t) decreases exponentially from 1150 K to 300 K
with a time constant of 20 ps ͑see dotted line͒.51 Interest-
ingly, the absorption response does not behave exponen-
tially. The deviation from an exponential behavior is most
evident at a frequency position of Ϫ2 cmϪ1, i.e., at the low-
frequency tail of the absorption line of the cold molecules:
Here, two phases are observed, starting with an initial ab-
sorption rise followed by a subsequent absorption decrease.
This response is a consequence of the interplay between the
temperature dependent band broadening and the frequency
shift.
The previous model calculations were obtained by using
one special mode of benzene. However, there are arguments
that the presented features and conclusions are general: The
anharmonic frequency shifts and broadening effects are ac-
cumulated effects depending not so much on the actual an-
harmonic constants xik of each specific bath mode but rather
on the average of all constants ͑weighted with its contribu-
tion according to the Bolzmann factor of each individual
mode͒. Even when using one fixed value x for all anhar-
monic constant xik , very similar results are obtained besides
k can be calculated. This was done for the ␯ mode of ben-
19
zene using the harmonic frequencies and anharmonic con-
stants reported in Ref. 44. The ␯ mode was selected since
19
this mode is directly related to the investigated vibrational
modes in azobenzene. In order to account for a limited spec-
tral resolution ͑for example, due to a homogeneous or inho-
mogeneous broadening of the transition or due to the limited
experimental resolution͒, the calculated curves are subse-
quently convoluted with a Gaussian line shape function with
a FWHM of 2 cmϪ1. The results are shown in Fig. 4 starting
at room temperature ͑300 K͒ and continuing with several
higher temperatures up to 1150 K. The latter value corre-
sponds to the situation where the total photon energy is dis-
sipated over all vibrational modes of azobenzene ͑frequen-
cies as reported in Ref. 39; two normal modes reported with
negative frequencies in Ref. 39 are set to ϩ10 cmϪ1͒. In Fig.
4͑a͒, the absolute absorption spectra A(T) are shown while
in Fig. 4͑b͒, the difference signals ⌬A(T)ϭA(T)ϪA͑300 K͒
are plotted. The spectra in Fig. 4͑a͒ correspond to the obser-
vation during the formation and cooling of an absorption line
of a photoproduct ͑i.e., a species which is not present prior to
excitation͒, while the plots of Fig. 4͑b͒ correspond to the
transient IR-difference spectra for the vibrational mode of
the reactant. Both sets of spectra are presented ͑although
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

526
Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
FIG. 5. Simulation of a kinetic experiment at several selected frequency
positions ͑marked by arrows in Fig. 4͒. Solid lines: Absorption changes ͑left
axis͒; dotted line: underlying temperature dependence ͑right axis͒ which was
assumed to be exponential. ͑a͒ Absorption spectrum A(T); ͑b͒ difference
spectrum ⌬A(T)ϭA(T)ϪA͑300 K͒.
FIG. 6. ͑a͒ Model calculation simulating the transient spectra of azobenzene
assuming a thermal energy distribution and an exponential decrease of tem-
perature from 1000 K to 300 K with a time constant of 20 ps. Open circles:
960 K ͑corresponds to 1 ps͒; gray squares: 720 K ͑corresponds to 10 ps͒;
filled triangles: 320 K ͑corresponds to 70 ps͒. This plot may be directly
compared to the experimental data of Fig. 2. ͑b͒ Simulation of the temporal
evolution at 1456 cmϪ1 ͓see arrow in ͑a͔͒. This plot may be directly com-
pared to the experimental data of Fig. 3͑b͒.
a smaller broadening effect. In this simple case, the fre-
quency shift depends linearly on this fixed value.
In the next step, the results of a model calculation
adopted directly to the time resolved difference spectra of
azobenzene are presented ͑see Fig. 6 and Fig. 7͒. The fol-
lowing model assumptions were used:
The spectra were calculated for a fully thermalized en-
ergy distribution. Consequently, an intramolecular tempera-
ture can be assigned to each spectrum ͑960 K: open circles;
720 K: gray squares; 320 K: filled triangles͒. These tempera-
tures are obtained at a delay time of 1 ps, 10 ps, and 70 ps if
a time constant of 20 ps for the decay of the intramolecular
temperature from 1000 K to 300 K is assumed. In this sense,
the model spectra of Fig. 6 may be directly compared with
the experimental data shown in Fig. 2͑a͒. The initial tem-
perature 1000 K is taken somewhat smaller than the maximal
value of 1150 K calculated from Eq. ͑4͒, since a fraction of
the excitation energy probably is transferred to the solvent
immediately during the initial large amplitude motion of the
molecule.
A
cis(T) the contribution from the hot cis-azobenzene mol-
ecules, and Acis͑300 K͒ the bleaching ground state contribu-
tion.
The frequencies of all coupled bath modes were used as
reported in Ref. 39.
As mentioned before, no anharmonic constants are
known for azobenzene. Consequently, in a simplified model
they are assumed to be equal for all investigated high-
frequency modes xikϭxi . In addition, a linear dependence of
the anharmonic constant xi on the frequency of bath mode i
is assumed, in approximate agreement with the numbers re-
ported for benzene in Ref. 44:
The frequencies, intensities, and bandwidths of both the
cis- and the trans-modes in the cold molecule were obtained
from a multi-Gaussian fit of the absolute spectra in Fig. 1.
The method of calculation is identical to that used in Fig.
4 summing up all investigated vibrational modes. The differ-
ence spectra are a superposition of three contributions
xikϭxiϭx•␻i .
͑6͒
Consequently, only one model parameter x remains which is
estimated from a separate FTIR experiment measuring the
absolute spectrum of trans-azobenzene ͑solved in DMSO͒ in
a heated cuvette: The absorption spectra recorded between
300 K and 400 K yielded a relative frequency shift of ϷϪ1
cmϪ1 for both phenyl ring modes. x is adjusted to reproduce
this frequency shift. A value of xϭ0.9ϫ10Ϫ3 is obtained in
good agreement with the corresponding averaged value of
⌬Atot T͒ϭ␩A
T͒ϩ 1Ϫ␩͒A T͒ϪA 300 K͒.
͑ ͑ ͑
cis cis
͑
͑
trans
͑5͒
␩ϭ0.5 is the isomerization quantum yield, Atrans(T) is the
contribution from the hot trans-azobenzene molecules,
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
527
experimentally observed band broadening is larger than pre-
dicted by the model, most probably due to the simplifying
assumption for the anharmonic constants.
2. Slow IVR and selective excitation of a distinct
vibrational mode
It was shown in the previous section that in the case of a
fully thermalized molecule, the off-diagonal anharmonic
constants dominate the anharmonic effects. On the other
hand, assuming a selective, highly nonthermal excitation of
one selected mode, the diagonal anharmonic terms xkk may
also become important. Three limiting cases shall be dis-
cussed in the following. Again the ␯ mode of the benzene
19
molecule will be treated where realistic anharmonic con-
stants are known.44 Shown in Fig. 7͑a͒ are different distribu-
tion functions a(nk) of the ␯ mode, Fig. 7͑b͒ presents the
19
corresponding absorption spectra A; and Fig. 7͑c͒ the result-
ing difference spectra ⌬AϭAϪA͑300 K͒.
In a first unrealistic limiting case only the ␯ mode is
19
highly excited, while the remaining bath modes are vibra-
tionally cold, i.e., in the ground state. Figure 7͑b͒ and ͑c͒
͑broken line͒ shows the absorption changes for a Gaussian
population distribution a(nk) centered around the nkϭ3
level with a width of ⌬nkϭ2 ͓see Fig. 7͑a͒, broken line͔.
The most pronounced feature is a negative signal around
⌬␻ϭ0 which is a consequence of the population inversion
giving rise to stimulated emission.
As a second model distribution, a much more realistic
situation is discussed: It is assumed that a selected mode is
excited according to a nonthermal one quantum excitation
͓Gaussian function centered at nkϭ1, width ⌬nkϭ1; see
Fig. 7͑a͒ dotted line͔ and that this mode is coupled to the
bath of the remaining modes which are thermally excited
according to a Boltzmann distribution ͑a temperature of 800
K is used as an example͒. The result is shown in Fig. 7͑b͒
and ͑c͒ as dotted lines. Again, a negative signal due to the
1→0-population inversion can be seen ͓Fig. 7͑b͔͒ which now
is less pronounced. In particular in the case of the situation
shown in Fig. 7͑c͒, it will be difficult to resolve the stimu-
lated emission signal experimentally since the bleaching cold
molecule contribution also gives rise to an additional strong
negative signal.
FIG. 7. Simulated shape of the ␯19 mode of benzene for non-thermal energy
distributions for this mode ͑broken line, dotted line, broken-dotted line, for
details see text͒ compared with the fully thermalized 800 K spectrum of Fig.
4 ͑solid line͒. ͑a͒ Assumed population density of mode ␯19 ; ͑b͒ resulting
absorption spectrum A(T); ͑c͒ resulting difference spectrum ⌬A(T)ϭA(T)
ϪA͑300 K͒.
1.3ϫ10Ϫ3 for the ␯19 mode of benzene. This procedure might
be viewed as a first calibration of the intramolecular ther-
mometer.
Qualitatively, the model spectra ͓Fig. 6͑a͔͒ and the ex-
perimentally obtained transient difference spectra ͑Fig. 2͒ are
in excellent agreement. All observed spectral features, i.e.,
the refill of the bleached ground state cis-bands, the late rise
of the product state bands, the decay, and the blue shift of the
hot-bands, are well reproduced by the model. Also, the non-
exponential, biphasic time dependence is well reproduced:
The simulation of a kinetic experiment in Fig. 6͑b͒ at the
A more moderate nonequilibrated population distribu-
tion without population inversion, i.e., which does not give
rise to stimulated emission, is obtained when assuming that
the ␯19 mode has a higher temperature ͑1600 K͒ than the bath
modes ͑800 K͒. However, this situation ͑Fig. 7, broken-
dotted line͒ yields a spectrum very similar to a pure thermal
peak of the ␯
mode of trans-azobenzene ͓arrow in Fig.
19a
6͑a͔͒ may be directly compared with the experimental data of
Fig. 3͑b͒. In this case, the biphasic behavior is caused by the
contribution of two different modes: The initial absorption
distribution where the ␯ mode as well as the bath modes
19
both have the same temperature of 800 K ͑Fig. 7, solid line͒.
An experimental distinction between both situations requires
very accurate experimental data and a good knowledge of the
anharmonic constants.
decrease is due to the early narrowing of the ␯
mode,
19a
while the subsequent absorption rise is due to the formation
of the cold ␯ mode.
19b
This analysis shows that the presented model is able to
qualitatively describe the experimental data. However, due to
the lack of more detailed model parameters ͑i.e., a complete
set of reliable anharmonic constants͒ we did not attempt to fit
the model function to the experimental data. In particular, the
A direct comparison of the slow IVR model situation
with the experimental results ͑as it was done before in Sec.
III A 1͒ is not possible since there are too many unknown
model parameters, i.e., the population distributions ␣(ni) of
both the observed high-frequency modes and the anharmoni-
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

528
Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
cally coupled low-frequency bath modes. Yet, one important
conclusion is possible: As seen from Fig. 7, a stimulated
emission signal would be a clear indication for a strong non-
thermal energy distribution which, however, is not observed
experimentally for azobenzene. Thus, at least a strong devia-
tion from a thermal energy distribution can be excluded for
the observed vibrational modes, although the absence of a
stimulated emission signal cannot show that the molecule is
fully thermalized.
emission signal, an unambiguous assignment of an anhar-
monic frequency shift to a nonthermal selective excitation of
one vibrational mode will be difficult. It is interesting to note
that not necessarily very particular and strongly coupled
modes like the central bending and torsional modes of
azobenzene or stilbene ͑see, for example, Ref. 13͒ are re-
sponsible for strong anharmonic effects. Also a great number
of only weakly coupled modes may give rise to considerable
effects, as shown here in the case of the rather rigid benzene
molecule. This is seen from the fact that the averaged value
of the anharmonic constants of the ␯ mode of benzene
19
IV. CONCLUSION
͑1.3ϫ10Ϫ3͒ is of the same order ͑even slightly larger͒ than
the estimated corresponding value necessary to reproduce the
experimental results in azobenzene ͑0.9ϫ10Ϫ3͒.
As seen in Fig. 6, the results on azobenzene can be ex-
plained without contradiction under the assumptions of a
thermal population distribution of the molecule in the inves-
tigated time range of Ͼ1 ps. There is no experimental evi-
dence for a stimulated emission signal which would be in-
dicative of a highly nonthermal energy distribution. Thus, a
strong deviation from a thermal distribution of these vibra-
tional modes seems to be very unlikely in terms of the
present model. On the other hand, the model involving ul-
trafast IVR explains the observed hot-bands with the help of
the anharmonic constants xij between the investigated vibra-
tional modes and the bath of the remaining modes very well.
Consequently, one basically observes the cooling of the
whole molecule due to the energy transfer from the molecule
to the solvent and not a mode selective de-excitation of the
investigated modes. The time scale of the cooling via inter-
molecular energy transfer ͑ca. 20 ps͒ is in a reasonable
range3,4 and compares well with the results of the transient
UV experiments in Ref. 37. The anharmonic frequency shifts
and broadening effects are a consequence of the intramolecu-
lar temperature and can be regarded as a intramolecular ther-
mometer which can be calibrated precisely with the help of
model calculations and also with steady-state experiments.
A clear distinction between thermal and a moderate non-
thermal energy distribution presently is not possible. In other
words, the concept of an intramolecular temperature eventu-
ally is a rough approximation. However, since this approxi-
mation readily can explain the experimental results as shown
in Sec. III A 1, this approach seems to be justified.
In conclusion, we have demonstrated here the concept of
a new intermolecular thermometer. The experimental data
obtained by transient IR spectroscopy combined with model
calculations give valuable qualitative insights into the effects
which can be expected when investigating the excitation of
vibrational modes initiated by a photoreaction. Future inves-
tigations going beyond this qualitative approach require sev-
eral improvements: ͑i͒ A higher time resolution on the order
of ca. 100 fs; ͑ii͒ smaller systems which can be modeled
theoretically with higher accuracy; ͑iii͒ selected vibrational
modes which, on the one side, have a large diagonal anhar-
monic constant and on the other side, are strongly coupled to
the internal conversion process; and ͑iv͒ an extension of the
frequency range into the Ͻ1000 cmϪ1 regime in order to
address for example torsional modes ͑found in this spectral
range͒ which might be expected to be strongly coupled
modes.
ACKNOWLEDGMENTS
The authors wish to thank Gerhard Stock, Eberhard
Riedle, Wolfgang Domcke, Paul Tavan, and Anne Myers for
very fruitful discussions, and Thomas Naegele, Werner Ga-
bler, and Joseph Wachtveitl for making the results of the UV
experiments available prior to publication. S.M.O. acknowl-
edges the support of a postdoctoral fellowship granted by the
Alexander von Humboldt Stiftung.
During the electronic excitation process, the Franck–
Condon active modes are excited, which may be observed by
transient Raman experiments. On the other hand, the tran-
sient IR experiments performed here investigates the ‘‘bath’’
modes which may have a different equilibration time than
the hot Franck–Condon modes.
The attempt to explain anharmonic frequency shifts only
with the diagonal anharmonic constants xkk which are ob-
tained when measuring the frequency of the overtone ͑as it
was done, for example, in Refs. 13, 16, 17, and 19͒ does not
explain the investigated experimental situation. Such a treat-
ment will give reasonable results only in the special situation
where the sum of the off-diagonal elements is smaller than
the diagonal element, i.e., ͑i͒ for very small molecules, ͑ii͒
for a special mode with extremely large diagonal anharmonic
constant term, or ͑iii͒ when energy flows selectively into
only one or very few modes. Without a clear stimulated
1 A. Lauberreau and W. Kaiser, Rev. Mod. Phys. 50, 607 ͑1978͒.
2 D. W. Oxtoby, Annu. Rev. Phys. Chem. 32, 77 ͑1981͒.
3 A. Seilmeier and W. Kaiser, in Ultrashort Laser Pulses, edited by W.
Kaiser ͑Springer-Verlag, New York, 1988͒, p. 279.
4 T. Elsaesser and W. Kaiser, Annu. Rev. Chem. Phys. 42, 83 ͑1991͒.
5 J. C. Owrutsky, D. Raftery, and R. M. Hochstrasser, Annu. Rev. Phys.
Chem. 45, 519 ͑1994͒.
6 R. Sension, S. Repinec, A. Szarka, and R. M. Hochstrasser, J. Chem.
Phys. 98, 6291 ͑1993͒.
7 K. Lenz, M. Pfeiffer, A. Lau, and T. Elsaesser, Chem. Phys. Lett. 229, 340
͑1994͒.
8 W. Zinth, C. Kolmeder, B. Benna, A. Irgens-Defregger, S. F. Fischer, and
W. Kaiser, J. Chem. Phys. 78, 3916 ͑1983͒.
9 S. J. Doig, P. J. Reid, and R. A. Mathies, J. Phys. Chem. 95, 6372 ͑1991͒.
10 W. L. Weaver, L. A. Hutson, K. Iwata, and T. L. Gustafson, J. Phys.
Chem. 96, 8956 ͑1992͒.
11 K. Iwata and H. Hamaguchi, Chem. Phys. Lett. 196, 462 ͑1992͒.
12 J. Qian, S. L. Schultz, R. G. Bradburn, and J. M. Jean, J. Phys. Chem. 97,
10638 ͑1993͒.
13 D. L. Phillips, J. M. Rodier, and A. B. Myers, Chem. Phys. 175, 1 ͑1993͒.
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions

Hamm, Ohline, and Zinth: Vibrational cooling after photoisomerization
529
14 M. Hofmann and H. Graener, Chem. Phys. 206, 129 ͑1996͒.
36 N. Biswas and S. Umupathy, Chem. Phys. Lett. 236, 24 ͑1995͒.
37
15 J. C. Owrutsky, Y. R. Kim, M. Li, M. J. Sarisky, and R. M. Hochstrasser,
Chem. Phys. Lett. 184, 368 ͑1991͒.
J. Wachtveitl, T. Nagele, B. Puell, W. Zinth, M. Kruger, S. Rudolph-
¨
¨
¨
Bohner, D. Oesterhelt, and L. Morode, Photochem. Photobiol. ͑in press͒;
16 P. O. Stoutland, R. B. Dyer, and W. H. Woodruff, Science 257, 1913
͑1992͒.
T. Nagele, W. Gable, W. Zinth, and J. Wachtveitl ͑in preparation͒.
¨
38
¨
¨
R. Kubler, W. Luttke, and S. Weckherlin, Z. Elektrochem. 64, 650 ͑1960͒.
17 S. K. Doorn, R. B. Dyer, P. O. Stoutland, and W. H. Woodruff, J. Am.
Chem. Soc. 115, 6398 ͑1993͒.
39 D. R. Armstrong, J. Clarkson, and W. E. Smith, J. Phys. Chem. 99, 17 825
͑1995͒, and references therein.
18 D. Raftrey, E. Gooding, A. Romanovsky, and R. M. Hochstrasser, J.
Chem. Phys. 101, 8572 ͑1994͒.
40 E. B. Wilson, J. C. Decius, and P. C. Cross, in Molecular Vibrations
͑Dover, New York, 1955͒.
19 T. Lian, S. E. Bromberg, H. Yang, M. Asplund, R. G. Bergmann, and C.
B. Harris, in Ultrafast Phenomena X, OSA Technical Digest Series, Vol.
8, Paper FE-27 ͑Optical Society of America, Washington, DC, 1996͒.
20 J. Owrutsky and A. Baonavskiu, in Ultrafast Phenomena X, OSA Tech-
nical Digest Series, Vol. 8, Paper PDP-4 ͑Optical Society of America,
Washington, DC, 1996͒.
41 T. Lian, Y. Kholodenko, B. Locke, and R. M. Hochstrasser, J. Phys.
Chem. 99, 7272 ͑1995͒.
42 H. H. Nielsen, Rev. Mod. Phys. 23, 90 ͑1951͒.
43 J. Pliva, J. Mol. Spect. 139, 278 ͑1990͒.
44 P. E. Maslen, N. C. Handy, R. D. Amos, and D. Jayatilaka, J. Chem. Phys.
97, 4233 ͑1992͒.
21 P. A. Anfinrud, C. H. Han, T. Lian, and R. M. Hochstrasser, J. Phys.
Chem. 95, 574 ͑1991͒.
45 A. Willettsm and N. C. Handy, Chem. Phys. Lett. 235, 286 ͑1995͒.
46 G. Herzberg, in Molecular Spectra and Molecular Structure. II. Infrared
and Raman Spectra of Polyatomic Molecules ͑Van Nostrand Reinhold,
New York, 1945͒.
22 P. Hamm, C. Lauterwasser, and W. Zinth, Opt. Lett. 18, 1943 ͑1993͒.
23 P. Hamm, S. Wiemann, M. Zurek, and W. Zinth, Opt. Lett. 19, 1642
͑1994͒.
47 In a more general form, Eq. ͑1͒ contains additional terms taking into
account the degeneracy and the vibrational angular momumentum quan-
tum numbers of the vibrational modes. Since azobenzene has no degener-
ate modes these terms can be omitted.
24 T. P. Dougherty and E. J. Heilweil, Opt. Lett. 19, 129 ͑1994͒.
25 F. Seifert, V. Petrov, and M. Woerner, Opt. Lett. 19, 2009 ͑1994͒.
26 P. Hamm, Chem. Phys. 200, 415 ͑1995͒.
27 K. Wynne and R. M. Hochstrasser, Chem. Phys. 193, 211 ͑1995͒.
48 R. M. Shelby, C. B. Harris, and P. A. Cornelius, J. Chem. Phys. 70, 34
͑1979͒.
28 T. Uzer and W. H. Miller, Phys. Rep. 199, 73 ͑1991͒.
29
R. Schneider, W. Domcke, and H. Koppel, J. Chem. Phys. 92, 1045
49 C. B. Harris, H. Auweter, and S. M. George, Phys. Rev. Lett. 44, 737
͑1980͒.
¨
͑1990͒.
30 L. Seidner and W. Domcke, Chem. Phys. 186, 24 ͑1994͒.
31 G. Stock, J. Chem. Phys. 103, 10 015 ͑1995͒.
32 T. Ikeda and O. Tsutsumi, Science 268, 1873 ͑1995͒.
33 H. Rau, in Photochromism: Molecules and Systems, edited by H. Durr and
H. Bouas-Lauran ͑Elsevier, Amsterdam, 1990͒, p. 165.
34 N. Siampiringue, G. Guyot, S. Monti, and P. Bortolus, J. Photochem. 37,
185 ͑1987͒.
50 C. B. Harris, R. M. Shelby, and P. A. Cornelius, Phys. Rev. Lett. 38, 1415
͑1977͒.
51 The description of the time dependence of the temperature by an expo-
nential function is a simple model assumption which may not be justified
in realistic cases. However, it is used as a reasonable assumption in the
present case where it will be shown that the transient absorption changes
may have a time response completely different from the time dependence
of the temperature.
35 R. Cimiraglia and H. J. Hofman, Chem. Phys. Lett. 217, 430 ͑1994͒.
J. Chem. Phys., Vol. 106, No. 2, 8 January 1997
Downloaded 24 Mar 2013 to 129.187.254.47. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/about/rights_and_permissions