Download Heterodynedetected timedomain measurement of I2 predissociation

Heterodynedetected timedomain measurement of I2 predissociation and vibrational
dynamics in solution
N. F. Scherer, L. D. Ziegler, and G. R. Fleming
Citation: The Journal of Chemical Physics 96, 5544 (1992); doi: 10.1063/1.462693
View online: http://dx.doi.org/10.1063/1.462693
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Heterodyne-detected time-domain measurement of 12 predissociation
and vibrational dynamics in solution
N. F. Scherer, L. D. Ziegler,a) and G. R. Fleming
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago,
Illinois 60637
(Received 21 October 1991; accepted 28 January 1992)
An understanding of the molecular mechanisms that
produce broad and structureless electronic absorption
spectra is central to studies of chemical dynamics in liquids
and solutions. 1,2 Such broadening often reflects the perturbation of the electronic and nuclear degrees of freedom of
the solute by the solvent medium. The spectral consequence of these interactions, however, is to mask the structural and dynamic information necessary to formulate molecular-level descriptions of chemical processes. The
preparation and detection of the evolution of coherent vibrational motion (Le., nuclear wave packets) of chromophores in solution by direct time-domain methods is an
experimental approach that facilitates the extraction of the
molecular vibrational spectrum. 3 (a) For photochemically
reactive species in liquid media, such studies may reveal
nuclear motion along the reaction coordinate and also
probe the role of the absorber-bath interactions.
With this goal in mind we have chosen to study a
simple molecular solvent and iodine as the (reactive) chromophore. The reaction is the predissociation of the B state
of 12, which is believed to occur via solvent-induced coupling of the B(Ou+ 3rI) and dissociative aeg 3rI) states. 4
It has been theoretically shown that vibrational coherences in both ground and excited electronic states, as well
as populations, are prepared when an ultrafast pulse interacts with an electronically resonant molecular sample. 3,5-7
In regions of optical transparency only impulsively excited
ground state vibrational coherences appear. 8- 1O Several experimental techniques have been demonstrated to detect
these vibrational coherences under conditions of electronic
resonance. 7,11-15 However, the ground or excited state assignment of these vibrational responses has not always
been clearly made, partiCUlarly for chromophores (Le., dye
modecules) in solution. The results reported here allow
clear assignment of all nuclear dynamic contributions to
the signal.
The timescales of iodine recombination and relaxation
following predissociation have been reported. Condensed
phase transient absorption l 6-19 and resonance Raman 20
studies have monitored the geminate recombination and
vibrational relaxation on the picosecond time scale. Harris
and co-workers established that B-state predissociation in
chlorinated methane solvents occurs in less than two
picoseconds. 19 The spontaneous B-X resonance Raman
scattering of 12 in a variety of solvents has been analyzed by
Sension and StraussY As a result of a Raman excitation
profile study, they conclude that the optical dephasing time
of 12 in n-hexane is about 300 fs and that the major line
broadening mechanism for the B-X transition in solution
is ascribed to inhomogeneity. However, early estimates of a
long excited state lifetime 18 resulted in uncertainty as to
the origin of the homogeneous broadening.
In this communication we report time-domain measurements of the ultrashort-pulse optically induced dichroism OfI2 in solution. The excitation and probe pulses at 580
nm are resonant with the broad B-X (630-450 nm) absorption band. Our approach is a form of polarization
spectroscopy,22 where the decay of the pump-pulse induced anisotropy is probed via optical heterodyne detection.
The time dependence of the heterodyne-detected optically induced transient dichroism signal for pump-probe
pulses separated in time by td is described b/2
(1)
where R(td) describes the overall rotational reorientation
relaxation of the anisotropy induced by the first pulse and
W(td) is the time-dependent change in the energy of the
signal field. In what follows we concentrate on W(td), the
work done on the detected optical field by the pump-probe
induced material polarization.
We have derived expressions for W(td) using a density
matrix treatment for a four-level system consisting of two
vibrational levels of two dipole-coupled electronic states
excited by pulses of finite duration but shorter than all the
relevant material dephasing times of the system. A full
account will be given elsewhere. 23 It is found that in dichroism measurements of such a four level system the energy of the probe beam will be transiently affected, in general, by three material responses of differing molecular
origin: (i) excited state population, (ii) excited state vibrational coherence, and (iii) ground state vibrational coherence. Since the amplitUde of the three contributions to the
signal are determined by products of the same FranckCondon factors it is anticipated that their initial contributions to the dichroic response will be similar in magnitude.
The optical dephasing time T2 does not affect such pumpprobe signals. 5
The sample is excited and probed by tunable 30 fs
FWHM Gaussian pulses at 100 kHz repetition rate. 24-26
The dichroic part of the molecular nonlinear response
function is selected by means of an in-phase local
oscillator27 that is derived from the probe pulse and is
adjusted to be 20 times the homodyne intensity. In practice, the dichroism is obtained by taking the difference of
two scans each with the same magnitude local oscillator
but of opposite sign. The 1T shift of the local oscillator
phase is obtained by rotating the polarization analyzer that
J. Chern.asPhys.
96 (7),
1 April
1992
5544
© 1992 American Institute of Physics
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Letters to the Editor
follows the sample by equal amounts in opposite directions. This differencing approach removes the homodyne
and any small residual birefringence signal from the dichroism measurement. 28 5 mM 12 (Aldrich) in n-hexane
(Baker spectrophotometric grade) was flowed in a 1 mm
cell to avoid thermal heating and lensing effects and has an
optical density of 0.15 at 580 nm. All measurements are
performed at 295 K. The energies of the pump and probe
beams at the sample are 3-4 nJ and 100-200 pJ, respectively. A mechanical chopper is used to amplitude modulate the pump beam. The induced modulation of the probe
beam transmitted through the analyzer is detected by a
photomultiplier tube and is processed in a lock-in amplifier
(SRS 530) referenced to the amplitude modulation. The
lock-in signal is recorded for each step of the optical delay
line (1 s accumulation) and approximately 4 scans are
averaged together.
The optically induced dichroism of 12 in n-hexane excited and probed by 30 fs pulses centered at 580 nm is
shown in Fig. I (a). Also shown in this figure is the intensity autocorrelation of these pulses. Following the time of
pump-probe overlap (::= 50 fs) and coherent artifact
effects,29 the most obvious feature of this dichroic response
is the oscillation with an ::= 150 fs period that persists for
several picoseconds. This oscillation corresponds to a level
spacing of 210 cm - 1 in the vibrational superposition.
Linear prediction singular value decomposition 30 analysis was used to determine the number of parameters for
the exponentially damped cosinusoidal terms that describe
the data set. This method of analysis has been used to
determine the frequency, phase, and time constant of vibrational wave packets in dye molecules. II Standard nonlinear least-squares approaches to data fitting are not very
reliable due to the number of parameters involved.
Figure 1(b) shows a singular value analysis performed
with the assumption (see below) that the experimental
data results from a sum of exponentially damped cosinusoidal functions
SUd)
=
L Ai cos (UJ;fd + cp;)e - t,lT; ,
(2)
i
where UJi is a vibrational frequency difference in either electronic state. The fit to the data for pump-probe time delays
td is excellent and the corresponding parameters are summarized in the figure caption. This analysis finds three
damped oscillatory components and two purely exponentially damped components. The oscillatory components are
identified with the ground state fundamental (Llv = 1),
211 cm - I, the first overtone (Llv = 2), 424 cm -I, and
with the excited state vibrational spacing of 107 cm - I.
The ground state frequencies of iodine in solution are
known from resonance Raman spectra while the observed
excited state frequency is almost the same as the B-state
gas phase value. 31 The vibrational coherence contributions
to the dichroic response are characterized by cosinusoidal
modulations whose phases are zero for the ground state
wave packet and nearly 'IT for the excited state wave packet,
respectively. Intuitively, a sign or 'IT phase shift in the signal
5545
reflects the gain!loss, i.e., absorptive vs emissive character
of the system response to the probe pulse.
The time constants (1) of the ground and excited state
components are significantly different. In the case that rotational reorientation is slow compared to vibrational
dephasing the damping constant is the vibrational dephasing time T 2v' When both times are similar the rotational
contribution must be removed from the damping constant
to obtain the vibrational dephasing time. As the fit in Fig.
1(b) demonstrates (see caption) these two conditions apply to the excited and ground state vibrational coherences
respectively.
A single exponential relaxation component (UJ = 0) of
comparable magnitUde, decay time and sign to the excited
state vibrational coherence is also clearly evident in the
data. This response is identified with the excited state population and decays with its characteristic TI relaxation
time. The other longer lived exponential term with the
same sign as the ground state oscillatory term is assigned to
rotational relaxation.
Figure 2 shows the real part of the Fourier transformed iodine dichroism response of Fig. 1. The real spectrum of the dichroism signal shows positive peaks at zero,
211 and 424 cm - I and negative peaks at ::.::: 12 and 107
cm - 1.32 Overtone bands appear in the dichroism signal for
the same reason they appear in the spontaneous resonance
Raman spectrum. In this case the overtone response is
stimulated since it falls within the spectral bandwidth of
the pump pulse. The sign of the peaks, in the case of
tpulse < T 2, indicates the electronic origin of the frequency
components.
The excited state parameters provide direct information about the subpicosecond predissociation dynamics of
the 12 B state in solution. The excited state vibrational
response decays via both popUlation loss and pure dephasing. Therefore, in general, the oscillatory and exponential
contributions to the excited state signal will decay with
different time constants. In the present case, however, we
find 12v::= TI ::=200 fs. This result implies that vibrational
dephasing results predominantly from population decay of
both excited state vibronic levels involved in the vibrational coherence.
The finding that pure dephasing is not the dominant
mechanism for the decay of the excited state vibrational
coherence is in accord with the resonant light scattering
studies of Sension and Strauss.21 No resonance fluorescence is discernible in their published spectra, indicating3
that pure dephasing is slow compared to the population
decay. This observation alone suggests that the lifetime of
the iodine B state (T1 ) should be !T2 or "'" 150 fs, a value
not inconsistent with our directly observed value of 200
± 50 fs. Experimental uncertainties aside, the two measurements refer to somewhat different quantities. The resonance Raman estimate represents an average over the
entire absorption band, whereas the induced dichroism signal samples only the portion of the excited state surface
accessible within the laser bandwidth.
Previous studies have found that the optical dephasing
rate of molecules in solution, such as CS2,33 azulene,34 and
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128.32.208.2 On: Thu, 29 May 2014 18:35:24
Letters to the Editor
5546
Optically-Induced Dichroism of Iodine in n-Hexane
5.0
4.5
4.0
SmM Iodine in n-Hexane
3.5
:;E
--ctS
3.0
2.5
2.0
c
1.5
U5
1.0
0>
Dichroism
Autocorrelation
0.5
0.0
-0.5
-1.0
-1.5
0.0
O.S
1.0
(al
1.S
2.0
2.S
3.0
Time (ps)
Linear Prediction-Singular Value Decomposition of Iodine Dichroism
0.8
+
0.6
+
0.4
0.2
~
0
+
.....~
rJ)
-0.2
-11'
,"" '
,, '',
,"' ," ,
,, '\ : ' ,," , ," , ," , ," , ,-,
,,
"
1
(bl
1.5
2
''\
,-
2.5
3
Time Cps)
FIG. 1. (a) Solid line, transient dichroic response of 12 in n-hexane. Dashed line, pump-probe pulse intensity autocorrelation. (b) Data analysis of
transient dichroism signal. Experimental data, +. Solid line, fitted curve. Fitting parameters frequency, amplitude, phase, time constant: WI = 211
em-I, Al =0.21, tPI =4±1O deg., TI = 940±100 fs; W2 = 424 em-I, A2 = 0.04, tP2= -19±20 deg., T2=900±I00 fs; W3= 111 em-I, A 3 =0.16,
tP3 = - IS5± 10 deg., T3 = 210±50 fs; W4 = 0 em -1, A4 = 0.43, tP4 = ISO deg., T4 = IS0±50 fs; Ws = 0 em - 1, As = 0.32, tPs = 0 deg., TS = 1350± 100
fs. Components 1, 3, and 4 have been plotted individually in the lower portion of the figure offset by - 0.6 units.
dyes,12,13 occurs on the time scale of 10-50 fs and results
primarily from pure dephasing. The present results for iodine stand in strong contrast with these observations for
electronically highly excited (or conjugated) po1yatomic
molecules with large transition dipole moments. A similar
conclusion was recently obtained for S02 in solution by a
resonance Raman approach. 35
In general, 1IT2 = ~(1ITle + 1IT1g ) + 1111', where e
J. Chern. Phys., Vol. 96, No.7, 1 April 1992
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Letters to the Editor
Deconvoluted Spectrum of Iodine Dichroism
5mM Iodine in n-Hexane
3.5
3.0
25
--
RealFFT
2.0
1.5
1.0
.. j····································i················ ............ .
,
,,,
,,
,,
0.5
0.0
~.5
-1.0
-50
i
t
0
,
t
50
,,
,,,
,
,,,
~
100 150 200 250 300 350 400 450 500 550 600
Frequency
FIG. 2. Deconvoluted real portion of the fast Fourier transform of the
iodine dichroism data of Fig. J. Arrows indicate the positive and negative
peaks of the real spectrum, referenced to the nuclear components discussed in the text and correspond to the five components from the linear
prediction analysis of Fig. l( b). The dashed horizontal line indicates the
contribution of the electronic (Il-function) response to the data.
and g refer to excited and ground states and 1! is the pure
dephasing contribution to the optical dephasing. In the
present case T lg>Tie and the lack of fluorescence emission
implies 11' > Tie' Therefore, the optical dephasing of iodine
appears to be entirely due to population decay, that is TI
processes, on the time scale of 200 fs. This population decay could be vibrational relaxation or dissociation of the B
state. Solution phase vibrational relaxation within the X
and A states of iodine occurs on the picosecond
timescale. 19 ,20 We therefore conclude that curve crossing
(i.e., reaction) takes place within three vibrational periods
(TI = 200 fs) with near unit quantum efficiency. The solvent dependence of the dissociation rate will be presented
in a future manuscript. 23 The slow pure dephasing of the
optical transition can be understood from the low-frequency spectral density of the solvent and the absence of a
change in charge character or dipole moment on B-X
excitation. 36-38
This work was supported by the National Science
Foundation. N.F.S. thanks the NSF for a postdoctoral fellowship. We thank Professor Glen Millhauser for providing us with the singular value decomposition routine. We
thank Min Cho for valuable discussions.
')Department of Chemistry, Northeastern University, Boston, MA 02115.
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Fleming, J. Chern. Phys. 96, 5033 (1992). This paper develops a collective-motion Brownian oscillator approach to self-consistently analyze
the solvent dynamics measured through fluorescence Stokes shift of a
dye molecule in acetonitrile and the nonresonant optically induced birefringent response of the neat acetonitrile solvent.
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