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The Influence of Vibrational Excitation on the Photoisomerization of trans-Stilbene in Solution† Kristin A. Briney, Leslie Herman, David S. Boucher, Adam D. Dunkelberger, and F. Fleming Crim* Department of Chemistry, UniVersity of Wisconsin-Madison, Madison, Wisconsin, 53706 ReceiVed: March 26, 2010; ReVised Manuscript ReceiVed: June 14, 2010
Preparing electronically excited trans-stilbene molecules in deuterated chloroform using both one-photon excitation and excitation through an intermediate vibrational state explores the influence of vibrational energy on excited-state isomerization in solution. After infrared excitation of either two quanta of C-H stretch vibration |2νCH〉 at 5990 cm-1 or the C-H stretch-bend combination |νCH + νbend〉 at 4650 cm-1 in the ground electronic state, an ultraviolet photon intercepts the vibrationally excited molecules during the course of vibrational energy flow and promotes them to the electronically excited state. The energy of the infrared and ultraviolet photons together is the same as that added in the one-photon excitation. Transient broadband-continuum absorption monitors the lifetime of electronically excited molecules. The lifetime of excited-state transstilbene after one-photon electronic excitation with 33 300 cm-1 of energy is (51 ( 6) ps. The excited-state lifetimes of (55 ( 9) ps and (56 ( 7) ps for the cases of excitation through |2νCH〉 and |νCH + νbend〉, respectively, are indistinguishable from that for the one-photon excitation. Vibrational relaxation in the electronically excited state prepared by the two-photon excitation scheme is most likely faster than the barrier crossing, making the isomerization insensitive to the method of initial state preparation. 1. Introduction Vibrational energy can dramatically influence the course of a chemical reaction or a photodissociation, as illustrated by the ability of excitation in a specific vibrational mode to promote one reaction pathway over another competing pathway.1–4 One example is the vibrationally mediated photodissociation of ammonia,2 in which photolysis from an excited symmetric N-H stretching state yields NH2 in its ground electronic state but photolysis from an asymmetric N-H stretching state yields NH2 primarily in its excited electronic state. The difference between the two reaction pathways lies in their sampling of the conical intersection between the excited- and ground-state surfaces. Such examples of vibrational selectivity in the gas phase motivate experiments that test the influence of vibrational excitation on reactions in solution. The flow of vibrational energy, both within an excited molecule and into the surrounding solvent, is a critical aspect of translating gas-phase measurements into solution. Couplings within a molecule, which control vibrational energy flow in isolated molecules, dominate intramolecular energy flow in relatively weakly interacting solvents even though fluctuating interactions with the solvent potentially alter the specific relaxation pathway.5 Interactions with the solvent are the dominant feature of intermolecular energy transfer, in which vibrational energy flows from the initially excited molecule into vibrations of the solvent molecules as well as into collective modes of the solvent.5,6 Because the first process is often faster, sequential relaxation in which intramolecular energy transfer precedes intermolecular relaxation is common. The key to vibrationally mediated photodissociation in isolated molecules is preparing a vibrational eigenstate with one †
Part of the “Reinhard Schinke Festschrift”. * To whom correspondence should be addressed. Email: fcrim@ chem.wisc.edu.
high-resolution laser pulse and subsequently exciting the molecule to an electronically excited state with a second pulse. Because the vibrationally excited eigenstate has different Franck-Condon factors for the transition to the electronically excited state than does the ground vibrational state molecule, the second pulse can prepare the electronically excited molecules with different initial vibrational motions. In the examples of ammonia2 and phenol,3 the vibrations accessed in the excited state alter the behavior at the conical intersection, as reflected in the state or energy distribution of the products. The situation is different in solution because of the frequent interactions with the solvent. Thus, in liquid phase experiments, we use an ultrashort laser pulse to prepare an initial vibration, which is not an eigenstate of the molecule but rather a set of the zero-order states, such as C-H stretching vibrations, that provide the oscillator strength for the vibrational transition.5 Because this initially prepared, nonstationary vibrational state rapidly relaxes by intramolecular and intermolecular energy flow,7 we must intercept the molecule early in its relaxation process and transfer it to an electronically excited state. In analogy to the gas-phase experiments, this approach prepares molecules in the electronically excited state with initial vibrational motions determined by the ground-state excitation and the Franck-Condon factors for the electronic transition. In these liquid-phase experiments, we follow a photoisomerization that involves a conical intersection analogous to those in ammonia and phenol by observing the excited-state absorption of the isomerizing molecule. Unraveling the influence of the initial vibrational excitation requires that we compare the decay time of excited-state molecules prepared through an excited vibrational state to that of molecules prepared by a one-photon excitation that adds the same total energy. We choose trans-stilbene for our first studies of the effect of vibrational energy on a condensed-phase photoisomerization because it is particularly well-characterized both experimentally8–19
10.1021/jp102752f 2010 American Chemical Society Published on Web 07/15/2010
Photoisomerization of Excited trans-Stilbene
J. Phys. Chem. A, Vol. 114, No. 36, 2010 9789 studies of the influence of vibrational excitation on condensedphase molecules that are analogous to those possible for isolated gas-phase molecules. 2. Experimental Approach
Figure 1. Schematic drawing of the potential energy curves for stilbene illustrating vibrationally mediated photoisomerization measurements. A pulse of infrared light (λvib) initially excites two quanta of C-H stretching vibration in the ground electronic state S0. As that vibrational energy flows into other modes, a pulse of ultraviolet light (λel) transfers some of the molecules to the electronically excited state S1. A third broadband continuum pulse (λprobe) monitors the excited state absorption (SN r S1) to determine the decay time τel for the electronically excited state. The numbers in the sketch give the fraction of the molecules following each of the indicated pathways.
and theoretically.20–25 Figure 1 is a schematic drawing of the energetics of the cis-trans isomerization of stilbene.8 Isomerization of trans-stilbene begins with excitation to the S1 surface on which it passes over a barrier and through a conical intersection to form either trans- or cis-stilbene in its ground electronic state.21 The arrows labeled λvib, λel, and λprobe in Figure 1 illustrate the preparation of vibrationally excited trans-stilbene molecules, their excitation to the electronically excited state, and their interrogation by excited state absorption. An infrared pulse (λvib) initially excites either a C-H stretching overtone, |2νCH〉, or a combination of the C-H stretch and bend, |νCH + νbend〉.26 After a period ∆t0 during which vibrational energy flows into other modes of the system, an ultraviolet pulse (λel) transfers molecules to the S1 excited state, and then a broadband continuum pulse (λprobe) monitors these excited molecules by excitation to a higher lying electronic state SN. Varying the time ∆t0 between the vibrational and electronic excitation pulses selects different subsets of vibrationally excited modes that potentially provide access to different portions of the S1 surface in the electronic excitation step. Monitoring the absorption on the SN r S1 transition at different intervals ∆t1 after the electronic excitation measures the lifetime of the electronically excited molecules. Comparing the decay rate of molecules excited through an intermediate vibrational state with that of molecules prepared by adding the same amount of energy through one-photon electronic excitation tests the influence of initial vibrational excitation on the excited state dynamics. These experiments show that a combination of well-characterized ground-state vibrational energy transfer with time-resolved electronic excitation and excited-state interrogation allows
A regeneratively amplified Ti:Sapphire laser system generates the infrared, ultraviolet, and broadband continuum pulses used in this experiment. The laser system produces 3.5 mJ, 35 fs pulses centered at 800 nm at a repetition rate of 1 kHz. We purposely chirp these short pulses to optimize subsequent nonlinear processes, obtaining measured instrument response times of 300-500 fs. Ten percent of the 800 nm light drives an optical parametric amplifier (OPA) that uses a 5 mm thick Type II β-barium borate (BBO) crystal cut at 27° to produce a total of 40 µJ of near-infrared light divided almost equally between signal and idler pulses. We tune the longer wavelength (idler) to excite either two quanta of C-H stretch |2νCH〉 at 5990 cm-1 or the stretch-bend combination |νCH + νbend〉 at 4650 cm-1. We double 30% of the 800 nm light to drive a noncollinear optical parametric amplifier (NOPA)27 that amplifies a portion of a white-light continuum in two sequential 1 mm thick Type I BBO crystals cut at 29°, producing up to 20 µJ of light at 480 nm. Mixing light from the NOPA with the shorter wavelength (signal) light from the OPA in a 300 µm thick 27° Type I BBO crystal generates 1-2 µJ of light between 350 and 365 nm. For the one-photon excitation measurements, we combine light from the NOPA with 300 µJ of 800 nm light in the same crystal to generate 0.5 µJ of 300 nm light. We rotate the polarization of the ultraviolet light with a half-wave plate. The probe continuum comes from focusing approximately 50 nJ of 800 nm light that leaks through a dielectric mirror into a 6 mm sapphire plate to produce a broadband continuum from 400-800 nm. The polarization of the 800 nm light, which we set with a half-wave plate, determines the polarization of the probe light. However, some depolarization that occurs during the continuum generation contributes to the uncertainty in the measured anisotropy. The infrared, ultraviolet, and continuum beams spatially overlap in a 1 mm thick flow cell. Lenses with focal lengths of 300 mm focus the infrared and ultraviolet beams, and a parabolic mirror with a focal length of 100 mm focuses the continuum beam. Two computer-controlled delay stages manage the relative timing of the pulses. We follow both the absorption of the ultraviolet light (λel) and that of the broadband continuum (λprobe). To monitor the S1 r S0 transition in trans-stilbene, we measure the absorption of λel with two photodiodes, one before and one after the sample cell. A 500 Hz chopper synchronized to the laser modulates the infrared light for background subtraction, and we obtain the absorption at each time delay by averaging the signal from 5000 laser pulses. To monitor the SN r S1 transition, we measure the absorption of λprobe separately at each time delay. A spectrometer collects the continuum beam that passes through the sample along with a reference beam that does not pass through the sample and disperses each of them onto separate 1024 element photodiode arrays.28 We accumulate the signal from 400 laser pulses on the photodiode arrays with and without the infrared light present to obtain a transient difference spectrum and then average between 40 and 75 of these spectra at each time delay. We determine the cross-correlation between the infrared vibrational excitation pulse (λvib) and the ultraviolet electronic excitation pulse (λel) to be either 300 fs for |2νCH〉 or 500 fs for |2νCH + νbend〉 by measuring the time-dependent two-photon mixing signal in a Type II 33° BBO crystal. We obtain an
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instrument response time of 500 fs for the continuum absorption experiments by measuring the chirp in the broadband continuum probe λprobe. The chirp is detectable as the time difference between the prompt rise in absorption for the red and blue edges of the broadband spectrum near ∆t1 ) 0 ps in a transient absorption trace. Trans-stilbene (96% purity) and the deuterated chloroform solvent (99.8% deuterated) come from SigmaAldrich, and we use them without further purification. Sample concentrations are 100 mM for all measurements. 3. Results Determining the influence of vibrational excitation on photoisomerization involves preparing a vibrationally excited molecule in the ground electronic state, promoting it to an electronically excited state during the course of vibrational energy flow, and following the evolution of the molecule in the excited state. Preparing the vibrationally excited molecule requires information about the energy flow in the ground electronic state, which we obtain by observing the S1 r S0 absorption at different times after the vibrational excitation. This technique of monitoring the time-dependent absorption of ultraviolet light by vibrationally excited molecules has proven useful for a variety of systems,29–35 and we have previously used it to observe vibrational energy flow in both trans- and cisstilbene.26 This approach amounts to observing the transient absorption of the ultraviolet photon used to transfer the vibrationally excited molecule from the ground electronic state S0 to the excited electronic state S1. Transient broadband absorption of the SN r S1 transition from the excited state to a higher lying state is our means of following the evolution of molecules in the excited state. To identify any changes in the lifetime of electronically excited state molecules arising from vibrational pre-excitation, we first measure the excited-state lifetime of molecules prepared by one-photon excitation from thermally populated states. With that information in hand, we can compare their time evolution to that of molecules prepared with the same amount of energy added by the combination of vibrational and electronic excitation. 3.1. Vibrational Energy Flow in the Ground Electronic State. Our previous studies using transient electronic absorption to probe energy transfer in vibrationally excited trans-stilbene show that energy deposited into the C-H stretch overtone |2νCH〉 or the stretch-bend combination |νCH + νbend〉 initially relaxes into a subset of states on two fast time scales. It then decays in approximately 10 ps into some combination of low frequency modes of stilbene and modes of the solvent.26 The two vertical arrows labeled λvib and λel in Figure 1 show a generalized scheme for the measurement, where the energy initially resides in the C-H stretching modes and subsequently flows into other modes. Selecting a long wavelength for λel, for which there is little absorption by ground vibrational state molecules, allows us to monitor the flow of energy out of the initially excited C-H stretching modes into other modes that absorb more strongly at that wavelength. The points in Figure 2 are the transient ultraviolet absorption measured after excitation of either the C-H stretch overtone |2νCH〉 (upper panel) or the combination band |νCH + νbend〉 (lower panel) in the experiments described here. In both studies, the S1 r S0 absorption rises and falls in less than 2 ps. (There is also a more slowly decaying weak absorption hidden within the noise of the data in the figure. Although it is more apparent in other measurements, it is not the focus of the experiments described here.) The Gaussian curves below each set of points show the measured cross correlation functions between the infrared and ultraviolet pulses.
Figure 2. Time evolution of the transient S1 r S0 electronic absorption ∆AS0 of vibrationally excited trans-stilbene. The upper panel shows the absorption at λel ) 366 nm (27 310 cm-1) following initial excitation of two quanta of C-H stretching vibration (|2νCH〉) at λvib ) 1.67 µm (5990 cm-1). The line through the points is a fit of the initial rise and decay of the absorption with the convolution of the measured instrument response function and a single exponential decay. The Gaussian curve below the data shows the instrument response, which has a width of 300 fs. The exponential decay time from the fit is τvib(2νCH) ) (410 ( 110) fs. The lower panel shows the absorption at λel ) 349 nm (28 650 cm-1) following initial excitation of the combination of one quantum of C-H stretching vibration and one quantum of bending excitation (|νCH + νbend〉) at λvib ) 2.15 µm (4650 cm-1). The line through the points is a fit of the initial rise and decay of the absorption with the convolution of the measured instrument response function and a single exponential decay. The Gaussian curve below the data shows the instrument response, which has a width of 500 fs. The exponential decay time from the fit is τvib(νCH + νbend) ) (260 ( 50) fs. The arrows mark the delay time at which we intercept the ground-state vibrational relaxation in the three-photon experiment.
We fit the initial rise and decay of the absorption with the convolution of the measured cross-correlation function and a single exponential decay. Because the zero of time is uncertain to within a few time steps, we initially adjust it to give the best qualitative agreement with the data and allow it to vary by up to one 50 fs time step in the final fits to the data. These fits yield decay times of τvib(2νCH) ) (410 ( 110) fs for the |2νCH〉 mode and τvib(νCH + νbend) ) (260 ( 50) fs for the |νCH + νbend〉 mode where the uncertainties are the standard deviation in the fit values for eight and nine traces, respectively. The time evolution we observe for 100 mM solutions is qualitatively similar to that observed previously for 500 mM solutions,26 but there are quantitative differences.36 The evolution of the transient absorption that we observe here and have observed previously is consistent with a cascade of vibrational energy out of the C-H stretching modes through tiers of coupled vibrational modes, {|n1〉} and {|n2〉}, and eventually into the solvent collective modes, {|g〉},
|2VCH〉 f {|n1〉} f {|n2〉} f {|g〉} The different Franck-Condon factors for each of the tiers produces an absorption that varies in time as the energy flows
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Figure 4. Time evolution of the rotational anisotropy r(t) for the S1 electronically excited state of trans-stilbene prepared by excitation of the S1 r S0 transition and probed by transient absorption on the SN r S1 transition. The single exponential fit gives a rotational diffusion time of τR ) (19 ( 3) ps and an initial anisotropy of r0 ) (0.28 ( 0.10).
ps after 300 nm excitation of trans-stilbene, which agrees with previous observations of the SN r S1 transition.12 The absorption of S1 trans-stilbene decays as a function of the time between the ultraviolet excitation pulse (λel) and the continuum probe (λprobe). The middle trace in the figure shows the time evolution of the 585 nm maximum with the effects of rotational anisotropy removed by taking the appropriate combination of the signals for perpendicular I⊥(t) and parallel I|(t) relative polarizations of the excitation and continuum probe pulses,37
S(t) ) (I| + 2I⊥)/3 ) Aele-t/τel Figure 3. (Upper Panel) Transient electronic SN r S1 absorption spectrum ∆AS1 for trans-stilbene excited to S1 from thermally populated vibrational states. The time interval between the S1 r S0 excitation and the measurement of the spectrum is ∆t1 ) 15 ps. The arrow above the spectrum marks the wavelength (λprobe ) 585 nm) used to probe the time evolution in the SN r S1 transient absorption. (Lower Panel) Time evolution of the transient SN r S1 electronic absorption ∆AS1 of electronically excited trans-stilbene at λprobe ) 585 nm following onephoton excitation at λel ) 300 nm (33 300 cm-1). The upper trace is the isotropic decay obtained by taking the combination of the measurements for perpendicular and parallel relative polarizations of the electronic excitation and probe light, as described in the text. The single exponential fit shown as a solid line gives a population lifetime of τel ) (51 ( 6) ps. The lower trace shows the time evolution for the two different relative polarizations with a solid line that is a fit to eq 3 or eq 4 using the rotational diffusion time of τR ) 19 ps. These fits give a population lifetime of τel ) (52 ( 6) ps.
through the states. Starting from the C-H stretch overtone or the stretch-bend combination, both of which have small Franck-Condon factors for the S1 r S0 transition, energy quickly flows into a set of modes {|n1〉} with larger FranckCondon factors, causing the initial rise in the absorption on a time scale that is comparable to or faster than the experimental resolution. We deduce that the energy quickly moves into a tier {|n2〉} with smaller collective Franck-Condon factors before eventually relaxing into a set of final states {|g〉} made up of solvent modes and possibly low frequency stilbene modes. We intercept the energy flow at the point of maximum ultraviolet (λel) absorption, which we associate with the first tier of strongly coupled states {|n1〉}. This electronic excitation potentially allows population of a different set of excited vibrations on S1 than prepared by single-photon excitation. 3.2. Excited-State Dynamics. The first step in monitoring the electronically excited molecules is preparing them by onephoton excitation and probing them by broadband continuum absorption on the SN r S1 transition. The upper panel in Figure 3 shows the absorption spectrum obtained at a time ∆t1 ) 15
(1)
Fitting this isotropic signal gives an excited-state population lifetime of τel ) (51 ( 6) ps for trans-stilbene in deuterated chloroform. The uncertainty in the excited-state lifetime is the standard deviation of the decay times from fitting five sets of isotropic data,38 and the lifetime we obtain in deuterated chloroform is consistent with measurements in other solvents.11,14,39 The decay in the signal reflects the movement of excited-state trans-stilbene away from the Franck-Condon region for the S1 r S0 transition. Similarly, we obtain the rotational diffusion time, τR, by constructing the rotational anisotropy, r(t),
r(t) ) (I| - I⊥)/(I| + 2I⊥) ) r0 e-t/τR
(2)
and fitting it to a single exponential decay where r0 is the initial anisotropy. Figure 4 shows a fit to the decay of the anisotropy r(t) that gives a rotational diffusion time of τR ) (19 ( 3) ps in deuterated chloroform with an initial anisotropy of r0 ) (0.28 ( 0.10). This anisotropy decay time agrees with the rotational diffusion times for trans-stilbene in other solvents of similar viscosity, 19 ps in methanol and 25 ps in octane.11,39 3.3. Vibrationally Mediated Photoisomerization. Initial vibrational excitation in S0 followed by electronic excitation to S1 and subsequent probing of the time evolution in S1 tests the influence of vibrational excitation on the isomerization of transstilbene. The arrows in Figure 1 illustrate the experiment. An infrared photon excites a ground-state vibration, either two quanta of C-H stretch |2νCH〉 at 5990 cm-1 or a stretch-bend combination |νCH + νbend〉 at 4650 cm-1, and after a short delay ∆t0 an ultraviolet photon promotes vibrationally excited molecules to the excited electronic state. The critical comparison is between this two-step preparation scheme and single-step excitation that adds the same total energy of 33 300 cm-1. After a second time delay ∆t1 we measure the vibrational excitationdependent transient absorption with a broadband continuum
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Figure 5. (Upper panel) Transient electronic SN r S1 absorption spectrum ∆AS1 for trans-stilbene excited to S1 following initial excitation of the C-H stretching overtone state (|2νCH〉). The time between the vibrational excitation in S0 and the electronic excitation to S1 is ∆t0 ) 0.25 ps, and the time between the S1 r S0 excitation and the measurement of the spectrum is ∆t1 ) 15 ps. The arrow above the spectrum marks the wavelength (λprobe ) 585 nm) used to probe the time evolution in the SN r S1 transient absorption. (Lower panel) Time evolution of the 585-nm transient SN r S1 electronic absorption ∆AS1 of trans-stilbene excited to S1 following initial excitation of the C-H stretching overtone state (|2νCH〉). The solid line through the points is a fit of eq 4 to the data using a rotational diffusion time of τR ) 19 ps and r0 ) 0.28. The fit gives a population lifetimes of τel ) (55 ( 9) ps.
pulse. A comparison of the excited-state lifetime obtained in this case to the value observed without vibrational excitation quantifies the effect of vibration on the time evolution in S1. We fix the first time delay at the maximum of the ultraviolet absorption near ∆t0 ) 0.25 ps in order to capture the vibrational energy early in its flow. The arrow in Figure 2 marks this delay, at which time the initial vibrational excitation is likely to reside in the subset of the most strongly coupled and, hence, most rapidly populated states. We measure the time evolution in the excited state by scanning the time delay between the ultraviolet photon and continuum probe, ∆t1, just as we did in the measurements on molecules without added vibrational energy. Continuum absorption from the excited state S1 after excitation through the C-H stretch overtone vibration |2νCH〉 or the stretch-bend vibration |νCH + νbend〉 in the ground electronic state S0 gives spectra, shown as the upper panels in Figures 5 and 6, which are similar to those obtained following one-photon excitation directly to S1. Rotational diffusion in both the intermediate vibrational state and excited state potentially makes the polarization dependence in a three-photon experiment more complex than in a two-photon measurement.41,42 However, the different time scales of vibrational energy flow and rotational diffusion largely mitigate this complication for our measurements. The similarity of the structure of trans-stilbene in its ground and first excited states23,43 suggests that the rotational diffusion time in the ground state is similar to the 19-ps diffusion time we measure in the excited state. Because we intercept the vibrationally excited molecules only 0.25 ps after their initial preparation, they do not rotate significantly before the ultraviolet photon λel transfers them to the excited state. Thus, there is no rotational diffusion of the vibrationally excited molecules, and we can analyze the time
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Figure 6. (Upper panel) Transient electronic SN r S1 absorption spectrum ∆AS1 for trans-stilbene excited to S1 following initial excitation of a combination state containing one quantum of C-H stretching vibration and one quantum of bending vibration (|νCH + νbend〉). The time between the vibrational excitation in S0 and the electronic excitation to S1 is ∆t0 ) 0.25 ps, and the time between the S1 r S0 excitation and the measurement of the spectrum is ∆t1 ) 15 ps. The arrow above the spectrum marks the wavelength (λprobe ) 585 nm) used to probe the time evolution in the SN r S1 transient absorption. (Lower panel) Time evolution of the 585-nm transient SN r S1 electronic absorption ∆AS1 of trans-stilbene excited to S1 following initial excitation of a combination state containing one quantum of C-H stretching vibration and one quantum of bending vibration (|νCH + νbend〉). The solid line through the points is a fit of eq 4 to the data using a rotational diffusion time of τR ) 19 ps and r0 ) 0.28. The fit gives a population lifetimes of τel ) (56 ( 7) ps.
evolution of the three-photon experiment exactly as we do the two-photon experiment. Even if we interrogate an unfavorable orientation of the infrared and ultraviolet transition moments, which both lie in the plane of the molecule,44,45 this situation only affects the fraction of molecules transferred to the excited state surface, not their time evolution in that state. We measure the time evolution in the excited state with both parallel and perpendicular relative polarizations of the ultraviolet excitation (λel) and continuum probe pulses (λprobe). However, the polarizations of the ultraviolet (λel) and infrared (λvib) pulses are always parallel for this experiment, and we can use the rotational anisotropy decay from the two-photon experiment in analyzing this more complicated situation. It is convenient to rewrite the signal for perpendicular and parallel orientation of the polarizations in the two-photon experiment in terms of the isotropic signal S(t) and the rotational anisotropy r(t),
I⊥(t) ) S(t)[1 - r(t)]
(3)
I|(t) ) S(t)[1 - 2r(t)]
(4)
The time evolution for either orientation is not a simple exponential decay but contains the time evolution of both the population and the anisotropy. It is clear from the lower panel in Figure 3, which shows the measured signals for the two orientations in the two-photon experiment, that rotational diffusion strongly influences the early time behavior for the different polarizations. However, using our measured values of r0 and τR, we can fit the corresponding expression for I|(t) or
Photoisomerization of Excited trans-Stilbene I⊥(t) to our data to extract a decay time τel ) (52 ( 6) ps that matches the value τel ) (51 ( 6) ps we obtained from combining the two signals to synthesize isotropic data. The two procedures are equivalent for the two-photon data, but the second approach, which incorporates a separate measurement of the anisotropy decay into the fit for a single polarization, is the one we use to analyze the three-photon experiment. We fit either eq 3 or eq 4, depending on the relative polarization of the continuum probe pulse, to the three-photon data using the measured values of r0 ) 0.28 and τR ) 19 ps to obtain the population lifetimes. The lower panel in Figure 5 shows the decay of the SN r S1 absorption at the band maximum of 585 nm obtained with the three pulses polarized parallel to one another for initial excitation of the C-H stretching overtone |2νCH〉 along with the fit to eq 4 shown as a solid line. Separately fitting data for both parallel and perpendicular polarizations yields an excited-state lifetime of τel ) (55 ( 9) ps, which is indistinguishable within experimental uncertainties to the (51 ( 6) ps lifetime measured for direct excitation. Similarly, the lower panel of Figure 6 shows the transient signal after excitation through the ground-state stretch-bend vibration |νCH + νbend〉 of trans-stilbene for parallel polarization of all the pulses. Fits of the data for both relative polarizations give an excited state lifetime of τel ) (56 ( 7) ps that is the same as the lifetime following direct excitation. Thus, the lifetime of trans-stilbene molecules prepared by electronic excitation following initial preparation of the |2νCH〉 C-H stretching state or the |νCH + νbend〉 stretch-bend combination is the same as that for molecules prepared by isoenergetic onephoton excitation. 4. Discussion Exciting vibrational modes that have a large component of motion along the reaction coordinate should have the largest effect on the isomerization rate. Calculations of a multidimensional surface find a broad minimum for trans-stilbene in S1 with a barrier to crossing into a gauche configuration that lies near the conical intersection.40 These calculations identify the coordinate for barrier crossing as a combination of changing the central dihedral angle and some torsion of the phenyl ring, similar to the isomerization coordinate of torsion and pyramidalization proposed by Quenneville and Martinez.21 Thus, vibrational motion along these two coordinates as well as energy in excess of the barrier should increase the rate of isomerization in trans-stilbene. Initially populating these barrier crossing modes is the key to changing the isomerization rate. Our initial ground-state vibrational excitation does not initially populate those modes. However, if vibrational energy flow prior to the electronic excitation step were to populate those modes, we would observe a substantial change in the excited-state decay. Thus, monitoring the excited-state decay provides an indirect view of the vibrational energy flow in the ground electronic state. The similarity of the lifetimes we observe with and without vibrational excitation suggests that we are not intercepting population in vibrational states that have good Franck-Condon factors for the isomerization modes. In addition, the extent of vibrational relaxation prior to barrier crossing in the excited state also moderates the influence of the initially excited modes. The details of the excited-state potential, shown schematically in Figure 1, are critical to both the barrier crossing and vibrational relaxation in the excited state. The low energy portion of the electronic transition to S1 from thermally populated vibrations of S0 in deuterated chloroform26 lies near 30 000 cm-1
J. Phys. Chem. A, Vol. 114, No. 36, 2010 9793 and is likely to access a region near the minimum on the excitedstate surface. Because fluorescence decay studies of isolated trans-stilbene19 and of stilbene in alkane solvents10,14 determine the excited-state barrier to be 1200 cm-1, we expect that our 33 300 cm-1 excitation energy prepares trans-stilbene with roughly 2000 cm-1 of energy above the barrier. Experiments at different levels of excitation show that this excess energy increases the rate of isomerization over that of molecules excited into the bottom of the S1 well because of the increase in the barrier crossing rate.10,19 The initial vibrational energy flow out of the C-H stretching modes in the ground electronic state is an intramolecular process dominated by low-order couplings that lead to the exchange of only a few quanta.26 Because we intercept the energy flow during this initial relaxation, identifying the modes that are nearby in energy and have low-order couplings provides the simplest picture of the vibrations from which the electronic excitation occurs. Using calculated energy values for the vibrational modes of stilbene,44,46,47 we identify modes that have low-order coupling to |2νCH〉 and |νCH + νbend〉. Because there are roughly 200 states coupled in third-order to the initially excited vibration, the initial rapid energy flow deposits energy into several different nuclear motions. The best candidates for low-order coupling to the initially excited C-H stretching states are relatively high frequency motions with energies in the range of 1200-1600 cm-1. Exchanging a quantum of C-H stretch for two quanta of these modes, which involve ethylenic C-C stretching, ring stretching and C-H rocking in the rings, ethylenic C-H rocking, or C-phenyl stretching motions,44 should be relatively efficient. However, none of these modes are the low frequency torsion or C-C-C bending motions that seem responsible for barrier crossing. Comparisons of the calculated and measured emission spectra of S1 trans-stilbene indicate that several states involving these strongly coupled motions have good Franck-Condon factors.48 Because π* r π excitation dominates the S1 r S0 transition, there should be a prominent progression in the CdC stretching vibration, and, indeed, the calculation finds that this progression determines the width of the band.48 Thus, we conclude that excitation from the strongly coupled vibrations in S0, which we intercept shortly after excitation of the C-H stretch, does not populate the modes that preferentially carry the system across the excited-state barrier toward the conical intersection. In this situation, the intramolecular flow of vibrational energy from the initially populated vibrational states of S1, which occurs within a few picoseconds, controls the population of the vibrational modes during the reaction. Several time-resolved Raman studies of trans-stilbene in alkanes and alcohols find two time scales of 1-5 ps49,50 and 9-12 ps49,51,52 for intramolecular vibrational relaxation in the excited state.53 Shortly after the electronic excitation, but long before the characteristic barrier crossing time of 51 ps, there is extensive vibrational relaxation in the excited state. Because even the fastest measured isomerization of trans-stilbene in solution, which occurs in the solvent methanol, requires 33 ps,11,14 it is difficult for nonselective excitation to drive the system across the barrier prior to vibrational relaxation. Thus, our observation of the same lifetime with and without initial vibrational excitation is consistent with the relatively low frequency pyramidalization and torsional modes being poorly coupled to the C-H stretches that we initially excite in the ground state. Molecules that move directly toward the conical intersection without intermediate barrier crossing, such as cis-stilbene, are better candidates for using
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vibrational excitation to influence the passage through the conical intersection. 5. Summary Comparing the lifetimes of electronically excited transstilbene molecules prepared by one-photon excitation with those of molecules prepared with the same total energy added by excitation through an intermediate vibrational state is a means of discovering the influence of vibrational energy on excited state isomerization. Using broadband continuum absorption to follow the electronically excited molecules, we measure a lifetime of (51 ( 6) ps for one-photon excitation that adds 33 300 cm-1 of energy. After excitation of either two quanta of the C-H stretch vibration |2νCH〉 at 5990 cm-1 or the C-H stretch-bend combination |νCH + νbend〉 at 4650 cm-1 in the ground electronic state, we intercept the vibrationally excited molecules during the course of vibrational energy flow and promote them to the electronically excited state with an ultraviolet photon selected to make the total energy added the same as in the one-photon preparation. The excited state lifetimes of (55 ( 9) ps and (56 ( 7) ps for the cases of |2νCH〉 and |νCH + νbend〉, respectively, are indistinguishable from those for isoenergetic one-photon excitation. The relatively high frequency, strongly coupled vibrational states rapidly populated by intramolecular vibrational energy flow in the ground electronic state are poorly coupled to the motions that carry the system across the excited state barrier. Thus, vibrational relaxation, which is faster in the electronically excited state than the barrier crossing, predominates and the isomerization rate does not depend significantly on the initial preparation of the system. Acknowledgment. We appreciate help from Katrin Sieferman with the early stages of these measurements, and we thank the Air Force Office of Scientific Research for support of this work. L.H. thanks the Belgian American Educational Foundation for a post-doctoral fellowship. References and Notes (1) Crim, F. F. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12654. (2) Hause, M. L.; Yoon, Y. H.; Crim, F. F. J. Chem. Phys. 2006, 125, 174309. (3) Hause, M. L.; Yoon, Y. H.; Case, A. S.; Crim, F. F. J. Chem. Phys. 2008, 128, 104307. (4) Kim, M. H.; Shen, L.; Tao, H. L.; Martinez, T. J.; Suits, A. G. Science 2007, 315, 1561. (5) Elles, C. G.; Crim, F. F. Annu. ReV. Phys. Chem. 2006, 57, 273. (6) Owrutsky, J. C.; Raftery, D.; Hochstrasser, R. M. Annu. ReV. Phys. Chem. 1994, 45, 519. (7) Nesbitt, D. J.; Field, R. W. J. Phys. Chem. 1996, 100, 12735. (8) Sension, R. J.; Repinec, S. T.; Szarka, A. Z.; Hochstrasser, R. M. J. Chem. Phys. 1993, 98, 6291. (9) Waldeck, D. H. Chem. ReV. 1991, 91, 415. (10) Courtney, S. H.; Fleming, G. R. J. Chem. Phys. 1985, 83, 215. (11) Courtney, S. H.; Kim, S. K.; Canonica, S.; Fleming, G. R. J. Chem. Soc., Faraday 2 1986, 82, 2065. (12) Greene, B. I.; Hochstrasser, R. M.; Weisman, R. B. Chem. Phys. Lett. 1979, 62, 427. (13) Greene, B. I.; Hochstrasser, R. M.; Weisman, R. B. J. Chem. Phys. 1979, 71, 544. (14) Kim, S. K.; Courtney, S. H.; Fleming, G. R. Chem. Phys. Lett. 1989, 159, 543. (15) Kim, S. K.; Fleming, G. R. J. Phys. Chem. 1988, 92, 2168.
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