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# Spectroscopic Tracking of Structural Evolution in Ultrafast Stilbene Photoisomerization

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Science  14 Nov 2008:
Vol. 322, Issue 5904, pp. 1073-1077
DOI: 10.1126/science.1160902

## Abstract

Understanding a chemical reaction ultimately requires the knowledge of how each atom in the reactants moves during product formation. Such knowledge is seldom complete and is often limited to an oversimplified reaction coordinate that neglects global motions across the molecular framework. To overcome this limit, we recorded transient impulsive Raman spectra during ultrafast photoisomerization of cis-stilbene in solution. The results demonstrate a gradual frequency shift of a low-frequency spectator vibration, reflecting changes in the restoring force along this coordinate throughout the isomerization. A high-level quantum-chemical calculation reproduces this feature and associates it with a continuous structural change leading to the twisted configuration. This combined spectroscopic and computational approach should be amenable to detailed reaction visualization in other photoisomerizing systems as well.

Molecular rearrangements in chemical reactions occur on a time scale comparable to nuclear vibrational periods (i.e., from 10 fs to 1 ps). This time scale is now accessible with advanced ultrafast vibrational spectroscopy (1), but, in almost all studies, we only observe structures in stationary (excited) states and the population transfer from one state to the other. Continuous changes of the molecular structure are seldom observed, especially for large polyatomic molecules. This situation often limits our understanding to a level of an oversimplified reaction coordinate (RC). To map structural evolution and elucidate true RCs, it is crucial to track molecular vibrations during reactions, which characterize the global motions of the whole molecule. Recently, femtosecond infrared spectroscopy has provided highly time-resolved vibrational spectra, but the technique is practically limited to the >1000 cm–1 region (2). Conventional spontaneous Raman is only applicable to picosecond or slower processes, because long and narrow-band pulses are utilized to achieve sufficient frequency resolution (<15 cm–1). This drawback in time resolution was improved by the introduction of a stimulated Raman process with femtosecond pulses (3). With the use of this technique, geometric changes of the retinyl chromophore in visual pigments were uncovered by monitoring hydrogen out-of-plane wagging vibrations in the 800- to 1000-cm–1 region (4). Common to these frequency-domain Raman approaches, however, is the challenge of observing low-frequency vibrations, given disturbance from strong Rayleigh scattering. Here we report a femtosecond resonance Raman probing at the impulsive limit to follow the low-frequency spectral change accompanying structural evolution in a cis-trans photoisomerization in solution.

Femtosecond transient impulsive Raman spectroscopy is explained as a combined pump-probe and time-domain Raman technique using three laser pulses (5, 6), as shown in Fig. 1A (7). In this experiment, we first generate a reactive excited-state molecule by a pump pulse (P1). After a certain delay (ΔT), we introduce an ultrashort pulse (P2) resonant with the excited-state absorption and impulsively induce a vibrational coherence of Raman active modes, which is driven by two frequency components contained in the spectrum of the P2 pulse. In other words, the P2 pulse initiates the motion of a nuclear wave packet in the reactive excited state. The third pulse (P3) monitors the excited-state absorption, whose intensity is modulated by the nuclear wave-packet motion. Fourier transformation of the resultant beating feature in the time-resolved absorption provides a spectrum of the molecular vibration with a detectable range reaching into the low-frequency terahertz region, which is inaccessible by other frequency-domain methods. For long-lived stationary states, this time-domain measurement gives vibrational information equivalent to that obtainable from conventional frequency-domain Raman (8, 9). However, for structurally evolving states in a picosecond, this method can afford vibrational spectra with the best possible time- and frequency-resolutions that are determined only by the vibrational coherence time of the transients.

Stilbene is an extensively studied paradigm of ultrafast olefinic photoisomerization (Fig. 1B). In particular, cis-stilbene exhibits nearly barrierless bond twisting in the excited state that is complete within ∼1 ps (1015). The photoisomerization mechanism of cis-stilbene has been often discussed on the basis of a traditional one-dimensional (1D) potential energy surface (PES) along the torsional coordinate of the central C=C bond in the first singlet electronic excited (S1) state (Fig. 1A) (16). The S1 PES is believed to have a rather flat feature on the cis side, where the excited molecule persists for ∼1 ps as an isomerization precursor showing strong SnS1 absorption in the 600- to 700-nm region (here, Sn is a higher-lying electronic excited state). Then, the molecule migrates to an S1/S0 conical intersection and relaxes to either the trans (product) or cis isomer in the ground (S0) state. However, spectroscopic studies have pointed to the inadequacy of this 1D rigid-twist model that does not take into account, for example, out-of-plane deformations of the ethylenic moiety (17, 18). Pyramidalization of one ethylenic carbon (sp2sp3 change of hybridization) was recently claimed to be essential in the structure at the S1/S0 conical intersection, indicating the importance of the multidimensionality of PES (19). For elucidation of the true RC of the polyatomic molecule, it is crucial to track the structural evolution by taking a temporal series of spectroscopic snapshots of the molecule.

To achieve this aim, we acquired femtosecond impulsive Raman data of cis-stilbene over the course of the isomerization. Figure 1C presents a time-resolved SnS1 absorption in the absence of the P2 pulse after excitation with the 267-nm P1 pulse. This signal shows a 1.3-ps decay, reflecting a decrease in the S1 population due to internal conversion/isomerization (1113, 15). With irradiation by the P2 pulse (11 fs, 620 nm) after a delay ΔT, the SnS1 absorption instantaneously changes, because the P2 pulse resonantly excites a fraction of the S1 molecules to the Sn state. The difference between the SnS1 absorption signals measured with and without the P2 pulse gives time-resolved impulsive Raman data, which include information about the nuclear wave-packet motion induced by the P2 pulse. With the P2 pulse tuned in rigorous resonance with absorption of the isomerization precursor, this impulsive Raman measurement selectively monitors the photoisomerization process, and the signal contribution from a minor photocyclization to 4a,4b-dihydrophenanthrene is negligible (20). We measured time-resolved impulsive Raman signals in hexadecane at three delays (ΔT = 0.3, 1.2, and 2 ps) to examine the temporal change of S1 vibrational structure (Fig. 2A). A strong beating feature is observed in each trace, which reflects the nuclear wave-packet motion induced in S1 cis-stilbene at each delay. A contribution from the Sn state is excluded because its lifetime is shorter than the damping time of the beating. The other features of the observed traces are represented by three exponential decay components that reflect the population dynamics after the P1 and P2 irradiation (21).

The inset of Fig. 2A shows the beating features extracted from the data by subtraction of the population component. Their Fourier transform power spectra (Fig. 2B) represent vibrational spectra of S1 cis-stilbene at the three ΔT delays. At ΔT = 0.3 ps, a broad band appears near 240 cm–1, together with several weak bands at 411, 533, and 752 cm–1. As the only band showing exceptionally large Raman intensity in the 200- to 300-cm–1 region, the predominant 240-cm–1 band is characteristic of S1 cis-stilbene; hence, it is straightforwardly associated with a broad band observed near 229 cm–1 in a picosecond frequency-domain Raman study (22). This vibration has been assigned to a mode that involves the motion of phenyl-C=C bending, ethylenic C=C torsion, and phenyl torsion. The nuclear wave-packet motion due to the same mode was also observed in previous ultrafast uv-pump/vis-probe measurements in this laboratory (23), which detected the nuclear wave-packet motion induced directly by photoexcitation.

The present Raman measurements reveal that the center frequency of the 240-cm–1 motion considerably downshifts with increasing ΔT delay, diminishing from 239 cm–1T = 0.3 ps) to 224 cm–1 (1.2 ps) to 215 cm–1 (2 ps). This large frequency downshift is directly apparent in the raw time-domain data. As shown in the inset of Fig. 2A, the intensity maxima of the three beating components gradually shift in time, manifesting a lengthening of the oscillation period with increasing delay. The data reveal that the frequency of the 240-cm–1 mode substantially changes while the isomerization proceeds. In other words, the 240-cm–1 mode probes the structural evolution of the molecule as a spectator through a large anharmonic coupling to the isomerization coordinate.

To confirm that the frequency downshift is directly related to the isomerization process, we carried out the same measurements in methanol, where the isomerization is accelerated and proceeds with a time constant of 0.48 ps (13, 15). The data obtained at ΔT = 0.3, 0.7, and 1.1 ps (Fig. 2, B and C) show that the 240-cm–1 mode exhibits a clear frequency downshift in methanol also. Figure 2D compares the temporal change of the center frequency of the mode in the two solvents. Clearly, the rate of the frequency downshift is higher in methanol than in hexadecane. With the change of solvent from hexadecane to methanol, the isomerization rate increases by a factor of 2.7 (0.77 to 2.08 ps–1), and the rate of the frequency downshift nearly doubles (14 versus 27 cm–1/ps). This strong correlation confirms that the frequency downshift of the 240-cm–1 mode arises from the structural evolution relevant to the isomerization of S1 cis-stilbene.

Linear fits to the frequency shifts observed in the two solvents both extrapolate to the same initial frequency (242 ± 2 cm–1) at zero delay (24). We independently evaluated the initial frequency of this mode in a uv-pump/vis-probe experiment (23) (where the nuclear wave-packet motion was directly induced by S1S0 photoexcitation) and found it to be 231 ± 3 cm–1 in both nonpolar (cyclohexane) and polar (methanol) solvents (25), which is 11 cm–1 lower than the value obtained from the extrapolation of the frequency shift after ΔT = 0.3 ps. This discrepancy indicates that the frequency of this mode first exhibits an upshift as the wave packet evolves on the S1 surface. In fact, we observed a shortening of the oscillation period in the uv-pump/vis-probe experiment (23), which demonstrates that the frequency upshift occurs within the vibrational coherence time. After this initial upshift, the mode shows a frequency downshift as observed in the present impulsive Raman experiment.

The vibrational period of the 240-cm–1 mode is approximately equal to 140 fs, which is well separated from the time scale of the isomerization (1.3 ps in hexadecane). Thus, the nuclear motion along the 240-cm–1 coordinate (q) can adjust adiabatically during the relatively slow temporal evolution of nuclear configurations due to the isomerization, with the instantaneous frequency of the 240-cm–1 mode decreasing as the isomerization proceeds. In other words, the vibrational force constant of the 240-cm–1 mode (k) decreases as the isomerization coordinate (Q) changes through the following anharmonic coupling relation (where V is potential energy) $Math$(1) Because the force constant is given by the curvature of the S1 PES along the 240-cm–1 coordinate (q), the present results reveal that the shape of the S1 PES changes along the isomerization coordinate (26), as illustrated in Fig. 3B. The experiment shows that the structure of S1 cis-stilbene continuously evolves within the S1 lifetime. It is noteworthy that the “averaged” frequency measured in a picosecond frequency-domain Raman study (229 cm–1) (22) lies in the middle of the range of the frequency shift (239 → 215 cm–1) observed here.

To associate the experimental observation with actual structural changes in S1 cis-stilbene, we calculated the PES and vibrational structure by density functional theory (DFT) and time-dependent DFT (TDDFT) using the Becke 1988 exchange + one-parameter progressive correlation functionals with long-range correction (27). The calculation gave a nonplanar optimized structure (C2 symmetry) for S0 cis-stilbene because of steric hindrances: The two phenyl groups are largely tilted (ϕβα12 ≈ 40°), although the ethylene moiety is nearly planar (θ1αα′1′ ≈ 5°). At this S0 geometry, an optically allowed transition to the S1 state, with a highest occupied molecular orbital → lowest unoccupied molecular orbital single-excitation character, was calculated at 4.90 eV, which agrees well with the experimental value (4.48 eV). Two almost-dark states were computed to lie above this bright S1 state. The S1 character, as well as the state ordering, is consistent with a recent calculation (28).

Starting from the S1 state with the structure optimized for the S0 state (Franck-Condon point), we gradually changed the geometry along the negative direction of mass-weighted energy gradients calculated at every point and searched the minimum energy path on the S1 PES. The RC, s, is defined as the path length along the thus-obtained minimum energy path (s = 0 at the initial Franck-Condon point). Figure 4A depicts the change of the S0 and S1 energies along the RC. The S1 energy first decreased rapidly (s < 0.5) and then exhibited a slower decrease (s > 0.5). This energy change reflects the biphasic structural evolution of the S1 state. As shown in Fig. 4C, the initial structural change (Qinit) in s < 0.5 is dominated by a prompt stretch of the central C=C bond due to ππ* electronic excitation and an out-of-plane motion of the two ethylenic hydrogens. In the later region of s >0.5, the two ethylenic hydrogens gradually move in opposite directions to a greater extent so that the twisting angle (θβαα′β′) of the C=C bond increases and the tilt angle (ϕβα12) of the phenyl group decreases (17, 18) (Fig. 4B). Consequently, a twisted structure having θβαα′β′ ≈ 49° and ϕβα12 10° is attained at s ≈ 5, which corresponds to a very shallow potential minimum leading to the conical intersection. The substantial twisting around the C=C bond is achieved mainly by the out-of-plane motion of the ethylenic hydrogens without extensive motion of the phenyl rings. This twisting motion in the second phase, which actually characterizes the isomerization, cannot be fully detected by the analysis of resonance Raman spectra of the S0 state (17), because it only sees the nuclear motions occurring within a very short electronic coherence time of the S1S0 transition (a few tens of femtoseconds).

To calculate the instantaneous vibrational frequency during the structural evolution of S1 cis-stilbene, we evaluated the force-constant matrix at different points along the RC and obtained the frequencies of the instantaneous normal modes. The calculated frequencies of six low-frequency modes are plotted against RC in Fig. 4D. Among these modes, the ν33 mode is uniquely assignable to the 240-cm–1 vibration observed in the experiment, on the basis of the frequency and Raman activity of this mode (29). The initial nuclear motion in s <0.5 (Qinit) involves a substantial component parallel to the ν33 coordinate (q), and this motion is smoothly connected to the ν33 mode in the second phase (s > 0.5) (Fig. 3C). After a steep increase from 278 to 353 cm–1, the ν33 frequency substantially decreases down to 318 cm–1 at the twisted geometry at s = 5. This behavior of the ν33 frequency almost perfectly reproduces the frequency shift of the 240-cm–1 mode observed experimentally, including the initial upshift measured by the ultrafast uv-pump/vis-probe measurement (23). The agreement strongly bolsters our conclusion that the present experiment tracks the structural evolution of cis-stilbene during the isomerization through accompanying changes in the vibrational structure. The frequency differences between the experiment and computation are attributed to the normal coordinate analysis (harmonic approximation) applied to the highly anharmonic S1 PES.

We thus achieved direct experimental tracking of the continuous structural evolution of a reacting polyatomic molecule by monitoring the evolving frequency of a spectator wave packet. The spectator frequency showed a gradual downshift over the course of the isomerization through a large anharmonic coupling to the isomerization coordinate. This observation arises from the gradual twisting of the olefinic moiety, realized by the out-of-plane motion of the two ethylenic hydrogens with minimal change in the molecular volume. The global molecular rearrangements visualized here lead to the structure at the S1/S0 conical intersection, which may be accompanied with further pyramidalization of one ethylenic carbon (19). Femtosecond time-domain Raman spectroscopy offers effective probing of complicated multidimensional RC of polyatomic molecules that cannot be tracked by conventional vibrational spectroscopy.

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