Femtosecond Stimulated Raman Exposes the Role of Vibrational

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Femtosecond Stimulated Raman Exposes the Role of Vibrational Coherence in Condensed-Phase Photoreactivity David P. Hoffman† and Richard A. Mathies* Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States CONSPECTUS: Femtosecond spectroscopy has revealed coherent wave packet motion time and time again, but the question as to whether these coherences are necessary for reactivity or merely a consequence of the experiment has remained open. For diatomic systems in the gas phase, such as sodium iodide, the dimensionality of the system requires coordinated atomic motion along the reaction coordinate. Coherent dynamics are also readily observed in condensed-phase multidimensional systems such as chromophores in proteins and solvated charge transfer dimers. Is precisely choreographed nuclear motion (i.e., coherence) required for reactivity in these systems? Can this coherence reveal anything about the reaction coordinate? In this Account, we describe our efforts to tackle these questions using femtosecond stimulated Raman spectroscopy (FSRS). Results of four exemplary systems are summarized to illustrate the role coherence can play in condensed-phase reactivity, the exploitation of vibrational coherence to measure vibrational anharmonicities, and the development of two-dimensional FSRS (2D-FSRS). We begin with rhodopsin, the protein responsible for vertebrate vision. The rhodopsin photoreaction is preternaturally fast: ground-state photoproduct is formed in less than 200 fs. However, the reactively important hydrogen out-of-plane motions as well as various torsions and stretches remain vibrationally coherent long after the reaction is complete, indicating that vibrational coherence can and does survive reactive internal conversion. Both the ultrashort time scale of the reaction and the observed vibrational coherence indicate that the reaction in rhodopsin is a vibrationally coherent process. Next we examine the functional excited-state proton transfer (ESPT) reaction of green fluorescent protein. Oscillations in the phenoxy C−O and imidazolinone CN stretches in the FSRS spectrum indicated strong anharmonic coupling to a low-frequency phenyl wagging mode that gates the ESPT reaction. In this case, the coherence revealed not only itself but also the mode coupling that is necessary for reactivity. Curious as to whether vibrational coherence is a common phenomenon, we examined two simpler photochemical systems. FSRS studies of the charge transfer dimer tetramethylbenzene:tetracyanoquinodimethane revealed many vibrational oscillations with high signal-to-noise ratio that allowed us to develop a 2D-FSRS technique to quantitatively measure anharmonic vibrational coupling for many modes within a reacting excited state. Armed with this technique, we turned our attention to a bond-breaking reaction, the cycloreversion of a cyclohexadiene derivative. By means of 2D-FSRS, the vibrational composition of the excited-state transition state and therefore the reaction coordinate was revealed. In aggregate, these FSRS measurements demonstrate that vibrational coherences persist for many picoseconds in condensed phases at room temperature and can survive reactive internal conversion. Moreover, these coherences can be leveraged to reveal quantitative anharmonic couplings between a molecule’s normal modes in the excited state. These anharmonic couplings are the key to determining how normal modes combine to form a reaction coordinate. It is becoming clear that condensed-phase photochemical reactions that occur in 10 ps or less require coordinated, coherent nuclear motion for efficient reactive internal conversion.

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INTRODUCTION With the advent of femtosecond laser pulses,1 researchers observed the production and evolution of coherent nuclear motioni.e., photogenerated wave packetsin both the gas phase2 and condensed phases.3−6 On the one hand, the fact that small molecules in the gas phase are vibrationally coherent for a long time is, in retrospect, predictable from their sharply peaked gas-phase linear spectra with resolved Franck−Condon (FC) profiles. On the other hand, the observation by Banin, Waldman, and Ruhman3 that both the excited-state reactants and products were vibrationally coherent in the solution-phase photodissociation of I3− was a surprise. Around the same time, others5,6 showed that vibrational coherences of individual modes could last for many picoseconds in condensed-phase molecules and proteins. Still, whether or not these coherences © XXXX American Chemical Society

are simply a consequence of the experimental design or play a role in the photoreactivity remained unresolved. At this point it is useful to clarify what is meant by “coherence” and to define the different types of coherences that will be discussed in this Account. A single-mode coherence is a one-dimensional harmonic system that is in a superposition state with nonstationary expectation values for the position and momentum operators. A multimode coherence is a multidimensional, approximately harmonic, vibrational system (i.e., a molecule) wherein all of the individual modes exhibit singlemode coherences and there is a well-defined phase relationship among them. Similarly, an ensemble coherence is a collection of Received: November 16, 2015

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Figure 1. Diagrams representing wave packet propagation in three distinct scenarios: (a) weak coupling (Kasha’s rule), (b) moderate coupling, and (c) strong electronic surface coupling. Reactants (green wave packets) are promoted via the absorption of a photon (green arrow) to the excited state (blue wave packets), and after evolving on the upper surface they return to the ground state as products (red wave packets) retaining varying degrees of vibrational coherence depending on the coupling strength and transition time. The left and right sides show early and late time wave packet dynamics, respectively. (d) Schematic energy ladder diagram illustrating the pulse shapes, durations, timings, and dominant interactions during the FSRS experiment. Thick black lines denote electronic states and thin ones vibrational states, and the dashed gray line represents a virtual state. Solid and dashed arrows indicate interactions of the electric field with the ket and bra, respectively.

time to completely dephase. From there the system can internally convert to the ground state (GS) through first-order Fermi’s golden rule transitions, leading to traditional exponential decay rates. If the coupling is sufficiently weak the ES population may persist long enough to produce a statistical (thermal) distribution of the ES vibrational levels before the transition. Figure 1b presents the moderate coupling case, which is pertinent for molecules such as green fluorescent protein (GFP)8 and charge transfer dimers.9 The reaction begins as before, but now there is an appreciable probability of a nonradiative transition as the wave packet passes near the conical intersection (CI) because the GS and ES surfaces are closer together. The right panel in Figure 1b depicts an additional oscillation within the excited-state potential energy well; the ES wave packet (blue) maintains coherence, and as it approaches the CI again, another pulse of product is formed

noninteracting systems in which each system exhibits a multimode coherence and there is a well-defined phase relationship between the systems. The demarcation between a multimode coherence and an ensemble coherence is somewhat vague: for example, one could consider a molecule as an ensemble of normal modes. In general, excited-state spectroscopy exploits large ensemble coherenceswhich are generated experimentally by the interaction of many independent systems with the same pulse of lightto gather information about the multimode coherenceswhich are generated “naturally” when a single system interacts with a photon. Photoreactions may be broadly classified into three groups on the basis of the strength and time scale of the electronic coupling between potential energy surfaces (PESs). Figure 1a presents the conventional weak-coupling case, e.g., Kasha’s rule,7 where the nonradiative decay time is much longer than ∼10 ps, so the excited state (ES) wave packet has sufficient B

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Figure 2. (a) FSRS of rhodopsin from 200 fs to 1 ps (black lines) in the HOOP region along with associated fits to a chirped vibrational coherence model10,31 (red lines). Above and below are resonance Raman spectra of the 11-cis-rhodopsin reactant and the bathorhodopsin product, respectively (shaded). (b) Calculated rhodopsin structures that correspond to the estimated instantaneous HOOP frequencies, showing that predictions of structural changes occurring faster than the vibrational dephasing time can be made from FSRS data. The 11 and 12 hydrogens are indicated in blue. Reproduced with permission from ref 10. Copyright 2005 AAAS.

(red). Pulsed formation of product continues until the excited state is depopulated or dephased. The kinetics for this scenario are no longer exponential but are instead predicted to exhibit product “quantum beats” for experiments with sufficient time resolution. Figure 1c presents the strong coupling case, e.g., rhodopsin,10 cis-stilbene,11,12 and cyclohexadiene.13,14 In these cases, the coupling is so strong that a single pass through the CI results in a significant nonradiative transition probability. Rhodopsin is the most extreme case: only a half period of torsional motion occurs in the excited state.15 Remarkably, there is only one product-producing “quantum beat” in the first step in vision. Over the past decade, our group and others have developed and used femtosecond stimulated Raman spectroscopy (FSRS)16−18 to study chemical reactions that belong to the second two cases.8−10,12,14,19−21 FSRS is a relatively simple three-pulse technique, for which an illustrative bra−ket energy ladder diagram is presented in Figure 1d. The actinic pump pulse (green) prepares an excited-state population that evolves for a period of time before interacting simultaneously with the narrow-bandwidth picosecond Raman pump pulse (red)22 and the broad-band, short-duration femtosecond Raman probe pulse (purple), which drive a vibrational coherence (Raman coherence, orange waveform). A successive interaction with the Raman pump pulse generates a Stokes-shifted photon. The short duration of the actinic pump and probe pulses allows precise timing of the coherence onset, while the narrow bandwidth of the Raman pump pulse provides high-resolution vibrational spectra. For a more nuanced discussion of time and frequency resolution in FSRS, the interested reader is referred to the papers by Dorfman et al.23 and Wu et al.24 Moreover, as in the case of any pump−probe spectroscopy, the actinic pump will impulsively generate a vibrational coherence (impulsive coherence) in any mode with a period shorter than the duration of the actinic pump. However, this impulsive

coherence may or may not still be present when the Raman pump/probe pair generates the Raman coherence. The interaction of the Raman and impulsive coherences can be used to directly measure anharmonic coupling between modes. This Account will focus on our frequent observation of longlasting multimode coherences in condensed-phase reactions and how we have exploited them to develop two-dimensional FSRS (2D-FSRS). We show that FSRS can be used to study the vibrational structure of chemically reacting molecules, revealing key details of the reaction coordinate in both high-energy GS products and reactive excited states. While Raman spectroscopy is not generally sensitive to all normal motions and some may not be observed, it is especially sensitive to modes with large excited-state displacements, precisely the modes of reactive importance in fast photochemistry. Importantly, these new structural details include the ES anharmonic couplings that mediate vibrational energy transfer. These data are crucial for mapping of reactive trajectories and the local portions of the potential energy surfaces that they traverse, offering detailed insight into the local shape and overall structure of reactive PESs, including in particular the locations of transition states and the vibrational composition of conical intersections. On the basis of these studies, we predict that most room-temperature condensed-phase photochemical reactions occurring on time scales shorter than ∼10 ps do not exhibit the phase space randomization implied by golden rule analysis but are instead governed by coherent vibrational dynamics.

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STRONG COUPLING

Ultrafast Chemistry of Vision: Rhodopsin

Vision begins with a quick double-bond isomerization, specifically, the photoinduced cis → trans isomerization of the C11C12 bond of the retinal chromophore buried within the transmembrane G protein-coupled receptor rhodopsin. This reaction is so quick, in fact, that the beginning of C

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Accounts of Chemical Research phototransduction is complete within ∼120 fs15,25 and the CI itself is transited in an amazing 50 fs.26 In part because of its speed, this photoisomerization is the most efficient photochemical reaction involving heavy-atom displacements known to date, with nearly two-thirds of the absorbed photons generating product.27 The combination of this high quantum yield with an enormous extinction coefficient allows the vertebrate visual system to detect single photons.28 Researchers knew that the high speed and efficiency of this reaction dictated that the ground and excited states be strongly coupled to one another. However, precisely which nuclear modes were responsible remained unclear. Early resonance Raman (RR) studies29 indicated that the initial reactive atomic motions are dominated by carbon backbone torsions and hydrogen out-of-plane (HOOP) wags. Subsequent picosecond time-resolved Raman experiments30 mapped out the later, slower, structural evolution after the formation of photorhodopsin. However, the structural changes occurring immediately before, during, and after internal conversion remained undetermined. FSRS offered an ideal way to probe rhodopsin’s reacting structure as a function of time. Figure 2 presents stimulated Raman spectra (black lines) of retinal’s HOOP region at selected time delays between 200 fs and 1 ps following photoexcitation at 500 nm. The time-resolved stimulated Raman spectra of the HOOP modes did not exhibit the expected Lorentzian line shapes but instead displayed dispersive line shapes that are partially positive and partially negative. Negative line shapes are possible in stimulated Raman spectroscopy because its heterodyne nature makes it sensitive to the phase of the vibrational coherence. One explanation for this surprising result is that the instantaneous vibrational frequency is changing during the vibrational dephasing time, i.e., the coherence is chirped. Using the coupled wave theory of FSRS,18 Kukura and co-workers10 modeled the spectra that would result from exponential chirp (red lines), and the results show excellent agreement with the data. Using the estimated instantaneous frequencies from the model in conjunction with electronic structure theory, the authors predicted the chemical structure of the chromophore as a function of time, demonstrating that FSRS can deduce structural changes that occur during the vibrational dephasing time. A snapshot of the predicted structure at 200 fs delay is presented at the right in Figure 2 along with the structures of 11-cis-rhodopsin and alltrans-bathorhodopsin. Furthermore, reanalysis by one of the authors31 improved the accuracy of the predicted ground-state formation time of photorhodopsin to 140 fs, in good agreement with recent high-time-resolution transient absorption data.15 Interestingly, while the model predicts that the GS forms in 140 fs, it also estimates that the vibrational dephasing time is 620 fs, more than 4-fold longer. This analysis together with the photoproduct multimode coherence observed by Wang et al.25 demonstrated that coherent nuclear motion survives passage through the reactive conical intersection. Another conclusion of the model is that the HOOP frequencies increase by approximately 100 cm−1 during the formation of photorhodopsin; such large changes in frequency suggest that the HOOP modes are strongly coupled to the reaction coordinate. Previous RR work29 indicated that the reaction coordinate is likely a collection of single- and doublebond torsional motions along the retinal backbone, with the C11C12 bond experiencing the largest change in combination with HOOP motions. Because of this coupling, their symmetry,

and their vibrational period (∼36 fs), Kukura et al.10 posited that it is the HOOP motions, together with the torsions, that drive the initial stages of the reaction by strongly coupling the ground- and excited-state surfaces, allowing for fast and efficient internal conversion. Once on the GS surface, the torsional motions take over, forming the all-trans photoproduct. In the language of conical intersections,32 the HOOP motions form the coupling coordinate that bridges the symmetry gap between the two surfaces, coupling them together, andin one picturethe torsional motions form the tuning coordinate that tunes the energy gap, allowing the two states to be formally degenerate. FSRS of rhodopsin demonstrated the ability to detect qualitative anharmonic couplings and use them to reveal the reaction coordinate; more generally, it has unequivocally confirmed what others have predicted and observed:25 that vibrational coherences can and do survive reactive internal conversion in the condensed phase.

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INTERMEDIATE COUPLING AND 2D-FSRS

Elucidating the Function of a Microscopy Workhorse: Green Fluorescent Protein

The discovery of GFP and its subsequent use as a genetically encodable marker33 heralded a new age for cellular biology in general and fluorescence microscopy in particular. Genetically encodable fluorescent proteins allow researchers to tag structures or processes of interest and follow their evolution through space and time in living systems. GFP epitomizes fluorescent protein design; it is stable, fluoresces without cofactors, and has a large absorption cross section and a high fluorescence quantum yield. A high fluorescence quantum yield indicates that the ES lifetime must be long, as suggested by Kasha’s rule.7 Early studies showed that GFP’s lengthy ES lifetime is due in part to an excited-state proton transfer (ESPT) reaction. However, how GFP’s protein pocket (shown in Figure 3b) makes this chromophore so bright was unknown. In an effort to answer that question, Fang et al.8 employed FSRS to probe the precise nuclear motions that drive ESPT. They found that the ES Raman frequencies and intensities of the C−O phenoxy stretch and the CN imidazolinone ring stretch residing on opposite sides of the chromophore’s conjugated system oscillate out of phase from one another with a period of 280 fs and that these oscillations persist for picoseconds (Figure 3a). To explain this peculiar behavior, it was argued that both the C−O and CN stretching modes are anharmonically coupled to an impulsively excited, coherently evolving low-frequency motion. With the aid of theoretical calculations it was determined that this motion likely corresponds to a phenyl wag. Figure 3b presents a representation of the chromophore’s predicted structural changes within the protein pocket (green), in particular the phenyl wag associated with the ESPT reaction. As the phenyl group moves up (orange structure) and down (cyan structure) from its equilibrium position (gray structure), it brings its hydroxyl moiety into and out of alignment with the beginning of the proton transfer chain (white dotted lines), thereby gating the reaction. Figure 3c presents a view of the predicted excited-state PES expressed in terms of the proton transfer coordinate and the phenyl wag phase. The yellowgreen wave packet represents the state of the ensemble, and the yellow dotted line represents its evolution. At t = 0 the phenoxy ring is in its equilibrium position and a significant barrier exists D

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along the proton transfer coordinate, restricting the wave packet to the reactant well. As the phenyl ring begins to wag, bringing the OH group into alignment with the proton transfer chain, the barrier to PT is greatly reduced, allowing part of the ensemble to reach the product well. As the phenyl group continues to wag, the barrier grows and shrinks with every oscillation, leading to pulsed formation of product; this process repeats about 10 times (∼3 ps) before the reaction is complete. GFP’s chromophore acts like a proton transfer diode, allowing the ESPT reaction to proceed in the forward direction only. The protein pocket ensures that the phenyl wagging motion is promoted while other nonradiative pathways are prevented, fostering the ESPT reaction. Once the wagging motion has relaxed, the reverse reaction is prevented, prolonging the ES lifetime and thus increasing the fluorescence quantum yield. FSRS of GFP allowed the crucial observation of anharmonic coupling between the phenyl wag and the C−O/CN stretches revealing that the ESPT reaction is coherently gated by the wag. It also showed not only that the coherent nuclear motion is necessary for the proper functioning of GFP but also that it persists for ∼3 ps. More generally, this experiment showed that anharmonic couplings in slower reactions can be measured and used to decipher the reaction coordinate, strongly hinting at the possibility of a true two-dimensional Raman spectroscopy based on FSRS. Developing 2D-FSRS and Characterizing a Conical Intersection: TMB:TCNQ

To further explore the concept of ES anharmonicity, we sought a simple model system that had a well-defined reaction coordinate as well as low-frequency motions that could easily be impulsively excited and were likely to influence the reaction coordinate. The charge transfer dimer formed between the electron donor tetramethylbenzene (TMB) and the electron acceptor tetracyanoquinodimethane (TCNQ) presents such a system. When mixed together in solution, TMB and TCNQ form a stable π-stacked charge transfer complex. Photon absorption in a charge transfer band results in the transfer of an electron from TMB to TCNQ to form the radical cation/anion pair, which equilibrates with the surrounding solvent on the picosecond time scale. We used FSRS to examine this relaxation and the mechanism of the electron back-transfer reaction.9 TMB:TCNQ has extremely large ES Raman cross sections, resulting in very high signal-to-noise ratio (SNR) data. This high spectral quality enabled the surprising observation that nearly all of the excited-state vibrational modes exhibit oscillations of both their center peak frequencies and amplitudes that persist for multiple picoseconds. As in the case of GFP, we recognized that the oscillations are due to anharmonic coupling between the high-frequency FSRS modes and the impulsively excited low-frequency modes in the excited state. Figure 4 illustrates how anharmonic coupling generates these oscillatory peak center frequencies in FSRS. It is important to note that FSRS does not measure the instantaneous frequency but rather the frequency averaged over the vibrational coherence induced by the combined action of the Raman pump and Raman probe; in essence, FSRS operates like an experimental short-time Fourier transform employing an exponential (Poisson) window function with a time constant determined by the length of the Raman pump pulse and/or the intrinsic dephasing time of the vibrational coherence. Unlike

Figure 3. (a) Oscillations in the frequencies of the C−O and CN stretches in the GFP chromophore after correction for averaging over the Raman pump envelope. (b) View inside GFP’s β-barrel showing the chromophore and residues involved in the GFP proton transfer chain. Reproduced with permission from ref 8. Copyright 2009 Nature Publishing Group. (c) Schematic potential energy surface along the proton transfer coordinate as a function of the phenolic wag phase from 0 to 3π (analogous to time). E

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instantaneous frequency analysis used in pump−probe spectroscopy,34−36 which is subject to analysis artifacts and confounding ground- and excited-state signals, FSRS applies the “window function” in the complex domain, before the inherent loss of information upon square-law detection and digitization. For our current instrument, the Raman pump pulse has a duration of 2.6 ps22 and a typical vibrational dephasing time is about 2 ps. This effect and that due to the finite duration of the actinic pump and probe pulses cause the observed changes in frequency to appear significantly smaller than the intrinsic ones (see ref 9 and the Supporting Information thereof for more details). All nominally harmonic nuclear motions are anharmonically coupled to one another to some extent, but particularly strong coupling can be indicative of reactive importance. To test this hypothesis, we devised a method to transform high-timeresolution FSRS data into a quantitative two-dimensional map (spectrum) of anharmonic couplings between the low- and high-frequency modes, which is presented in Figure 5. In electron transfer reactions, it is important to identify and characterize the coupling and tuning modes that span the branching space of the conical intersection. Examination of the anharmonic coupling map for TMB:TCNQ in Figure 5d reveals that only two fundamental modes are strongly coupled and have the correct symmetry to play a role in the branching space: the non-totally symmetric 1271 cm−1 CC rocking motion (the coupling mode) and the totally symmetric 323 cm−1 CCN bending motion (the tuning mode).

Figure 4. Generalized model of excited-state anharmonic coupling probed in 2D-FSRS. (top) Time slices along the high-frequency normal mode of a wave packet evolving on an anharmonic potential energy surface (gray). Here the curvature and therefore the resonant frequency of the high-frequency mode depend linearly on the coordinate of the low-frequency motion. Probing the frequency of the high-energy mode as a function of time after impulsive excitation of the low-energy mode reveals low-frequency modulations. (bottom) Illustrative spectra of the high-frequency mode when the lowfrequency mode is at its minimum (red), maximum (blue), or equilibrium (purple) position. The equilibrium spectrum is shown in all of the plots for reference.

Figure 5. Analysis of 2D-FSRS signals of the TMB:TCNQ photoinduced charge transfer reaction. (a) Raw FSRS data at a 2 ps delay (gray shading) are fit to a sum of line shape functions (black line) and a polynomial baseline (dotted line). (b) The center frequencies of the peaks are extracted from the fit for each time point, and the slow, exponential population dynamics are removed so that only the oscillatory component remains (red dashed line). The oscillatory dynamics, which persist beyond 2.5 ps, are modeled by a linear prediction with singular value decomposition (LPSVD) algorithm (blue line), which directly yields the frequency, amplitude, phase, and dephasing time of each oscillatory component. (c) These parameters can be transformed into the frequency domain to yield a conventional power spectrum. (d) Alternatively, the data from all of the peaks can be visualized as a 2D plot. Here the area and horizontal and vertical positions of each circle represent the magnitude (Δω), oscillatory frequency (ω), and parent peak frequency (ω0) of each component. After the corrections mentioned in the text, the quantity Δω/ω0 is directly proportional to the first-order anharmonic coupling between the impulsively excited low-frequency modes in the excited state and the high-frequency skeletal modes. Adapted from ref 9. Copyright 2014 American Chemical Society. F

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enough distortion to break the symmetry barrier to reactive internal conversion (red wave function). In summary, while the FSRS peaks themselves report on the local harmonic curvature of the reactive PES, the anharmonic couplings extend our view further into the surrounding multidimensional energy landscape. In addition, it is clear that multimode coherences not only survive for relatively long times (>3 ps) in condensed-phase systems but also can be leveraged to provide new insights into the character of reaction coordinates.

Figure 6 presents a representation of the TMB:TCNQ charge transfer/recombination reaction branching space.

Watching a Bond Break in Real Time: ModCHD

To test the hypothesis that most, if not all, fast photoinduced condensed-phase reactions are vibrationally coherent, we turned our attention to bond cleavage reactions. Cyclohexadiene (CHD) ring opening37 is a classic reaction whose stereochemistry is described by the Woodward−Hoffmann orbital symmetry rules;38 however, the reaction is extremely fast (complete in ∼80 fs),13 and the short wavelengths required are outside the capabilities of our instrument. Therefore, we studied a modified cyclohexadiene, 1,2-bis(2,4-dimethyl-5phenyl-3-thienyl)perfluorocyclopentene (ModCHD), which reacts much slower than its parent because of the presence of an ES transition state barrier and has a visible absorption. Previous studies39 interested in photochromic molecular switches showed that the transition state is crossed in about 3 ps and that internal conversion occurs in ∼9 ps. The slower reaction and competition from nonreactive pathways results in a quantum yield of 5%, compared with 50% for cyclohexadiene. Figure 7a presents the 2D-FSRS map of photoexcited ModCHD that was produced in exactly the same way as the one for TMB:TCNQ. In contrast to TMB:TCNQ, there are no overtone or combination bands, resulting in a simplified picture of five strong anharmonic couplings. This significant anharmonic coupling likely indicates which modes are involved in crossing the ES transition state. To determine which modes were and were not reactive, we examined three characteristics; coupling, symmetry, and alignment with a hypothetical reaction coordinate (RC). The modes with conrotatory symmetry,38 good alignment with our hypothetical RC, and strong coupling with one another were deemed reactive (colored blue). Those modes that are strongly coupled to one another but have disrotatory symmetry, are largely orthogonal to our RC, and have displacement distant from the central CHD moiety were deemed unreactive (colored red). Figure 7b presents the molecular structure of ModCHD highlighting the locations of the reactive (blue) and unreactive (red) modes. Reactive modes are localized on the central ring, precisely where the reaction occurs, whereas the unreactive motions are located on the periphery of the molecule, effectively funneling energy away from the reactive center. Figure 7c presents an enlarged view of the central ring showing the reactive modes, including the 191 cm−1 methyl wag that is anharmonically coupled to the 467 cm−1 C−C bend and the 1333 cm−1 C−C stretch. We hypothesize that all three modes must move coherently (i.e., concertedly) through phase space in order to reach and pass the ES transition state barrier and drive the ring-opening reaction. This study of ModCHD demonstrates that multimode coherence is not just a unique feature of fast reactive internal conversion but also occurs when navigating ES transition states. Here we exploited the unique ability of 2D-FSRS to offer insight into the ES nuclear structure and dynamics beyond the

Figure 6. Schematic potential energy surface in the branching space of a conical intersection that connects the charge transfer excited state (yellow surface) with the neutral ground state (gray surface) in the TMB:TCNQ dimer. Nuclear displacements (structures, red arrows) of TCNQ’s totally symmetric CCN bending coordinate, the tuning coordinate (black), and the non-totally symmetric CC rocking motion, the coupling coordinate (magenta), are shown at the lower left and right, respectively. Vibrational wave functions along the coupling mode are shown in both the FC region (blue) and near the conical intersection (red). As a result of the extensive mixing of the electronic states near the conical intersection (green dot), the nuclear surfaces are no longer harmonic, and the initially excited tuning mode can share its energy with the coupling mode, providing the distortion necessary to perturb the nuclear symmetry such that the system can change electronic states. Adapted from ref 9. Copyright 2014 American Chemical Society.

Schematic ground (gray) and excited (yellow) PESs of the TMB:TCNQ charge transfer dimer are shown in terms of the 323 cm−1 totally symmetric CCN bending mode (black) and the 1271 cm−1 ungerade CC rocking mode (magenta). TCNQ structures with mode-specific nuclear displacements (red arrows) are shown at bottom left for the CNN bending mode and bottom right for the CC rocking mode. Upon excitation, the dimer is promoted from the neutral GS to the charge transfer ES. The nuclear wave packet oscillates along the highly displaced CCN tuning coordinate, bringing the system into and out of the region surrounding the conical intersection (green sphere). Because the coupling coordinate is non-totally symmetric, its wave function in the FC region (blue) is initially a totally symmetric replica of its ground state wave function because it cannot be displaced. However, as the multimode wave packet approaches the anharmonic region surrounding the CI, the highly excited low-frequency CCN bend mode can share energy via anharmonic coupling with the non-totally symmetric high-frequency CC rock motion, generating G

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Figure 7. (a) 2D-FSRS analysis of a modified cyclohexadiene (ModCHD) that shows strong anharmonic coupling of the asymmetric molecular bend and methyl wag with various high-frequency skeletal modes. The anharmonic coupling, in combination with other mode characteristics, allows the vibrations to be divided into reactive (blue) and unreactive (red) modes. (b) The structure of ModCHD: red highlighting indicates the location of the unreactive modes, and blue highlighting indicates the reactive ones. The anharmonic couplings measured by 2D-FSRS indicate that the two sets of motions compete for the exciting photon’s energy. ModCHD’s reduced quantum yield can be explained by energy that is funneled to the unreactive motions on the molecular periphery at the expense of the reactive ones. (c) Schematic depiction of how the C−C stretching, CCC bending, and methyl wagging motions combine to drive the molecule along the conrotatory ring-opening reaction coordinate. Dynamic motion along these modes must be properly phased to successfully drive the reaction. Reproduced with permission from ref 14. Copyright 2015 The PCCP Owner Societies.

simple first-order kinetics of product appearance times, deducing the suite of modes that are anharmonically coupled to fashion the multidimensional ring-opening reaction coordinate.

space, the coupling and tuning coordinates, which are linear combinations of the system’s normal modes. The system does not, and in fact for fast reactions cannot, explore the full extent of phase space. This picture implies that the transition probabilities from excited-state reactant to product are dependent on the system’s position in phase space and will therefore exhibit product “quantum bumps” as the system passes the CI (assuming that it is probed with sufficient time resolution). More generally, we suggest that all types of fast photoreactive internal conversion including proton transfer, charge transfer, electron transfer, energy transfer, and isomerization reactions also do not involve full phase space randomization and will exhibit vibrationally coherent characteristics. The 2D-FSRS experiments performed to date have not yet approached the limits of the technique; FSRS vibrational peaks below ∼500 cm−1 and impulsive signals for modes higher than ∼450 cm−1 have not yet been observed. It is difficult to remove the residual 800 nm light from the probe when performing FSRS spectroscopy below 500 cm−1 but this problem could be alleviated by altering the Raman pump wavelength or generating the probe continuum with 400 nm light. Alternatively, pump−dump probe techniques11,41 are ideally suited to measure the low-frequency excited-state spectrum in the time domain. The impulsive excited state preparation is limited by the long duration of our actinic pump; a shorter ∼7 fs pump would impulsively excite modes over ∼2000 cm−1, covering the entire range of interesting fundamental vibrational transitions. Moreover, higher time resolution should allow accurate determination of the phase of each coupling, meaning that not only the magnitude but also the sign of each coupling can be recorded. We expect that an instrument with these capabilities will be able to record a complete cross-coupling map from 0 to 2000 cm−1 along both the FSRS and impulsive

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SUMMARY AND OUTLOOK 2D-FSRS is a unique tool that exposes and exploits the apparent ubiquity of coherent vibrational motion in fast photochemical reactive dynamics. From extremely fast reactions with very large vibronic coupling, as exemplified by rhodopsin, to much slower, more weakly coupled reactions such as the charge recombination reaction in TMB:TCNQ, we have explored the role of coherent nuclear motion in reactivity. In some cases, such as rhodopsin, it is evident that coherent nuclear motion is necessary and critical for reactivity. Precisely phased HOOP and torsional motions combine to enable fast passage through the CI in a coordinated twisting motion.40 In more weakly coupled systems such as TMB:TCNQ and GFP, the multimode coherence may simply provide a vibrationally resolved picture of the anharmonic coupling. In either circumstance, we are able to exploit the multimode coherences to identify the specific ES nuclear motions involved in the reaction coordinate. Furthermore, through our investigations it has become clear that most, if not all, photochemical reactions that occur in 10 ps or less in the condensed phase are vibrationally coherent. When a photoreaction occurs this quickly, the system must pass through an area of phase space with large electronic surface couplingsthat is, it must encounter a CI. As CIs are points in a two-dimensional branching space (a four-dimensional phase space), reaching them cannot be achieved expeditiously by random or even chaotic motion. The CI is better approached by precisely choreographed or coherently phased movement along the two molecular coordinates that span the branching H

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Accounts of Chemical Research

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axes. This achievement of the vibrational equivalent of a 2DNMR spectrum should allow researchers to precisely pinpoint the phase space locations of critical features such as conical intersections and transition states that control chemical reactivity.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (510) 642-4192. Present Address †

D.P.H.: Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA 20147, United States. Notes

The authors declare no competing financial interest. Biographies David P. Hoffman completed a B.Sc. degree in chemistry from McGill University in 2008 and was awarded a Ph.D. from the University of California Berkeley in 2014 working under the direction of Richard A. Mathies. He is currently a postdoctoral associate with Eric Betzig at HHMI’s Janelia Research Campus. Richard A. Mathies completed undergraduate studies at the University of Washington, Seattle before pursuing a Ph.D. at Cornell University under the direction of Andreas Albrecht. After postdoctoral research at Yale with Lubert Stryer, he was appointed to the faculty of the Department of Chemistry of UC Berkeley, where he is now a Professor of the Graduate School.

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ACKNOWLEDGMENTS This work was supported by the Mathies Royalty Fund. The authors thank their current and former group members, with special thanks to S. R. Ellis, R. R. Frontiera, C. Fang, J. Dasgupta, D. Valley, P. Kukura, and D. W. McCamant.

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