Multidimensional Vibrational Coherence Spectroscopy
Multidimensional vibrational coherence spectroscopy has been part of laser spectroscopy since the 1990s and its role in several areas of science has continuously been increasing. In this contribution, after introducing the principals of vibrational coherence spectroscopy (VCS), we review the three most widespread experimental methods for multidimensional VCS (multi-VCS), namely femtosecond stimulated Raman spectroscopy, pump-impulsive vibrational spectroscopy, and pump-degenerate four wave-mixing. Focus is given to the generation and typical analysis of the respective signals in the time and spectral domains. Critical aspects of all multidimensional techniques are the challenges in the data interpretation due to the existence of several possible contributions to the observed signals or to optical interferences and how to overcome the corresponding difficulties by exploiting experimental parameters including higher-order nonlinear effects. We overview how multidimensional vibrational coherence spectroscopy can assist a chemist in understanding how molecular structural changes and eventually photochemical reactions take place. In order to illustrate the application of the techniques described in this chapter, two molecular systems are discussed in more detail in regard to the vibrational dynamics in the electronic excited states: (1) carotenoids as a non-reactive system and (2) stilbene derivatives as a reactive system.
KeywordsUltrafast laser spectroscopy Multidimensional spectroscopy Raman Vibrational spectroscopy Coherence spectroscopy Excited states Vibronic coupling Photoisomerization
The dynamics and function of complex molecular systems can be understood as resulting from the interaction between three different interacting sub-units composed of the electronic, vibrational, and environmental degrees of freedom. Focusing particularly on photoreactions—i.e., excited state reactions—they may be described as (non radiative) transitions between distinct electronic states of one or several molecules. Depending on the nature of the coupling responsible for such a transition in a given case, the photoreaction may correspond to a charge or energy transfer, or an internal conversion, an intersystem crossing, etc. Within the Born–Oppenheimer (BO) approximation, electronic states are characterized by multidimensional electronic potential energy surfaces (PESs) representing the energy of the electronic subsystem as a function of all internal nuclear coordinates (3 N-6 for N nuclei) treated as fixed, external parameters. The vibrational degrees of freedom, which drive the molecular system along the photoreactive path from the Franck–Condon state (i.e., initially produced by the photon absorption) to the photoproduct, contribute to the reaction coordinate. All other molecular (and solvent, in condensed phase) vibrational degrees of freedom constitute a large thermal bath—the environment—responsible for very fast energy relaxation and dissipation. There is not only fundamental interest in understanding how these three sub-units interact to perform a given photoreaction and govern its quantum yield, but also in understanding how such interactions shape the molecular functionality.
The mechanism of photoreactions may be elucidated by identifying the conformations and vibrational dynamics of transient electronic states successively populated, from the Franck–Condon state to the vibrationally and thermally relaxed photoproduct. Vibrational spectroscopies (i.e., Raman and IR spectroscopies) have long been exploited to reveal vibrational activity and conformations of stationary or transient molecular states. In this contribution, we will review recent experimental developments, which implement in various ways stimulated Raman scattering to monitor vibrational dynamics along the course of a photoreaction, with a time resolution typically below 100 fs, therefore allowing to resolve the vibrational activity accompanying ultrafast photoreactions. In condensed phases, the vibrational energy relaxation and dissipation to the environment occurs on the 0.1–10 ps time scale, which is in many cases faster than the photoreaction itself. We shall consider as “ultrafast” the photoreactions occurring on a similar time scale or faster. One difficulty inherent to their investigations comes from the fact that there is no time scale separation between the various relevant processes.
To investigate the dynamics and functions of molecular systems on ultrashort time scales, time-resolved UV–VIS spectroscopy has been used since the advent of femtosecond laser light sources. Time-resolved transient absorption—or so-called pump-probe spectroscopy—exploits the non-linear response of the complex system described above upon interaction with coherent laser light pulses. More generally, in the regime of weak-field light–matter interaction, the use of short, coherent laser pulses enables the preparation of controlled, coherent superpositions of molecular (i.e., electronic and vibrational) quantum states. The quantum evolution of these initial coherent states may be followed spectroscopically, i.e., interrogated by the interaction with another laser pulse, until decoherence (interaction with the bath) occurs on typical time scales of a few femtoseconds (electronic decoherence) up to a few picoseconds (vibrational decoherence) [1, 2, 3, 4]. After electronic decoherence has occurred, the time evolution of the laser-induced populations can be further observed spectroscopically.
Over the last decade, the investigation of coherence in molecular processes occurring in the condensed phase has become a frontier research topic in molecular quantum physics [5, 6, 7, 8, 9, 10, 11]. In this chapter, we will describe an application of femtosecond coherent multidimensional spectroscopy which engineers vibrational coherence in molecular systems and uses it as a spectroscopic tool. More precisely, the goal is to follow in time the vibrational coherence imprinted in the electronic excited states by the non-linear interaction with coherent laser light and exploit the peculiar spectroscopic signatures of such vibrationally coherent molecular states. This type of spectroscopy can be performed under several distinct experimental implementations, which have been named differently. Here we will summarize all these implementations under the name multidimensional vibrational coherence spectroscopy, or multi-VCS. This contribution does not deal, however, with other kinds of vibrational spectroscopies based on so-called rephasing mechanisms like 2D Raman or 2D infrared spectroscopies. These topics are reviewed in different contributions in this collection.
We will first shortly describe how VCS results from the third-order interaction (and higher-order for multi-VCS) of the molecular system with femtosecond light pulses. This initial description will assist the reader in understanding how the higher-dimensional versions of VCS are able to report on structural dynamics in excited states. The main experimental implementations in the time-domain (pump-Impulsive Vibrational Spectroscopy-pump-IVS, pump-Degenerate Four Wave Mixing-pump-DFWM, and Population-controlled IVS) and in the frequency-domain (Femtosecond Stimulated Raman Scattering-FSRS) will be discussed and compared. Finally, we will illustrate the success of multi-VCS at revealing a mechanistic understanding of ultrafast photoreactions in a selection of molecular systems: carotenoids and stilbene derivatives.
2 Introduction to Vibrational Coherence Spectroscopy (VCS)
The principle of vibrational coherence spectroscopy was demonstrated in molecules as soon as picosecond and then femtosecond laser pulses became available. In particular, laser pulses which are shorter than the period of nuclear motions in a molecule have a spectrum larger than the corresponding vibrational level spacing. With such a laser pulse, coherent superposition of vibrational levels, also referred to as vibrational wavepackets, may be produced impulsively in essentially any molecule. The spectroscopic signature of such vibrational wavepackets allows tracking molecular structural dynamics accompanying ultrafast photoreactions in molecules. Early investigations of vibrational wavepacket signatures in simple molecules in gas phase have pioneered the so-called field of femtochemistry .
In the sequential pump-probe scheme discussed here (i.e., the probe pulse does not overlap temporally with the pump pulse), the first two interactions with the pump field are followed, after a “waiting” time τ, by a third interaction with the probe field, as illustrated in Fig. 1c. The latter couples (i.e., creates a “coherence” between) the pump-induced population and another electronic state. The resulting (third-order) polarization of the molecular system radiates a field that builds up constructively in a fourth wave (to be detected), which propagates in a specific direction k1 − k2 + k3 imposed by the phase matching condition . In the present case, where the first two interactions occur with the same pump pulse k1 = k2, the fourth wave propagates collinearly with the probe pulse k3. Hence, one detects the co-propagating third and fourth waves, which means detecting the fourth wave heterodyned by the incident probe field. Finally, this experiment may be described as the measurement of the linear absorbance of the probe beam (i.e., first order in the probe field), by the non-stationary population induced (at the second order of perturbation) by the pump .
The vibrational wavepackets produced by the quantum superposition of vibrational states results in the classical oscillation of the vibrational degrees of freedom (bonds elongations, torsions, etc.). These oscillatory molecular motions induce an oscillatory modulation of all the linear optical properties of the system such as absorbance, dichroism, birefringence, etc. [15, 22]. Hence, the pump-induced change in the spectrum or polarization state of the transmitted probe oscillates accordingly as a function of the waiting time τ. The sequential pump-probe experiment described here and performed with ultrashort laser pulses, so as to generate and probe vibrational wavepackets both in the ground and excited states, is referred to as impulsive vibrational spectroscopy (IVS). Fourier transformation of the oscillatory signals reveals the Raman activity of the system. For a ground-state wavepacket—RISRS or ISRS—the resulting vibrational spectrum coincides with the molecular Raman spectrum as measured directly in the frequency domain by conventional Raman spectroscopy [27, 28, 29]. The limited bandwidth of the laser pulses may, however, result in the attenuation of the relative intensity of the highest-frequency vibrational modes or even prevent from detecting them. In practice, 10–12 fs pulses are short enough to trigger and detect vibrational activities up to the 3000 cm−1 range. Hence, VCS of ground-state wavepackets is a time-domain equivalent of frequency-domain Raman spectroscopy. For excited-state wavepackets, time–frequency representations of mode-specific coherent oscillations was recently proposed as a spectroscopic tool for detecting CInt’s .
Alternatively, VCS may also be performed directly in the frequency domain according to an experimental scheme implementing stimulated Raman scattering and illustrated in Fig. 2c. The major difference is that the pump pulse is temporally significantly longer (typically a few ps) and spectrally narrower than the probe pulse, and both pump and probe pulses overlap temporally, in contrast to the sequential scheme discussed above. The typical non-linear process at work in this implementation is the following. The vibrational wavepacket is produced by one interaction with the pump pulse (k1) and one with the probe pulse (k2). This vibrational wavepacket is subsequently interrogated by another interaction with the long, spectrally narrow pump pulse (k3). The signal is here again detected in the direction of the probe (i.e., self-heterodyned). The result of this interaction mechanism is that the probe spectrum is amplified at frequencies that correspond to the difference between the pump frequency and the frequencies of the vibrational mode initially populated with the probe pulse. This coherent stimulated Raman technique reveals in the frequency domain the spectroscopic signatures of vibrational wavepackets in both the ground and excited state,  thus providing, in principle, the same spectroscopic information as IVS does in the time domain. In this frequency-domain VCS approach, the Raman pump-pulse duration is the observation window which limits the achievable spectral resolution, in the same way as the time window considered for Fourier transformation with respect to the waiting time τ limits the spectral resolution of Raman spectra recorded in the time domain.
A fundamental difference between time-domain and frequency-domain VCS is that in the latter case, the three light–molecule interactions are no longer engineered sequentially as in IVS or DFWM, but the interaction with the probe wave may occur at any moment before, between or after both interactions with the pump pulse. In fact, these various time-ordering options correspond to distinct terms in the third-order perturbative expansion, and all of them contribute to the third-order polarization  while in the sequential scheme by experimental design, only those where the probe interaction is the last one contribute. Hence, a drawback of the frequency-domain VCS is the background signal generated by contributions other than the stimulated Raman signal of interest. The features and challenges of each technique will be presented in more detail in the next section.
3 Multidimensional Vibrational Coherence Spectroscopy (Multi-VCS)
All the VCS approaches introduced above engineer a third-order light–molecule interaction which simultaneously reveals the vibrational activity of both electronic states coupled by a resonant pump laser field, i.e., the ground and the Franck–Condon excited state. This may pose a challenge to distinguish between vibrational signatures specific of each electronic state. Above all, this does not generally give access to the vibrational signatures of other possible transient states produced along the course of a photoreaction. In this regard, VCS has been further developed to be sensitive specifically to the excited states and to successive transient states by adding an “actinic” pulse. The role of this actinic pulse is to trigger a photoreaction prior to generating and probing a vibrational wavepacket by a subsequent third-order VCS scheme applied after a given time delay T. The vibrational activity can thus be monitored along the successive structures and electronic states achieved by the molecular system during the course of its photoreaction. This leads to the multidimensional character of the VCS, where usually one axis displays Raman frequencies while the other axis shows the photoreaction time delay T.
Independent of the technique, the actinic pulse always excites the electronic population via two interactions with its electric field. Since these first two interactions originate from a single actinic beam, they do not affect the phase matching of the subsequent VCS signal: kmulti-VCS = ka − ka + k1 − k2 + k3. Strictly speaking, multi-VCS engineers a fifth-order light–molecule interaction , but again within a sequential scheme, the initial actinic pulse first triggers a photoreaction, i.e., creates a non-stationary excited-state population, which is subsequently probed by a third-order VCS scheme revealing the Raman activity as a function of the photoreaction time T. Importantly, the transition dipole moment, which operates in the T-delayed VCS scheme, does not necessarily involve the ground state anymore. This is a major difference between VCS and multi-VCS. Indeed, with multi-VCS, vibrational activity may be triggered and probed in a transient state by using laser spectra on resonance with one specific electronic transition of this very state, which may not be resonant with the ground state absorption. This allows taking advantage of the so-called resonant enhancement for generating a vibrational wavepacket specifically in this transient state.
For completeness, we note that another implementation of multi-VCS uses what we call here the actinic pump to specifically trigger a vibrational wavepacket in the ground state (by ISRS), followed by the subsequent three-pulse VCS scheme to generate and monitor an excited-state vibrational wavepacket from this non-stationary ground state population. This enables correlating the vibrational activity on the excited state to that of the ground state in a so-called two-dimensional resonance Raman (2DRR) spectroscopy. Another chapter in this collection is dedicated to this technique. Therefore here, we limit the discussion to a scheme where the effect of the actinic pulse can be simply understood as initiating a photoreaction by populating an excited state.
3.1 Femtosecond Stimulated Raman Scattering (FSRS)
FSRS is a frequency-domain spectroscopy based on stimulated Raman scattering generated after an actinic pulse (Fig. 3, top panel). The signal is generated in the same direction as the probe beam, leading to a self-heterodyne detection geometry. The delay T between the probe pulse and the actinic pulse is scanned and Raman spectra are detected in dependence of this delay. The first implementation of FSRS in its three-beam configuration used a 10-Hz laser and had a Raman resolution of only 76 cm−1 . After almost 25 years of experimental development, the state-of-the-art FSRS setup nowadays offers a Raman resolution of about 10 cm−1 while using actinic pulses with durations of less than 100 fs, and covering the whole ultraviolet and visible spectral range [47, 48, 49, 50].
The probe pulse is spectrally broad and usually red-shifted with respect to the narrow spectrum of the Raman pump. The advantage of a broadband implementation is that a full Raman spectrum, i.e., typically from 200 to 3000 cm−1, can be directly recorded and the high peak intensity of femtosecond pulses enhances the efficiency of the stimulated Raman process generating vibrational wavepackets . While the actinic pulse is electronic resonant with the ground-state absorption, the Raman pump-probe pair is usually off-resonant in most experiments. The ability of tuning the spectrum of the Raman pump-probe pair allows to probe specific electronic transitions, other than those involving the ground state . Thus, all Raman modes in the excited state or subsequent transient states can be measured, not only those Franck–Condon active. Being a spectral domain technique where only the scan of the actinic pulse T delay is required, the acquisition of several spectra is intrinsically faster than time domain techniques where an additional probe τ delay must be scanned (Fig. 3). While FSRS has been already demonstrated with a single laser shot acquisition , typical acquisition times of FSRS transients are only a few minutes .
Pump-IVS is based on the combination of impulsive stimulated Raman scattering (ISRS) with an actinic excitation. As FSRS, it can be easily implemented since the signal is generated in the direction of the probe beam. However, it requires scanning two time delays, namely the photoreaction time T between the actinic pulse and the “repump” pulse (or Raman pump, or even impulsive pump, simply called “pump” hereafter), and the waiting time τ between the pump and probe pulse, during which the wavepacket dynamics evolve. Typical acquisition times for pump-IVS are of several tens of minutes for laser systems with kHz repetition rates. The acquired data must then be post-processed by Fourier transformation along τ to reveal the T-dependent impulsive Raman spectrum. The spectral range of the Raman spectrum depends exclusively on the bandwidth of the pump spectrum and the length of the transients measured along the τ delay. The pump bandwidth limits the highest upper Raman frequency and the length of the τ scanning interval defines the lowest detectable Raman frequency. Raman spectra from as low as few tens of wavenumbers up to 3000 cm−1 have been demonstrated with pump-IVS [19, 57, 58]. Detection of very low frequency Raman modes (< 200 cm−1) is another central advantage of time-domain methods in comparison with spectral domain methods like FSRS, which are constrained by optical filters to spectrally cut the Raman pump from the Raman spectrum. Moreover, since the probe spectrum in pump-IVS is normally spectrally resolved via a grating spectrometer, Raman spectra can be obtained at several detection wavelengths, depending only on the bandwidth of the probe spectrum.
Pump-degenerate four-wave mixing is based on the same concept as pump-IVS, but the two interactions with the second pulse in pump-IVS (repump) is split in two pulses. This four-beam geometry offers several advantages with respect to the three beams used in pump-IVS. One of them is the delay between the two “repump” field interactions (called here “pump” and “Stokes”), which can be used for selective nonlinear response preparation and to separate optical beating artifacts from molecular vibrations . The four-beam geometry generates the signal in a background-free configuration (homodyne detection), i.e., not in the direction of the probe as in pump-IVS, which typically leads to a superior signal-to-noise ratio and shorter acquisition times .
As briefly mentioned above, pump-DFWM differs from pump-IVS and FSRS in the signal detection and the dependence on the molecule concentration in the sample. The pump-DFWM signal is detected in a homodyne configuration. This contrasts to the self-heterodyne detection used in the other two techniques, where the signal created in the sample is generated in the same direction as the (Raman) probe beam. (Self-)heterodyne detection offers amplification of weak optical signals (see the contribution “Introduction to State of the Art Multidimensional Time-resolved Spectroscopy Methods” in the collection), but its signal-to-noise ratio often suffers from local oscillator fluctuations, inserting random noise as well as signal distortion that can only be corrected under e.g., specific balanced detection and averaging schemes [30, 61]. Pump-DFWM is not prone to such signal distortions, instead it may suffer from interferences (see below on the Challenges in Multidimensional VCS) leading to an ambiguous assignment of (low) frequency modes and artificially broadened Raman lines . The second major difference between pump-DFWM and other techniques is the nonlinear concentration dependence: while pump-IVS and FSRS depend linearly on the probed concentration, pump-DFWM (as any other homodyne nonlinear technique) shows a quadratic dependence. This nonlinear dependence leads to a distortion of the evolution of the amplitude of Raman modes during the T delay, which can only be linearized by using a heterodyne detection . A major drawback of such nonlinear concentration dependence is the difficulty of detecting minor components in a multi-component sample, since the contribution of major component(s) will dominate the signal.
4 Challenges in Multidimensional VCS
A fundamental challenge of multi-VCS in the detection of vibrational coherence in the electronically excited manifold is the small amount of excited-state population compared to the ground state or other non-actinic activated molecules (like solvent or buffer molecules). The amount of excited molecules can be changed by the actinic pulse energy, but in general is well below 20–30% to avoid saturation or other nonlinear effects. Usually, it is the interplay of the involved transition dipole moments (i.e., resonant or non-resonant with the ground state or with the small excited-state population) and the spectral overlap with optical signals originated by other states, that will determine whether a VCS signal of a given electronic state is detectable or not. In practice, very seldom a VCS signal will contain the vibrational signature of only one single electronic state. The only exception for that is electronically nonresonant experiments involving only the electronic ground state (no actinic pump). In spectrally resonant experiments, for example, the VCS spectrum is often resonant with distinct transitions during the course of a photoreaction, since the involved transition dipole moments and FC overlap with higher lying states are continuously changing. This leads inevitably to a modulation of the VCS signal due to a modification of the resonance enhancement conditions. The overlap of VCS signals originated by different electronic states is one of several causes for the interpretation challenges in VCS experiments and has been the motivation of new techniques to disentangle them.
One approach to assist the assignment of a Raman mode to the ground- or excited-state manifold is directly related to the properties of the oscillatory signal itself. Ground-state vibrational modes often show a longer-living dynamics than transient excited states, where the dephasing may be faster, due to e.g., a photoinduced reaction or internal conversion to the ground state [63, 64]. In time-domain techniques, this leads to vibrational wavepackets with shorter dephasing times (or broader Raman peaks in spectral domain techniques like FSRS) normally associated to excited state modes, while longer dephasing times are taken as coming from the ground state. Of course, longer and shorter are relative quantities, which can only correctly be interpreted when taking into account the duration of other vibrational modes and electronic population times of the involved electronic states. An additional approach often used to identify the nature of vibrational wavepackets is to rely on the phase of the oscillatory signal [13, 66, 67, 68]. For example, in spectrally dispersed time-resolved experiments, probing at wavelengths red- and blue-detuned from the center of the absorption spectrum often leads to oscillatory signals with a π-phase difference due to vibrational wavepacket dynamics. This information, when combined with the ground- and excited-state absorption bands, may assist in the assignment of a Raman mode to the respective electronic state (see e.g. ).
An additional central aspect in the signal interpretation of VCS-detected signals is interferences between signal contributions. Several kinds of interferences can be experimentally observed which may overlap with the vibrational coherences of interest [73, 74, 75]. For example, interference beats originate from the interference between vibrational modes of two different electronic states, and are an intrinsic beat of electronically resonant techniques, since vibrational coherence will be excited on both electronic states involved. Polarization beats originate from interference between nonlinear polarization contributions at the detector and are thus a pure optical effect. The origin of the polarization beating can be e.g., the emission, by different kinds of molecules, of polarizations oscillating at different vibrational frequencies and interfering at the detector. We refer the reader to references [20, 31] for more technical details.
5 Application of Multidimensional VCS
5.1 How can Multidimensional VCS Help a Chemist?
The most natural way of describing how multi-VCS can assist a chemist is by comparing it to Raman spectroscopy. In its essence, multi-VCS delivers a sequence of Raman spectra obtained after an actinic pulse interacts with the sample. In Raman spectroscopy, structural and interaction information comes from the energy, width, and amplitude of Raman bands, which assist in the identification of specific molecular species and conformations. Multi-VCS provides the same information and goes beyond by measuring how Raman frequencies shift and amplitudes evolve in time (for example, Refs. [88, 89]). Hence, it reveals time-resolved structural information on transient molecular species along the course of a photoreaction. In this regard, multi-VCS follows the same conceptual approach as transient spontaneous Raman measurements with picosecond pulses [91, 92, 93] pioneered by Lauberau et al. more than four decades ago . Multi-VCS differs from transient picosecond Raman spectroscopy, however, in many aspects. The first one is the signal intensity of the spontaneous Raman signal detected in the transient picosecond Raman spectroscopy, which is intrinsically much weaker than the coherent/stimulated signal detected in multi-VCS methods. The second one is related to the Fourier relation between the spectral resolution and pulse duration. Transient picosecond Raman spectroscopy is limited to molecular processes much slower than picoseconds due to the intrinsic time duration of the narrow-band Raman pulse, if a spectral resolution of few wavenumbers is desired. For example, a 1-ps Raman probe pulse leads to an intrinsic band broadening of more than 10 cm−1. It is also interesting to note that the vibrational content in multi-VCS can be very similar to the one detected by transient infrared absorption spectroscopies, in particular for complex systems where symmetry rules are relaxed and vibrations can be probed by Raman as well as infrared interactions.
Generally, following how the frequency of Raman bands change in dependence of the actinic pulse time delay T gives information on how bond strengths are modified during a photochemical reaction [37, 89, 95]. Frequency blue-shifts indicate stiffening of the vibrational motion or relaxation within an anharmonic potential, while red shifts may hint at elongation of a given chemical bond. On the other hand, the lack of any shift or amplitude changes is usually taken as the signature of non-reactive coordinates. The changes in the amplitude of Raman bands in multi-VCS report on the formation and breaking of chemical bonds after interaction with the actinic pulse. When correlated with frequencies changes, they become the central feature in the mapping of structural changes during photochemical reactions. Moreover, the evolution of the amplitude of a band does not need to follow a first-order kinetics and decay or grow exponentially, it can also show very complex dynamics. For example, modulation of the amplitude of a Raman band with the frequency of another Raman band has been identified as the signature of anharmonic vibrational coupling between the two corresponding modes . Information on how vibrational energy redistributes can be retrieved from the width as well as frequency changes of Raman bands. Strong coupling between molecular vibrations leads to strong dephasing and damping of specific bands and can be exploited to record how e.g., intramolecular vibrational relaxation (IVR) and vibrational cooling—e.g., solute–solvent interaction—take place in complex systems [97, 98]. Initially, very fast photoreactive systems evolve within few tens or hundreds of femtoseconds away from the Franck–Condon region, leaving very broad multi-VCS bands in the Raman spectrum.
Selected molecular systems investigated with multidimensional VCS in the last decade
Based on carotenoids
Based on retinal
Based on stilbene
Dye molecules in solution
Aromatic amino acid residues
Green fluorescence protein
Photoactive yellow protein
A seminal example in multi-VCS, which depicts many of the points mentioned above, is the pioneering FSRS investigation of the photoinduced, sub-ps structural evolution of the protonated Schiff base of retinal (PSBR) in the rhodopsin protein, the visual sensor . Upon light excitation to S1, the C11=C12 bond of PSBR extends and acquires a single-bond character. This enables a very fast torsional motion to drive the system within ~ 100 fs to a CInt , where it decays to S0, with a predicted C11=C12 bond twist of ~ 90°. By implementing FSRS, the vibrational frequencies associated to the hydrogen out-of-plane motions (in the 800–900 cm−1 range) of both hydrogen atoms linked to the H–C11=C12–H isomerizing bond could be observed as a function of time, after decay to the S0. This experiment revealed a rapid (300-fs time scale) blue shift of the H wagging frequencies by ~ 100 cm−1, which is the signature of a large structural reorganization of PSBR occurring on the ground state PES S0. More specifically, the blue shift is shown to reveal the stiffening of these vibrations resulting from the planarization of the PSBR backbone, i.e., completion of the C11=C12 isomerization (torsional) motion towards the first vibrationally relaxed photoproduct intermediate, called bathorhodopsin.
5.2 Ultrafast Vibrational Dynamics in the Excited States of Carotenoids
Carotenoids have been an important class of molecules investigated by multi-VCS due to their central role in several biological functions . As chromophores in light-harvesting complexes (LHC), for example, carotenoids are involved in the initial absorption of light and energy transfer to other chromophores (e.g., bacteriochlorophylls). The very strong absorption from the ground state S0 is due to the π–π* transition to the second electronic state labeled S2. The transition from the S0 to the first electronic S1 state is not one-photon allowed, making the S1 state a “dark” electronic state. Upon light absorption to S2, the electronic relaxation to S1 is very fast (within 100–200 fs for all-trans-β-carotene and lycopene). Further electronic relaxation from S1 to S0 takes place in the picosecond time scale, varying with the number N of effective conjugated C=C double bonds. For example, the S1 state in all-trans-β-carotene (N ~ 10.5) decays with about 9 ps, while in lycopene (N = 11) decays faster with about 4.1 ps . The S2 to S1 relaxation mechanism has been intensely debated in the last decades (see for example Ref. [124, 125, 126, 127, 128]). One source of discussion has been, for example, the nearly identical lifetime of the S2 state for several open-chain carotenoids with different numbers N of effective conjugated C=C bonds, which has been interpreted as the result of additional electronic dark states between the S2 and S1 states. The experimental identification of these dark states via transient absorption, nevertheless, has been extremely challenging due to the high spectral overlap of the respective absorption bands, the ultrashort time scales involved, but also due to the couplings [130, 131] between these states.
One of the first experimental observations of the evolution of the totally symmetric C=C stretching mode at about 1800 cm−1 has been pioneered by Hashimoto et al. using an actinic pulse to promote all-trans-β-carotene to S2 and followed by a stimulated Raman scattering scheme . With a temporal resolution of 300 fs, the energy flow between the S2 and the S1 states was followed. The initial vibrational relaxation until the v = 1 level of the totally symmetric C=C mode of the S1 state was found to be very fast, while further relaxation from v = 1 to v = 0 was much slower than the internal conversion to the ground state S0. This has been explained by the presence of an additional electronic dark state, which assisted the vibrational relaxation to v = 1 of the S1 state. The presence of an electronic dark state being populated within 20 fs in the decay between S2 and S1 states has been also proposed in lycopene based on extensive modeling of the spectroscopic signal observed by pump-DFWM .
The vibrational relaxation during the internal conversion between the S2 and S1 states for all-trans-β-carotene has been also explained by pure vibrational cooling, challenging the presence of any additional electronic dark state assisting this relaxation. The first FSRS measurements of all-trans-β-carotene showed that the S1 C=C stretching mode at 1798 cm−1 relaxes via a two-step process identified by two distinct frequency up-shift kinetics . A fast time constant (200 fs) was related to a strong coupling followed by a slower equilibration process (450 fs) to the complete set of vibrational normal modes. Although these first FSRS measurements were not able to resolve the initial 250 fs of the dynamics, more recent comprehensive studies using pump-DFWM and pump-IVS with improved temporal resolution corroborated the ultrafast initial step of the vibrational cooling model of the S1 C=C. A similar ultrafast vibrational cooling step was also observed for the C=C 1525 cm−1 mode for all-trans-β-carotene  and in other carotenoids . Cooling of the S1 C=C mode was also observed for carotenoids in a light-harvesting complex by applying FSRS to spirilloxanthin in the native LH1 of Rhodospirillum rubrum . After the actinic excitation, the frequency at 1740 cm−1 evolved to 1767 cm−1 with a time constant of 300 fs.
The vibrational relaxation after deactivation of the S2 state has been recently further addressed for a series of open-chain carotenoids (like lycopene) with increasing conjugated length N by using pump-DFWM . The simple picture of vibrational cooling, accounted for by a bi-exponential frequency up-shift as discussed in the previous paragraph for all-trans-β-carotene, is actually only observed for longer open-chain carotenoids (N = 11 and 13). Short open-chain carotenoids (N = 9 and 10) show a down-shift of the C=C stretching mode from about 1580 to about 1510 cm−1, which has been explained as a further indication of coupling between the S2 and an additional electronic dark state (between the S1 and S2 states).
A very intriguing observation in the vibrational dynamics of carotenoids is the additional observation of two vibrational bands in the 1800 cm−1 spectral region in several experiments. These bands have been observed with e.g., FSRS at 1770 and 1800 cm−1 as well as at 1770 and 1790 cm−1 [132, 135], and at 1740 and 1785 cm−1 with pump-IVS and pump-DFWM  for all-trans-β-carotene. In the latter case, they have been explained as the result of vibrationally hot C=C levels of the typical S1 C=C mode contributing to the signal (agreeing with the above picture). More recently, FSRS has been applied to spirilloxanthin (N = 13) and two bands at 1743 and 1771 cm−1 have been also observed . However, the much longer life time (3 ps) detected for 1771 cm−1 in comparison to the S1 lifetime (1.5 ps) has been interpreted as the signature of an electronic state of another carotenoid conformer present already in the ground state and also excited by the actinic pulse. Whether these two bands are due to inhomogeneous S0 conformational distributions or to vibrationally hot bands in the S1 manifold is still unclear.
Finally, low-frequency contributions have also been investigated in carotenoids [20, 51, 58]. Low-frequency bands are notoriously complicated to detect in any multi-VCS, in particular for short-lived electronic states as the S2 state of carotenoids like all-trans-β-carotene and lycopene. Nevertheless, low-frequency modes of the S2 state were reported by applying resonant stimulated Raman scattering, i.e., without an actinic pump for all-trans-β-carotene . The bands at 200, 400, and 600 cm−1 in the S2 have larger amplitude compared to ground state modes, hinting at strong anharmonicities and mixing of low frequencies in the S2 state (Fig. 13b).
In spite of being investigated by several techniques, the ultrafast vibrational dynamics in the excited states of carotenoids still poses a challenge for multi-VCS and will require in the future additional experimental and theoretical work to clarify it. Nevertheless, the application to carotenoids illustrates the ability of multi-VCS at revealing the signatures of vibrational dynamics involved in ultrafast, non-reactive, internal conversion. We will describe below another example of application of multi-VCS to the investigation of photoreactive vibrational dynamics.
5.3 Photoisomerization of Stilbene and Derivates
Both the cis and trans isomers of stilbene, named “c” and “t”, respectively, undergo C=C double bond photoisomerization via a common, so-called “phantom” dark state [142, 143], which is a perpendicular S1 transient structure named p*, from which further pyramidalization rapidly drives the system to decay to S0 via a conical intersection (CInt) [145, 146] in a similar way in both cases. Upon photoexcitation of the planar t isomer, the formation of the p* transient state from the t* Franck–Condon state takes ~ 100 ps due to a significant S1 energy barrier. Photoexcitation of the non-planar c isomer leads either (1) to ultrafast, further C=C bond torsion and sub-ps formation of the same transient p* state, or (2) to planarization enabling a cyclization reaction and dihydrophenanthrene (DHP) formation. Accurate time-resolved structural information along the S1 reactive paths has long been sought after in order to decipher the photoreaction mechanism in condensed phase [37, 77, 148, 149].
Multi-VCS of cis-stilbene was also carried out similarly, but its very short c* lifetime increases the experimental challenge [37, 148, 149], as portrayed above for the excited states of carotenoids. A seminal pump-IVS experiment demonstrated the ability of multi-VCS to reveal quantitative structural information along the ultrafast isomerization pathway from c* to the CInt . Following actinic UV excitation, a 620-nm, 11-fs pulse (repump) on resonance with ESA and SE of c* was used to impulsively trigger and subsequently probe a S1 vibrational wavepacket. A dominant oscillation is detected with a frequency around 240 cm−1, which down-shifts by up to 30 cm−1 on the ps time scale as a function of the waiting time between actinic and repump pulses. This mode, previously observed in the form of a Franck–Condon activated vibrational wavepacket in a conventional pump-probe experiment  and by ps-resolved Raman spectroscopy , is attributed to a spectator mode whose frequency shift reveals the anharmonicity and gradual topography change of the excited state PES as the system evolves from the FC point towards the CInt. FSRS experiments performed with a Raman pump on resonance with the c* ESA band  revealed Raman peaks broadened by the very short c* lifetime, but the background subtraction (inherent to FSRS data, see above) is in this case particularly challenging, leading the authors to consider the data with caution.
While both c and t photoisomerizations have long been postulated to occur via the same transient perpendicular p state , its experimental evidence and spectroscopic characterization in condensed phase came four decades later . Recently, further characterization of the p* state was made by investigating stilbene derivatives where the formation and decay time of the p* state vary by more than two orders of magnitude, while its characteristic UV absorption band is invariably observed at 350 ± 20 nm depending on the substitutions [111, 158, 159]. The dependence of the p* lifetime on the solvent polarity is interpreted as the signature of its zwitterionic nature. Multi-VCS was performed on the trans- 1,1′-dicyanostilbene, which features a nearly 30-ps-long-lived p* state in n-hexane, thus facilitating the elucidation of some of its vibrational spectroscopic signatures thanks to a very sensitive FSRS set-up . Three Raman peaks of a few μOD signal amplitude and characterized by a 20–30 ps decay kinetics were attributed to the transient p* species, including a 1558 cm−1 mode which was tentatively assigned to the phenyl quadrant vibrations, in the absence of any computational prediction of the p* vibrational modes.
Finally, another common feature of substituted trans-stilbene derivatives is the existence of ground state, sub-populations of rotamers resulting from the thermally activated phenyl ring rotations . While the various rotamers may not easily be distinguished by their steady-state UV–Vis spectroscopic signatures, they may feature distinct photoreaction kinetics and vibrational signatures. Multi-VCS was recently applied to the investigation of a family of di-fluorinated stilbene compounds . This work demonstrates the efficiency of multi-VCS at discriminating the vibrational signatures and photoreaction kinetics of distinct subpopulations. Chemical and/or structural heterogeneity is a common feature of complex molecular systems in condensed phase. One present challenge of time-resolved non-linear spectroscopy and of physical chemistry is to resolve such heterogeneity, and multi-VCS is a promising spectroscopic tool for that.
The detection of Raman spectra as a function of photoreaction time is one of the most natural ways to investigate structure changes and interactions at the molecular level. Multi-VCS has achieved this goal by detecting stimulated Raman scattering (SRS) after the interaction with an actinic pulse triggering the photoreaction of interest. SRS is a third–order non-linear spectroscopy technique which exploits coherent light–matter interactions to prepare vibrational wavepackets in one (or two) electronic states and to probe their spectroscopic signatures either in the spectral domain or in the time domain. The examples discussed in this contribution portrayed how such stimulated Raman spectra are acquired by Multi-VCS and used to (1) map structural dynamics along a photoreaction, (2) identify transient molecular species, and (3) reveal chemical/structural heterogeneity of complex molecular systems in condensed phase. In particular, the ability to directly follow Raman shifts of only a few wavenumbers as well as Raman amplitudes during a photoreaction is a central feature of time- as well frequency-domain Multi-VCS methods.
The recent success of multi-VCS in clarifying the dynamics of a myriad of molecular system is mainly due to advances in key optical technologies of ultrashort pulse generation and the ability of tuning the excitation and probing spectra. On the one hand, multi-VCS in the time domain requires short pulses, i.e., below 15 fs to effectively induce high-frequency vibrational coherence. On the other hand, spectral tuneability has been shown to be a central piece when disentangling e.g. ground from excited-states vibrational dynamics as well as addressing different chromophores. These two aspects have become experimentally more accessible in recent years by the combination of commercial non-collinear optical parametric amplifiers (nc-OPA) and broadband chirped mirrors. As also shown in this contribution, this has enabled the application of multi-VCS to a wide range of different chromophores absorbing from the UV, over the visible and up to the near-infrared spectral region. Present experimental developments, e.g., towards microscopy, are the promise for turning multi-VCS into a so-called “high-content” analytical technique [167, 168]. In particular, the combination of e.g., multi-VCS with super-resolution microscopy exemplifies the ability to identify chemical compounds with spatial resolutions beyond the diffraction limit without any chemical labeling .
In spite of the success of multi-VCS, there are still several ongoing research topics. One of these topics is the extraction of the pure excited state vibrational dynamics. The complexity of molecular signal extraction is present in all multi-VCS methods and can be due to different causes (spectral overlap between ground- and excited-state absorptions, signal distortion due to other optical signals contributions, etc.). The development of cautious data post-processing, for example, to isolate reliably the specific stimulated Raman spectra of interest is still an intense research topic.
Another ongoing research topic in multi-VCS is the calculation of the evolution of Raman spectra in excited molecular states. Compared to other multidimensional techniques like 2D electronic or 2D infrared spectroscopies, the application of theoretical methods to calculate the evolution of Raman spectra in excited molecular states still is in its infancy, and in the overwhelming majority of the experimental cases, analysis of multi-VCS spectra is still done in a very qualitative way. From the theoretical point-of-view, models (like sum-over-states (SOS) and multimode Brownian oscillator) and nonlinear signal calculation techniques are well known, but there have been very few examples where the experimental optical signal in multi-VCS has been completely numerically simulated . A major challenge for accurate modeling of third-order non-linear spectroscopy signals (VCS or UV–Vis 2DES) obtained in complex molecular systems still resides in the accurate quantum chemical simulation of excited molecular states and of their photoreaction dynamics. The contribution by Segarra-Martin et al. in this collection reviews the present state-of-the-art theoretical developments for the simulation of 2DES spectroscopy signal in complex molecular systems. Rapid progress in theoretical development is opening new horizons towards quantitative modeling of experimental signal based on realistic models of complex systems.
In conclusion, multi-VCS is now established as one of the state-of-the-art non-linear spectroscopy techniques for the investigation of ultrafast photoreactivity in molecules. More specifically, it is a technique of choice for monitoring vibrational dynamics in excited states with unparalleled time resolution. It is our belief that the combination of multi-VCS methods with recent and rapid theoretical developments will further enhance the impact of multi-VCS in unraveling ultrafast photoreaction mechanisms.
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