Slow Intramolecular Vibrational Relaxation Leads to Long-Lived

Aug 10, 2016 - intramolecular vibrational relaxation (IVR). Slow IVR indicates weak mode−mode coupling and therefore weak anharmonicity of the poten...
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Slow Intramolecular Vibrational Relaxation Leads to Long-Lived Excited-State Wavepackets Shahnawaz Rafiq and Gregory D. Scholes* Frick Chemistry Laboratory, Princeton University, Princeton, New Jersey 08544, United States ABSTRACT: Broadband optical pump and compressed white light continuum probe were used to measure the transient excited-state absorption, ground-state bleach, and stimulated emission signals of cresyl violet solution in methanol. Amplitude oscillations caused by wavepacket motion in the ground and excited electronic states were analyzed. It was found that vibrational coherences in the excited state persist for more than the experimental waiting time window of 6 ps, and the strongest mode had a dephasing time constant of 2.4 ps. We hypothesize the dephasing of the wavepacket in the excited state is predominantly caused by intramolecular vibrational relaxation (IVR). Slow IVR indicates weak mode−mode coupling and therefore weak anharmonicity of the potential of this vibration. Thus, the initially prepared vibrational wavepacket in the excited state is not significantly perturbed by nonadiabatic coupling to other electronic states, and hence the diabatic and adiabatic representations of the system are essentially identical within the Born−Oppenheimer approximation. The wavepacket therefore evolves with time in an almost harmonic potential, slowly dephased by IVR and the pure vibrational decoherence. The consistency in the position of node (phase change in the wavepacket) in the excited-state absorption and stimulated emission signals without undergoing any frequency shift until the wavepacket is completely dephased conforms to the absence of any reactive internal conversion.

1. INTRODUCTION Photoexciting a molecule using a spectrally broad (temporally short) pulse prepares a superposition of Franck−Condon active vibrational levels called a wavepacket, which subsequently evolves in time according to the displacement of the excitedstate potential and loss of coherence. Wavepacket dynamics on an ultrafast time scale has regained attention recently, as researchers discover and elucidate quantum coherent effects initiated by short laser pulses. Earlier, wavepacket dynamics were explored to reveal the photophysics of small molecules like ethylene cation, pyrazine, and NO2.1−4 The passage of a nuclear wavepacket from one electronic surface to another was explained by theories for conical intersections between the two adiabatic surfaces enabled by coherent nuclear motion.1−9 Electron transfer in the photosynthetic reaction center was found to occur, while vibrational eigenstates were still in a coherent superposition and eventually led to an increased interest in the quantum aspects of energy and electron transfer in photosynthetic systems.10−12 Quantum coherences were recently proposed to drive the charge separation in the photosynthetic reaction center and in the organic photovoltaics.13−18 In parallel, energy-transfer dynamics in photosynthetic light-harvesting complexes in plants and algae have been examined using ultrafast spectroscopy to detect coherent dynamics involving excitonic and nuclear degrees of freedom.19−32 Wavepacket dynamics were originally detected after shortpulse excitation of small molecules isolated in the gas phase. Those experiments provided insights into time scales and © XXXX American Chemical Society

mechanisms of intramolecular vibrational relaxation (IVR) in excited electronic states.33−40 In large molecules in condensed phase at ambient temperature, IVR normally occurs rapidly, typically in a few picoseconds, by redistributing energy among vibrational modes and also dissipating the energy to the solvent.41−46 Dephasing of the wavepacket therefore has a strong contribution from IVR (population relaxation), which is why excited-state vibrational wavepackets dephase much more quickly than those in the ground electronic state. Here we report a study of vibrational coherences in cresyl violet (CV) dissolved in methanol at ambient temperature. Using a white-light probe we resolved the ripples in the groundstate bleach (GSB), stimulated emission (SE), and excited-state absorption (ESA) transient signals caused by wavepacket motion and thereby isolated its contribution in modulating the ground- and excited-state populations. This explicit assignment of wavepacket motion to the ground and excited electronic states were confirmed by detection of nodes in the phase of coherent oscillations along the probe frequency axis. These nodes are essentially a manifestation of phase change in the wavepacket, as it passes through the minimum of the potential whose phase space it occupies. Careful Fourier filtering and continuous wavelet transform analyses provided detailed information helping to revise a recent proposition that the excited-state wavepacket branches at the seam of conical Received: August 2, 2016 Revised: August 10, 2016

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Figure 1. (a) Absorption and corrected fluorescence spectra of CV perchlorate in methanol are shown as black and red solid lines with respective maxima at 16 830 cm−1 (594 nm) and 16 030 cm−1 (623 nm). The pump pulse spectrum is shown as yellow transparent shaded area, and the compressed white light probe spectrum is shown as a cyan color shaded area. (b) A contour map of pump probe raw data showing the oscillatory modulation on top of ground- and excited-state population dynamics.

Figure 2. (a) Pump probe map showing residual oscillations after subtracting population kinetics obtained from biexponential fitting. In addition to the GSB/SE spectral region, oscillations are very prominent in ESA. (b) Power spectrum map obtained by Fourier transformation of the data in plot (a). Several oscillatory frequency components in GSB/SE and ESA spectral regions are revealed. Owing to relatively small amplitude of oscillations in ESA, the power spectrum in the range defined by the horizontal arrow is scaled fivefold relative to the GSB/SE region. (c) Fourier transform of the time domain traces at probe frequencies predominantly from GSB/SE, SE, and ESA spectral regions. It shows that 587 and 593 cm−1 are the frequencies of excited- and ground-state wavepackets, respectively. (d) Fourier filtering of the strong Franck−Condon active mode at 587/593 cm−1 by applying a super-Gaussian filter shows clearly the oscillations of this particular mode in the time domain.

conclusions rely on the time-dependent dynamics of nodes in terms of their invariable spectral position and not undergoing any frequency shift along the waiting time until the wavepacket

intersection between the ground and excited electronic states of CV.47 Small frequency shifts due to a difference in the shape of the ground- and excited-state potentials are observed. Our main B

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dynamics contributions are removed by performing exponential fitting at each probe frequency, and the residual of the fitting represents the coherent oscillations. The fitting is started at 50 fs to isolate the coherent artifact arising from pulse overlap effects. Residuals at each probe frequency are plotted as a function of probe frequency and waiting time in Figure 2a, which provides visual representation of the phase of these coherent oscillations.48 These periodic oscillations can be Fourier transformed along t2 into their respective frequencies. The resulting power spectrum map resolves oscillatory frequencies as a function of probe frequency as shown in Figure 2b. The advantage lies in the information it provides about the origin of these oscillations in terms of which transient signal is modulated. The measurements resolved 341, 468, 486, 522, 567, 670, 821, 1036, 1174, 1232, 1359, 1519, 1644 cm−1 frequencies, including a particularly strong amplitude modulation at ∼590 cm−1 spreading over the GSB, SE, and ESA bands. To avoid any ambiguity due to the solvent contributions, control experiments performed on neat methanol confirmed that no Raman active modes due to the solvent were detected in the 600 cm−1 region. 3.1. Assignment of Excited-State Vibrational Coherences. In broad band pump probe-type experiments, a wavepacket is generated by projecting the ground-state population into the excited state through an impulsive excitation by ultrashort laser pulse.33,49−51 The wavepacket represents a superposition of vibrational states encompassing multiple nuclear modes and carries all the frequencies under its envelope, like ripples created when a ball is thrown in a pond. This field matter interaction not only generates a wavepacket on the excited electronic state but also projects a minor wavepacket on the ground state through the impulsive stimulated Raman process.3,52 The nuclear wavepacket of a mode is launched on one side of the displaced potential energy curve, and its motion as a function of the normal coordinate to the other side of the potential and back is detected as a function of probe frequency. During the motion of wavepacket along the displaced potential, a phase shift of the oscillations is noted at a probe frequency corresponding to the minimum of the potential curve, manifest as a node of zero amplitude.10,48,53,54 Therefore, wavepacket motion in the ground electronic state potential produces a node in GSB at the absorption maximum, while if the wavepacket is on the excited-state potential then the phase change in SE signal will appear at the fluorescence maximum. With transform-limited pulses, an excited-state wavepacket is generated with a large displacement and hence strongly modulates the excited-state amplitude, while a groundstate wavepacket is generated with a small displacement and hence weaker oscillations.55,56 Also, the generated superposition of vibrational eigenstates on the ground state can reduce the effective energy gap between the ground and excited states, and hence the node in the GSB may be shifted to slightly lower energy. Contrarily, the superposition of vibrational eigenstates generated on the excited electronic state can increase the effective energy gap, and hence the node in the SE may be slightly shifted toward higher energy.57 The spectral position of the node is thus a useful indication of the source of the wavepacket,53,58 although sometimes overlapping signal from a major wavepacket on the excited state (SE) and a minor on the ground state (GSB) biases the apparent spectral position of the node, decided by interference effects and also the relative amplitude of the two wavepackets.53 Phase change (node) in the oscillatory components of each

dephases completely, while the dephasing is primarily controlled by significantly slow IVR dynamics.

2. EXPERIMENTAL SECTION Cresyl violet (Exciton Inc, USA) solution was prepared in methanol with an optical density of ∼0.2 at its absorption maximum, 16 830 cm−1 (594 nm) in a 1 mm glass cuvette. The normalized absorption and the fluorescence spectra of the CV solution is shown in Figure 1a as black and red solid curves, respectively. For broad band transient absorption spectroscopic measurements, the experimental setup is explained in detail elsewhere;48 however, a brief description is provided here. Pulsed laser light (800 nm, 150 fs) from a Ti:sapphire seeded regenerative amplifier (Spectra-Physics, Spitfire) was used to pump a home-built nonlinear optical parametric optical amplifier (NOPA). The desired NOPA pulse spectrum was compressed into a folded grating compressor and a two-prism compressor, respectively. The pulses centered at 16 400 cm−1 (∼610 nm) were compressed to ca. 13 fs full width at halfmaximum as diagnosed with polarization-gated frequency resolved optical grating (PG-FROG) in a 1 mm path length methanol solvent. The pump spectrum is shown in Figure 1a as a semi-transparent yellow color filled curve. The compressed output was split into three beams by a wedge beam splitter. Two beams reflected from the front and back surfaces of the wedge, having ca. 1% of total incident intensity, were used as reference and probe beams, respectively. The transmitted beam was used as a pump beam and had a translation stage in its path to control the arrival of pump pulses relative to the probe pulses. For the transient absorption measurements with a broader probe spectral range, a separate white light arm was put in place and before sending the generated white light continuum (Figure 1a, cyan color filled curve) from sapphire plate into the transient absorption setup, it was pre-compressed by inserting a pair of chirped mirrors in its path to remove the temporal chirp. In general, the measurements can also be performed without putting chirped mirrors in the white light path, as it does not affect the temporal resolution of individual wavelengths. The normalized differential intensity (not the differential absorbance) of the probe as a function of its wavelength along the waiting time (tmax = 6 ps) is measured in the usual way.48 The 2 positive-signed transient features represent GSB or SE and negative features indicate ESA. In Figure 1b, the red colored contours represent GSB and SE, while as the blue colored contours represent ESA. The main purpose of using white light continuum as a probe instead of the replica of pump spectrum was to access the ESA transient signal, as it is outside of the spectral range provided by the output of NOPA spectrum. 3. RESULTS AND DISCUSSION The transient absorption map of CV (Figure 1b) shows prominent GSB and SE signals overlapped in the spectral region from 15 000−19 000 cm−1, with a maximum at 16 000 cm−1. A distinct ESA band extends from 19 000 to 21 000 cm−1, peaked at 20 000 cm−1 (500 nm). The ripples appearing on top of the transient signals in Figure 1b are a manifestation of the wavepacket motion modulating the population in the ground and excited electronic states. These coherent oscillations contain information about the Franck−Condon active nuclear modes populated during an electronic excitation. Population C

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the overlapping (oppositely signed) tail of the bleach. The tail is apparent in the absorption spectrum (Figure 1a). 3.3. Conical Intersection or Not. Recently, Brazard et al. made the fascinating suggestion that the presence of a conical intersection between the S1 and S0 electronic states in CV branches the wavepacket at the seam, so that an abrupt bifurcation in the SE node detects the conical intersection associated with reactive internal conversion.47 The conclusions of that study were based on sudden appearance of new nodes in the GSB/SE region after a waiting time of 2 ps. The work raises interesting questions because based on the fluorescence lifetime and quantum yield of CV we would expect the radiationless transitions to occur on the nanosecond time scale, relatively slower than the radiative rate.60,61 Is there a fast radiationless relaxation channel enabled by coherent wavepacket motion or hot vibrational excitation in S1? Two time-frequency analysis procedures were implemented to analyze carefully the spectral and temporal dependence of the node position. The time dependence of the SE and ESA node position can provide information about the timedependent location of the wavepacket. If a wavepacket faces a reactive crossing on its path, it will change its location from the initial state to the final state and thereby affect directly the spectral position of the node from the minimum of initial state to the minimum of the final state. Fourier filtering based timefrequency analysis was performed on the 587 cm−1 (strongest) vibration in the SE and ESA region of our data (Figure 2d). This nuclear mode was proposed to be the coupling mode between excited and ground state enabling population relaxation through conical intersection in the work of Brazard et al.47 In addition, continuous wavelet transform analysis was also performed to follow the time evolution of the node position at the SE and ESA signals as a function of probe frequency and Fourier transformed frequency (Figure 3).53,62,63 Briefly, wavelet analysis allows us to map the temporal evolution of the frequency spectrum within the limits of the frequency-time uncertainty relation. It uses a zero mean and short-time oscillating function called a “mother wavelet”, to decompose a multidimensional (real) signal into different frequency bands known as scales, which are then subsequently converted into oscillatory frequencies. More details are provided in ref 63. Remarkably, the branching of the wavepacket at the seam of the presumed conical intersection reported in ref 47 were not reproduced under our experimental conditions. In contrast, the node positions at 16 100 and at 19 640 cm−1 in the respective SE and ESA signals remained consistent through the waiting time window up to 6 ps (Figure 2d and Figure 3) without undergoing any visible change. The spectral position of the node in SE signal (at 16 100 cm−1) remains at the fluorescence maximum, and the node in ESA signal (at 19 640 cm−1) continues to be there without undergoing any shift in its position. We did not detect the disappearance of the initial node at 16 100 cm−1 after a waiting time of 2 ps and subsequent branching of the node toward the absorption and fluorescence maximum as reported in ref 47. Note that another kind of node is also seen in Figure 2d at 18 360 cm−1. That node is not related to wavepacket motion; rather, it is the probe frequency where GSB and ESA signals perfectly cancel each other. In the work of Brazard et al, the experiments were conducted by using a broader excitation pulse than what we used in our experiments, and therefore the possibility may arise that the wavepacket branching might occur to a high-energy

Franck−Condon active nuclear mode in the GSB/SE signal (from 15 000−19 000 cm−1) appears at a probe frequency of 16 100 cm−1 (621 nm), as shown in Figure 2a,b. This probe frequency is slightly shifted toward higher energy (by 2 nm) with respect to the fluorescence maximum of CV in MeOH (623 nm). As indicated above, this slight blue shift is most likely due to increase in effective energy gap between the excited and ground state when a superposition of vibrational eigenstates is generated in the excited electronic state. The wavepacket motion can therefore be explicitly ascribed to the excited electronic state. A small difference in the frequency of the oscillatory mode at ∼590 cm−1 on either side of the node at 16 100 cm−1 is evident in the data (Figure 2b), and we propose that the integrated peak at ∼590 cm−1 possibly contains two frequencies instead of one. The frequency on the lower wavenumber side, where SE is the predominant transient signal, is 587 cm−1 (Figure 2c), while on the higher-energy side, which contains a mix of GSB and SE signals, two frequencies, 587 and 593 cm−1, are resolved (Figure 2c). Such small difference in the frequency between the fluorescence side (587 cm−1) and the absorption side (593 cm−1) reveals a small frequency change of this nuclear mode in the excited electronic state compared to that of the ground state. Such a small frequency change is common and comes from a decrease in the force constant of the excited state compared to the ground-state potential of this normal mode. We assign 587 cm−1 to the excited-state frequency and 593 cm−1 to the ground-state frequency, consistent with Raman scattering measurements.59 Such frequency shifts were not observed for other nuclear modes possibly due to the predominant contribution of excited-state wavepacket. 3.2. Direct Probing of Excited-State Coherences. It is always cumbersome to isolate the contribution of ground- and excited-state wavepacket motions while dealing with transient signals from the two electronic states overlapping in the same spectral region. In case the transient signature of a particular electronic state is spectrally separate and distinct from other signals, it can provide clear evidence about the contribution of wavepacket motion toward that state. In CV, the excited-state absorption signal is spectrally separated from the GSB and SE signal (Figures 1 and 2), peaked at 20 000 cm−1 (500 nm). This spectral region is not accessible by the bandwidth of our NOPA pulse. To detect this signal required us to use the white light continuum as a probe instead of probing by an attenuated replica of the pump pulse as mentioned above. The amplitude of the oscillations in ESA region (Figure 2a) are observed to be smaller than those in SE region, likely indicating a smaller displacement of the normal modes and smaller extinction from the S1 to S2 transition. Fourier transformation reveals that all the frequencies observed in the SE signal are replicated in the ESA region (Figure 2b) and that the mode that was earlier identified to have a frequency of 587 cm−1 in the excited state and 593 cm−1 in the ground state has a frequency of 587 cm−1 in the ESA region (Figure 2c, blue trace). This clearly identifies 587 cm−1 as the excited-state frequency and 593 cm−1 as the ground-state frequency of this particular nuclear mode. A distinct phase change is also observed in ESA signal both in the residual map (Figure 2a) and the power spectrum (Figure 2b) at 19 640 cm−1 (509 nm), which is shifted from the apparent ESA maximum of 20 000 cm−1. We propose that the node shows more accurately the peak frequency of the ESA, because the ESA band in the pump−probe spectrum is blue-shifted by D

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between the absorption and fluorescence maxima. Depending on the relative proportion of the excited- and ground-state wavepackets, the node position will be biased toward the fluorescence maximum or the absorption maximum. At earlier times, the excited-state wavepacket having stronger amplitude predominates, but once that wavepacket starts dephasing, it loses amplitude, and the ground-state wavepacket, which has an inherently longer dephasing time, contributes strongly. This results in a shift of the node position from fluorescence side toward the absorption side. Such an apparent shift of the node position is however not due to the transfer of wavepacket from excited to ground state through some reactive curve crossing, but rather due to the fact that excited-state wavepacket loses phase coherence earlier than the ground-state wavepacket.53 3.4. Wavepacket Dephasing and Intramolecular Vibrational Relaxation. A remarkable observation from our study is the consistency in the node position at the SE maximum and the ESA maximum along the waiting time, which predicts the absence of any reactive internal conversion (conical intersection) process between the excited and the ground state. Usually, in molecular systems where coherent motion along a specific nuclear mode brings an initially prepared state toward the point of degeneracy with the final state, the wavepacket sloshes through the crossing point as the population is transferred.9 The lifetime of these coherent oscillations on the “initial state” is limited by the time scale of the process itself, and there is a possibility that some of the nuclear modes, promoter or spectator, can survive these reactive processes and continue oscillating coherently on the “final state”. An important aspect of the motion of wavepacket through these crossings is that the wavepacket changes its electronic state, and hence the node position will be shifted depending on the initial and final locations of the wavepacket. It is though very wellestablished that the processes that are directly controlled by the coherent nuclear motion occur significantly faster (in less than 10 ps) and that the population in the initial state does not outlive the survival time of coherent oscillations. In other words, these coherent nuclear motions drive the nonradiative transfer of population from one state to another in a highly nonexponential manner depending on the extent of electronic coupling between the two states. For example, in the strong coupling case of rhodopsin, a single pass through the conical intersection results in significant nonradiative relaxation,8 while as in the intermediate coupling regime, like proton transfer in Green Fluorescent Protein (GFP)71 or charge transfer in tetramethylbenzene-tetracyanoquinodimethane π-stacked charge-transfer complex,72 there is still an appreciable nonradiative transition probability, as the two state are close together, but the rate is relatively slower (10 ps. The slow dephasing of the vibrational wavepacket in the excited state and the invariable node position is a reflection of slow intramolecular vibrational relaxation, which in turn suggests weak coupling of this normal mode to other modes of CV (i.e., very weak anharmonicity). The system is an ideal example of a weak coupling regime, wherein the excited and ground electronic states interact weakly with each other, and hence coherent nuclear motion generated in the excited state stays there until it dephases completely without facing a reactive internal conversion. The system instead internally converts to the ground state through Fermi’s golden rule transition following exponential rates.

vibrational coherences are found to survive for more than the experimental waiting time window of 6 ps (Figure 4), which is

Figure 4. Amplitude oscillations extracted at the excited-state absorption transient signal by inverse Fourier filtering of the two frequencies; 522 and 587 cm−1. The red trace shows the periodic oscillations of the two frequencies within the experimental waiting time window of 6 ps. The blue trace starting from time zero is the fitting function composed of two damped cosines for 522 and 587 cm−1, which provides 2.2 and 2.4 ps as the respective dephasing time constants. Extending the fitting function up to 10 ps shows that the oscillations have not yet completely dephased. (inset) Blue trace starting at 5 ps indicates the enlarged portion of the fitted trace to highlight the fact that oscillations have not even completely dephased by 10 ps.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +1-609-258-0729. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through Grant No. DE-SC0015429. S.R. thanks M. Koch for reviewing a draft of the manuscript.

relatively longer than the reported lifetime of excited-state vibrational coherences in the stronger and intermediate coupling regimes.9 The fitting of time domain data in the ESA region (to probe excited-state coherences explicitly) by two damped cosines for two modes, 522 and 587 cm−1, suggest that by extending the fitting range to 10 ps, the coherences have still not dephased fully as shown in Figure 4. The dephasing time constants of the two nuclear modes is found to be 2.2 and 2.4 ps, which is relatively longer than the estimated dephasing time constants of coherent modes in GFP (