Excited-state Raman spectroscopy with and without

Excited-state Raman spectroscopy with and without actinic excitation: S 1 Raman spectra of trans-azobenzene A. L. Dobryakov, M. Quick, I. N. Ioffe, A. A. Granovsky, N. P. Ernsting, and S. A. Kovalenko Citation: The Journal of Chemical Physics 140, 184310 (2014); doi: 10.1063/1.4874854 View online: http://dx.doi.org/10.1063/1.4874854 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Femtosecond Raman spectra of cis-stilbene and trans-stilbene with isotopomers in solution J. Chem. Phys. 137, 244505 (2012); 10.1063/1.4769971 Coupled-cluster and density functional theory studies of the electronic excitation spectra of trans-1,3-butadiene and trans-2-propeniminium J. Chem. Phys. 131, 024301 (2009); 10.1063/1.3158990 Ultrafast excited-state dynamics in photochromic N-salicylideneaniline studied by femtosecond time-resolved REMPI spectroscopy J. Chem. Phys. 121, 9436 (2004); 10.1063/1.1801991 Structure of the triplet excited state of bromanil from time-resolved resonance Raman spectra and simulation J. Chem. Phys. 115, 6106 (2001); 10.1063/1.1398304 Spectroscopy and ultrafast dynamics of the 2A 1 state of Z-hexatriene in gas phase J. Chem. Phys. 106, 2205 (1997); 10.1063/1.474080

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THE JOURNAL OF CHEMICAL PHYSICS 140, 184310 (2014)

Excited-state Raman spectroscopy with and without actinic excitation: S1 Raman spectra of trans-azobenzene A. L. Dobryakov, M. Quick, I. N. Ioffe,a) A. A. Granovsky,b) N. P. Ernsting, and S. A. Kovalenko Department of Chemistry, Humboldt-Universität zu Berlin, Brook-Taylor-Str. 2, D-12489 Berlin, Germany

(Received 11 March 2014; accepted 23 April 2014; published online 9 May 2014) We show that femtosecond stimulated Raman spectroscopy can record excited-state spectra in the absence of actinic excitation, if the Raman pump is in resonance with an electronic transition. The approach is illustrated by recording S1 and S0 spectra of trans-azobenzene in n-hexane. The S1 spectra were also measured conventionally, upon nπ * (S0 → S1 ) actinic excitation. The results are discussed and compared to earlier reports. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4874854] I. INTRODUCTION

Femtosecond stimulated Raman (FSR) spectroscopy has been developed1–7 to study short-lived intermediates in the condensed phase. Here a femtosecond actinic pulse is applied to create population in an excited electronic state. After a delay t, a picosecond Raman and femtosecond probe pulse act simultaneously to produce and record a stimulated Raman signal. The technique combines high temporal (0.1 ps) and spectral (10 cm−1 ) resolution and therefore is very useful in Raman spectroscopy of non-stationary states. In the absence of actinic excitation and far from resonance, FSR records conventional Raman spectra, with the advantage that even strong sample fluorescence does not affect the quality of the signal. Furthermore, in the resonance case FSR ground-state spectra should contain contributions from higher electronic states.8–11 In other words excited-state Raman spectroscopy without actinic excitation may be realized. Although first demonstrated in 1981 with coherent antiStokes Raman scattering (CARS),8, 9 this opportunity has not been explored systematically, partly because the focus was on different aspects, partly due to imperfect laser technology. In this regard, FSR is ideally suited for the problem of interest, as shall be clarified in the present paper. We report S1 and S0 spectra of trans-azobenzene recorded with and without actinic excitation. The resulting S1 spectra are compared to each other and to earlier reports. Trans-azobenzene was chosen since its absorption bands are well accessible with our Raman6, 7 and transient absorption12–15 setups. In addition, azobenzene spectra are of great interest, as the compound is important for many nanotechnological applications.16–20 II. EXPERIMENTAL

The experimental setups have been elsewhere.6, 7, 12–15 The Raman pump (0.2 μJ, 10 cm−1 width) was tunable in the wavelength = 495–590 nm. The actinic (λac = 460 nm, 30

described 920 Hz, range λR fs, 1 μJ),

a) Also at Department of Chemistry, Lomonosov Moscow State University,

Moscow, Russia

b) Also at Firefly Project, Moscow 117593, Russia

0021-9606/2014/140(18)/184310/5/$30.00

probe (30 fs, 1000 cm−1 in width, chirped), and Raman beams were focused on a flow sample cell in the boxcar geometry. The spot size was about 100 μm for the actinic and probe beam, and about 30 μm for the Raman beam. The polychromator dispersion was adjusted to cover a 1000 cm−1 probe range. In the measurements with/without actinic excitation, the signal was recorded by chopping the Raman pump with the open/blocked actinic excitation. In this registration scheme, signals at negative pump-probe delays correspond to the ground-state Raman and solvent contributions. For positive delays, these contributions are eliminated by subtracting the signals at negative delays. 50–100 pump-probe scans were averaged to achieve a sufficient signal-to-noise ratio. III. CALCULATION OF RAMAN SPECTRA

Raman spectra were calculated with the PRIRODA software21 that features a fast implementation of the resolution-of-identity (RI) technique for the GGA functionals. We used the built-in TZ2P basis set ((11s6p2d)/[6s3p2d] for the first row atoms and (5s1p)/[3s1p] for hydrogens) and the PBE xc functional.22 Both S0 (density functional theory, DFT) and S1 (linear response time-dependent (TD) DFT with analytic gradients) were optimized to high accuracy (above 10−5 Ha/Bohr) without symmetry restrictions, revealing the apparent C2h symmetry in both cases. The hessian was computed analytically for S0 and by numerical differentiation of the analytic gradients for S1 . To obtain the non-resonant Raman intensities, the normal modes were combined with the static polarizability derivatives computed for both states via numerical differentiation of the energy gradient over the electric field. IV. GROUND AND EXCITED-STATE ABSORPTION SPECTRA

Ground-state absorption spectra of trans-azobenzene in n-hexane are displayed in Fig. 1, top. They show a strong π π * band peaked at 316 nm, and a weak nπ * band due to the S0 → S1 transition at 448 nm. In the ground-state measurements without actinic excitation, the Raman pump was in the range

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extinction and transient aborption of trans-azobenzene

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probe wavelength λ (nm) FIG. 1. Extinction spectra of trans-azobenzene in n-hexane, and a transient absorption spectrum at t = 0.12 ps upon nπ * (S0 → S1 ) excitation. An excited-state absorption (ESA) band about 530 nm corresponds to S1 → Sn , while stimulated emission (SE) is associated with S1 → S0 . By definition, ESA is positive and SE is negative. The SE band, schematically drawn in red, is not visible as negative signal because of the stronger ESA contribution. Actinic excitation was at 460 nm, and Raman pump was tunable in the range of 495–590 nm.

of 495–590 nm. A transient absorption spectrum at t = 0.12 ps upon nπ * excitation is shown in Fig. 1, bottom. The excitedstate absorption (ESA) band at 530 nm is associated with S1 → Sn . The stimulated emission (SE) band shown by the red curve corresponds to S1 → S0 . The SE band is not directly seen because it is overlaid by stronger ESA. This observation, which is important for the following, can be expressed by an inequality μ1n > μ10 for the corresponding transition dipole moments. In our measurements with actinic excitation, the Raman pump was in the region of 540–590 nm, simultaneously in resonance with S1 → Sn and S1 → S0 . We shall see that the knowledge of both ground-state and excited-state absorption is crucial to correctly evaluate the resonance Raman signal, either without or with actinic excitation. V. STIMULATED RAMAN DIAGRAMS

Further we consider only the Stokes FSR signal. It can be written as a sum A = Ai over the stimulated Raman diagrams drawn in Fig. 2 (the full A expression is detailed in Ref. 24). The energy level diagrams used here are advantageous over conventional double-sided Feynman diagrams, as they visualize Raman shifts, help to easily distinguish Stokes and antiStokes signals, and even provide “by eye” the relative weight of various contributions, as shall be detailed further below. Diagrams 1-3 (upper row) start in S0 and therefore contribute without actinic excitation. Diagram 1 describes con-

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FIG. 2. Stokes stimulated Raman diagrams for the third-order polarization P(3) . “Bra” and “ket” interactions correspond to solid and dashed arrows, blue and orange being Raman pump and Stokes probe, respectively. A positive sign is for probe absorption, and negative for probe emission. Vibrational coherence is created by the first two interactions, either in S0 (1, 8) or S1 (2–7). Diagrams 1–3 start in S0 and thus contribute without actinic excitation; diagram 1 corresponds to usual ground-state Raman scattering; diagrams 2 and 3 (commonly not considered) show S1 contributions. Diagrams 4–8 describe signals upon actinic excitation (not shown); diagram 8 probes S0 , while diagrams 4–7 reveal S1 contributions. Note that formally diagrams 4–8 are of fifth order P(5) , due to two additional interactions with the actinic field. Here these interactions are skipped by considering that an S1 population is already available.

ventional S0 scattering while diagrams 2 and 3 reflect S1 contributions. Far from the S0 → S1 resonance only diagram 1 survives (classical nonresonant scattering) whereas diagrams 2 and 3 disappear because they require excited-state population. Diagrams 2a, 2b and 3a, 3b appear always in pairs10, 11 because they allow the permutation of the Raman pump and probe fields. Vibrational coherence is created by the first two interactions either in S0 or in S1 . Usually the coherence lives longer in the ground than in the excited electronic state. The Raman signal depends on the ratio between the probe pulse duration and coherence lifetime. The signal is higher when the probe becomes shorter. In the opposite case of long probe pulses, the signal is suppressed. Note that diagrams enter A with different sign, “plus” for probe absorption and “minus” for probe emission, the convention being taken from transient absorption spectroscopy. Importantly, in spontaneous Raman scattering (stationary or picosecond) diagrams 2 and 3 disappear due to zero probe fields, so that only diagram 1 contributes. Thus, ground-state spontaneous resonance Raman cannot deliver excited-state spectra. Lower diagrams (4–8) start in S1 and hence require actinic excitation (which is not shown). Sn coherencies are neglected because of their very short lifetimes. Diagrams 8a and 8b probe S0 and must be visible in absorption, while diagrams 4–7 reveal different S1 contributions. Comparing diagrams 2 and 3 and taking into account μ1n > μ10 derived earlier, one gets |A2a | > |A3a | and |A2b | > |A3b |. That is the full S1 signal should be positive (absorption) in the absence of actinic excitation. On the contrary, with actinic excitation the S1 signal will be negative because |A4 | < |A5 | and


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|A7 | < |A6 |. Note that far from the Sn resonance, Ai (i = 4, 8) would be all positive, while without actinic excitation the corresponding Ai (i = 1, 3) would be negative. In the case of spontaneous picosecond Raman, diagrams 4–8 are all operative, because the probe field is available from spontaneous S1 fluorescence.

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FIG. 3. Raman spectra from trans-azobenzene in n-hexane measured without actinic excitation, as function of Raman pumping wavelength λR . The sample concentration was 0.05–0.1 M. Negative bands correspond to the conventional S0 signal (diagram 1), while positive peaks originate from S1 (diagrams 2 and 3). The S1 contributions vanish when the Raman pump is detuned farther from the S0 → S1 resonance. The signal A is in (mOD): 1 mOD corresponds to a gain 0.0023.

We now turn to experimental results. Fig. 3 shows resonance ground-state spectra measured without actinic excitation. Raw data are displayed on top, and backgroundcorrected spectra are given at the bottom, with different detuning of the Raman pump from the S0 → S1 resonance. The high-frequency Stokes range is dominated by conventional S0 scattering (diagram 1) seen in emission (negative). At low frequencies, this contribution becomes extremely weak. Here one finds in addition positive peaks which, on the basis of the above discussion, are to be ascribed to S1 coherencies. The positive peaks decrease and disappear when the Raman pump goes farther from the resonance, as expected for the S1 contributions (diagrams 2 and 3). VII. FSR SPECTRA UPON ACTINIC EXCITATION

Next, consider FSR spectra recorded upon actinic excitation. They are shown in Fig. 4. The spectra at negative delays (top) originate from S0 (diagrams 1–3) and also include the hexane contribution (magenta curve). In the left graph, the

Raw transient FSR spectra of trans-azobenzene in hexane with λAc=460 nm, λR=590 nm 0.22

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FIG. 4. FSR spectra of trans-azobenzene in n-hexane upon S0 → S1 (nπ ∗ ) actinic excitation (λAc = 460 nm) nm, and Raman pump at λR = 590 nm. The spectra at negative delays (yellow, top right) are due to S0 (diagrams 1–3) and also include a hexane contribution (magenta). Transient Raman spectra (bottom) reveal negative S1 bands (marked by arrows, diagrams 4–7). Strong positive peaks in the high-frequency range (at right) are due to S0 coherencies (diagram 8). Note a 3 cm−1 shift between the positive and negative S0 peaks that may be due to a difference in the vibrational frequencies as seen from S0 or S1 .


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hexane subtraction was done with different weights resulting in yellow, black, and red curves. Regions 300–450 cm−1 and 700–900 cm−1 are strongly affected by the weighting parameter, because the hexane signal is relatively strong here. Other regions like 215 or 610 cm−1 are insensitive to the weighting, therefore the Raman lines there can be ascribed to transazobenzene in S0 . Transient FSR spectra are shown at the bottom upon subtracting signals at negative delays. In such a way all groundstate (diagrams 1–3) and solvent contributions are eliminated. The spectra at low frequencies (left) and also around 1550 cm−1 (right) reveal negative bands marked with arrows, which should be ascribed to S1 (diagrams 4–7). Note that the sign of the signal agrees with the prediction. In the highfrequency region, the spectra are dominated by strong positive bands, which are very similar to those from the ground state. Apparently, the positive bands originate from S0 by diagram 8. It is necessary to mention here a different explanation of the positive signal, as due to bleaching the ground-state by the actinic pulse. The extent of bleach is estimated as nph /nAz , where nph is the number of absorbed photons and nAz is the number of azobenzene molecules in the active volume V = 0.1 × 0.1 × 0.3 mm3 = 3 × 10−9 L. For our 0.6 μJ actinic pulses, and azobenzene concentration cAz = 0.08 M one gets nph = 1.4 × 1012 , nAz = 1.4 × 1014 , and nph /nAz = 0.01. But the real ratio of the positive bands (bottom right) to those in the ground state (top right) is about 0.2. Hence the bleach can contribute only weakly, while the main signal comes from S1 due to diagram 8.

VIII. DISCUSSION

Fig. 5 summarizes our results by comparing experimental and calculated DFT spectra for S0 and TDDFT ones for S1 . Ground-state spectra are displayed on top. The low-frequency range shown here was not reported previously. Main features in the higher-frequency range are correctly reproduced by the calculation. Interestingly, our tests with popular hybrid-GGA functionals did not show a clear advantage over PBE: for example, they tended to assign highest intensity rather to the rightmost band in the triplet at 1400-1500 cm−1 . Reproduction of the range below 1000 cm−1 still remains a challenging task. The bottom frame shows S1 spectra recorded without (black) and with (red) actinic excitation. For better comparison, the real intensity of the black spectrum is reduced 10 times, illustrating the power of the ground-state measurements. Note general agreement between the two spectra, both in the band frequencies and intensities. The bands at 1550 cm−1 are absent in the black spectrum (without actinic excitation), because they are too far from the resonance even with our bluest 495 nm Raman pump. Generally, the S1 spectrum shows much stronger Raman activity in the low frequency range than the S0 spectrum. This is easy to understand, as molecules are usually more rigid in the ground than in excited state. A similar observation was made also for trans-stilbene.7, 24

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FIG. 5. Measured and calculated Raman spectra of trans-azobenzene in n-hexane, S0 (top) and S1 (bottom), from resonance Raman measurements without actinic excitation (black), and upon actinic excitation (red). The real intensity of the black spectrum is reduced 10 times. A shift between the positive and negative peaks reflects a difference in S1 frequencies as seen from S0 and S1 . The calculated S0 spectra (cyan) are in reasonable agreement with the experiment. The calculated S1 frequencies (green) at 190, 300, 650, 850, and 1550 cm−1 are also well reproduced although the Raman intensities are too weak in the low-frequency range.

Next, there is an appreciable (up to 30 cm−1 ) shift between the corresponding “black” and “red” bands. We believe that the shift is real and reflects differences in the S1 frequencies when they are probed from S0 (diagrams 2 and 3) or S1 (diagrams 4–7). A much weaker 3 cm−1 shift was also observed for the S0 frequencies when being probed from S0 (diagram 1) or S1 (diagram 8). The calculated S1 frequencies are in satisfactory agreement with the experiment (see Fig. 5 and Fig. S7 in the supplementary material24 ). At least the modes at 190, 300, 650, 850, and 1550 cm−1 are well reproduced, although the Raman intensities in the low-frequency part still desire improvement. We plan to further address this issue with more advanced computational methodology. Previous S1 Raman spectra of trans-azobenzene were measured by picosecond spontaneous Raman, upon actinic excitation at 273 nm and Raman pump at 410 nm.23 Only the frequency range 600–1600 cm−1 was reported. In this range the 650 and 850 cm−1 bands are close in position to ours (although of different intensities) while others, at 980, 1139, and 1430 cm−1 are not observed in our measurements. The reason may be in the intense S0 contributions there, which prevent isolation of the weaker S1 signals. On the other hand the S0 and S1 spectra in Ref. 23 are surprisingly similar in the frequency and intensity pattern. In fact, the spectra are more or less a replica of each other (see Fig. S8 in the supplementary material24 ). Generally such similarity is not expected


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as the S0 and S1 polarizabilities (and hence spectra) should differ due to electronic charge redistribution upon optical excitation. For example, in trans-stilbene Raman S0 and S1 spectra are strongly different,7, 24 and the same is true for our measured and calculated spectra of trans-azobenzene (Fig. 5). It is therefore conceivable that the S1 spectra in Ref. 23 suffer from inadequate subtraction of the ground-state contributions. ACKNOWLEDGMENT

We thank the Deutsche Forschungsgemeinschaft for financial support (Er 154/10-3). I.N.I. and A.A.G. are thankful to the computational support by the Supercomputing Center of the Lomonosov Moscow State University.25 1 M.

Yoshizawa and M. Kurosawa, “Femtosecond time-resolved Raman spectroscopy using stimulated Raman scattering,” Phys. Rev. A 61, 013808 (1999). 2 P. Kukura, D. W. McCamant, S. Yoon, D. B. Wandschneider, and R. A. Mathies, “Structural observation of the primary isomerization in vision with femtosecond-stimulated Raman,” Science 310, 1006 (2005). 3 P. Kukura, R. Fronteira, and R. A. Mathies, “Direct observation of anharmonic coupling in the time domain with femtosecond stimulated Raman scattering,” Phys. Rev. Lett. 96, 238303 (2006). 4 P. Kukura, D. W. McCamant, and R. A. Mathies, “Femtosecond stimulated Raman spectroscopy,” Annu. Rev. Phys. Chem. 58, 461–88 (2007). 5 J. M. Rhinehart, J. R. Challa, and D. W. McCamant, “Multimode chargetransfer dynamics of 4-(dimethylamino)benzonitrile probed with ultraviolet femtosecond stimulated Raman spectroscopy,”J. Phys. Chem. B 116, 10522–10534 (2012). 6 S. A. Kovalenko, A. L. Dobrykov, and N. P. Ernsting, “An efficient setup for femtosecond stimulated Raman spectroscopy,” Rev. Sci. Instrum. 82, 063102 (2011). 7 A. L. Dobryakov, I. Ioffe, A. A. Granovsky, N. P. Ernsting, and S. A. Kovalenko, “Femtosecond Raman spectra of cis-stilbene and trans-stilbene with isotopomers in solution,” J. Chem. Phys. 137, 244505 (2012). 8 Y. Prior, A. R. Bogdan, M. Dagenais, and N. Bloembergen, “Pressureinduced extra resonances in four-wave mixing,” Phys. Rev. Lett. 46, 111– 114 (1981).

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R. Andrews and R. M. Hochstrasser, “Thermally induced excited-state coherent Raman spectra of solids,” Chem. Phys. Lett. 82, 381–385 (1981). 10 S. Mukamel, “Stochastic theory of resonance Raman line shapes of polyatomic molecules in condensed phases,” J. Chem. Phys. 82, 5398–5408 (1985). 11 S. Mukamel, Principles of Nonlinear Spectroscopy (Oxford University Press, USA, 1995), pp. 281–282. 12 S. A. Kovalenko, A. L. Dobryakov, J. Ruthmann, and N. P. Ernsting, “Femtosecond spectroscopy of condensed phases with chirped supercontinuum probing,” Phys. Rev. A 59, 2369 (1999). 13 S. A. Kovalenko, R. Schanz, H. Hennig, and N. P. Ernsting, “Cooling dynamics of an optically excited molecular probe in solution from femtosecond broadband transient absorption spectroscopy,” J. Chem. Phys. 115, 3256 (2001). 14 S. A. Kovalenko, A. L. Dobryakov, I. Ioffe, and N. P. Ernsting, “Evidence for the phantom state in photoinduced cis-trans isomerization of stilbene,” Chem. Phys. Lett. 493, 255 (2010). 15 M. Quick, F. Berndt, A. L. Dobryakov, I. N. Ioffe, A. A. Granovsky, C. Knie, R. Mahrwald, D. Lenoir, N. P. Ernsting, and S. A. Kovalenko, “Photoisomerization dynamics of stiff-stilbene in solution,” J. Phys. Chem. B 118, 1389 (2014). 16 H. Finkelmann, E. Nishikawa, G. G. Pereira, and M. Warner, “A new optomechanical effect in solids,” Phys. Rev. Lett. 87, 015501 (2001). 17 T. Hugel, N. B. Holland, A. Cattani, L. Moroder, M. Seitz, and H. E. Gaub, “Single-molecule optomechanical cycle,” Science 296, 1103–1106 (2002). 18 Y. Yu, M. Nakano, and T. Ikeda, “Directed bending of a polymer film by light,” Nature (London) 425, 145 (2003). 19 J. Li, G. Speyer, and O. F. Sankey, “Conducting switching of photochromic molecules,” Phys. Rev. Lett. 93, 248302 (2004). 20 W. R. Browne and B. L. Feringa, “Making molecular machines work,” Nat. Nanotechnol. 1, 25–35 (2006). 21 D. N. Laikov, “Fast evaluation of density functional exchange-correlation terms using the expansion of the electron density in auxiliary basis sets,” Chem. Phys. Lett. 281, 151–156 (1997). 22 J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996). 23 T. Fujino and T. Tahara, “Picosecond time-resolved Raman study of transazobenzene,” J. Phys. Chem. A 104, 4203–4210 (2000). 24 See supplementary material at http://dx.doi.org/10.1063/1.4874854 for the calculation of Raman diagrams and additional experimental results. 25 V. Sadovnichy, A. Tikhonravov, Vl. Voevodin, and V. Opanasenko, Contemporary High Performance Computing: From Petascale toward Exascale (CRC Press, Boca Raton, USA, 2013), pp. 283–307.
