Phase-Resolved Heterodyne-Detected Transient Grating Enhances

Article pubs.acs.org/JPCA

Phase-Resolved Heterodyne-Detected Transient Grating Enhances the Capabilities of 2D IR Echo Spectroscopy Geun Young Jin and Yung Sam Kim* Department of Chemistry, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Korea S Supporting Information *

ABSTRACT: 2D IR echo spectroscopy, with high sensitivity and femtosecond time resolution, enables us to understand structure and ultrafast dynamics of molecular systems. Application of this experimental technique on weakly absorbing samples, however, had been limited by the precise and unambiguous phase determination of the echo signals. In this study, we propose a new experimental scheme that significantly increases the phase stability of the involved IR pulses. We have demonstrated that the incorporation of phase-resolved heterodyne-detected transient grating (PR-HDTG) spectroscopy greatly enhances the capabilities of 2D IR spectroscopy. The new experimental scheme has been used to obtain 2D IR spectra on weakly absorbing azide ions (N3−) in H2O (absorbance ∼0.025), free of phase ambiguity even at large waiting times. We report the estimated spectral diffusion time scale (1.056 ps) of azide ions in aqueous solution from the 2D IR spectra and the vibrational lifetime (750 ± 3 fs) and the reorientation time (1108 ± 24 fs) from the PR-HDTG spectra.

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INTRODUCTION Two-dimensional infrared (2D IR) spectroscopy was first reported using narrow-band pump/broad-band probe in 1998.1 Ever since this time, this nonlinear spectroscopic method has undergone extensive development, in terms of both experiments2−8 and theory,9−11 and been widely applied to investigate structure and ultrafast dynamics of molecules, ranging from small molecules12−16 to large biomolecules.17−19 Two different methods of data acquisition are widely used in 2D IR spectroscopy: (i) the four-wave mixing (FWM) echo method2 and (ii) the pump−probe (PP) method1 including the recently introduced acousto-optic pulse shaping.7 The FWM echo method has certain advantages over the PP method in terms of sensitivity, polarization control of the involved pulses, and separation of the rephasing and nonrephasing signals.20,21 The FWM method, however, is severely limited by the difficulty in determining the absolute phase of the 2D IR signals and maintaining high phase stability of the involved pulses during the data collection.22,23 The phase of the 2D IR spectrum is typically determined by matching the projection of the spectrum onto the ωt (probe) frequency axis to the corresponding broadband PP spectrum.24−26 For weak signals, however, a reliable PP spectrum with a satisfactory signal-to-noise (S/N) ratio is extremely difficult to obtain, thereby limiting the accurate determination of the phase of the 2D IR spectrum. The exponential decrease of the signal at larger waiting times (T’s), determined by the vibrational lifetime, makes it very challenging to obtain 2D IR spectra of weakly absorbing samples. Phase-resolved heterodyne-detected transient grating (PR-HDTG) spectra contain essentially the same information as the PP spectra, but with a much higher S/N ratio, and therefore can play a critical role in the determination of the © 2017 American Chemical Society

phase of the 2D IR spectra of weak signals, especially at large T’s. In addition, PR-HDTG spectra can be directly used to obtain information on the dynamics of molecular systems more effectively than PP spectra. PR-HDTG studies have been previously reported in the optical regime.27−29 HDTG experiments in the IR regime were also reported30,31 to extract the vibrational lifetime, however, they were not phase resolved. To the best of our knowledge, an experimental implementation of PR-HDTG in the IR regime has never been reported. To obtain PR-HDTG spectra the following conditions should be satisfied: (i) the relative phase of the signal to a reference pulse must be maintained during the data acquisition; and (ii) the phase of an HDTG spectrum must be determined accurately at least for one T. By designing an experimental setup that satisfies aforementioned conditions, we have successfully collected PR-HDTG spectra for a very dilute solution of sodium azide (NaN3) in H2O with an absorbance of ∼0.025 in the azide (N3−) asymmetric stretch region. The PR-HDTG spectra have been used as references for determining the phase of 2D IR spectra at large T’s and also provide information on vibrational lifetime and reorientation dynamics of N3− dissolved in H2O. In this article, we present our PR-HDTG study and show that incorporation of PR-HDTG spectroscopy can enhance the capabilities of 2D IR echo spectroscopy, specifically in increasing the S/N level and unambiguous phase determination.

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EXPERIMENTAL METHODS Samples. A solution of 20 mM NaN3 dissolved in H2O and pure H2O were used for FTIR, PP, PR-HDTG, and 2D IR Received: December 18, 2016 Published: January 9, 2017 1007

DOI: 10.1021/acs.jpca.6b12713 J. Phys. Chem. A 2017, 121, 1007−1011

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The Journal of Physical Chemistry A experiments. The samples were contained in a cell composed of 2 CaF2 windows separated by a 5-μm Teflon spacer. NaN3 was purchased from Sigma-Aldrich and used without further purification. All reported spectra were collected at room temperature (22 °C). Linear IR Spectroscopy. FTIR spectra were collected on a Shimadzu IRTracer-100 spectrometer with 0.25 cm−1 resolution. 2D IR Spectroscopy. The 2D IR experimental scheme (Figure 1 and Figure S1) and data-processing procedures were

Figure 1. Schematic diagram of the experimental setup used for the collection of PR-HDTG and 2D IR spectra. TSn’s indicate translation stages. The arrow-headed solid lines represent the beam paths for three excitation pulses and a reference pulse (local oscillator), and the arrow-headed dotted line represents the beam path for signal. A detailed optical layout is presented in Figure S1.

performed essentially the same way as reported previously.26,32 For these experiments, IR pulses (60 fs in width and a repetition rate of 1 kHz; see Figure S2, Supporting Information) were centered at ∼2045 cm−1. Briefly, three excitation pulses with wave vectors k1, k2, and k3 at time interval τ between the first and second, and T between the second and third, were used to generate signal in a phase-matched direction of −k1 + k2 + k3. The generated signal and a heterodyning pulse (local oscillator) preceding it by ∼1 ps were combined at the focal plane of a monochromator (TRIAX-190) combined with a 64-element MCT array detector (IR Associates), enabling the signal to be measured as a function of detection time, t. The processing of the heterodyned signal leads to a 2D IR spectrum S(ωτ, ωt; T) for each T. The range of τ scanned was −3 to +3 ps in 2 fs steps, where negative and positive values represent nonrephasing and rephasing schemes, respectively. Variation in T was done by movement of only the TS5 in Figure 1. All 2D IR spectra were collected with parallel polarization and represent the real part of the absorptive (correlation) spectra. The data collection time for an absorptive 2D IR spectrum was 20 min. Phase-Resolved Heterodyne-Detected Transient Grating Spectroscopy. The optical layout for PR-HDTG experiments was the same as that for 2D IR experiments. The delay τ was fixed at 0 while T was scanned from 0 to 5 ps with 2 fs steps. The signal generated in a phase-matched direction of −k1 + k2 + k3 was heterodyned by a local oscillator and processed the same way as the 2D IR signal. A set of PR-HDTG spectra was collected for 15 min and two sets of PR-HDTG spectra were collected consecutively to check whether there was phase drift during the data collection period. The phase difference between the two sets of PR-HDTG spectra was less than 0.2% of a cycle. The phase of the PR-HDTG spectra was determined by matching to the PP spectra at earlier T’s (50 to 150 fs). PR-HDTG spectra of even weakly absorbing

Figure 2. (a) Linear IR spectrum. (b) PP spectra. (c) PR-HDTG spectra. (d) Decay profiles of the spectra in parts b and c along T at (top) ωt = 2049.5 cm−1 (v = 0 → 1 transition) and (bottom) ωt = 2019 cm−1 (v = 1 → 2 transition). The spectra in parts b and c are plotted in the T range of 100 to 4000 fs with 100 fs steps. The insets in part d are magnified views by 10 times in the range 2.5−5 ps. The magnitude of the PR-HDTG signals in part d was adjusted to be overlapped with the PP traces. 1008

DOI: 10.1021/acs.jpca.6b12713 J. Phys. Chem. A 2017, 121, 1007−1011

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at a probe delay of 200 ps and subtracted from the PP spectra.

Table 1. Population Relaxation Time (T1), Reorientation Time (TR), and Magnitude Factor (a) for N3− in H2Oa parameters

prof ile_01_PR‑HDTG (at ωt = 2049.5 cm−1)

prof ile_12_PR‑HDTG (at ωt = 2019 cm−1)

weighted average

T1 (fs) TR (fs) a (mOD)

745 ± 2 757 ± 12 1.256

750 ± 3 1108 ± 24 −0.7317

750 ± 2 890 ± 10 1.000

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RESULTS AND DISCUSSION A typical setup for the 2D IR echo method contains four translation stages (TS’s), one each for the three excitation pulses with wave vectors k1, k2, k3, and one for the reference pulse (local oscillator) with wave vector kLO (−k1 + k2 + k3). We need to simultaneously move 2 of the 4 TS’s, either the TS’s for k1 and k2 or those for k3 and kLO, to obtain HDTG spectra. The movement of multiple TS’s, however, causes non-negligible phase instability between the signal and the reference pulses, which hinders us from retrieving the phase information on the HDTG signal, thereby preventing us from obtaining the PR-HDTG spectra. We have devised a new experimental scheme, as shown in Figure 1, with an additional common TS (TS5) for k1 and k2. TS5 enables simultaneous change of the arrival time of the first (k1) and second (k2) pulses at the sample by the same amount. This experimental design enables us to move only one TS (TS5) and leads to a significant decrease in phase instability and allows collection of T-dependent HDTG or 2D IR spectra at various T’s.

The fitting function, f(T), is in the form of f(T) = a·exp(−T/T1)· [4/9·exp(−T/TR) + 5/9] and the weighted average is (prof ile_01_PR‑HDTG − 1.606· prof ile_12_PR‑HDTG)/2.431. a

samples could be obtained by an increase in the S/N ratio of corresponding PP spectra. Pump−Probe Spectroscopy. The pulses with wave vectors k3 and k2 were used as the pump and probe beams, respectively. The intensity of the probe beam was attenuated by two wire-grid polarizers to reach about half of the detector-saturation level. While PP spectra were collected, the pump (k3) beam was chopped with half the repetition rate. The probe beam was scanned in the range 0−5 ps with 1 fs steps. Background signal was also collected

Figure 3. (a) 2D IR spectra and (b) comparison of PP, PR-HDTG spectra, and 2D IR projections at 4 waiting times (T = 0.1, 0.5, 1, and 3 ps). The dotted line in each 2D IR spectrum in part a represents the nodal line. 1009

DOI: 10.1021/acs.jpca.6b12713 J. Phys. Chem. A 2017, 121, 1007−1011

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(major component) and 0.182 ps (minor component); a constant offset has been considered for the fit.43,44 The time scale of 1.056 ps for the slower (major) component is in excellent agreement with previous results by Maekawa et al. (1.2 ps for N3− in H2O)44 and by Hamm et al. (1.3 ps for N3− in D2O).43

Linear IR, PP, and PR-HDTG spectra of 20 mM NaN3 in H2O with a 5-μm spacer are presented in Figure 2, parts a, b, and c, respectively. For the spectra in Figure 2, solvent (H2O) spectra were collected separately and subtracted from solution (NaN3 in H2O) spectra. The solution and solvent spectra are presented in Figure S3, with their phase-calibration curves in Figure S4. The PP and PR-HDTG spectra in Figures 2b and 2c, respectively, look apparently very similar, however, there is noticeable difference in their S/N ratio, which is clearly visualized by the decay profiles shown in Figure 2d. The decay profiles directly reflect population relaxation of v = 1 state and orientation relaxation. The two profiles are denoted by prof ile_01_PR‑HDTG (for the v = 0 → 1 transition) and prof ile_12_PR‑HDTG (for the v = 1 → 2 transition). To extract information on the relaxation dynamics, we fitted the prof ile_01_PR‑HDTG and prof ile_12_PR‑HDTG as well as a weighted average of the two profiles with doubleexponential functions that include both population and orientation relaxation.33,34 The results of the fits are summarized in Table 1. The obtained parameters for the prof ile_12_PR‑HDTG, T1 = 750 ± 3 fs and TR = 1108 ± 24 fs, are in good agreement with the reported values of T1 of 810 ± 60 fs and TR of 1300 ± 300 fs by Zhong et al.35,36 Details of the fitting results are presented in Supporting Information (Figure S5). Figure 3a shows 2D IR spectra collected at four different T’s (0.1, 0.5, 1, and 3 ps). 2D IR spectra for more T’s are presented in Figures S6 and S7. The magnitude of the 2D spectrum at T = 3 ps is ∼1.5% of that at T = 0.1 ps, as can be seen from the color bars of the 2D IR spectra in Figure 3a. The phase of the extremely weak signal in the 2D IR spectrum at T = 3 ps could be accurately determined with the help of the PR-HDTG spectra (Figure 2c). Comparisons of the PP spectra, PR-HDTG spectra, and the 2D IR projections at the 4 T’s are shown in Figure 3b. The shape of the peak pairs in the 2D IR spectra changes from rather tilted along the diagonal to vertically upright as T increases. Such change in the peak shape is a manifestation of spectral diffusion in the time scale of picoseconds, which is believed to originate from the H-bond dynamics between azide and water.37−39 The inverse slope of the nodal line in the overlap region of the positive and negative peaks of the 2D IR spectrum has been measured to quantify the spectral diffusion time scale.40−42 The plot for the values of the inverse slope as a function of T along with the single- and double-exponential fits are shown in Figure 4. The measured time constants for the double-exponential fit are 1.056 ps

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CONCLUDING REMARKS In this work, we have demonstrated that the capabilities of 2D IR echo spectroscopy can be enhanced significantly with the incorporation of PR-HDTG spectroscopy. To accurately determine the phase of the HDTG signals, a new experimental scheme has been designed to move a single TS during the HDTG data collection and increase the phase stability of the involved pulses. To check the performance of the new scheme, we have collected PR-HDTG spectra of N3− dissolved in H2O with a maximum absorbance of ∼0.025 in the asymmetric stretch region. The PR-HTDG spectra showed a much higher S/N ratio than their corresponding PP spectra and were used as references for phasing the 2D IR spectra, especially for those at large T’s. Our estimated time constant for the spectral diffusion of N3− in H2O to be 1.056 ps from the 2D IR spectra agrees well with previously reported results.43,44 We have also estimated the population relaxation time (T1 of 750 ± 3 fs) and reorientation time (TR of 1108 ± 24 fs) directly from the PR-HDTG spectra.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b12713. Optical layout of 2D IR apparatus, the IR pulse spectrum, linear IR, and PR-HDTG spectra of solution and solvent, phase calibration curves, detailed fitting results, linear IR and T-dependent 2D IR spectra, and comparison of linear and 2D IR spectra with and without subtraction of solvent spectra (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(Y.S.K.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (Grant No. 2011-0015061). We thank Dr. Sayan Bagchi for helpful discussions.

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