Frequency Generation (HD 2D SFG) Spectroscopy

Home , Spectral line shape

Adding a dimension to the infrared spectra of interfaces using heterodyne detected 2D sum- frequency generation (HD 2D SFG) spectroscopy

Wei Xiong, Jennifer E. Laaser, Randy D. Mehlenbacher , and Martin T. Zanni1

Department of Chemistry, University of Wisconsin-Madison, Madison, WI 53706

Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved October 13, 2011 (received for review September 13, 2011)

In the last ten years, two-dimensional infrared spectroscopy has of carbon monoxide on polycrystalline platinum. Pt-CO is studied become an important technique for studying molecular structures extensively to better understand electrochemical catalysis (13– and dynamics. We report the implementation of heterodyne de- 16). The linear SFG spectrum of Pt-CO has been measured many tected two-dimensional sum-frequency generation (HD 2D SFG) times previously. The spectrum is almost always fit to a Lorent- spectroscopy, which is the analog of 2D infrared (2D IR) spectro- zian line shape (14–16), from which one concludes that Pt-CO is scopy, but is selective to noncentrosymmetric systems such as vibrationally narrowed, meaning that the structural dynamics interfaces. We implement the technique using mid-IR pulse shap- of the CO and its surrounding environment are so fast that the ing, which enables rapid scanning, phase cycling, and automatic system is homogeneous. By resolving the 2D line shape of Pt-CO, phasing. Absorptive spectra are obtained, that have the highest we find that there is a significant inhomogeneous contribution, frequency resolution possible, from which we extract the rephas- which indicates that there is a slow component to the vibrational ing and nonrephasing signals that are sometimes preferred. Using dynamics. Heterogeneity could be caused by some combination this technique, we measure the vibrational mode of CO adsorbed of surface crystallinity and weak hydrogen bonding of water to on a polycrystalline Pt surface. The 2D spectrum reveals a signifi- CO. Either way, the HD 2D SFG spectrum allows one to quantify cant inhomogenous contribution to the spectral line shape, which the heterogeneity, which leads to a fundamentally different con- is quantified by simulations. This observation indicates that the clusion about the nature of the Pt-CO interface. surface conformation and environment of CO molecules is more To implement HD 2D SFG spectroscopy, we have used many complicated than the simple “atop” configuration assumed in pre- tricks-of-the-trade from the fields of 2D IR and 2D visible spec- vious work. Our method can be straightforwardly incorporated troscopy, including mid-IR pulse shaping, passive phase stabiliza- into many existing SFG spectrometers. The technique enables one tion, and phase cycling. We collect absorptive spectra, which have to quantify inhomogeneity, vibrational couplings, spectral diffu- the highest frequency resolution (17), while also showing how one sion, chemical exchange, and many other properties analogous to can extract out the rephasing and nonrephasing signals that are 2D IR spectroscopy, but specifically for interfaces. sometimes preferable (18, 19). Another important piece of the methodology is heterodyne detection (20–24). Recently, land- multidimensional spectroscopy ∣ vibrational spectroscopy ∣ mark 2D SFG spectra were reported (25, 26). Those experiments, surface-sensitive ∣ Pt catalysis ∣ CO monolayer along with related pump-probe SFG experiments (27–29), proved that the signal strengths are sufficient for performing higher- olecular spectroscopies are some of the best tools for study- order nonlinear spectroscopy at interfaces. However, one cannot Ming structures and dynamics. Two particularly useful interpret those spectra in the same manner as a 2D IR spectrum variants are sum-frequency generation (SFG) and two-dimen- because the spectra are distorted by a complicated convolution of sional infrared (2D IR) spectroscopy. SFG spectroscopy provides signals, as we discuss below. In contrast, HD 2D SFG spectra are a vibrational spectrum of molecular systems that lack an inversion mathematically analogous to 2D IR spectra, but with surface sen- center (1), and so has become a valuable tool for probing inter- sitivity and a few other interesting and informative differences faces because no signal arises from the bulk. SFG spectroscopy that we outline below. has helped reveal the surface structure of liquids, characterize the surfaces of materials, and probe membrane proteins, to name Qualitative Description of Pulse Sequences and Spectra only a few applications (2–5). 2D IR spectroscopy is also a vibra- To provide a basis for comparison, we present a simplified de- tional spectroscopy, although not interface specific. 2D IR spec- scription of the pulse sequences and spectra for each of the three troscopy spreads the infrared spectrum into a second coordinate techniques that we discuss in this article. Consider a system that so that coupled vibrational modes are correlated by cross peaks, has molecules in both the bulk and attached to a surface, such as vibrational dynamics quantified by 2D line shapes, and energy CO in contact with a platinum plate illustrated in Fig. 1A. If one transfer or chemical exchange revealed from peak intensities measures a SFG spectrum, one obtains a vibrational spectrum of (6–8), in addition to many other capabilities not possible with the CO absorbed to the Pt because it is oriented. CO in the bulk linear one-dimensional (1D) vibrational spectroscopies like SFG electrolyte generates no signal because it is isotropic on length spectroscopy. 2D IR spectroscopy is now being used to study pro- scales comparable to the visible pulse wavelength (30). There are tein structure and dynamics, solvent dynamics, charge transfer in many ways to generate an SFG spectrum, but they all use an semiconductors, and many other processes (9–12). These two

techniques might be considered the core technologies of modern Author contributions: W.X., J.E.L., and M.T.Z. designed research; W.X., J.E.L., and R.D.M. infrared spectroscopy. performed research; W.X. contributed new reagents/analytic tools and performed In this article, we combine the surface sensitivity of SFG simulations; W.X. and J.E.L. analyzed data; and W.X., J.E.L., and M.T.Z. wrote the paper. spectroscopy with the multidimensional capabilities of 2D IR The authors declare no conflict of interest. spectroscopy in a technique that we call heterodyne detected This article is a PNAS Direct Submission. (HD) 2D SFG spectroscopy. With this technique, one obtains 2D 1To whom correspondence should be addressed. E-mail: [email protected]. vibrational spectra of noncentrosymmetric systems. We demon- This article contains supporting information online at www.pnas.org/lookup/suppl/ strate our approach by measuring the HD 2D SFG spectrum doi:10.1073/pnas.1115055108/-/DCSupplemental.

20902–20907 ∣ PNAS ∣ December 27, 2011 ∣ vol. 108 ∣ no. 52 www.pnas.org/cgi/doi/10.1073/pnas.1115055108 Downloaded by guest on September 30, 2021 the anharmonic shift of the vibrational mode (Δ ¼ ω12 − ω01). The width of the peaks along the diagonal gives the total vibrational line width while the antidiagonal width gives the homogeneous line width. As a result, peaks that are inhomogeneously broadened are elongated along the diagonal (7, 8). Shown in Fig. 1F is the pulse sequence that we use to collect a HD 2D SFG spectrum. Notice that it is the SFG pulse sequence with an additional two excitation pulses. That way, one correlates the t1 and t3 vibrational coherences by measuring the interfero- metric SFG spectrum as a function of t1 and then Fourier transforming the data into a 2D spectrum. As we show mathematically below, the t1 and t3 vibrational coherences for HD 2D SFG spectroscopy are identical to those in 2D IR spectroscopy, barring a difference in polarizability vs. transition dipoles. As a result, one will obtain two peaks that are 180° out-of-phase and sepa- rated by Δ, just like in a 2D IR spectrum. However, the signs of the peaks may be reversed from those in a 2D IR spectrum, because the signs in heterodyned SFG spectroscopy also depend on the absolute orientation of the molecule (which is why centrosymmetric signals average to zero). As we show below, the HD 2D SFG spectrum can be interpreted in the same way as a 2D IR Fig. 1. Schematics of the molecular system, pulse sequences and spectra spectrum, but will only report molecules near the interface that of linear SFG, 2D IR and HD 2D SFG spectroscopies. (A) The regions that signal are preferentially oriented. is generated from for each technique. The pulse sequence and schematic spectrum, respectively, for (B, C) linear (1D) SFG, (D, E) 2D IR and (F, G)HD Results E E A 2D SFG spectroscopy. n are mid-IR pulses, vis is the visible upconversion Shown in Fig. 2 is the linear SFG spectrum of a CO monolayer E pulse, and LO is the local oscillator pulse. The coherences used to generate on a polycrystalline Pt surface using the pulse sequence shown the spectra are shown dashed. In the 2D spectra, the phases of the peaks are in Fig. 1B. Because heterodyne detection is phase sensitive, both labeled “þ” and “−“. the imaginary and real parts of the spectra are measured (20–23). We focus on the imaginary spectrum (solid) because it has an infrared pulse that is on-resonance with the vibrational mode and absorptive line shape. In Fig. 2B, the spectrum is fit to both a a visible pulse to generate an emitted field with a frequency that is Lorentzian and a Gaussian function, convoluted with the electric – B the sum of the two (2 4). Shown in Fig. 1 is a pulse sequence field of the visible pulse. Fits give full-width-at-half-maxima that uses a fs infrared pulse and a ps visible pulse (31). In the (fwhm) of 25 and 36 cm−1 for the two line shapes, respectively, experiments reported here, we use a dichroic filter to frequency which are similar to previous reports (15, 16). Neither fit is ideal, narrow the visible pulse, which is why it is asymmetric and broad but most previous reports used Lorentzian fits (14–16), thereby CHEMISTRY in the time-domain pulse sequence. The goal is to measure the indicating homogeneous dynamics. A Gaussian line shape would vibrational free induction decay that is created by the infrared indicate an inhomogeneous environment or structural distribu- pulse (dashed). The ps pulse has a narrow spectrum so that when tion. The spectrum can also be fit to a Voigt, but the fit is not the emitted field is sent through a spectrograph, one obtains a unique. Thus, one cannot conclude with certainty the nature of spectrum of the free induction decay. This pulse sequence also the vibrational dynamics from the SFG spectrum, which is a contains a local oscillator pulse at the same frequency as the typical difficulty with standard linear spectroscopies. emitted field, which heterodynes the free induction decay by interfering with it on the detector, allowing both the real and imaginary parts of the emitted field to be measured (20–23). The imaginary part produces a vibrational spectrum like that shown in Fig. 1C, which only contains signal from noncentrosymmetric CO at or near the surface. Shown in Fig. 1 D and E is a 2D IR pulse sequence and schematic spectrum. There are many ways to collect a 2D IR spectrum, but the most common and most accurate method uses four femtosecond infrared pulses, where the first three pulses excite the vibrational modes of the molecule and the fourth pulse is the local oscillator that heterodynes the emitted field (dashed). The emitted field is analogous to the vibrational free induction decay in the SFG pulse sequence, but the 2D IR emitted field may include a vibrational echo (7). The additional pulses in the 2D IR pulse sequence generate another vibrational coherence during t1, which modulates the emitted field. Thus, by measuring the heterodyned spectrum as a function of t1, one obtains a correlation between t1 and t3, which is often visualized in frequency space (ω1, ω3) by Fourier transforming the data. A schematic 2D IR spectrum is given in Fig. 1E, which consists of two peaks that are out-of-phase by 180°. The negative peak on the diagonal is cre- ω ν 0 → 1 ated by transitions at the fundamental frequency 01ð ¼ Þ Fig. 2. Linear and HD 2D SFG scans of CO on polycrystalline Pt. (A) The real, while the positive peak is created by sequence transitions at imaginary and absolute SFG spectra. (B) Fittings to the imaginary 1D SFG frequency ω12ðν ¼ 1 → 2Þ. Thus, the difference in frequencies be- spectrum. (C) Pump-probe spectrum. (D) The time evolution of the funda- tween the positive and negative peaks along the probe axis gives mental peak at 2;090 cm−1 with 20 fs and (inset) 10 fs time steps

Xiong et al. PNAS ∣ December 27, 2011 ∣ vol. 108 ∣ no. 52 ∣ 20903 Downloaded by guest on September 30, 2021 Shown in Fig. 2C is one particular time delay from the dataset binations is one way of producing the two types of spectra using the HD 2D SFG pulse sequence in Fig. 1F. The spectrum (18, 19). Instead, we use spectral interferometry (7, 20–22) to ob- shown has t1 ¼ 0, which makes it equivalent to a pump-probe tain the complex HD 2D SFG signal and then Fourier transform spectrum (27, 28). This spectrum contains both negative and po- it along t1 to retrieve the rephasing and nonrephasing spectra sitive peaks, which are due to the ν ¼ 0 → 1 and ν ¼ 1 → 2 tran- in different quadrants, which are shown in Fig. 3 B and C. The sitions, respectively, as discussed above. Shown in Fig. 2D is the rephasing spectra are oriented along the diagonal while the non- −1 amplitude of the spectrum at ω3 ¼ 2;090 cm as a function of t1. rephasing spectra are oriented perpendicular to the diagonal. The amplitude oscillates with a period of 80 fs, rather than the Both spectra are phase twisted, because both spectra contain 16 fs period that corresponds to the natural vibrational frequency absorptive and dispersive components, which is why they are much −1 of 2;090 cm , because the data was collected in the rotating broader than the absorptive spectrum. The ratio between the re- frame (19, 32). The inset shows a few periods measured in smaller phasing and nonrephasing spectra is 1.7, which is another indicator time steps to better illustrate the vibrational coherences. that the system is inhomogeneously broadened. For homogeneous Fourier transforming the spectrum along t1 produces the HD line shapes, the intensities of the two spectra are equal. 2D SFG spectrum shown in Fig. 3. The 2D spectrum resembles the schematic spectrum in Fig. 1G. There is a negative peak on Discussion the diagonal and a positive peak shifted off the diagonal along the In this section we present the mathematical formalism that we use ω3 axis. It is also apparent that the spectra are elongated along to interpret the HD 2D SFG spectrum and extract the homoge- the diagonal. Thus, by simple inspection, we get an estimate of neous and inhomogeneous line widths. We contrast the signal to the anharmonic shift of the CO stretch and learn that the line that measured by 2D IR spectroscopy. shape is inhomogeneously broadened. The 2D spectrum in Fig. 3A has absorptive line shapes in both Formalism of HD 2D SFG Spectroscopy dimensions and thus the optimal frequency resolution. To obtain Each laser pulse interacts with the system either through the absorptive 2D spectra, one must sum together spectra collected vibrational transition dipole μ or the electronic polarizability α 4 with rephasing and nonrephasing pathways in order to cancel to create a fourth-order macroscopic polarization, Pð ÞðtÞ (7, 8). their individual phase twists (17). Because the first two excitation Neglecting the polarization of the laser pulses, which will be a 4 pulses in our experimental setup are collinear, both signals are topic for a future article, Pð ÞðtÞ is written generated in the same phase matching direction, detected simul- Z Z Z Z taneously, and automatically summed, in an analogous manner ∞ ∞ ∞ ∞ 6 ð4Þ 3 ð4Þ P ðtÞ ∝ μ α dt4 dt3 dt2 dt1 Rn ðt4;t3;t2;t1Þ to collecting 2D IR spectra in the pump-probe beam geometry 0 0 0 0 ∑ (33, 34). However, it is sometimes advantageous to inspect the n¼1 × E t − t E t − t − t E t − t − t − t rephasing and nonrephasing spectra separately because corre- visð 4Þ 3ð 4 3Þ 2ð 4 3 2Þ lated frequency fluctuations and cross peak patterns are different × E t − t − t − t − t ; [1] in the two types of spectra. Cycling the relative phase of the first 1ð 4 3 2 1Þ π two infrared pulses between 0 and 2 and taking their linear com- where the integrals convolute over the pulse envelopes and ð4Þ Rn are the Feynman paths associated with the fourth-order molecular response functions. In this equation, we have written the infrared transition dipoles, μ, and the Raman polarizability, α, in front of the integrals rather than in the response functions themselves, for reasons that become apparent below. Because the electronic molecular response associated with the nonreso- nant visible pulse is short lived, we approximate it as a Dirac delta ð4Þ function δðt4Þ so that Rn becomes

ð4Þ ð3Þ Rn ðt4;t3;t2;t1Þ¼Rn ðt3;t2;t1Þ · δðt4Þ; [2]

ð3Þ where Rn are the third-order responses that are measured in 2D IR spectroscopy. As a result, [1] simplifies to Z Z Z ∞ ∞ ∞ 6 Pð4Þ t ∝ μ3αE t dt dt dt R ð3Þ t ;t ;t ð Þ visð Þ 3 2 1 n ð 3 2 1Þ 0 0 0 ∑ n¼1

× E3ðt − t3ÞE2ðt − t3 − t2ÞE1ðt − t3 − t2 − t1Þ: [3]

Because the mid-IR pulses are fs in duration compared to the ps molecular response, it is valid to use a semiimpulsive approximation for the pump pulse durations, EnðtÞ ∼ δðtÞ, which elimi- nates the convolutions in [3], illustrating that the macroscopic polarization closely resembles the desired molecular responses

6 Pð4Þ t ; t ;t ;t ∝ μ3αE t ; t Rð3Þ t ;t ;t : [4] ð 3 2 1 visÞ visð 3 visÞ · ∑ ð 3 2 1Þ n¼1

In [4], we have included the experimentally controlled pulse Fig. 3. Experimental and simulated HD 2D SFG spectra of a CO monolayer on delays as dependent variables as a reminder of which time vari- a polycrystalline Pt surface. (A–C) Experimental absorptive, rephasing, and ables are manipulated experimentally. The polarization creates ð4Þ ð4Þ nonrephasing spectra with (D–F) their corresponding simulations. an emitted field, E ðt3Þ ∝ i P ðt3Þ, that is spatially overlapped

20904 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1115055108 Xiong et al. Downloaded by guest on September 30, 2021 E with the local oscillator pulse LO. Both the signal and local approximation is valid and that the metal surface does not appre- oscillator are sent through a spectrograph that Fourier transforms ciably weaken the Born-Oppenheimer approximation at these the fields, which are then measured on a square-law detector to energies (36). generate the actual Shet signal 2DSFG Vibrational Dynamics of Pt-CO and Its Structural het ð4Þ 2 Implications S2 ðω ; t1;t2;t Þ¼jF½E ðt3Þ þ F½E ðt3Þj DSFG SFG vis LO Using the formalism above, we have fit the experimental 2D and F E t 2 F Eð4Þ t 2 −1 ¼j ½ LOð 3Þj þj ½ ð 3Þj linear SFG spectra to obtain Δ ¼ −22 cm , T2 ¼ 610 fs, and ð4Þ 1∕δΩ ¼ 588 fs. The simulated spectra are shown in Fig. 3 D–F. þ 2RefF½E ðt3Þ ⊗ E ðt3Þg; [5] LO The fits reproduce the diagonal and antidiagonal line widths and predict a ratio of 1.4∶1 for rephasing:nonrephasing spectra. where ⨂ represents a convolution. The first term is just the spec- Thus, the simulations quantify the homogeneous and inhomoge- trum of the local oscillator, which is subtracted off. The second neous contributions to the line width. term is the homodyne detected fourth-order response, which is Shown in Fig. 2B is the simulated linear SFG spectrum. Be- very weak and carries no phase information. The last term is the cause the simulations include both T2 and δΩ, the line shape desired one, because it provides the actual fourth-order electric is a Voigt profile, rather than purely a Lorentzian or Gaussian. field. Because this field is scaled by E , it is much larger than the LO The inhomogeneous contribution accounts for about 40% of homodyne response, which we ignore. A semiimpulsive approx- the total line width. Thus, inhomogeneity is a major contribution imation is also appropriate for the last term (20), E δ t ,so LO ¼ ð Þ to the vibrational dynamics. The inhomogeneous distribution that the final signal is could be caused by the crystallinity of Pt or water hydrogen bond- 6 ing to the CO or both. Previously, features in the OH stretch Shet ω ; t ;t ;t ≈ μ3αE ω ; t ⊗ R ð3Þ ω ;t ;t : 2DSFGð SFG 1 2 visÞ visð vis visÞ ∑ n ð 3 2 1Þ region have been attributed to H2O molecules coadsorbed with n¼1 the CO monolayer (37). Moreover, recent DFTcalculations have [6] shown that there are strong/weak hydrogen-bonding interactions between the coadsorbed H2O and the bridge/atop-adsorbed CO To shift the spectra back to the IR region, one applies the re- molecules (38). Our results might provide further evidence of lation ω3 ω − ω to the spectra. From this equation it is ¼ SFG vis these hydrogen-bonding interactions between CO and H2O apparent that HD 2D SFG spectroscopy measures the third- around it. R ð3Þ order molecular responses, n , just like 2D IR spectroscopy. While the line shape now better reflects the dynamics, it is still The differences are that the last interaction in HD 2D SFG spec- not a perfect fit to the linear SFG spectrum. Bloch dynamics is α μ troscopy depends on instead of , and the HD 2D SFG signal is usually a poor approximation of vibrational dynamics, because convoluted with the visible pulse that is absent in a 2D IR experi- the dynamics of most vibrational modes tend to evolve on a ment. We show below that this convolution leads to a distorted few ps time scale due to solvent and structural motions. Forcing signal. If a fs instead of a ps visible pulse is used, then the con- fits into rigorous homogeneous and inhomogeneous contribu- volution drops out, the spectrum is undistorted, and the HD 2D tions can be quite inaccurate (39). A better way is to actually mea- CHEMISTRY SFG signal is identical to the 2D IR signal except for the scaling sure the evolution of the vibrational dynamics by collecting a factors. We have not taken that route here because then one must series of HD 2D SFG spectra as a function of the t2 time delay t actively scan the 3 delay, rather than use a spectrograph to mea- and measuring the change in the ellipticity and nodal slope of t sure the entire 3 response at once (20). The 2D spectrum is gen- the peaks (40). These parameters are related to the vibrational Shet t erated by collecting 2DSFG for a series of 1 delays, which is then frequency fluctuation correlation function, which captures the ω ω Fourier transformed to give a correlation between 1 and 3. spectral evolution of the line shape. Waiting time experiments Following the notation above, we can simulate the third-order should also be able to distinguish between the two origins of vibrational response just as we do for 2D IR spectroscopy. We the inhomogeneity because crystallinity effects would not be time start by drawing the Feynman diagrams from which the response dependent, but hydrogen bonding would cause spectral diffusion. R ð3Þ t SI Text functions n ð Þ can be written (see ) (7). Because the Waiting time experiments may also provide evidence for vibron experimental spectra are close to symmetric along the diagonal, hopping (41). While potentially very interesting, these dynamical we use a second-order Cumulant expansion and Bloch dynamics, “waiting time” experiments lie outside the scope of this initial which approximate the vibrational dynamics with a homogeneous report on HD 2D SFG spectroscopy. It would also be interesting T lifetime ( 2) that includes time constants for both pure dephasing to compare the inhomogeneous distributions of CO in the atop and vibrational lifetime and an inhomogeneous broadening con- configuration on Pt(111) which may be more ordered. stant, δΩ. With these approximations, the third-order vibrational response for the rephasing and nonrephasing pathways are Heterodyne Detection and Spectral Distortions 2D IR spectroscopy was originally implemented using a ps pump t t 2 2 3 − 3þ 1 δΩ ðt3−t1Þ ð Þ −iω01ðt3−t1Þ −iððω01−ΔÞt3−ω01t1Þ T − pulse (6), but most researchers now only use fs pulses because R ðt3;t1Þ¼iðe − e Þe 2 e 2 reph there is less distortion to the spectrum (33, 42). To understand [7a] E the effects of the ps vis pulse on the HD 2D SFG spectrum, we present simulations in Fig. 4 A and B. Fig. 4A is a reproduction t t 2 2 3 − 3þ 1 δΩ ðt3þt1Þ of Fig. 3B, but plotted with expanded axes. This spectrum ð Þ −iω01ðt3þt1Þ −iððω01−ΔÞt3þω01t1Þ T − R ðt3;t1Þ¼iðe − e Þe 2 e 2 : E eiωt−t∕T T 600 nonreph was generated using vis ¼ with ¼ fs, so that the [7b] visible pulse has a fwhm of 18 cm−1, which matches the Raman filter that we use in our experimental setup. In Fig. 4B, we set E eiωt T ∞ In the equations above we also used the harmonic approxima- vis ¼ ð ¼ Þ so that the spectrum is an exact measurement tion, which makes the ratio of the response functions of the fun- of the response. Notice that the 2D spectrum is unaltered along ω ω E damental and sequence transitions in HD 2D SFG spectroscopy 1 but broadened along 3. In essence, vis is acting as a window equal, just as in 2D IR spectroscopy, because α depends linearly function on the vibrational coherence during t3 (20), by artificially μ E on the vibrational coordinate just as does (35). Because the ex- decreasing the homogeneous lifetime. Clearly, one wants vis to perimental spectra have fundamental and sequence peaks of perturb the spectrum as little as possible, which is why we used equal (but opposite) intensities, we conclude that the harmonic the narrowest Raman filter that can be commercially purchased.

Xiong et al. PNAS ∣ December 27, 2011 ∣ vol. 108 ∣ no. 52 ∣ 20905 Downloaded by guest on September 30, 2021 Conclusions We have demonstrated the direct analog of 2D IR spectroscopy with surface-selective sensitivity. It is straightforward to implement HD 2D SFG spectroscopy, because one can either add a mid-IR pulse shaper to an existing HD SFG spectrometer or add an upconversion pulse and visible local oscillator to a 2D IR spectrometer. Instead of a pulse shaper, one could use an etalon or two individual pump pulses, although etalons will distort the spectra along ω1 (33, 42) while individual pumps pulses will require an Fig. 4. Simulated HD 2D SFG spectra. Simulated result using visible upcon- additional phasing process (34), and both techniques lack the E eiωt−t∕T A T 600 version pulse approximated as vis ¼ for ( ) ¼ fs (spectrum is identical to Fig. 3B) and (B) T ¼ ∞ so that the spectrum is an exact Fourier many benefits of pulse shaping. To estimate the difficulty in per- transform of the molecular response. (C) Simulated experimental spectrum forming a HD 2D SFG experiment on a particular system, one when the local oscillator is a linear SFG spectrum rather than an independent can approximate the expected nonlinear SFG response from local oscillator. the ΔOD of a 2D IR signal for a similar system, because the difference for both is μ2, excluding the orientational contribution. Smaller bandwidths can be obtained using gratings, although Considering that our experiments were performed with only a gratings will act as a Gaussian window function and thus produce few μJ of mid-IR pulse energy, whereas most modern SFG spec- a different 2D line shape (20), which may or may not be prefer- trometers generate 15–20 μJ, there are many systems that will able. An alternative would be to use a fs E pulse, but then one vis have easily measureable HD 2D SFG signals. Of course, this pa- needs to scan t3 in the time-domain (20). Previous experiments that produced 2D plots of SFG spectra per has only probed an isolated vibrational mode, but HD 2D did not add an independent local oscillator pulse, but instead SFG spectra will also exhibit cross peaks in coupled systems. heterodyned the fourth-order 2D SFG signal with the second- Along with theoretical developments (44, 45), we believe that order SFG signal (25, 26). Using the second-order SFG signal HD 2D SFG spectroscopy will become another useful tool in as a local oscillator leads to nonintuitive features, as has been the fields of surface science and multidimensional spectroscopy. previously reported (43). To describe those experiments math- E Eð2Þ 5 Methods ematically, we replace LO by in Eq. ., but now the semiimpulsive approximation cannot be made. As a result, the Detailed information about the experiment and a schematic of the instru- interference term becomes ment is provided in SI Text. In brief, E1 and E2 are generated by a mid-IR pulse μ E μ E μ E shaper that together are 0.5 J. 3 is 0.1 J. vis is at 800 nm and 2 J. LO is 6 created using a 5%Mg:LiNbO3 crystal in a phase stable design with a beam Shom ω ; t ;t ;t ≈ μ3α E ω ; t ⊗ R ð3Þ ω ;t ;t geometry for heterodyne detection. All pulses are P-polarized. The hetero- 2DSFGð SFG 1 2 visÞ ½ visð vis visÞ n ð 3 2 1Þ ∑ 400 × 1;340 t 2 5 n¼1 dyned signal is dispersed on a CCD camera. LO ¼ . ps, which is controlled by a pair of ZnSe wedges while t2 ¼ tvis ¼ 0. Data are collected ð1Þ E ω ; t ⊗ R ω3 ; [8] ½ visð vis visÞ ð Þ with φ1 ¼ 0 and π, which are subtracted to remove the linear SFG spectrum and background scatter. Phase cycling is also used to shift the apparent where the second bracketed term is the linear SFG signal. Thus, response frequency to 326 cm−1, which has a 80 fs period. We collect ω the spectrum is highly modulated along the 3 axis, because the t1 ¼ 0 to 2,000 fs in steps of 20 fs (7). E3 is not passively phase stabilized, caus- “ ” local oscillator is now a very complicated function. In fact, the ing φ3 to drift at about 2°∕ min (20), which we monitor with reference linear response will not necessarily contain all the frequencies scans of the linear SFG spectrum every 80 s that are used to phase correct needed to heterodyne the entire fourth-order signal. This effect the data. The local oscillator and homodyned signal are removed by Fourier is illustrated in Fig. 4C, which uses the same Bloch parameters transforming the measured spectrum along ω3, filtering out the zero fre- that are obtained from simulating the experimental spectrum quency component, and inverse Fourier transform back to frequency space. (Fig. 3). Notice that the sequence peak is now much weaker than the fundamental and the line shapes are distorted. The sequence ACKNOWLEDGMENTS. We thank Prof. Robert Hamers and Rose Ruther for the ð1Þ peak is weak because R ðω3Þ does not contain overtone frequen- loan of a potentiostat and their suggestions on setting up the electrochemi- cies. The only reason that the sequence peak is apparent at all cal cell. We appreciate Prof. Dana. D. Dlott, Dr. Prabuddha Mukherjee and is because the anharmonic shift is comparable to the line width Robert Kutz for their advice on the Pt-CO surface. The authors thank the so that the sequence band spectrally overlaps a little with the fun- National Science Foundation (NSF) for financial support through the Univer- sity of Wisconsin-Madison Materials Research Science and Engineering damental. In fact, one can get the wrong signs of peaks, or as Center (DMR-0520527), the Center of Excellence for Materials Research and noted previously, fake cross-peaks (43). In comparison, an inde- Innovation (DMR-1121288), and single-investigator grant CHE-1012380. pendent LO pulse allows the 2D spectrum to be cleanly inter- J.E.L. is supported by the NSF Graduate Research Fellowship Program preted and simulated. (DGE-0718123).

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