Relative Phase Change of Nearby Resonances in Temporally

Nov 12, 2012 - ... spectroscopy has been previously shown to benefit from a finite time ... Benjamin L. Strick , Regan J. Thomson , Victor S. Batista ...
0 downloads 0 Views 764KB Size
Download PDF
Letter pubs.acs.org/JPCL

Relative Phase Change of Nearby Resonances in Temporally Delayed Sum Frequency Spectra Fadel Y. Shalhout, Sergey Malyk, and Alexander V. Benderskii* Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States S Supporting Information *

ABSTRACT: Surface-selective sum frequency generation (SFG) spectroscopy has been previously shown to benefit from a finite time delay between two input laser pulses, which suppresses the nonresonant background and improves spectral resolution. Here we demonstrate another consequence of the time delay in SFG: depending on the magnitude of the delay, nearby resonances (e.g., vibrational modes) can “flip” their relative phase, i.e., appear either in-phase or out-of-phase with one another, resulting in either constructive or destructive interference in SFG spectra. This is significant for interpretation of the SFG spectra, in particular because the sign of the resonant amplitude provides the absolute molecular orientation (up vs down) of the vibrational chromophore. We present results and model calculations for symmetric and asymmetric CH-stretch modes of the methyl-terminated Si(111) surface, showing that the phase flip occurs when the delay matches half-cycle of the difference frequency between the two modes. SECTION: Spectroscopy, Photochemistry, and Excited States

S

chromophore moiety (e.g., CH3 group orientation with hydrogens up vs down).5,8−12 While optical heterodyne detection can provide both amplitude and phase of the SFG signal5,7,12−15 and thus allows one to separate the resonant and NR signals,9,10,12 in many cases it is desirable to suppress the NR background. As first demonstrated by Lagutchev et al.,16 this can be achieved for broad-band17,18 IR+visible vibrational SFG (BB-SFG) by realizing that the NR signal is instantaneous in the timedomain while the resonant response has a finite (vibrational) dephasing time and thus can be up-converted with a delayed time-asymmetric picosecond visible pulse following a broadband (femtosecond) IR pulse. Stiopkin et al. showed how the time delay between the IR and visible pulses and the spectral width and temporal shape of the visible pulse affect the spectroscopic line shapes, resolution, and the signal level of SFG.19 Although suppression of the NR background has proven to be a major improvement in the analysis of the vibrationally relevant information,9,16,19 Curtis et al. demonstrated that suppression of the NR signal can lead to other distortions in the SFG signal, which can complicate the analysis of the SFG spectra.20 In this Letter we present both experimental measurements and theoretical analysis of the effect of the time delay on the broad-band SFG spectra of a surface with two nearby vibrational resonances (frequency offset by Δω ≈ 70 cm−1). We show that the relative phase between the two coherently

um frequency generation (SFG) is rapidly becoming a standard tool used in chemistry, physics, and biology for characterizing structure, orientation, and dynamics of molecules at surfaces and interfaces.1−6 The surface-selectivity of SFG, which results from the second-order susceptibility χ(2) vanishing in centrosymmetric media under the electric dipole approximation, readily allows vibrational spectroscopy and orientational analysis to be performed with monolayer and submonolayer sensitivity. The detection limits can be further lowered to percent monolayer levels by using optical heterodyne detection.7 Although SFG from interfaces between two isotropic media is generally free from bulk-phase contribution to the signal, in practice it is rarely a completely background-free measurement. Because of the relatively small number of surface molecules, their resonant signatures in SFG spectra are always contaminated by the nonresonant (NR) background signal arising, for example, from electronic response of the substrate (2) material. The resonant χ(2) R (ω) and NR χNR signals interfere because SFG is a coherent optical technique, (2) ISFG(ω) ∝ |χ (2) |2 = |χNR + χR(2) (ω)|2

(1)

which complicates the spectroscopic analysis. The NR signal varies depending on the sample, but its amplitude is often comparable or stronger than the molecular vibrational resonances, and the interference makes it difficult to subtract the NR contribution. On the other hand, this interference can also be useful, for example in allowing one to determine the phase (e.g., positive or negative sign) of the resonant features. The sign of the resonant signal carries useful molecular information such as absolute orientation of the vibrational © 2012 American Chemical Society

Received: September 17, 2012 Accepted: November 12, 2012 Published: November 12, 2012 3493

dx.doi.org/10.1021/jz3014437 | J. Phys. Chem. Lett. 2012, 3, 3493−3497

The Journal of Physical Chemistry Letters

Letter

excited vibrational modes “flips” for certain values of the time delay: the two modes can appear with the same sign (e.g., as two “dips” against the NR background) for zero delay, but with opposite signs (one “dip” and one “peak”) at certain finite values of the delay. Clearly, such behavior can affect the molecular interpretation of the SFG spectra and thus needs to be understood quantitatively. This frequency-dependent phase shift has been previously described for other coherent spectroscopies such as 2D IR21 and noted in the time-domain theoretical calculations of SFG spectra.13 The model system chosen for this study is the methylterminated Si(111) surface, CH3−Si(111). The BB-SFG spectra of the symmetric and asymmetric stretch vibrational modes of the methyl recorded with time delay τ = 0 fs and τ = 300 fs between the broad-band IR and narrow-band visible pulses are shown in Figure 1. The polarization combination is

the central frequency, line width, and the apparent amplitude of ith resonant band, respectively. Although a truly nonresonant signal would be purely real, in practice, electronic resonances of the substrate (in the visible or UV region) impart a phase on this part of the response, as reflected in eq 2. The last term in eq 2 is the spectral shape of the IR pulse EIR(ω), which is approximated by a Gaussian with central frequency ωg, and width σg. The Lorentzian spectral shape of the visible pulse Evis(ω) (produced by an etalon), is assumed to be convoluted into the Lorentzian line shapes of the resonances (i.e., Γi are not the true Lorentzian line widths of the transitions). CH3−Si(111) surface features two vibrational modes in the C−H stretch region: a CH3 symmetric stretch (r+) at ∼2907 cm−1 and a CH3 asymmetric stretch (r−) at ∼2979 cm−1. The BB-SFG spectrum with no IR-visible delay (τ = 0 fs) (Figure 1a) shows a large NR signal, with both resonant bands clearly appearing as dips against the NR background, with negative Lorentzian amplitudes B′r+ = −1.0 and B′r− = −0.63 (a.u.). The BB-SFG spectrum for τ = 300 fs delay (Figure 1b) has little NR background because there is almost no time-domain overlap between the IR and the time-asymmetric visible pulse produced by an etalon. We note that (1) our visible pulse, shown in Figure 2b, is not ideally flat at early times: there is a

Figure 1. Experimental SFG spectra of CH3−Si(111) for IR−vis delay τ = 0 fs (a) and τ = 300 fs delay (b). Solid black lines show fits to eq 2, and dashed lines show decomposition of the fit into a Gaussian (NR) envelope and two resonant Lorentzian terms, per eq 2, with resonant amplitudes B′r+ = −1.0 and B′r− = −0.63 (a.u.) for τ = 0 fs spectrum (a) and B′r+ = +0.38 and B′r‑ = −0.28 (a.u.) for τ = 300 fs delay spectrum (b).

Figure 2. (A) Frequency-resolved cross-correlation of the femtosecond IR and picosecond visible pulses. (B) Temporal profile of the narrow-band visible pulse. (C) Frequency-domain spectrum (red line) of the narrow-band visible pulse produced by passing the compressed pulse through the etalon. Blue line shows a Lorenztian fit.

PPP (parallel to the plane of incidence for IR, visible, and SFG beams), although the polarization combination should not affect the observed phase flip. We note that CH3−Si(111) exhibits 3-fold azimuthal rotational anisotropy, described in detail elsewhere.22 The NR signal due to the Si response changes significantly with the azimuthal angle. Here we show the BB-SFG spectra for the azimuthal angle 50° with respect to one of the mirror planes of the C3v symmetry of Si(111) surface where the NR amplitude is near its maximum,22 for which the relative phase flip behavior is most pronounced. The BB-SFG spectra in Figure 1 are fit by assuming Lorentzian profiles for the two vibrational resonances contributing to χ(2) R (ω), which interfere with the frequencyindependent NR background contribution χ(2) NR:

small (∼ 1%) intensity “bump” before the sharp rise, and (2) the IR pulse may also have similar magnitude “wings” at 300 fs. This contributes a nonzero NR background contribution to the signal. The BB-SFG spectrum at τ = 300 fs delay can only be fit with the amplitudes of the two resonant bands having opposite signs, B′r+ = +0.38 and B′r− = −0.28 (a.u.). The complete set of fitting parameters is provided in the Supporting Information. The theory of BB-SFG spectroscopic line shapes was presented in detail elsewhere.13,19,23,24 Here we only briefly describe the main equations used to calculate the signals. In the SFG process, two laser pulses combine on the surface to induce the second-order polarization P(2)(t)

I SFG(ω) = |χ (2) (ω)E IR (ω)◦Evis(ω)|2 iϕ

= ANR e +

∑ i

B′i ω − ωi + i Γi

⎛ (ω − ω )2 ⎞ g ⎟ exp⎜⎜ − ⎟ 2 σg ⎝ ⎠

2

P(2)(t ) =

∞

∞

∫−∞ dt1 ∫−∞ dt2S(2)(t1, t2)E(t − t1) E(t − t 2 − t1)

(2)

(3)

The laser pulses interact with the surface at times t − t1 and t − t2 − t1 and S(2)(t1,t2) is the second-order response function. In the case of IR+visible vibrational SFG, a mid-infrared pulse

where ANR is the NR amplitude, ϕNR is the relative phase between the NR and the resonant signal, and ωi, Γi, and Bi′ are 3494

dx.doi.org/10.1021/jz3014437 | J. Phys. Chem. Lett. 2012, 3, 3493−3497

The Journal of Physical Chemistry Letters

Letter

of the input broad-band Gaussain visible pulse. When τvis > τRT, the pulses in the output train overlap significantly in time, producing a smooth envelope that has a sharp leading edge and decays exponentially in time. In the frequency domain, pulses interfere resulting in a narrowed, nearly Lorentzian line shape (the exact line shape is given by the Airy formula26). The IR pulse shape was approximated by a single Gaussian-type pulse with zero-chirp

EIR(t) resonantly excites molecular vibrations at the surface, creating the first-order polarization P(1)(t) P(1)(t ) =

∞

∫−∞ dt1S(t1)EIR (t − t1)

(4)

where S(t1) is the first-order response function. The IR pulse is followed, after a time-delay τ, by the visible pulse Evis(t − τ). The second interaction is nonresonant (i.e., instantaneous) and thus the molecular response is a δ-function with respect to the visible field, S(2)(t1,t2) = S(t1)δ(t2), which removes the second integration step in eq 3, (2)

(1)

P (t , τ ) = P (t )Evis(t − τ )

⎛ t2 ⎞ 0 E IR (t ) = E IR exp⎜ − 2 ⎟ exp( −iωIR t ) ⎝ τIR ⎠

with the carrier frequency ωIR = 2907 cm and pulse duration τIR = 80 fs. The BB-SFG spectra simulated using eqs 7−10 are shown in Figure 3. While the exact fit would require the accurate

(5)

The SFG signal field is emitted by the second-order polarization in the phase-matched direction, such that the signal intensity (in the time domain description) is ISFG(t , τ ) ∝ |P(2)(t , τ )|2

(10)

−1

(6)

In the frequency-domain measurement, the BB-SFG signal is Fourier transformed by a monochromator ∞

ISFG(ω , τ ) ∝ |

∫−∞ P(2)(t , τ)·eiωt dt|2 ∞

=|

∫−∞ P(1)(t )Evis(t − τ)·eiωt dt|2

(7)

The first-order time-domain molecular response function that characterizes evolution of the system after a single interaction with the vibrationally resonant IR field can be written as19,23,25

Figure 3. Simulated SFG spectra for IR-visible delay τ = 0 fs (a) and τ = 300 fs (b). Solid black lines show fits to eq 2, and dashed lines show fit decompositions.

S(t1) = ANR exp(iφNR )δ(t1) − iθ(t1) ∑ Bi Γi i

exp( −iωit1 − Γit1)

(8)

where θ(t1) is a Heaviside step function, and ANR is the amplitude of the NR signal with the phase ϕNR. The second term represents the resonant molecular response, and Bi, Γi, and ωi are amplitude, line width, and central frequency of the resonant response for ith vibrational molecular mode. The Fourier transform of the response function (eq 8) and substitution into eqs 4−7 yields the BB-SFG spectral shape as a set of coherently added Lorentzians interfering with the NR background, as per eq 2. Note, however, that, unlike the frequency-domain expression (eq 2), the response function (eq 8) explicitly accounts for the time evolution of the optical phase of the vibrational coherences, which then translates into the interference in the frequency-domain BB-SFG spectra recorded with a delayed visible pulse (eq 7). In order to qualitatively simulate the BB-SFG spectra obtained in the experiment, the time-domain electric field of the narrow-band visible pulse Evis(t) transmitted through the etalon is represented as a sum of a train of replicas of the input broad-band Gaussian visible pulse spaced in time by round-trip time τRT = 2d/c = 32fs where d is the air gap between mirrors16,19,26

knowledge of the IR and visible laser field pulse shapes, our goal here is to illustrate the relative phase flip phenomenon observed in the experimental spectra. The convolution was performed by numerical integration over the time interval from −3 ps to +3 ps with 0.2 fs step. The values for the duration and bandwidth of the IR and visible pulses were chosen to match their measured spectra and cross-correlation measurements (Figure 2) and were not adjusted during the simulation of the SFG spectra. The resonant amplitudes Bi for the asymmetric and symmetric stretch modes were set to have a ratio Br−/Br+ = 0.7. The other molecular response parameters for the symmetric (r+) and asymmetric (r−) CH3 stretch modes (the full list provided in Supporting Information) were adjusted to obtain the best qualitative agreement with the experimental spectra in Figure 1. In particular, in our simulation we could not accurately simulate the low intensity tail of the narrow-band visible field at early times (Figure 2b, from −1.0 to −0.3 ps). To compensate for this, ANR and φNR were adjusted independently for both delays. The simulated BB-SFG spectra for both τ = 0 fs and τ = 300 fs delays faithfully reproduce the phase flip as the function of the IR−visible delay. At zero delay, both symmetric and asymmetric methyl stretches appear as dips against the NR background. When the delay time between IR and visible pulses increased to τ = 300 fs, the NR contribution decreases and the lower-frequency symmetric stretch resonance becomes a peak. However, the higher frequency asymmetric stretch still appears as a dip.

100 ⎛ (t − nτ )2 ⎞ etalon 0 RT ⎟· Evis (t ) = Evis (1 − R ) ∑ Rn exp⎜ − 2 τvis ⎠ ⎝ n=0

exp( −iωvis(t − nτRT))

(9)

Here R = 0.953 is reflectivity of etalon mirrors, τvis = 50 fs, and ωvis = 12563 cm−1 are the duration and central frequency 3495

dx.doi.org/10.1021/jz3014437 | J. Phys. Chem. Lett. 2012, 3, 3493−3497

The Journal of Physical Chemistry Letters

■

The simulated spectra were also fitted with eq 2, with the fits shown as solid black lines in Figure 3 and the full set of fitting parameters provided in the Supporting Information section. As with the experimental spectra, fitting of the τ = 0 fs spectrum shows the same (negative) sign for the amplitudes of the symmetric and asymmetric stretch modes, B′r+ = −1.0 and B′r− = −0.63 (a.u.). Fitting the τ = 300 fs simulated spectrum requires that the two Lorentzians have opposite signs, B′r+ = +0.39 and B′r− = −0.50 (a.u.). The value and sign for the symmetric and asymmetric stretch amplitude were not adjusted during the simulation. Thus, change in the sign for the fitted Lorentzian can be attributed to the phase shift of the symmetric versus asymmetric modes accumulated during the τ = 300 fs delay time due to their different carrier frequencies. Indeed, the frequency offset between the two modes, Δω ≈ 70 cm−1, corresponds to the phase difference of Δφ = (ωr− − ωr+)τ ≈ 1.1π accumulated during the τ = 300 fs delay. Thus, the symmetric and asymmetric modes are almost exactly out-ofphase at τ = 300 fs, assuming they were in-phase at 0 fs delay. Other time-delaying approaches used to minimize the NR background and improve spectral resolution and signal level19 should also capture this phase flip effect. For instance, a timedelayed Gaussian visible pulse would also result in a phase-flip between two resonances if the time delay coincides with the half-period of the phase oscillation. However, for timesymmetric pulses with duration longer than the period of the phase oscillation between the nearby resonances, the phase would be averaged over many oscillations and thus diminish the effect. The phase flip of nearby resonances recorded with a timedelayed visible pulse is the frequency-domain manifestation of the quantum beats observed in the time-domain SFG free induction decay (SFG-FID) measurements on two or more vibrational modes.25,27 All modes coherently excited by a short IR pulse initially oscillate in-phase, and undergo the free induction decay. However, if the vibrational dephasing time τv is comparable or longer than the frequency offsets between the modes, τv ≳ 1/Δω, the modes go in- and out-of-phase before the vibrational dephasing is complete, beating against one another at the differences between their central carrier frequencies Δω. The phase-flip in the SFG spectra recorded using a time-delayed up-conversion visible pulse captures this behavior in the frequency domain. This paper demonstrates the importance of the time-domain description of the coherent spectroscopic processes such as SFG. The phase-flip phenomenon described in this paper would be entirely missed by a purely frequency-domain description such as eq 2. Our experimental and simulated spectra show that in the case when the NR signal is not fully suppressed by offsetting the IR-visible delay, the two resonant modes may appear in- or out-of-phase, depending on the time delay used for the measurement. Without taking these timedomain effects into account, eq 2, which is normally used for fitting SFG spectra, could give the wrong sign of the resonant amplitude. The phase of the SFG signal carries molecular information, e.g., on the absolute orientation of the vibrational chromophore. In this case, the “standard” orientation analysis model28−30 that is commonly used in SFG spectroscopy for experimental fits would not give “true” amplitude ratios, which is important to determine the molecular orientation. Thus, without proper time-domain analysis, the time delay effects can lead to wrong chemical interpretation of the SFG spectra.

Letter

EXPERIMENTAL METHODS A detailed description of our SFG setup is given elsewhere.22 Briefly, our SFG setup is based on a Ti:sapphire amplifier that outputs >100 fs pulses at 800 nm wavelength with an average power of 4 W at 1 kHz repetition rate. We split the fundamental beam into two parts: 60% is sent to a compressor to produce 65 ± 5 fs pulses that are used to pump an optical parametric amplifier (OPA), and the remaining portion is first compressed in another compressor and then sent through an etalon to produce narrowband (fwhm ∼17 cm−1) picosecond visible pulses. The signal and idler pulses generated from the OPA are difference frequency mixed in a nonlinear crystal to generate broad-bandwidth (fwhm ∼300 ± 50 cm−1) IR pulses from 2 to 20 μm (5000−500 cm−1) wavelength range. The IR and visible pulses are overlapped temporally and spatially on the sample to generate the SFG signal. The polarizations of the IR, visible, and SFG pulses are controlled by waveplates. The signal is spatially and spectrally filtered before entering a LNcooled charge-coupled device (CCD). The details of the methyl-terminated Si(111) samples preparation are described in a separate publication.22

■

ASSOCIATED CONTENT

S Supporting Information *

Experimental fitting and simulation parameters. This material is available free of charge via the Internet http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research is supported by AFOSR Grant No. FA9550-09-10547. We thank Prof. Nathan S. Lewis and Ms. Leslie O’Leary (Cal Tech) for providing methyl-terminated Si(111) samples.

■

REFERENCES

(1) Shen, Y. R. Surface-Properties Probed by 2nd-Harmonic and Sum-Frequency Generation. Nature 1989, 337, 519−525. (2) Richmond, G. L. Molecular Bonding and Interactions at Aqueous Surfaces as Probed by Vibrational Sum Frequency Spectroscopy. Chem. Rev. 2002, 102, 2693−2724. (3) Eisenthal, K. B. Liquid Interfaces Probed by Second-Harmonic and Sum-Frequency Spectroscopy. Chem. Rev. 1996, 96, 1343−1360. (4) Bain, C. D. Sum-Frequency Vibrational Spectroscopy of the Solid−Liquid Interface. J. Chem. Soc., Faraday Trans. 1995, 91, 1281− 1296. (5) Shen, Y. R.; Ostroverkhov, V. Sum-Frequency Vibrational Spectroscopy on Water Interfaces: Polar Orientation of Water Molecules at Interfaces. Chem. Rev. 2006, 106, 1140−1154. (6) Nihonyanagi, S.; Ishiyama, T.; Lee, T.; Yamaguchi, S.; Bonn, M.; Morita, A.; Tahara, T. Unified Molecular View of the Air/Water Interface Based on Experimental and Theoretical χ(2) Spectra of an Isotopically Diluted Water Surface. J. Am. Chem. Soc. 2011, 133, 16875−16880. (7) Stiopkin, I. V.; Jayathilake, H. D.; Bordenyuk, A. N.; Benderskii, A. V. Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy. J. Am. Chem. Soc. 2008, 130, 2271−2275. (8) Rao, Y.; Comstock, M.; Eisenthal, K. B. Absolute Orientation of Molecules at Interfaces. J. Phys. Chem. B 2006, 110, 1727−1732. (9) Stiopkin, I. V.; Weeraman, C.; Pieniazek, P. A.; Shalhout, F. Y.; Skinner, J. L.; Benderskii, A. V. Hydrogen Bonding at the Water 3496

dx.doi.org/10.1021/jz3014437 | J. Phys. Chem. Lett. 2012, 3, 3493−3497

The Journal of Physical Chemistry Letters

Letter

Surface Revealed by Isotopic Dilution Spectroscopy. Nature 2011, 474, 192−195. (10) Ji, N.; Ostroverkhov, V.; Chen, C. Y.; Shen, Y. R. PhaseSensitive Sum-Frequency Vibrational Spectroscopy and Its Application to Studies of Interfacial Alkyl Chains. J. Am. Chem. Soc. 2007, 129, 10056−10057. (11) Mondal, J. A.; Nihonyanagi, S.; Yamaguchi, S.; Tahara, T. Three Distinct Water Structures at a Zwitterionic Lipid/Water Interface Revealed by Heterodyne-Detected Vibrational Sum Frequency Generation. J. Am. Chem. Soc. 2012, 134, 7842−7850. (12) Mondal, J. A.; Nihonyanagi, S.; Yamaguchi, S.; Tahara, T. Structure and Orientation of Water at Charged Lipid Monolayer/ Water Interfaces Probed by Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy. J. Am. Chem. Soc. 2010, 132, 10656−10657. (13) Laaser, J. E.; Xiong, W.; Zanni, M. T. Time-Domain SFG Spectroscopy Using Mid-IR Pulse Shaping: Practical and Intrinsic Advantages. J. Phys. Chem. B 2011, 115, 2536−2546. (14) Pool, R. E.; Versluis, J.; Backus, E. H. G.; Bonn, M. Comparative Study of Direct and Phase-Specific Vibrational Sum-Frequency Generation Spectroscopy: Advantages and Limitations. J. Phys. Chem. B 2011, 115, 15362−15369. (15) Nihonyanagi, S.; Yamaguchi, S.; Tahara, T. Direct Evidence for Orientational Flip-Flop of Water Molecules at Charged Interfaces: A Heterodyne-Detected Vibrational Sum Frequency Generation Study. J. Chem. Phys. 2009, 130, 204704/1−204704/5. (16) Lagutchev, A.; Hambir, S. A.; Dlott, D. D. Nonresonant Background Suppression in Broadband Vibrational Sum-Frequency Generation Spectroscopy. J. Phys. Chem. C 2007, 111, 13645−13647. (17) van der Ham, E. W. M.; Vrehen, Q. H. F.; Eliel, E. R. SelfDispersive Sum-Frequency Generation at Interfaces. Opt. Lett. 1996, 21, 1448−1450. (18) Richter, L. J.; Petralli-Mallow, T. P.; Stephenson, J. C. Vibrationally Resolved Sum-Frequency Generation with BroadBandwidth Infrared Pulses. Opt. Lett. 1998, 23, 1594−1596. (19) Stiopkin, I. V.; Jayathilake, H. D.; Weeraman, C.; Benderskii, A. V. Temporal Effects on Spectroscopic Line Shapes, Resolution, and Sensitivity of the Broad-Band Sum Frequency Generation. J. Chem. Phys. 2010, 132, 234503/1−234503/9. (20) Curtis, A. D.; Burt, S. R.; Calchera, A. R.; Patterson, J. E. Limitations in the Analysis of Vibrational Sum-Frequency Spectra Arising from the Nonresonant Contribution. J. Phys. Chem. C 2011, 115, 11550−11559. (21) Hamm, P.; Zanni, M. Concepts and Methods of 2D Infrared Spectroscopy; Cambridge University Press: Cambridge, U.K., 2011. (22) Malyk, S.; Shalhout, F. Y.; O’Leary, L. O.; Lewis, N. S.; Benderskii, A. V. A Vibrational Sum Frequency Spectroscopic Investigation of the Azimuthal Anisotropy and Rotational Dynamics of Methyl-Terminated Silicon(111) Surfaces. J. Phys. Chem. C 2012, submitted for publication. (23) Bordenyuk, A. N.; Benderskii, A. V. Spectrally- and TimeResolved Vibrational Surface Spectroscopy: Ultrafast HydrogenBonding Dynamics at D2O/CaF2 Interface. J. Chem. Phys. 2005, 122, 134713/1−134713/11. (24) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford University Press: New York, 1995. (25) Bordenyuk, A. N.; Jayathilake, H.; Benderskii, A. V. Coherent Vibrational Quantum Beats As a Probe of Langmuir−Blodgett Monolayers. J. Phys. Chem. B 2005, 109, 15941−15949. (26) Born, M.; Wolf, E. Principles of Optics, 7th ed.; Cambridge University Press: Cambridge, U.K., 1999. (27) Star, D.; Kikteva, T.; Leach, G. W. Surface Vibrational Coherence at the CaF2/Air Interface: Vibrational Wave Packet Dynamics as a Probe of Interface Inhomogeneity. J. Chem. Phys. 1999, 111, 14−17. (28) Hong, S. C.; Oh-e, M.; Zhuang, X. W.; Shen, Y. R.; Ge, J. J.; Harris, F. W.; Cheng, S. Z. D. Orientations of Side Chains and Adsorbed Liquid Crystal Molecules on a Rubbed Polyimide Surface

Studied by Optical Second Harmonic Generation. Phys. Rev. E 2001, 63, 051706/1−051706/7. (29) Zhuang, X.; Miranda, P. B.; Kim, D.; Shen, Y. R. Mapping Molecular Orientation and Conformation at Interfaces by Surface Nonlinear Optics. Phys. Rev. B 1999, 59, 12632−12640. (30) Wang, H. F.; Gan, W.; Lu, R.; Rao, Y.; Wu, B. H. Quantitative Spectral and Orientational Analysis in Surface Sum Frequency Generation Vibrational Spectroscopy (SFG-VS). Intl. Rev. Phys. Chem. 2005, 24, 191−256.

3497

dx.doi.org/10.1021/jz3014437 | J. Phys. Chem. Lett. 2012, 3, 3493−3497