Communication: Spectroscopic phase and lineshapes in high-resolution broadband sum frequency vibrational spectroscopy: Resolving interfacial inhomogeneities of “identical” molecular groups

The extent to which one can characterize the structure and dynamics of surface species directly relies on experimental and computational tools able to selectively and accurately probe molecular entities residing in the interfacial layers. Sum frequency generation vibrational spectroscopy (SFG-VS), in particular, continues to grow as one of the preferred techniques to perform such investigations.^1–3 Furthermore, we report that SFG vibrational spectra with sub-wavenumber spectral resolution and large signal-to-noise ratio (SNR) can be obtained by means of high-resolution broadband SFG-VS (HR-BB-SFG-VS) with the characteristically short acquisition times of BB-SFG.⁴ These attributes make the detailed study of SFG vibrational lineshapes possible and, when in combination with a polarization/experimental configuration analysis of the structure-related optical phase in SFG (i.e., the sign of the individual vibrational contributions to the second-order susceptibility), a coherent dissection of molecular interfaces into their fine spectral and structural details becomes feasible, as first demonstrated here for the case of nearly degenerate methyl groups at the vapor/dimethyl sulfoxide (DMSO) liquid interface.

In a typical SFG-VS experiment, a visible (VIS) and an infrared (IR) laser beams are focused simultaneously and coincidentally on the sample surface. The vibrational spectrum of interfacial molecular species can then be determined from the optical signal emitted at the sum-frequency in the momentum-conserved direction. Technically, there are two basic approaches to an SFG-VS experiment: (i) scanning the IR frequency of a picosecond (or nanosecond) pulsed laser (so-called scanning SFG-VS) or (ii) making use of the broad bandwidth of a femtosecond (fs) IR laser pulse (so-called broadband SFG-VS or BB-SFG-VS); with the later gaining popularity in recent years due to its ability to obtain smoother spectral lineshapes in a relatively shorter time and to perform ultrafast dynamic studies.^4–6 In both cases, nonetheless, extracting meaningful quantitative information requires high-quality data (i.e., sufficient resolution and SNR) as well as a fair understanding of the SFG tensor components and underlying molecular symmetry.^3,7–10

Despite the aforementioned advantages, the spectral resolution in BB-SFG-VS is typically limited to 10–20 cm⁻¹, with lineshapes further complicated by convolution with the VIS pulse. Fundamentally, the molecular SFG response can be understood in terms of the free induction decay (FID) of the coherent vibrational polarization created by a resonant broadband femtosecond IR pulse, subsequently followed by electronic upconversion with a VIS pulse through a Raman transition.^11–14 Since the lifetime of a vibrational polarization is usually of several picoseconds (ps), Raman transitions probing the longer portions of the FID can often occur at a time interval which is on the same order or significantly longer than the duration of typical VIS pulses used in current BB-SFG systems (1–5 ps). Thus, this leads to truncation of the upconverted SFG field in the time domain, which unavoidably translates into lineshape distortion and spectral broadening in BB-SFG-VS. With this knowledge, some groups recently reported clever, but rather sophisticated, ways of alleviating this limitation by balancing the time-domain effects on the frequency-resolved spectra.^13–15 In principle, these intricate procedures can be avoided by using a VIS pulse with a duration long enough to last for several times the FID process.¹¹ In practice, however, obtaining extraordinarily long pulses with sufficient peak powers and good mode quality by the shaping of a fs fundamental pulse can be prohibitively challenging. Therefore, we find that the use of an independent laser, synchronized to the fs IR pulse train, becomes technically necessary. As such, we employ in this work ∼87 ps VIS pulses operating with high stability and TEM₀₀ mode, synchronized to the broadband IR pulses with extremely low jitter. By these means, undistorted spectra with resolution as high as 0.6 cm⁻¹ can be readily achieved with a high signal-to-noise ratio.¹⁶ 

In Figure 1, the unsmoothed, z-cut-quartz normalized,^16,17 HR-BB-SFG-VS spectra of DMSO at the vapor/neat-DMSO liquid interface are displayed for the C–H stretching region in three polarization combinations (ssp, ppp, and sps, where the indexing order correspond to the SFG, VIS, and IR beam polarization, respectively) and two experimental configurations: (I) β_VIS = 65°, β_IR = 55° and (II) β_VIS = 45°, β_IR = 55°. The IR incident angle (β_IR = 55°) is deliberately kept unchanged because the ssp and ppp spectral lineshapes and relative intensities are rather insensitive to it.^9,10 The ssp intensities are significantly stronger than in the ppp and sps spectra. While the ssp and sps spectral lineshapes are remarkably similar for both sets of experimental angles,^16,17 the two ppp spectra are dramatically different from each other, especially for the symmetric stretching band ∼2918 cm⁻¹. The ssp spectra reported here are, other than being significantly narrower, consistent with previous SFG reports,^18,19 having a strong methyl symmetric stretch, r⁺, band at ∼2918 cm⁻¹, and a much weaker asymmetric stretch, r⁻, contribution centered at ∼3000 cm⁻¹.

Figure 2(a) highlights the clear linewidth disparity in the r⁺ region between the ppp (FWHM = 4.7 cm⁻¹) and ssp (FWHM = 8.8 cm⁻¹) spectra obtained at β_VIS = 65°. In the β_VIS = 45° spectra, however, the ssp (8.8 cm⁻¹) and ppp (8.4 cm⁻¹) linewidths are nearly identical as seen in Figure 2(b). A simultaneous lineshape fitting analysis of the β_VIS = 65° (configuration I) ppp and ssp spectra to the square modulus of the sum of complex Lorentzians¹⁶ decidedly reveals two sub-peaks centered at ω₁ = 2916.88 ± 0.07 and ω₂ = 2919.66 ± 0.06 cm⁻¹, with FWHM (2Γ_q) of 7.2 ± 0.1 and 5.9 ± 0.1 cm⁻¹, respectively, thus rendering the high-resolution and the high SNR in these data essential for capturing such fine spectral features.

As in Table I, the susceptibility strength factors (A_q) obtained for these two peaks in the fitting of the (β_VIS = 65°) ppp spectrum are unambiguously of opposite sign (phase shift of π) and with nearly equal peak areas. With this in hand, we rationalize the apparent ppp spectral narrowing as a phase-dependent effect resulting from the destructive interference between the two closely spaced contributions. In the ssp polarization, nonetheless, both peaks are necessarily with the same relative phase in order to correctly reproduce the lineshape, a solid indication that the two methyl groups are pointing in the same overall direction since this phase is directly related to the orientational structure. This directionality is in agreement with previous reports stating that the DMSO vapor/liquid interface does not form an antiparallel double layer structure²¹ and that both methyl groups point into the vapor side.^18,22,23 No adequate results were obtained when the simultaneous fitting of the β_VIS = 65° ssp and ppp data were restricted to maintain an equal relative phase between these two peaks in the ppp spectrum,¹⁶ ruling out for this particular case, the possibility of the non-unique spectral fitting phase paradox postulated by Shen and co-workers.²⁴ The simultaneous fitting limited to a single peak contribution in this region also failed to reproduce the β_VIS = 65° ppp lineshape.¹⁶ 

We would like to point out that even though it is impossible to experimentally assign the absolute spectral phase without performing a phase-sensitive SFG measurement,^25,26 knowing a priori that the interfacial DMSO methyl groups are pointing away from the liquid phase^18,22,23 is sufficient to determine the absolute phase of all the methyl spectral features in this study.

As shown in Figure 3(b), we calculated the orientational dependence of the SFG phase and intensity for the symmetric stretch mode of the DMSO methyl groups under the two polarization and incident angles discussed in this work.^9,10 These calculations show intensity ratios in good agreement with the experimental data in Figure 1. It can be immediately noticed that while the ssp response is remarkably similar under the two configurations, the ppp orientational angle dependence is dramatically different, especially the change in phase predicted in the β_VIS = 65° curve for methyl orientation angles larger than ∼40°, whereas the complete absence of such phase flip is evident in the ppp curve at β_VIS = 45° (configuration II). This alone suggests that if the π-phase shift observed for the two closely spaced contributions in the ppp spectrum at β_VIS = 65° is orientational in nature (i.e., corresponding to interfacial methyl groups with two distinctive orientation angles as in Figure 3(a)), the ppp spectrum generated at β_VIS = 45° would have a structural phase scenario where the bluer (ω₂) peak has the same sign as the redder (ω₁) contribution, and the later being significantly stronger (see Figure 3(b)). As listed in Table I, the lineshape fitting analysis of the two ppp spectra, directly compared in Figure 2(c), provided excellent fit results with strength factors and relative structural phases in full agreement with this prediction. Combined, therefore, these two sets of data provide compelling evidence for the two peak constructive/destructive interference picture as described above. It is worth mentioning that a simultaneous fit of the β_VIS = 45° ssp and ppp spectra using two fully unrestricted Lorentzians in this region failed to yield unique parameters, in sharp contrast to the fitting of either curve (or both) simultaneously with the ppp spectrum in configuration I, which indicates that this particular ppp lineshape at β_VIS = 65° is in fact the anchoring point around which all other spectra are assessed in order to unambiguously determine their spectral composition. In principle, a similar analysis could be used for discerning subtle inhomogeneities of “identical” groups in more complex interfacial environments.

The susceptibility strength factors (peak areas) in Table I and the calculated intensity and phase relationships shown in Figure 3(b) allow, in addition, for the orientation angles of the two classes of methyl groups (or specifically their transition dipoles) to be determined with respect to the surface normal, yielding 28° ± 3° and 60° ± 4° for ω₁ and ω₂, respectively, assuming a δ-function distribution as displayed in Figures 3(a) and 3(b). These two angles give an orientational parameter D = 1.7 ± 0.1 (D = 〈cos θ〉/〈cos ³θ〉), which is in good agreement with the recent experimental value of D = 1.65 for the aqueous DMSO interface using the Polarization Null Angle (PNA) method.^3,18,27 Because the experimental D value contains the orientational angle distribution information, this agreement indicates that the assumption of a δ distribution is reasonable, suggesting that the orientational distributions for these two methyl groups are, as far as we can tell, relatively narrow, as otherwise the two methyl groups would have been spectroscopically indistinguishable in direct contradiction with the results obtained in this work. In spite of this agreement, the two angles directly determined in this work from the multiple relative intensity ratios, are somewhat different from the values reported in the PNA studies (27° ± 4° and 70.4° ± 4°) which assumed that θ₁ + θ₂ = ∠CSC = 97.4°, implying that the plane containing the two methyl groups is perpendicular to the surface, an assumption more appropriate for planar molecules, such as acetone, than for the non-planar DMSO.²⁷ Without an additional constrain such as θ₁ + θ₂ = ∠CSC, PNA is not able to generate two independent orientational angles.

In addition to these orientational observables, the spectral splitting of 2.78 cm⁻¹ provides further evidence that the two methyl groups of surface DMSO molecules, considered identical in the isotropic liquid phase, are in fact under different chemical environments and interactions at the intrinsically anisotropic interface. The nature of the frequency shift and the small linewidth difference of the two methyl groups warrant further investigation.

In summary, the data reported in this work show striking evidence that the vapor/liquid SFG spectra of dimethyl sulfoxide (DMSO) contains unambiguous vibrational features arising exclusively from the optical interference between the coherent sum-frequency signals generated by each of the two “identical” methyl groups of interfacial DMSO molecules. The nature of this interference is dictated by their structural spectroscopic phase relationships and revealed for the first time by the high-quality spectral lineshapes obtained in HR-BB-SFG-VS for different polarization combinations and experimental configurations. Such analysis enabled the determination of their fine frequency splitting and interfacial molecular orientation. As an even-order nonlinear process, the SFG susceptibility is a pseudotensor required to have a sign property (i.e., change sign under inversion). Most importantly, this sign is directly related to the orientation of the molecular transition dipole. Such structure-phase relationship is unique to the SFG process, thereby opening new directions in the understanding of spectral, structural, and dynamic details of molecular interfaces.

L.V. and H.F.W. are grateful to Yi Rao (Columbia), Gang Ma (Hebei University), and Dehong Hu (PNNL) for their helpful discussions and suggestions. This work was supported by the Pacific Northwest National Laboratory (PNNL) LDRD program and was conducted at the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL), a national scientific user facility located at the Pacific Northwest National Laboratory and sponsored by the Department of Energy's Office of Biological and Environmental Research (BER). X.Y.Z. is supported by the PNNL Alternative Sponsored Fellow (ASF) program.