The adsorption of molecules at solid surfaces is a key step in heterogeneous catalysis. The binding energy of a molecule is frequently determined by temperature-programmed methods, such as temperature-programmed desorption (TPD). Mass spectroscopic (MS) measurements of desorbing species, combined with suitable models (such as the Redhead approximation [1]), allow to even discriminate adsorbed species with different binding energy. However, for the identification of their molecular structure and binding sites, temperature-dependent spectroscopic studies are required. Among the methods used are vibrational (infrared (IR) or electron energy loss (EELS)) and electron (X-ray photoelectron) spectroscopies [2].

Apart from the mere binding energy of a molecule, its molecular orientation on the surface, which reveals important information about physical and chemical properties, as well as interactions between the adsorbates and substrates [3], is critical for "activating" it for catalysis. A prime example is ethylene adsorption on noble metal surfaces. Using low energy electron diffraction (LEED) surface crystallography, π and di-σ bonded C₂H₄ and ethylidyne C₂H₃ were identified, with their abundance and adsorption sites depending on temperature and type of metal [4-6]. There is also a vast body of work of CO adsorption geometries (e.g. hollow, bridge and on-top CO) and (ordered) structures on (typically) low Miller index single crystal surfaces [7]. Further work induces orientation analysis by near-edge X-ray absorption fine structure (NEXAFS) [8]. One has to confess, however, that most studies were carried out under ultrahigh vacuum (UHV) at cryogenic temperatures, which somewhat limits the transferability of these results to technological conditions.

The analysis of molecular orientation can also be carried out by nonlinear optical sum frequency generation (SFG) vibrational spectroscopy. Due to its surface/interface specificity, it can not only characterize adsorbed species at solid or liquid surfaces/interfaces, but can also distinguish the interfacial molecules from chemically identical species in the bulk (liquid or gas phases).

SFG has already been utilized as a powerful tool to probe the surface molecular structure and orientation of adsorbates on solid surfaces relevant for catalytic reactions, including the adsorption of CO and NO on single crystals [9-14], metal oxides [12], polycrystalline electrodes [9], and nanoparticles [15], as well as methanol dissociation (e.g. coverage-dependent, aerobic and anaerobic conditions) on TiO₂ [16, 17]. Additionally, two types of formates with tilted and perpendicular orientations, which were formed during the decomposition of formic acid on Ni(111), had been detected using SFG [18, 19]. The orientation (i.e. tilting and twist angles) of a (CO₂ reduction) catalyst on single crystal TiO₂ [20] and gold slide [21] were also obtained by SFG. Furthermore, SFG can be applied to even more complex liquid surfaces, for instance, electrolyte (inorganic ions) aqueous [22-24] and organic (methanol) solutions [25] and polyelectrolyte aqueous solutions [26]. Additionally, water surfaces with monolayer or bilayers of biomolecules (e.g. lipids, peptides, proteins) [27-31], thermosensitive polymers [32], and zwitterionic polymers [33, 34] under the influence of pH, salts and nanoparticles, can be measured as well. These studies are of great importance in the fields of e.g. environmental chemistry or biochemistry. SFG even shows advantages in revealing the molecular orientations of organic ions at the air/water interface [35], the arrangement of polymers (macromolecules) at buried surfaces [36, 37], as well as the structure of irregular and complex surfaces of polymers roughened by mechanic grinding [38].

Recent studies at the Dalian Institute of Chemical Physics (DICP) reported that the coverage of (intercalated) CO confined between h-BN and Pt(111) was higher than on open Pt(111) [39]. Comparing molecular structure and orientation on confined and open catalysts would be a challenge for SFG.

Herein, we discuss recent results of molecular orientation analysis of adsorbates at gas/solid, air/liquid and solid/liquid interfaces. The effects of experimental configurations and molecular (interface) properties, which have been not treated in detail so far, are thoroughly examined. After illustrating typical experimental configurations and spectroscopic cells, we discuss the basic SFG theory with a focus on the parameters critical for orientation analysis. Selected case studies are then presented to catch a glimpse of state-of-the-art SFG spectroscopy, providing guidelines for future studies.

In a SFG process, two light waves at different frequencies interact in a medium spatially and temporally, and then generate a wave at the sum of their frequencies [3, 40, 41]. Generally, one input beam is tunable in the mid-IR range (ω_IR), and the second beam is in the visible range with a fixed frequency (ω_Vis). As illustrated by the energy level diagram in Fig. 1(a), when the IR beam is tuned through a vibrational resonance of the surface molecules, it induces a vibrational transition from the ground state (ν = 0) to an excited state (e.g. ν = 1). Simultaneously, the visible beam induces a transition to a higher-energy virtual state. When the virtual state relaxes, a new light is generated at a sum frequency of two incident optical fields (ω_SFG = ω_IR + ω_Vis). This can be treated as an IR-single resonant SFG process. By continuously tuning ω_IR and monitoring the intensity of output SFG, a vibrational spectrum of surface molecules is obtained as a plot of the SFG intensity against IR wavenumber (Fig. 3).

SFG is a second-order nonlinear optical process, which is forbidden under the electric-dipole approximation in the bulk of centrosymmetric media with inversion symmetry. Thus, SFG is surface specific and sensitive since the centrosymmetry is broken at the surface or interface. The SFG intensity (I_SFG) is proportional to the square of the effective surface nonlinear susceptibility (χ_eff⁽²⁾), and the intensities of two incident laser beams (I_IR and I_Vis) [40, 41].

(1)

SFG has polarization dependence, because the laser beams can be switched between S and P polarizations as shown in Fig. 1(b). SSP (SPS, PSS and PPP) polarization combinations are typically written in the order of relative laser energies, i.e. SFG, visible and IR beams. For the co-propagation geometry, i.e. visible and IR beams are incident within the same quarter in the xz plane and SFG signals are collected in a reflected direction (Fig. 1(b)), the polarization-dependent χ_eff⁽²⁾ for an achiral and rotationally isotropic interface can be expressed by the macroscopic susceptibilities χ_ijk⁽²⁾ through [42]:

(2)

L_ii (i=x, y, z) terms are the Fresnel factors for the local field corrections,

(3)

with α_i and γ_i being the incidence and refraction angles with respect to the surface normal, respectively, for the output SFG, incident visible and IR beams (Fig. 1(b)). The laser beam path determines the definition of the interface. n₁(ω_i), n₂(ω_i) and n′(ω_i) are the refractive indices of bulk medium 1, bulk medium 2 and interfacial layer, respectively. One can see that L_ii is a constant when refractive indices, incidence angles (α_i) and refraction angles (γ_i) are known.

The values of n′(ω_i) are usually difficult to measure. Herein, they were estimated by the modified Lorentz model, which is usually used for the three-layer model [41]:

(4)

F_ijk terms contain the coefficients of L_ii and cosine/sine of α_i, which are also constant within certain experimental conditions.

The macroscopic susceptibilities χ_ijk⁽²⁾ in the laboratory coordinates system λ(x, y, z) are related to the molecular hyperpolarizability β_i'j'k'⁽²⁾ in the molecular coordinates system λ'(a, b, c) through the Euler transformation [41, 42]. For example, the χ_ijk⁽²⁾ of molecules with C_3v symmetric stretching (_SS) mode (e.g. -CH₃) simplified by the integration over the twist angle and azimuthal angle of Euler angles can be expressed as:

(5)

Where N_s is the effective number density of surface molecules, θ is the tilting angle, which is the angle between the main molecular axis in the molecular coordinates system λ′(a, b, c) and the z axis in the laboratory coordinates system λ(x, y, z) (i.e. the surface normal). The tilting angles of CO and methanol molecules were defined in Figs. 2a and 2b. β_ccc is the molecular hyperpolarizability, and R is the molecular hyperpolarizability ratio (R = β_aac/β_ccc = β_bbc/β_ccc), which can be calculated by the Raman depolarization ratio (ρ) [25, 42]. For the symmetric stretching modes of C_2v groups, R_a=β_aac/β_ccc≠R_b=β_bbc/β_ccc are generally calculated with the bond polarizability derivative model [43, 44], but there is still controversy [42]. The expressions of χ_ijk⁽²⁾ of molecules with a C_∞v symmetry (e.g. CO) are the same as Eq. (5) with R equal to the bond-polarizability derivative ratio (r) [41, 42, 44]. ⟨⟩ denotes ensemble average over molecular tilting angle. In this paper, a δ-function distribution for tilting angle was assumed in the simulations (modeling).

From Eqs. (2‒5), one can see that the χ_eff⁽²⁾ of surface molecules depends on the factors of polarizations (P or S), laser angles of incident and output beams, refractive indices of two bulk media and their interface, surface number density, orientation and molecular microscopic hyperpolarizability (IR transition dipole moment and Raman polarizability) of molecules. The former three factors are included in the defined F_ijk factor, which is a constant under certain experimental conditions. The latter three factors are the intrinsic properties of molecules, which are contained in the macroscopic susceptibility χ_jik⁽²⁾. The independence of F_ijk and χ_jik⁽²⁾ terms will make the following analysis of the effects of incidence angles, refractive indices and R-values on the SFG intensity and molecular orientation much easier.

A picosecond SFG spectrometer (commercial system by EKSPLA [45]) is comprised of three parts: the PL2241 laser, the harmonics unit and the parametric generation/difference frequency generation unit PG501/DFG. The PL2241 laser system, a diode-pumped mode locked neodymium-yttrium-aluminum-garnet (Nd: YAG), generates a fundamental laser beam at 1064 nm (e.g. 30 ps, 50 Hz, 30 mJ/pulse), a portion of which is frequency doubled to 532 nm by a harmonic crystal (deuterated potassium dihydrogen phosphate, K*DP) in the harmonics unit. One part of the 532 nm beam is directly used as the visible beam for the SFG process. Another part of the 532 nm beam (max. 10 mJ) is used for parametric generator PG, which consists of double-pass OP generator (OPO) and double-pass OP amplifier (OPA). Tunable signal (0.68‒1.064 µm) and near-IR idler (1.064‒2.3 µm) parametric pulses are generated by OPO crystal (BBO-1), diffraction grating (DG) and OPA crystal (BBO-2). Another portion of 1064 nm (max. 10 mJ) and the near-IR idler pulses are spatially and temporally overlapped in a difference frequency generation (DFG) crystal (AgGaS₂), which generates the tunable mid-IR beam (2.3‒10 µm) for the SFG process. The polarizations of incident laser beams and of generated SFG signals can be typically adjusted to/collected in S or P polarizations. The SFG signal is detected by a highly sensitive photomultiplier tube (PMT) after passing through optical filters and a monochromator.

As mentioned, SFG measurements can be carried out in any surface/interfaces such as gas (UHV)/solid, air/liquid and solid/liquid interfaces as shown in Fig. 2. Being an excellent surface-specific spectroscopy, SFG has already provided molecular information for many gas or liquid phases, and in ultra-high vacuum (UHV) (e.g. Fig. 3). However, some details of the experimental measurements need to be noted before discussing results.

For surface science studies of catalysis, preparing a clean and ordered catalyst surface is typically an important step. Generally, the solid sample (e.g. Pt(111) single crystal) mounted on a dedicated holder (Fig. 2(a)), is inserted into the spectrometer system through a load lock, which is connected to the UHV chamber. Using a magnetic transfer rod, the sample is transferred to the UHV chamber, in which cleaning (e.g. sputter and annealing) and characterization (e.g. LEED, Auger electron spectroscopy (AES)) are performed. Finally, again under UHV, the sample is transferred to the UHV-compatible high pressure SFG cell [46, 47], which also allows to introduce gases [48]. For CO, removal of Ni- and Fe-carbonyls by a Cu-based carbonyl scrubber is essential [2]. Generally, CaF₂ and quartz windows serve as entrance and exit ports for the incident (IR and visible) laser beams and outlet SFG radiation, respectively. The IR and visible laser beams are overlapped spatially and temporally on e.g. the disk-like Pt(111) surface (6 mm outer diameter) in a co-propagation geometry to interact with a surface (e.g. CO) molecule, and instantaneously a third beam at the sum of the two frequencies is emitted in the reflection direction as shown in Fig. 2(a). For examples of SFG spectra of CO adsorption on Pt(111), Pd(111) (Fig. 3) and Pt-ZrO₂ nanoparticle model catalysts performed in our recently designed SFG system refer to refs [11, 48].

In a study of air/liquid interfaces, organic contaminations of samples or sample cells have a crucial impact on SFG spectra. For example, the dangling O-H stretching of pure water (~3700 cm^‒1) disappears in the presence of some organic molecules spreading on the surface. For salt solutions, although some commercial salts contain less than 1% impurities, e.g. ACS grade or ultrapure grade, trace amounts of organic contaminations still significantly affect the interfacial water spectrum [49]. In order to exclude the unwanted interference of contaminations in salts, salts must be pretreated (e.g. by recrystallization, baking and/or filtration) before use. In addition, any container in touch with the sample must also be clean. Teflon cells, due to high chemical and physical stability as well as corrosion resistance (except XF solutions and molten (strong) alkali (metal)), are good materials for these measurements (Fig. 2(b)). The containers can be cleaned by immersion in freshly prepared Piranha solution (e.g. H₂SO₄: H₂O₂ ≈ 3:1 volume ratio) for several hours (timing allows to cool down since it is an exothermic reaction), followed by rinsing with conductively pure (Millipore) water (18.2 MΩ·cm) [50]. The SFG setup on the optical table is usually covered in a plastic housing to reduce the airflow when measured in air [51].

In an SFG study of solid/gas, solid/liquid and solid/solid interfaces, transparent substrates with small non-resonant SFG signals, such as fused quartz (SiO₂), sapphire (Al₂O₃), CaF₂ and BaF₂, in the form of windows or prisms (e.g. hemi-cylinder (Fig. 2(c)), triangular and dome) are usually chosen when designing experiments [37]. However, the chemical stability (e.g. inertness towards liquid phases) and transmission cutoff wavelengths of the selected materials must be carefully considered. For example, SiO₂ and Al₂O₃ substrates have higher chemical stabilities (e.g. higher hardness and better acid resistance) than CaF₂ and BaF₂ substrates. The latter may react with some acids (e.g. H₂SO₄) and even dissolve in water. However, due to the lower transmission cutoff wavelength, BaF₂ (770 cm^‒1) and CaF₂ (as low as 1000 cm^‒1) prisms still hold big advantages for studies of low vibrational modes, compared to the cutoff wavelengths of SiO₂ @ 2380 cm^‒1 and Al₂O₃ @ 2000 cm^‒1 [37]. One of the setups designed for solid/liquid interfaces, e.g. a SiO₂ hemi-cylinder prism in close contact with e.g. NaCl aqueous solutions (in a Teflon cell) (the entire arrangement held together by a metal bracket), is shown in Fig. 2(c).

SFG spectroscopy has been applied to many catalytic processes, including molecular (e.g. CO, C₂H₄) adsorption, oxidation and hydrogenation on single crystal surfaces [52, 53], (oxide-supported) nanoparticles [54-58], (graphene-supported) nanoclusters [59] and biomimetic crystals [60]. CO was often used as a probe molecule in the research of surface chemistry and catalysis, but most of the SFG studies were carried out in PPP geometry only, which prevents molecular orientation analysis. Recently, SSP and PPP spectra in the C‒O stretching vibration region of CO adsorbed on Pt(111) at 4 mbar and 300 K have been obtained [11] and are shown in Fig. 3(a) (upper panel). It is worth noting that the infrared polarization was always kept at P, because an S-polarized: field is canceled on a metal surface [61].

There are two peaks in PPP spectra, both attributed to the linearly bonded CO molecules (i.e. carbon atom bound on top of a single Pt atom, Fig. 4), but adsorbed at different sites of the single crystal surface. The sharp peak at 2092 cm^‒1 characterizes on-top CO adsorbed on terrace sites, whereas the smaller shoulder at 2073 cm^‒1 originates from species adsorbed on the step sites (Fig. 4). In turn, the appearance of 2073 cm^‒1 also reveals the existence of defects (steps or kinks) on Pt(111) crystal. In SSP spectra, only on-top CO at terraces was detectable and the signal was much smaller than that in PPP spectra, while step-sites CO was not observed because of its lower surface number density (N_s) [11]. Thus, SFG can not only probe various species adsorbed on different sites of crystals, but also evaluate the smoothness or defectivity of a surface [63, 64].

Already two decades ago, Baldelli et al. also reported polarization-dependent SSP and PPP spectra of CO on Pt(111) and polycrystalline Pt electrodes at different electrode potential. Interestingly, for CO on Pt(111) single crystal electrode, there was only one peak of on-top CO in PPP spectra, whereas two peaks respectively assigned as three-fold hollow and on-top CO appeared in SSP spectra [9]. Subsequently, SSP, SPS and PPP spectra of CO on PMMA-supported Pt nanoparticle arrays and films were also measured. However, Badelli et al. [15] attributed the difference in these polarization-dependent spectra to the changing dielectric properties of the surface as the Pt coverage increased, rather than probing different orientations of CO, i.e. the orientation information was not deduced for nanoparticles.

Even though the SSP spectral intensity is much smaller than PPP intensity, the spectra still have a good signal-to-noise ratio (Fig. 3(a), upper panel). The intensity ratio (I_PPP/I_SSP) can be utilized to quantitatively calculate the molecular hyperpolarizability ratio (R) or tilting angle (θ) of CO molecules, and an exact value of R = 0.49 was previously determined, assuming that the CO molecules were oriented perpendicular to the surface [11].

However, no SSP signal was obtained for CO on Pd(111) at 300 K. The experimental conditions were the same for CO on Pt(111) (I_SSP_Pt(111) < I_PPP_Pt(111)) and Pd(111) in Fig. 3(a), but their PPP intensities differed largely (I_PPP_Pd(111) < I_PPP_Pt(111) under similar CO pressure, lower panel). This suggests that the expected SSP intensity of CO on Pd(111) is also much smaller than that of Pt(111), and thus difficult to measure (despite simulations indicated nearly equal SSP intensities for Pt and Pd [11]).

In contrast to Pt(111), on Pd(111) bridge- (or hollow-) bonded CO (i.e. carbon atom bound to two/three Pd atoms, Fig. 4) at 1923 cm^‒1 rather than on-top CO at 2071 cm^‒1 dominated the PPP spectra, accompanied by a small shoulder at lower vibrational frequency (~1899 cm^‒1) [2, 65] as shown in Fig. 3(a) (lower panel). The latter may also indicate hollow-bonded CO.

Distinctly different from CO on Pd(111) at 300 K (α_Vis = 58.5°, α_IR = 55°), Galletto et al. [10] reported that at lower temperature (90 K) the signal of on-top CO (α_Vis = 54°, α_IR = 56°) dominated in both SSP and PPP spectra, whereas the signals of bridge- and hollow-bonded CO were nearly at the noise level. This spectral difference does not result from the experimental conditions, because similar incidence angles of visible and IR laser beams were employed. However, at lower temperature (90 K), the higher coverage of CO molecules and the different cross-section of on top and hollow species [66] explains the SFG spectra at 90 K. Similarly, when coverage decreases and the mobility increases at higher temperature, instead of on top, bridge-bonded CO molecules dominated the PPP spectra at 300 K, with CO preferring to bind two Pd atoms (Fig. 3(a), lower panel).

Furthermore, carbon-based materials, e.g. carbon nanotubes [67, 68], graphene-based supercapacitors [69], chemical reaction confined under graphene [70], as well as nanoparticles/nanoclusters deposited on carbon (graphene/HOPG) layer has recently attracted surface scientists [71, 72]. These studies will provide a new field for the SFG technique, studying more complex catalysts and processes. For instance, SFG has recently performed outstandingly in the study of CO-induced restructuring of Pt nanoclusters grown on graphene [59], as well as of the structure of self-assembled 2D crystal supported on graphene, which was proven to sustain long-lived excitons [60].

Methanol at the air/liquid interface was the first molecule studied by SFG, but only SSP vibrational spectra were obtained [73]. Subsequently, the air/methanol interface was intensively studied as a benchmark interface system, by SFG [25, 74-77] and molecular dynamics (MD) simulations [78-81]. These studies were related to the changes of structure (e.g. hydrogen-bonded network), orientation (of methyl group), adsorption isotherm, and the surface enrichment of ions, upon addition of water molecules and salts.

Fig. 3(b) shows the SSP and PPP spectra in the C-H stretching vibration region of air/methanol in the absence and presence of NaI (3M) salts. Three peaks centered at ~2840, ~2920 and ~2940 cm^‒1 in SSP spectra were assigned to the methyl symmetric stretching (CH₃-SS) mode and two Fermi resonance bands of the CH₃-SS mode with overtones of the CH₃ bending modes [73]. Due to the low surface number density, the Fermi resonance at 2920 cm^‒1 was at the noise level in PPP spectra. Different from the spectra of CO on Pt(111), the signal of methanol at the air/methanol interface is much larger in SSP than in PPP. After adding NaI salts (3M), both the SSP and PPP spectral intensities increased. This not only indicated that the interfacial methanol molecules became better ordered, but also confirmed the existence of ions at the interface. The ratio of I_SSP/I_PPP remained almost the same as for pure methanol, meaning an unchanged orientation. However, it was reported that methanol molecules were reoriented by NaI salts, more than 10° closer to the surface. Moreover, this first demonstrated the importance of refractive indices and Raman depolarizability ratio ρ (hyperpolarizability ratio, R) in the quantitative analysis of SFG spectral intensity and molecular orientation at the air/liquid interface [25].

Water is ubiquitous and the most important liquid on the earth. The understanding of its interfacial properties is crucial for the advances of many disciplines in science and technology. Since Shen and co-workers reported the first vibrational SFG spectrum of the air/water interface in the O-H stretching vibration region [82], a vast number of SFG studies emerged, dealing with interfacial structures and orientations of water molecules affected by inorganic ions at the air/liquid [22-24, 32, 49, 83] and solid/liquid [62, 84, 85] interfaces. These studies focused on the determination of relative surface propensities of ions through the changes of orientation of the "free-OH" group (non-hydrogen-bonded, at the top-most layer of air/liquid interface) and the hydrogen bonding of interfacial water molecules. Fig. 3(c) shows the SSP spectra of O-H stretch vibrations of the SiO₂/water interface for a series of concentrations of NaCl salts. Only two broad peaks near 3200 and 3400 cm^‒1 are observed (because "free-OH" was terminated by SiO₂), which are characteristic of interfacial water. They had been assigned to e.g. the ice-like/water-like [23, 82, 86] or stronger/weaker hydrogen-bonded OH [87], and donor-bonded OH of interfacial water with DA, DDA, DAA, or DDAA (D and A refer to donor-and acceptor bonds, respectively, with which a water molecule bound to its neighbors) [88, 89]. Even though the assignments remain controversial, they certainly originate from the interfacial water molecules more coupled to the bulk phase and are distinct from the top-most layer of the air/water interface [22].

Obviously, the water structures were significantly perturbed upon increasing the ionic strengths, according to the apparent drop of SFG signals in Fig. 3(c). Even though Hore and co-workers [84] later pointed out that both the real and complex parts of refractive indices of NaCl solutions at 3200 and 3400 cm^‒1 changed with the concentrations, it was a pity that the influence of changes of refractive indices were not considered in the discussion of disruption of solvent ordering especially at high concentrations. Because a slight increment (1.333 to 1.378) of the refractive indices of bulk solutions result in a significant reduction or disappearance of I_SSP [90].

Since there is no report concerning the effects of incidence angles, refractive indices (bulk substrates or solutions), and hyperpolarizability ratio on the quantitative analysis of SFG spectra at the gas/solid (catalysts), air/liquid and solid/liquid interfaces, an intensity/orientation analysis in light of these factors is presented in the following section.

Polarization- and experimental configuration-dependent sum frequency generation (SFG) vibrational spectroscopy is not only an excellent tool for the analysis of structures and orientations of molecules on various surfaces or interfaces, but it can also reveal spectral splitting and the existence of multiple orientations of the interfacial molecules (e.g. [bmim] cations) [50]. However, the changes in the SFG spectra, particularly those of the spectral intensities, must be carefully analyzed because many factors affect them. As discussed in Section 2, the SFG intensity contains contributions of "external" experimental conditions including refractive indices, laser incident angles and polarizations, and "internal" molecular properties, i.e. molecular macroscopic second-order nonlinear susceptibility (χ_ijk⁽²⁾), which is determined by the surface number density (Ns), microscopic hyperpolarizability tensors and average tilting angles (θ) of surface/interfacial molecules. Unfortunately, in the quantitative analysis of SFG spectra, changes of refractive index of medium 2 (n₂) and molecular hyperpolarizability ratio (i.e. R-values) were usually ignored, despite having a significant influence on the SFG intensity [90] and orientation [25] analysis, particularly in the study of concentrated salt solutions. Neglecting either the variations of "external" experimental or "internal" molecular factors may lead to misinterpretation of the property of surface molecules.

In the following, we thus separately discuss the influence of (1) incidence angles of visible and IR laser beams (α_IR and α_Vis) and bulk refractive indices on the SFG intensity, and of (2) bulk refractive indices and R-values on molecular orientation, at gas/solid, air/liquid and solid/liquid interfaces. Pt(111), Pd(111), pure H₂O, pure methanol, 5M NaCl aqueous solution and 3M NaI methanol solution served as the comparative solid substrates and liquid phases, respectively.

The contributions of refractive indices of bulk phases (n₁, n₂) and interface (n'), laser incident angles and polarizations can be contained in a defined F_ijk coefficient, which can be extracted from the χ_ijk⁽²⁾ item. As shown in Eq. (2), only F_yyz is involved in χ_{eff, SSP}⁽²⁾, therefore, changes of F_yyz can be employed to evaluate the influence of refractive indices on SSP spectral intensities due to I_SSP∝|χ_{eff, SSP}⁽²⁾|²∝|F_yyz|². However, χ_{eff, PPP}⁽²⁾ is a combination of four F_ijk factors (F_xxz, F_xzx, F_zxx and F_zzz) and four χ_ijk⁽²⁾ items, it is thus hard to evaluate the contribution of refractive indices to the PPP intensity on the basis of a single F_ijk term, but F_zzz was reported to be the dominant factor in PPP, especially when α_Vis is close to the critical angles of solid/liquid interfaces [90]. Since F_ijk will be a complex number when refractive indices contain imaginary parts (Table 1), the modulus of F_ijk, i.e. |F_ijk|, was adopted in the simulations. Fig. 5 shows the changes of |F_yyz| of gas/solid interface, air/liquid interface and solid/liquid interface as a function of incidence angles. Apparently, proper experimental configuration, i.e. incidence angles (α_IR and α_Vis), plays an important role in obtaining SFG spectra with good signal-to-noise ratio.

For the gas/solid (e.g. Pt) interface (n₁ = 1, and n₁ < n₂) (Fig. 5(a)) and incidence angles (α_IR and α_Vis) smaller than 54°, the values of |F_yyz| at different α_Vis with a fixed α_IR = 55° (red line) are larger than those at different α_IR with a fixed α_Vis = 55° (blue line). However, their difference decreases with increasing incidence angles. This is because |F_yyz| increases for α_IR < 73° but then decreases, while it decreases monotonically with α_Vis. When incidence angles change from 35° to 65° (commonly adopted range), the changes of |F_yyz| to α_Vis (yellow band) are almost three times larger than that to α_IR (green band), indicating SSP spectral intensity is much more sensitive to α_Vis. Previous studies also indicated the ratio of I_PPP/I_SSP is more sensitive to α_Vis [11]. Therefore, only |F_yyz| vs. α_Vis with a fixed α_IR = 58° of the air/liquid and solid/liquid interface are discussed in the following.

For the air/liquid interface (n₁ = 1, and n₁ < n₂), the curve of |F_yyz| vs. α_Vis (Fig. 5(b)) is similar to that of gas (UHV)/solid interface since n₁ is identical. However, the values of |F_yyz| decrease significantly because the Fresnel factors decrease with increasing n₂. For example, |F_yyz|_Pt of gas/solid interface are about two orders of magnitude smaller than |F_yyz|_H₂O of air/liquid interface (Fig. 5(a) vs. 5(b)) because of n₂ (Pt) > n₂ (H₂O). However, weak resonant SFG signals can be enhanced by a strong nonresonant background through heterodyne amplification, especially for metals due to their free electrons [91, 92]. Even though the nonresonant signal can be high and helpful to increase the SFG signal in certain polarization combinations [93], it can also interfere with the resonant signal and result in a distortion of the spectral line shape.

Even a slight increment of n₂ at air/liquid interface, e.g. ~a 3% increment of n₂ (Vis) (i.e. from 1.333 (H₂O) to 1.378 (5M NaCl, i.e.) at room temperature, can cause a 8%–15% decrement of |F_yyz| (black line), which corresponds to a 15%–28% drop of I_SSP in the whole range of α_Vis (black line). Previous SFG studies at air/liquid interfaces, particularly on concentrated salt solutions that involve a non-negligible change in refractive index, should thus be reassessed.

For the solid (e.g. SiO₂)/liquid interface (n₁ > 1 > n₂) in Fig. 5(c), which also used water and 5M NaCl aqueous as liquid phases (i.e. same n₂ as Fig. 5(b)), the values of |F_yyz| are much larger because the Fresnel factors (Eq. 5) are enhanced for bigger n₁. This indicates a stronger SFG signal of water at the SiO₂/water interface than at the air/water interface in case of an identical experimental configuration, particularly, when α_Vis is close to the critical angle (~67°) of the total internal reflection (TIR). However, to minimize the IR dispersion, α_IR is suggested to be away from the critical angle if the refractive index of the transmitted or reflected medium is a complex value [94]. Similarly, a significant decrease of |F_yyz| is caused by just a 3% variation of n₂, especially, when α_Vis ≈ 67°, it yielded about 50% decrement of |F_yyz| (i.e. 75% drop of I_SSP). The SFG intensity is enhanced at higher α_Vis, but the influence of refractive index is also amplified. Thus, ignoring the changes of refractive index may cause an incorrect interpretation of the molecular property at surfaces/interfaces. For instance, the refractive index of deuterated sulfuric acid (D₂SO₄) at 20 ^oC is 1.423, thus, the refractive index of 5M D₂SO₄-D₂O solutions should be much higher than pure D₂O (n₂ = 1.33). The vanished SFG signal at 5M D₂SO₄/mica surface may not be fully attributed to the reported disappearance of the ordered hydrogen-bonding network [85]. The probable drop of SFG intensity caused by a higher refractive index should also be considered.

Therefore, incidence angles (especially α_Vis) and refractive indices play an important role in the analysis of (SSP-) SFG intensity at interfaces. Particularly, one must be very careful when employing a TIR geometry at solid/liquid interfaces.

SFG intensity is a function of higher orders of cosθ function (Eq. 5), indicating that it is more sensitive to molecular orientation (tilting angle) than the linear IR and Raman spectroscopies. Besides the refractive indices, the molecular hyperpolarizability ratio (R) of solutions is also strongly changed in the presence of salts. For example, the value of R is 1.7 for the CH₃-SS group of pure methanol [42], while it is 2.0 in the presence of 3M NaI [25]. To calculate the precise orientation angle, non-negligible changes of these factors should be carefully taken into account.

As discussed above, slight changes of refractive index have a great effect on the SFG intensity, thus it may also affect orientation analysis using the ratio of χ_{eff, PPP}⁽²⁾/χ_{eff, SSP}⁽²⁾. Even though the n₂(ω_IR) and n′(ω_IR) should vary significantly across the spectral region because of the dispersion, their influence on the orientation analysis will not be significant. Because ω_SFG and ω_Vis are not in resonance with the interfacial molecules, χ_xzx⁽²⁾=χ_zxx⁽²⁾ is generally valid [42]. Moreover, ω_SFG is much closer to ω_Vis, the χ_xzx⁽²⁾ and χ_zxx⁽²⁾ terms of χ_{eff, PPP}⁽²⁾ can nearly cancel out especially when α_IR and α_Vis are equal, making an insignificant contribution to χ_{eff, PPP}⁽²⁾ with a co-propagating geometry [40]. Thus, only two terms of χ_xxz⁽²⁾ and χ_zzz⁽²⁾ are left in χ_{eff, PPP}⁽²⁾ (Eq. 5). Fortunately, the n₂(ω_IR) and n′(ω_IR) only exist in L_zz(ω_IR) term (Eq. 3), which can be canceled by the ratio of χ_{eff, PPP}⁽²⁾/χ_{eff, SSP}⁽²⁾. However, the contributions of χ_xzx⁽²⁾ and χ_zxx⁽²⁾ to χ_{eff, PPP}⁽²⁾ in the counter-propagating geometry are still quite important [42].

Based on Eqs. (2‒5), the R-value or tilting angle (θ) of surface molecules can be therefore determined at certain experimental conditions via the ratio of χ_{eff, PPP}⁽²⁾/χ_{eff, SSP}⁽²⁾, given one of them is known. For instance, the R-value (R = 0.49) of CO molecules, which can be hardly obtained by Raman depolarizability ratio or the bond polarizability model, can also be deduced from the experimental value of I_PPP/I_SSP, assuming that CO molecules stand upright on the surface of Pt(111) [11], and vice versa. Similarly, assuming an upright orientation, Baldelli et al. [9] reported the R-values (based on the I_SSP/I_PPP of CO on Pt(111) electrode) were 0.6 and 1.5 for CO adsorbed on on-top and three-fold hollow sites, respectively. Moreover, a value of 0.1 for the on-top CO on Pd(111) single crystal at lower gas pressure (10^‒6 mbar, 0.75 ML) and temperature (90 K) was reported, but it was speculated to change with coverage [10]. Anyway, the non-uniform experimental R-values of adsorbed CO molecules are also quite different from the static hyperpolarizability ratio (~0.25) of the free CO (obtained by DFT calculations) [100], suggesting that the R-value of molecules has a dependence on the substrate, temperature and gas pressure (coverage) if the tilting angles remained unchanged. Nevertheless, previous pressure-dependent SFG spectra of CO on Pt(111) at 300 K showed a constant value of I_PPP/I_SSP [11], which would demonstrate an independence of R on the coverage presuming a constant (upright) orientation of CO molecules.

Fig. 6 shows the influence of R-values and refractive indices (n₁ and n₂) on the I_PPP/I_SSP as a function of tilting angle (θ) at gas/solid (CO on Pd vs. Pt single crystals), air/liquid (pure methanol vs. 3M NaI) and solid/liquid (pure methanol vs. 3M NaI) interfaces. Most of the refractive indices contain imaginary part (Table 1) so that χ_eff⁽²⁾ will also be a complex number, the I_PPP/I_SSP = |χ_{eff, PPP}⁽²⁾|/|χ_{eff, SSP}⁽²⁾|² was therefore used in the simulations. Again, the lineshapes of I_PPP/I_SSP vs. θ of gas/solid (Fig. 6(a)) and air/liquid interfaces (Fig. 6(b)) are similar due to an identical n₁. I_PPP/I_SSP decreases monotonically with increasing θ.

Under identical experimental conditions at the gas/solid interface, molecules with R = 0.30 (blue line) adsorbing on the Pt surface, the I_PPP/I_SSP is obviously larger than that of CO molecules (R = 0.49) on Pt (red line) if θ < 51° (Fig. 6(a)). It demonstrates that SSP spectra of molecules having smaller hyperpolarizability ratio (R) or bond-polarizability derivative ratio (r) would be much more difficult to measure in case that their PPP spectral intensities are similar. For example, the r values for C-H group of simple halogenoalkyls and carboxyl acids are in the range of 0‒0.25 [44], and for the free OH group of water is about 0.32 [82]. Similarly, CO molecules adsorbing on a Pd surface (which has smaller refractive indices than Pt, Table 1), the larger value of I_PPP/I_SSP (black line) also suggests a weaker SSP signal. This can be confirmed by the experimental result that I_SSP (Pt) < < I_PPP (Pt) (Fig. 3(a)), i.e. SSP intensity is much smaller than PPP, and I_PPP (Pd) < < I_PPP (Pt) (Fig. 3(b)), so that I_SSP (Pd) should be much smaller than I_SSP (Pt). When I_PPP/I_SSP = 20, the values of θ are 24°, 36° and 44° corresponding to molecules with R = 0.49 on Pt, R = 0.3 on Pt and R = 0.49 on Pd, respectively. These results show that when the I_PPP/I_SSP ratio is identical, molecules with a larger R will have a smaller orientation (tilting) angle on Pt when θ < 51°. Additionally, CO molecules on Pd would tilt much closer to the surface (larger θ) than on Pt.

Furthermore, when the ratio of I_PPP/I_SSP decreases, θ increases. For example, I_PPP/I_SSP decreases from 20 to 10, and the tilting angle has an increase of 27°, 15° and 27° for molecules with R = 0.49 on Pt, R = 0.3 on Pt and R = 0.49 on Pd, respectively. This indicates that the SFG spectral intensity is more sensitive to the molecular orientation for molecules with a larger hyperpolarizability ratio or bond-polarizability derivative ratio. However, the orientation variations of CO molecules seem to be independent of the substrates (Pt vs. Pd).

Similarly, the changes of R and refractive index (n₂) of solutions at the air/liquid interface should not be ignored either (Fig. 6(b)). As reported before, even though both SSP and PPP spectral intensities of methyl symmetric stretching vibration (CH₃-SS) of methanol were obviously enhanced after adding 3M NaI salts, the ratio of I_PPP/I_SSP (i.e. χ_PPP⁽²⁾/χ_SSP⁽²⁾ = -0.346) was almost identical [25]. This means the tilting angles (θ = 30°) should be unchanged supposing an unchanged value of R and refractive index, i.e. R = 1.7, n₂ = 1.326 (red line). Unfortunately, both increased in the presence of NaI salts. The tilting angle of air/3M NaI methanol solutions increased to 41° with R = 2.0 and n₂ = 1.398 (black line), which is over 10° higher than that of pure methanol. The methanol molecules not only become better ordered (based on the increased SSP and PPP intensity), but they also tilt much closer to the surface under the influence of 3M NaI salts [25]. The tilting angle still had a 6° increase even when only considering the variation of n₂ (blue line). The orientation analysis of salt solutions with a constant value of I_PPP/I_SSP should thus be performed carefully. For example, the large difference in refractive index between pure water (n = 1.33) and [bmim][MS] (n = 1.48) (a complex ionic liquid) [51] indicates a strong dependence on the concentration.

Unlike the air/liquid interface, the value of I_PPP/I_SSP (> 1) is much bigger and increases with increasing θ at the solid/liquid interface (Fig. 6(c)). As |F_yyz| (I_SSP) is larger at solid/liquid than at air/liquid interface and I_PPP is bigger than I_SSP at solid/liquid interface, SFG signals of methanol are stronger at the solid/methanol interface. A constant θ = 35 ± 7° was obtained for all methanol concentrations at octyltrichlorosilane (OTS)-covered SiO₂/methanol-water mixture interfaces [101], which corresponds to I_PPP/I_SSP =2.6 (in case that the refractive index of SiO₂ was unchanged by the OTS monolayer). Similar to Fig. 6(b), θ of 3M NaI methanol solutions became 44°, which also shows that the methanol molecules at SiO₂/liquid interfaces orient almost 10° away from the surface normal under the influence of NaI.

Finally, even though the SFG intensity is proportional to the square of molecular surface number density, higher molecular coverage can also lead to some unwanted effects. Previous studies by SFG and DFT predicted a strong dependence of Raman activities or non-linear effects on the coverage of adsorbates [66]. The SFG and IR adsorption spectra also indicated a coverage dependence of the Raman tensor involved in the SFG hyperpolarizability tensor [102]. Moreover, a higher coverage of adsorbates on catalysts may destabilize the molecular configuration due to larger repulsive lateral interactions, which would fundamentally change the SFG response [103]. Therefore, any potential changes of factors that influence the SFG spectral analysis must be carefully considered.

SFG has been proven to be well suited for characterization of interfacial molecules in the C-O, C-H and O-H stretching vibration regions. SFG can not only detect molecules adsorbed at terrace or step sites of single crystals (catalysts) and at liquid interfaces, but it can also evaluate the smoothness or defectivity of catalysts as well as the enrichment/depletion of ions at the interface. An accurate understanding of molecular interfaces depends on the correct interpretation of SFG vibrational spectra, however. Illustrated by examples of CO adsorption on Pt(111) and Pd(111) at gas/solid interfaces, NaI salts effects on the methanol orientation at air/liquid interfaces and the influence of NaCl ionic strength on the disruption of water at solid/liquid interfaces, the analysis of SFG spectral intensity and orientation is illustrated, strongly depending on several parameters and factors. Influences of incidence angles, refractive index and molecular hyperpolarizability ratio (R) on the analysis of SFG intensity and molecular orientation at gas (UHV)/solid, air/liquid and solid/liquid interfaces were separately discussed. When I_PPP/I_SSP is identical, molecules with a larger R will have a smaller orientation angle on Pt (assuming θ < 51°). Moreover, CO molecules on Pd(111) tilt much closer to the surface than on Pt(111) (for identical I_PPP/I_SSP). At the gas/solid interface, the changes of orientation are much more sensitive to the molecular R value rather than depend on the type of substrate (Pt vs. Pd). The SFG intensity will be enhanced by a TIR geometry, but the influence of refractive index at solid (SiO₂)/liquid interface is also increased, much stronger than that at the air/liquid interface. In contrast, the refractive index and R-value cause similar effects on the orientation of NaI methanol solutions at air/liquid and solid/liquid interfaces. The analysis of SFG intensity and orientation with a constant value of I_PPP/I_SSP of salt solutions (especially concentrated solutions) must thus be carefully performed.

Conflict of Interest: The authors declare no competing financial or personal relationships with other people or organizations.

This work was in part supported by the Austrian Science Fund FWF through projects ComCat (I 1041-N28) and DK+ Solids4Fun (W1243) and by TU Wien via the Innovative Project "SFG Spectroscopy". X. Li acknowledges the doctoral candidate Jian Hou at Institute of Chemistry, Chinese Academy of Sciences for providing the picture of experimental setup in Fig. 2c.