Water Solutions via Sum Frequency

Article pubs.acs.org/JPCC

Surface Structure of Methanol/Water Solutions via Sum Frequency Orientational Analysis and Molecular Dynamics Simulation Takashi Ishihara,† Tatsuya Ishiyama,‡ and Akihiro Morita*,†,§ †

Department of Chemistry, Graduate School of Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan Department of Applied Chemistry, Graduate School of Science and Engineering, University of Toyama, Toyama 930-8555, Japan § Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan ‡

ABSTRACT: Polarization dependence of sum frequency generation (SFG) spectroscopy has been widely discussed to detect molecular orientation at surfaces. The present work examines the orientational analysis by molecular dynamics (MD) simulation of methanol/ water mixture surfaces with varying concentrations. We calculated by MD the surface structure of the solutions and their SFG spectra in the methyl C−H stretching region, and directly analyzed the relations. The MD calculations reported that (i) the SFG signal of the methyl symmetric stretching exhibits a turnover behavior with increasing concentration and (ii) the polarization ratio is almost invariant over the concentration, while (iii) the orientation of the methyl group significantly randomizes in high concentration. The present work elucidated these three findings in a consistent manner by analyzing the MD calculations.

1. INTRODUCTION The structure of a liquid surface is generally different from that of the bulk liquid because of the locally asymmetric environment.1 Molecules at the liquid surface pose a certain orientational structure in response to the anisotropic environment. Local density at the surface, or concentration of solute in the case of solution surface, may be different from that in the bulk phase. Generally speaking, principal structural features of liquid surfaces are characterized with the above two fundamental properties, i.e., molecular orientation and local density or concentration. However, detailed understanding of these features at liquid surfaces is still far from complete, mainly because of experimental difficulties to probe the liquid surfaces in comparison to solid ones. Molecules at liquid surfaces are more mobile and diffusive, and they are generally hard to investigate under vacuum condition due to evaporation and condensation. In contrast to detecting distinctive adsorbed species at solid surfaces, probe techniques for liquid surfaces have to distinguish the surface molecules from chemically identical species in the bulk liquid. However, most widely used spectroscopic methods, such as infrared absorption and Raman scattering, are not capable of distinguishing the surface signal from the bulk one. To overcome those experimental difficulties associated with the liquid surfaces, sum frequency generation (SFG) spectroscopy is quite suitable.2−6 SFG is allowed only at the surface where the inversion symmetry breaks down in the dipole approximation. Such an optical method is readily applicable to liquid surfaces in ambient conditions. SFG spectroscopy provides vibrational spectra of surface species, which allow us to assign the chemical moieties and local environment at the surface. Though SFG spectroscopy has ideal surface selectivity, observed spectra are often challenging to interpret. To © 2015 American Chemical Society

understand the SFG signals quantitatively, we often encounter a problem to analyze the SFG intensity unambiguously into two factors: orientation and local density. One useful way to detect the molecular orientation by SFG spectroscopy is to make use of the polarization of the incident and generated light.5−9 Such decomposition is based on the assumption that the polarization dependence should be solely governed by the molecular orientation, since the local density should commonly influence the SFG intensities of different polarizations. Though the polarization dependence of the SFG spectra is quite useful for discussing the orientational structure, the accuracy of the conventional analysis procedures to derive microscopic orientational angles may be questionable due to inherent assumptions that are not fully corroborated. In the present paper we examine SFG measurements of methanol and water mixtures with molecular dynamics (MD) simulation. Methanol and water were the first two liquids investigated by SFG spectroscopy,10,11 and SFG measurements of the mixtures have been reported by other groups since then.12−16 These systems provide a very good opportunity to analyze the orientation and local density. The SFG intensity of the methyl symmetric stretching vibration initially increases and then decreases with increasing concentration of methanol. This turnover behavior invoked a lot of discussion about the interpretation of surface structure.12−17 The local density of methanol at the surface of the mixture is arguably larger than that in the bulk solution, which is supported by the surface tension measurement with varying concentration.18 One may assume that the initial increase of the SFG signal is due to the increasing density of methanol, and the turnover is caused by Received: February 5, 2015 Revised: April 7, 2015 Published: April 15, 2015 9879

DOI: 10.1021/acs.jpcc.5b01197 J. Phys. Chem. C 2015, 119, 9879−9889

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The Journal of Physical Chemistry C

of the media and optical geometry of measurement. The effective nonlinear susceptibility depends on the polarization combinations. In the SSP and PPP cases, for example, χ(2) eff is represented by5,7

the randomized orientation of methanol molecules in higher density.12−14,19 However, the polarization measurement of SFG suggested that the orientation is nearly invariant over the concentration range,15,16 which implies that the turnover is not indicative of the randomized orientation. Consequently, the decreased SFG signal in relatively high concentration might be presumably explained with a double-layer structure of methanol with opposite orientation,15 though such a structure of opposite orientation was not apparently supported by MD simulation.20,21 To unambiguously understand the structure and spectra, further reliable analysis is strongly called for. MD simulation can provide detailed atomistic information on the structure and dynamics at liquid surfaces, and has been intensively applied to water and methanol mixtures.19−23 These previous MD studies show a generally consistent picture about the surface structure. The concentration of methanol is locally enhanced at the topmost layer. The methanol molecules there tend to point the methyl group to the vapor side, though the tilt angle distribution of the methyl group from the surface normal is fairly broad. However, it was not so straightforward to connect the surface structure obtained by MD simulation to observed experimental SFG spectra. Recent development of the SFG theory and computational methods6,24−29 advanced our understanding of SFG spectra with the help of MD simulation. We demonstrated that the MD simulation reliably reproduces the experimental SFG spectra of water and methanol by developing elaborate flexible and polarizable molecular models. 30−32 Therefore, the present paper aims at a comprehensive understanding of the surface structure and the SFG spectra of methanol/water mixtures using MD simulation on the same footing. The unified understanding will provide a valuable general insight into the SFG analysis of orientation and local density at liquid surfaces. The remainder of this paper is constructed as follows. Section 2 summarizes the theoretical background of the orientational analysis in SFG spectroscopy, which will be examined in this paper. Section 3 describes the MD conditions for methanol/water mixtures, and presents the MD results on the surface structure. Section 4 provides the calculated SFG spectra and their polarization dependence. Based on the MD results and calculated SFG spectra, section 5 discusses the accuracy and limitation of the conventional orientational analysis. Concluding remarks follow in section 6.

(2) (2) χeff,SSP = L YY (Ω) L YY (ω1) LZZ (ω2) sin β2 χYYZ (Ω, ω1 , ω2) (2) χeff,PPP = −LXX (Ω) LXX (ω1) LZZ (ω2) cos β cos β1 sin β2 (2) χXXZ (Ω, ω1 , ω2) + LZZ (Ω) LXX (ω1) LXX (ω2) sin β cos β1 cos β2 (2) χZXX (Ω, ω1 , ω2) + LZZ (Ω) LXX (ω1) LXX (ω2) sin β cos β1 cos β2 (2) χZXX (Ω, ω1 , ω2) + LZZ (Ω) LZZ (ω1) LZZ (ω2) sin β sin β1 sin β2 (2) χZZZ (Ω, ω1 , ω2)

(1)

In eq 1, the space-fixed coordinates X, Y, and Z are defined so that the interface is normal to the Z axis, and the light wavevectors propagate on the XZ plane. ω1 and ω2 are the frequencies of visible and infrared light, respectively, and Ω = ω1 + ω2 is the sum frequency. χ(2) IJK(Ω, ω1, ω2) denotes the frequency-dependent second-order nonlinear susceptibility tensor of the interface system. β, β1, and β2 are the incident or reflection angles from the interface normal of the sum frequency, visible, and infrared light, respectively. LXX(ω), LYY(ω), and LZZ(ω) are the diagonal tensor elements of the Fresnel factor at the frequency ω, which depend on the incident angle and the refractive index of the liquid and the interface. The explicit formulas of the Fresnel factor elements are presented in refs 5 and 7. Comparing the experimental SFG measurement using PPP and SSP polarizations yields the ratio (2) IPPP/ISSP or the ratio χ(2) eff,PPP/χeff,SSP. On the other hand, MD simulation allows us to straightforwardly calculate the second-order nonlinear susceptibility tensor χ(2) IJK(Ω, ω1, ω2). The second-order nonlinear susceptibility consists of the vibrationally resonant and (2),res nonresonant terms, χ(2) + χ(2),nonres , and the former is IJK = χIJK IJK represented using the time correlation formula by26 (2),res χIJK =

2. THEORY OF ORIENTATIONAL ANALYSIS The orientational analysis in SFG spectroscopy is routinely conducted by using different polarization combinations. The polarization combination in SFG is denoted with three letters, such as SSP or PPP, where the letters (S or P) denote the polarization of the sum frequency, visible, and infrared light, respectively. In the present case of methanol, the ratio of SSP and PPP has been utilized for the CH3 symmetric stretching vibrational mode.5,16 In this section we summarize the essential procedure of the orientational analysis, which will be thoroughly examined in comparison with MD simulation. The following discussion on the orientational analysis is presented using an example of the CH3 symmetric stretching of methanol, though application to other molecules is straightforward. 2.1. Polarization Dependence. The SFG intensity is proportional to the square of the effective nonlinear 2 susceptibility, I ∝ |χ(2) eff | , which is governed by the nonlinear susceptibility of the interface as well as the dielectric properties

iω2 kBT

∫0

∞

dt exp(iω2t )⟨AIJ (t ) MK (0)⟩

(2)

where kB and T are the Boltzmann constant and temperature. AIJ and MK are the polarizability and the dipole moment of the interface system, and ⟨ ⟩ denotes the statistical average. In the CH3 symmetric stretching vibration of methanol, the nonresonant term is neglected. Equation 2 has been extensively utilized to calculate SFG spectra.6,26,30,32,33 In combination with the calculated second-order nonlinear susceptibility tensor by eq 2 and the definition of the effective susceptibility of eq 1, the (2) ratio χ(2) eff,PPP/χeff,SSP is evaluated by the MD calculation. The calculated ratio corresponds to the polarization dependence of SFG measurement, and will be utilized to examine the orientational analysis. 2.2. Relation to Molecular Orientation. In section 2.1 we discussed the ratio of the effective nonlinear susceptibility, (2) (2) χeff,PPP /χeff,SSP , which is often used to derive microscopic molecular orientation at the surface. In the case of a methyl group, the orientation is usually characterized with the tilt angle θ of the methyl group from the surface normal. We summarize the procedure of deriving the tilt angle θ from the observed 9880


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The Journal of Physical Chemistry C (2) ratio χ(2) eff,PPP/χeff,SSP with noticing inherent assumptions (i), (ii), etc. We introduce the frequency-dependent hyperpolarizability of a methanol molecule βijk in a molecule-fixed coordinate in Figure 1, where the methyl O−C bond is along the c axis and

On the other hand, the molecular orientation can be directly investigated by the MD simulation without resorting to the above assumptions. MD can calculate the nonlinear susceptibility tensor by eq 2, and thereby allow for tracing the procedure of the orientational analysis. Such discussion on the orientational analysis will be presented in section 5.

3. MD SIMULATION OF LIQUID SURFACES This section describes the MD procedures and the calculated results on the surface properties of methanol/water mixtures, including density profiles, orientation, and surface tension. These results will be utilized to discuss SFG in section 4. 3.1. MD Conditions. The MD simulation for the surface of methanol/water mixtures was performed in the following conditions. We prepared the methanol/water mixtures with varying concentration from pure water (mole fraction x = 0) to pure methanol (x = 1) with a 0.1 interval of the mole fraction x. These molecules at each concentration x are enclosed in a periodic rectangular unit cell of LX × LY × LZ = 30 Å × 30 Å × 150 Å with three-dimensional periodic boundary conditions. The total numbers of molecules contained in a unit cell were set to 1000 for x < 0.5 and 500 for otherwise. These numbers were chosen to be sufficient to distinguish the surface structure from the bulk. These molecules form a slab geometry in the periodic cell so that two liquid−vapor interfaces are generated normal to the Z axis on both sides of the slab. The molecular models of methanol31 and water30 in the present work have been developed in our previous works of SFG calculations. These models are flexible and polarizable, and the electronic polarization is implemented with the charge response kernel (CRK) model.37 The present models allow for varying partial charges and charge response kernel with intramolecular vibrations.30,31 The long-range Coulombic interactions were treated with the Ewald summation. The MD trajectories were generated at a constant temperature of 298.15 K using the Berendsen thermostat with the damping constant of 0.4 ps.38 The time development was carried out by the velocity Verlet algorithm39 with a time step set to 0.61 fs. Initial configurations of constituent molecules at each concentration were randomly generated in a restricted region of the cell along the Z direction. For the pure methanol, for example, 500 methanol molecules were put in −18.9 Å < Z < 18.9 Å. The range in Z was chosen so that the density of the restricted region coincides with that of the bulk liquid at each concentration x. Before the MD equilibration, steepest descent relaxation was conducted to eliminate unphysical overlap among the random molecular configurations. Then the MD equilibration was performed in the restricted region for 12.2 ps, during which the centers of mass of the constituent molecules were confined in that region and the velocities were scaled every 20 MD steps to fit them to the given temperature. This equilibration allows the interior of the slab system to relax with the constraint of the bulk density. Subsequently the restriction along the Z direction was removed, and equilibration was further carried out for more than 150 ps with the Berendsen thermostat. After we confirmed that the density profiles of the species along the Z direction are converged during the latter stage of equilibration, we performed the MD sampling of the SFG spectra and other properties of the liquid surface for 183 ps. We prepared 256 independent initial configurations at each mole fraction x, and performed the subsequent equilibration and sampling calculations using parallel computers. Accord-

Figure 1. Molecule-fixed coordinates a, b, and c of methanol. The red arrows illustrate the normal-mode coordinate q of the methyl symmetric stretching in the positive direction.

the C−O−H bond is on the ac plane. (i) The nonlinear susceptibility χ(2) IJK is represented by (2) χIJK =

Ns

∑ ∑ +Ii(l) +Jj(l) +Kk(l) βijk(l) l

i ,j,k

(3)

where l is the suffix of constituent methanol molecules, and + is the rotation matrix.34 (ii) The methyl group is assumed to be a C3v moiety with the principal c axis. Hence the molecular hyperpolarizability βijk at the CH3 symmetric stretching mode has two independent elements in the molecule-fixed coordinate, βaac = βbbc and βccc.35 (iii) The hyperpolarizability ratio R = βaac/ βccc can be experimentally evaluated by the Raman depolarization ratio. It was reported to be R = 1.7 for methanol.5,12 (iv) The rotation matrix + in eq 3 is determined with the three Euler angles, ϕ, θ, and ψ,34 while we focus on the tilt angle θ to characterize the surface orientation. Therefore, we need to average out the other two angles, ϕ and ψ, in eq 3. Using the above assumptions (i)−(iv), the nonlinear susceptibility tensor at the CH3 stretching vibration is represented in the following forms.5,36 (2) (2) χXXZ = χYYZ N ≈ s βccc {(1 + R )⟨cos θ ⟩ − (1 − R )⟨cos3 θ ⟩} 2 N (2) (2) χXZX = χZXX ≈ s βccc (1 − R ){⟨cos θ ⟩ − ⟨cos3 θ ⟩} 2 (2) χZZZ ≈ Nsβccc {R⟨cos θ ⟩ + (1 − R )⟨cos3 θ ⟩}

(4)

We notice that a ratio of arbitrary tensor elements in eq 4 does not include Ns and βccc, but is described with two parameters, R and ⟨cos θ⟩/⟨cos3 θ⟩. Since R is known with the Raman depolarization ratio, the only unknown parameter involved in the ratio is ⟨cos θ⟩/⟨cos3 θ⟩ = D. Therefore, it can be uniquely determined from the experimentally measured ratio χ(2) eff,PPP/ χ(2) eff,SSP with the help of eq 1. The average tilt angle Θ is estimated from the derived value of D by assuming a certain cos θ distribution. (v) If the distribution is given with a delta function at Θ, δ(cos θ − cos Θ), ⟨cos θ⟩ ≈ cos Θ and ⟨cos3 θ⟩ ≈ cos3 Θ hold, and thus Θ is estimated to cos Θ ≈ 1/D1/2. We could assume some other cos θ distribution instead. 9881


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The Journal of Physical Chemistry C ingly, the total statistical sampling amounts to 183 ps × 256 ≃ 46.8 ns at each mole fraction x. During the sampling simulation, the local density of the constituent species and their orientational structure near the surface were sampled at both sides of the slab. These results were represented as a function of a common depth coordinate Ẑ , where Ẑ = 0 corresponds to the Gibbs dividing surface of water and Ẑ > 0 (Ẑ < 0) refers to the vapor (liquid) side. The location of (Ẑ = 0) is determined to negate the surface excess of water, except at pure methanol. In the case of pure methanol, Ẑ = 0 is defined so as to set the surface excess of methanol to be zero. The surface tension was also evaluated by calculating the anisotropy of the pressure tensor,39 and the calculated results were compared to the experiment with varying mole fraction x. The frequency-dependent nonlinear susceptibility tensor χ(2),res was calculated by eq 2. The computational protocol of IJK χ(2) is given in refs 30−32 in detail, and we followed the same protocol in the present computation. To briefly describe the procedure, the two sides of the slab were treated as independent samples of the surface in the calculation of χ(2). The instantaneous values of AIJ(t) and MK(t) in eq 2 were calculated with the same CRK models of water and methanol mentioned above. As the CRK models are fully based on nonempirical quantum chemical calculations, these models are designed to reproduce the quantum chemical values of molecular polarizability and dipole at an arbitrary molecular conformation. The polarization interactions and local field effects were considered in a self-consistent manner to evaluate the instantaneous values of AIJ and MK. The performance of reproducing the SFG spectra has been thoroughly examined and corroborated in those studies.30−32 3.2. Surface Structure: Local Density and Orientation. Figure 2 displays the calculated density profile of methanol as a function of the depth coordinate Ẑ at various mole fractions x. The local density of methanol (green lines) ρ is apparently enhanced near the surface, and this enhancement becomes conspicuous in a low mole fraction x.20,21,40 Such a locally enhanced concentration is consistent with the concentration dependence of the surface tension γ. Figure 3 shows that the surface tension decreases with increasing x, and the calculated surface tension well reproduces the experimental result in a semiquantitative sense. The negative slope of the surface tension γ indicates a positive surface excess of methanol Γ according to the Gibbs equation on surface tension:41 Γ=−

a ∂γ x ∂γ ≈− kBT ∂a kBT ∂x

Figure 2. Density and orientational profiles of methanol/water mixtures as a function of the depth coordinate Ẑ . Mole fraction of methanol (a) x = 0.1, (b) x = 0.4, and (c) x = 0.8. The black lines denote the density of water ρ(water) (units g cm−3), green lines denote the density of methanol ρ(meoh) (g cm−3), red lines denote the average ⟨cos θ⟩ of the methyl tilt angle θ, and purple lines denote the product of ρ(meoh) and ⟨cos θ⟩ (g cm−3).

(5)

where a is the activity of methanol. The last form of eq 5 assumes the unit activity coefficient with respect to the mole fraction x. Figure 2 also shows the average ⟨cos θ⟩ of the CH3 orientation near the surface with the red lines. The ⟨cos θ⟩ profile shows a positive region near the surface, indicating that the hydrophobic CH3 groups point themselves to the vapor side of the surface. Such preferential orientation near the surface decays in the bulk liquid, and accordingly the average ⟨cos θ⟩ approaches zero in the sufficiently deep region, e.g., Ẑ ≲ −10 Å, due to randomized orientation (see below). Figure 2 also displays the profile of w(Ẑ ) = ρ(Ẑ )⟨cos θ(Ẑ )⟩, the product of local concentration ρ and the average ⟨cos θ⟩ of methanol, with the purple lines. These lines show a positive region near the surface about −5 Å < Ẑ < 5 Å. The w(Ẑ ) profile

Figure 3. Calculated surface tension of methanol/water mixtures as a function of the mole fraction of methanol x. Units: mN/m. The inset shows the experimental results.16 (Reprinted from ref 16. Copyright 2005 American Chemical Society.)

qualitatively indicates the anisotropic region detected by SFG spectroscopy. We could estimate the effective surface thickness associated with the SFG spectra with the w(Ẑ ) profile. The orientational distribution of the methyl group is further investigated in the following. Figure 4 shows the probability distribution of cos θ, P(cos θ), near the surface at various mole 9882


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note that the mole fraction of methanol at x = 0.8 is high enough that the SFG intensity of the methyl symmetric stretching decreases with increasing x, which was referred to the turnover behavior in section 1. Figure 5 shows that the upright CH3 orientational structure at the surface layer decays until Ẑ > −5 Å, and the orientation becomes randomized below the layer. This two-dimensional distribution does not indicate a distinctive second layer below the surface layer where the reverse CH3 orientation is preferred. This conclusion is highly relevant to discussion of the turnover behavior in section 4. Figure 4. Distribution functions P(cos θ) of the methyl tilt angle θ for various mole fractions of methanol x from x = 0.1 to x = 1.0. The coloring scheme for x is indicated in the legend.

4. COMPUTATION OF SFG SPECTRA Here we present the calculated effective nonlinear susceptibility χ(2) eff of different polarizations, and we discuss its implications to the orientational analysis of methyl group using the MD simulation. 4.1. Calculated SFG Spectra. The calculation of the effective nonlinear susceptibility χ(2) eff in eq 1 requires the following three factors: (i) the frequency-dependent nonlinear susceptibility χ(2), (ii) incident and reflection angles, and (iii) the Fresnel factor elements. (i) χ(2) was calculated by the MD simulation in section 3.1. (ii) The incident angles of visible and infrared light were taken from the work of Sung et al.:16 β1 = 49° and β2 = 60°. The visible wavelength was set to ω1/(2πc) = 532 nm, and the reflection angle of SFG β is determined by the law of momentum conservation. (iii) The Fresnel factor includes the dielectric properties of the media.5,7 The optical refractive indices of methanol/water mixtures at various mole fractions were taken from the literature.42 The infrared refractive indices of the mixtures were estimated by interpolating those of pure methanol and water.43,44 The refractive indices in the interface are estimated by the simple average of those of gas and liquid. Though the dielectric properties of the interface could be estimated in a more accurate manner,45 we confirmed that the following discussion on the polarization ratio and the concentration dependence is actually insensitive to the estimation of the dielectric properties of the interface. Figure 6 shows the calculated imaginary parts of χ(2) eff for both SSP and PPP polarizations with varying mole fraction x. To facilitate comparison with experimental SFG spectra, we took the square of the absolute value to yield the SFG intensity spectra. Figure 7 shows the calculated SFG spectra in the SSP polarization with varying mole fraction x. These calculated spectra well reproduce the experimentally reported spectra in the CH stretching region.14,16 They generally have two bands at about 2830 and 2950 cm−1. The former band is assigned to the CH3 symmetric stretching, and the latter is assigned to a Fermi resonance.5,8,14 We confirmed these assignments of SFG spectra in our previous MD study of methanol,32 though sometimes the latter band has been assigned to the CH3 asymmetric stretching after the IR spectrum of methanol.46,47 The MD study revealed that the phase (sign of the imaginary part of χ(2)) of the CH3 asymmetric stretching contribution is opposite to that of the Fermi resonance contribution and thus the two contributions overlap in a destructive manner, though the Fermi resonance contribution dominates the 2950 cm−1 band of the SFG spectrum.32 Figure 7 also indicates that the peak intensity at the former 2830 cm−1 band first increases and then slightly decreases with increasing x. Such turnover behavior is consistent with the previous experimental observations.12,13,16

fractions x. Each curve of the probability distribution P(cos θ) is normalized along the cos θ coordinate, i.e. 1

∫−1 P(cos θ) d(cos θ) 1

∫−1 d(cos θ)

=

1 2

1

∫−1 P(cos θ) d(cos θ) = 1 (6)

Accordingly, P(cos θ) = 1 corresponds to fully random orientation, and deviation from unity means that the orientation of the molecules is not completely randomized and has some anisotropy. The cos θ distributions in Figure 4 are averaged over the depth coordinate Ẑ with the weighting factor w(Ẑ ) (purple lines in Figure 2). These P(cos θ) profiles exhibit the following two features: (1) the upright CH3 orientation, cos θ = 1, is generally preferred over all the concentration range, while (2) this orientational preference becomes weaker and the orientational distribution is more randomized in higher mole fraction x. The average ⟨cos θ⟩MD derived from the MD results of P(cos θ) in Figure 4 ⟨cos θ ⟩MD =

1 2

1

∫−1 cos θ P(cos θ) d(cos θ)

(7)

varies from ⟨cos θ⟩MD = 0.52 for x = 0.1 to ⟨cos θ⟩MD = 0.28 for x = 1. (This variation of ⟨cos θ⟩MD(x) relative to that of the pure methanol is illustrated as a function of x in Figure 9b.) Figure 5 displays the two-dimensional distribution of methanol, P(cos θ, Ẑ ), at x = 0.8, where P(cos θ, Ẑ ) is normalized to unity in the isotropic, uniform bulk liquid. We

Figure 5. Two-dimensional density distribution P(cos θ, Ẑ ) of methanol at x = 0.8. The density is normalized with that in the isotropic uniform bulk solution. The contour lines range from P = 0.1 to 2.1 with 0.2 interval. 9883


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54 (2) Figure 6. Calculated imaginary parts of (a) χ(2) The coloring scheme for x follows that in eff,SSP and (b) χeff,PPP spectra for various mole fractions x. Figure 4.

characterized with ρ and the orientation with ⟨cos θ⟩ as a function of the depth Ẑ . Thus, ρ and ⟨cos θ⟩ at the surface are plotted in parts a and b, respectively, of Figure 9, with varying mole fraction x. In Figure 9a,b, ρ and ⟨cos θ⟩ at the surface were obtained by averaging their profiles over the depth Ẑ with the weighting factor w(Ẑ ). Figure 9a shows that the local density ρ quickly rises in low concentration x and then gradually increases and saturates in high concentration, indicating that the positive surface excess of methanol is pronounced in low concentration. On the other hand, Figure 9b shows that ⟨cos θ⟩ decreases with increasing concentration x. This behavior can be understood in terms of the randomized CH3 orientation in higher concentration, as we argued in section 3.2. Figure 9c displays ρ⟨cos θ⟩ with varying x, where each value was obtained by integrating the weighting factor itself, w(Ẑ ) = ρ⟨cos θ⟩, over Ẑ . Figure 9c shows the turnover behavior of ρ⟨cos θ⟩ quite analogous to that in Figure 8a. This agreement is understandable since ρ⟨cos θ⟩ is the product of the local density and orientation, and thus mimics the SFG amplitude. From the above argument, the turnover behavior is clearly understood with the two factors mentioned above. The initial rise in lower concentration x is due to the enhanced local density of methanol at the surface, while the decreased amplitude in higher x is attributed to the randomized orientation of methanol.

Figure 7. Calculated SFG intensity spectra in the SSP polarization for various mole fractions x. The coloring scheme for x follows that in Figure 4.

To clarify the turnover behavior, we measured the imaginary −1 amplitude of χ(2) in Figure 6a as a function of eff,SSP at 2830 cm the mole fraction x, and the results are plotted in Figure 8a. On the other hand, the imaginary amplitude of χ(2) eff,PPP is shown in (2) −1 Figure 6b, and the ratio of χ(2) is also eff,PPP to χeff,SSP at 2830 cm plotted in Figure 8b. The ratio is found to be almost invariant over the mole fraction x, which is also consistent with the experimental findings.5,16 In section 4.2 we elucidate the turnover behavior and the invariant ratio of the amplitudes in Figure 8 by analyzing the MD simulation. 4.2. Turnover Behavior: Effects of Density and Orientation. As we argued in section 1, the SFG amplitude generally consists of two factors, local density and orientational order. Thus, we elucidate the turnover behavior in Figure 8a in terms of the two factors with the help of MD simulation. We have discussed the local density and orientational order at the surface in section 3.2, where the local density is

5. DISCUSSION ON ORIENTATIONAL ANALYSIS The above interpretation about the turnover behavior is in accord with our intuitive understanding, though it appears at odds with the orientational analysis. As indicated by the experiment and also by our calculated results of Figure 8b, the ratio of PPP and SSP is nearly constant over the concentration

(2) (2) −1 Figure 8. (a) SSP amplitudes χ(2) as a function of the methanol mole fraction x. In (a) eff,SSP and (b) ratios of PPP to SSP (χeff,PPP/χeff,SSP) at 2830 cm the amplitudes are normalized with that of pure methanol (x = 1). Red symbols denote the results of MD calculation, and purple symbols denote the results of eq 4 with R = 1.7.

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The Journal of Physical Chemistry C βijk = −

1 ⎛ ∂αij ⎞⎛ ∂μk ⎞ 1 ⎜ ⎟⎜ ⎟ 2mω ⎝ ∂q ⎠⎝ ∂q ⎠ ω2 − ω + iγ

(8)

where αij and μk are the polarizability and dipole moment of the methanol molecule. q denotes the normal-mode coordinate for the CH3 symmetric stretching mode; ω, m, and γ are the angular frequency, reduced mass, and damping constant for the CH3 stretching mode. (Note that γ in eq 8 is different from that in eq 5.) Thus, the hyperpolarizability ratio R is given as

R=

βaac

=

βccc

∂αaa ∂q ∂αcc ∂q

(9)

which coincides with the ratio of Raman tensor elements. With the C3v assumption, βaac = βbbc and ∂αaa/∂q = ∂αbb/∂q should hold. This parameter R is often estimated by the Raman depolarization ratio. We calculated the derivative quantities in eq 8 with the B3LYP functional49,50 and the aug-cc-pVTZ basis set51,52 using Gaussian 09.53 The molecular geometry was optimized with this level of calculation, and the molecule-fixed coordinates are defined in Figure 1, where the c axis is along the O−C bond, and the ac plane is chosen as the Cs symmetry plane. The normal-mode coordinate q is obtained by the Hessian calculation and scaled to set the reduced mass to be unity, m = 1. The derivatives with respect to q were carried out numerically using five-point differentiation. The calculated values are summarized in Table 1. By diagonalizing the ∂αij/∂q matrix, we obtain the three principal components as 0.1666, 0.2152, and 0.0970 au. Table 1. Calculated Derivatives of (a) Polarizability and (b) Dipole of Methanol with Respect to the CH3 Symmetric Stretching Mode q at the B3LYP/aug-cc-pVTZ Level of Theorya

Figure 9. (a) Surface density of methanol ρ(meoh), (b) average ⟨cos θ⟩ of the tilt angle θ, and (c) the product ρ(meoh)⟨cos θ⟩ as a function of the methanol mole fraction x. These values are normalized with those of pure methanol (x = 1), and the colors of the lines correspond to those in Figure 2.

(a) ∂αij/∂q

x. This result implies that the orientational structure should be unchanged over the concentration. Thus, we need to examine the orientational analysis to resolve this problem in this section. In the orientational analysis mentioned in section 2.2, the nonlinear susceptibility ratios are expressed with two parameters, R and D = ⟨cos θ⟩/⟨cos3 θ⟩. We examine these parameters by electronic structure and MD calculations. In what follows, we find that strictly quantitative comparison between the experimental orientational analysis and theoretical computation is difficult, presumably because the theoretical calculations could not fully reproduce the experimental conditions of measurement and/or the experimental measurement itself may involve significant uncertainties. Nevertheless, the following discussion will provide valuable insight into the characteristics of the orientational analysis. 5.1. Anisotropy of Raman Tensor. In modeling molecular properties of the methyl group, the C3v assumption is often invoked,35,36 which greatly simplifies the modeling of the hyperpolarizability tensor. Here we discuss the hyperpolarizability tensor in a more fundamental treatment. The resonant term of the molecular hyperpolarizability βijk to the CH3 symmetric stretching mode is represented by48

(b) ∂μk/∂q

(i,j)

a

b

c

k

a b c

0.132 643 0 0.034 338

0 0.215 199 0

0.034 338 0 0.131 829

a b c

−0.001 697 0 −0.005 705

a The molecule-fixed coordinates (a, b, c) and the sign of the normalmode coordinate q are shown in Figure 1. q is normalized to unit reduced mass. Unit: atomic unit.

In the above calculated results of Table 1, first we find that the deviation from the C3v symmetry of the methyl group is evident in the difference between ∂αaa/∂q and ∂αbb/∂q or between the two principal components, 0.1666 and 0.2152. Thus, R in eq 9 is not well-defined by the quantum chemical calculation as it is based on the assumption of cylindrical symmetry. Nevertheless, we tried to estimate the hyperpolarizability ratio using the three principal components as R≃

(0.1666 + 0.2152)/2 = 1.95 0.0970

(10)

which is fairly consistent with R = 1.7 derived from the Raman depolarization ratio. However, the breakdown of the C3v assumption on the hyperpolarizability elements will have significant implications in section 5.3. 5.2. Orientational Parameter. The parameter D = ⟨cos θ⟩/⟨cos3 θ⟩ plays an important role in the orientational analysis 9885


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consistent with the MD results and experiment. The χ(2) model of eq 4 is valid in a semiquantitative sense, though the quantitative values have some discrepancy. The above argument provides clear evidence that the apparently constant polarization dependence of the SFG measurement does not necessarily mean that the orientational structure is unchanged. Experimental information derived from the polarization measurement is not sufficient to fully characterize the orientational structure at the surface. 5.3. Role of Cylindrical Angle. Molecular orientation is determined with three Euler angles, ϕ, θ, and ψ, while we have dealt with only the tilt angle, θ. Thus, we discuss the role of the other two angles in the polarization analysis of the SFG spectra. Here we employ the y-convention of the Euler angles,34 and consequently ϕ and θ are the two polar angle coordinates of the c axis in the space-fixed coordinate. ψ is the cylindrical angle of the molecule around the c axis, defined as a dihedral angle between the H1−O2−C3 plane of the methanol molecule and the plane consisting of the surface normal and the O2−C3 vector. (The atomic numbering is shown in Figure 1.) The definition of ψ is illustrated in the inset of Figure 11.

in eq 4. Here we derive this property directly by MD simulation from the orientational distribution of methanol. Figure 10

Figure 10. Orientational parameter D = ⟨cos θ⟩/⟨cos3 θ⟩ calculated by MD simulation as a function of x (solid line). Its analogue ⟨cos θ⟩/ ⟨cos θ⟩3 is also plotted with the dashed line. Note the different scales of the ordinates.

displays the calculated D = ⟨cos θ⟩/⟨cos3 θ⟩ at the surface with varying concentration x. This parameter D at the surface is derived by averaging over the depth coordinate Ẑ with the weighting factor w(Ẑ ) in the same way as in Figure 9. Figure 10 shows that the D parameter is almost constant at about 1.6 over the concentration x. This behavior is rather deceptive, since the ⟨cos θ⟩ value in Figure 9b or the distribution P(cos θ) in Figure 4 shows significant variation over the concentration x. If we further neglected the distribution of cos θ, D = 1.6 could be interpreted by cos Θ/ cos3 Θ = (cos Θ)−2 ≈ 1.6 and thus cos Θ ≈ 0.79 (or Θ ≈ 38°). On the other hand, we have discussed in section 3.2 that the MD results of Figure 4 yielded the average ⟨cos θ⟩MD ranging from ⟨cos θ⟩MD = 0.52 (or θMD = 59°) at x = 0.1 to ⟨cos θ⟩MD = 0.28 (or θMD = 74°) at x = 1.0 (see Figure 9b). This range of ⟨cos θ⟩MD is not consistent with the estimated angle Θ by polarization mentioned above. If we estimated the D parameter on the assumption of the δ function distribution, the D parameter should range from ⟨cos θ⟩MD/⟨cos θ⟩MD3 = 3.7 at x = 0.1 to ⟨cos θ⟩MD/⟨cos θ⟩MD3 = 12.8 at x = 1.0, as shown with the dashed line in Figure 10. The large deviation comes from the fact that the actual cos θ distributions are far from a δ function as shown in Figure 4. It is also apparent that the cos θ distributions in Figure 4 are not described with a Gaussian function. We also note that the D values reported by experimental measurements may include uncertainties. The conventional method based on the polarization dependence of SFG intensity yielded D < 1.8, while a polarization null angle method gave D ≃ 1.0.5 The reason for discrepancy is not clear at present, though the MD result is rather consistent with the former. The bottom line here is that the latter measurement also showed that the D value is invariant over the concentration x. Now we understand that the apparent invariance of the ratio of χ(2) eff,PPP and χ(2) eff,SSP in Figure 8b is attributed to the invariant D parameter over the concentration x. To examine the validity of (2) the χ(2) model in eq 4, we estimated the ratio of χ(2) eff,PPP/χeff,SSP 3 using eq 4 and the calculated values of D = ⟨cos θ⟩/⟨cos θ⟩ in Figure 10. To facilitate comparison with MD results, all other parameters including the incident angles and dielectric constants were set to be common with those in section 4.1. The ratio derived from eq 4 is also plotted in Figure 8b. The plotted result based on the χ(2) model of eq 4 also reproduced the qualitative invariance over the concentration x, which is

Figure 11. (a) Distribution function P(ψ) on the cylindrical angle ψ of surface methanol with the tilt angle θ = 38° fixed. The definition of ψ (2) is also illustrated in the panel. (b) Calculated ratio of χ(2) eff,PPP/χeff,SSP as a function of ψ.

Among these Euler angles, ϕ is the azimuthal angle around the space-fixed Z axis. Therefore, the distribution around ϕ should be uniform for symmetric reasons in a surface having the macroscopic C∞v symmetry. This C∞v condition is satisfied for most liquid surfaces, including those of methanol/water mixtures. However, the distribution around the cylindrical angle ψ is not necessarily uniform due to the symmetry requirement, unless the molecule itself has cylindrical symmetry around the c axis. Surely it is not the case for the methanol molecule. We recall that cylindrical averaging has been assumed to derive the χ(2) tensor model in eq 4, as mentioned in section 2.2. The effect of the cylindrical averaging is clearly seen in the (2) different ratios χ(2) eff,PPP/χeff,SSP in Figure 8b between the MD results (red line) and the χ(2) model of eq 4 (purple line). The difference is attributed to the approximations contained in the χ(2) model of eq 4, since these ratios were derived from the 9886


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interpret the SFG signals from microscopic surface structure. Once we find that the MD results of the SFG signals are reasonable, then we step further and examine the orientational analysis procedure which connects the calculated SFG polarization dependence to the microscopic molecular orientation. The second stage of the orientational analysis is almost free from the uncertainties about experimental conditions, since all the calculated information about the SFG polarization dependence and orientational structure are available by the MD simulation. The present work on the orientational analysis revealed a number of features about the surface structure of methanol/ water mixtures as well as some limitations of conventional orientational analysis. Some important findings are summarized below. 1. The CH3 symmetric stretching SFG signal shows a turnover with increasing concentration of methanol x. The initial rise is due to the enhanced local surface density of methanol in low x, while the decreased signal in high x reflects randomized orientation. The hypothesis of forming a second layer with reverse orientation of methanol was not supported by the MD calculation. 2. The intensity ratio of PPP and SSP is almost constant over the concentration x. This behavior should not be interpreted that the orientational structure is unchanged. The MD simulation showed that the average tilt angle changes from ⟨cos θ⟩MD = 0.52 (x = 0.1) to ⟨cos θ⟩MD = 0.28 (x = 1.0). 3. The tilt angle estimated from the polarization analysis (cos Θ ≈ 0.79) significantly deviates from the average orientation by MD simulation (0.52−0.28). This deviation is arguably due to the broad orientational distribution which is far from a δ function or a Gaussian. 4. The C3v assumption of the CH3 group is of limited accuracy in the polarization analysis of methanol. This is because deviation from the C3v symmetry is considerable both in the hyperpolarizability tensor and in the orientational distribution of methanol. The orientational analysis of CH3 group is of broad importance in relation to many organic molecules. For example, the orientation of alkyl chains is often discussed in terms of the orientation of the terminal CH3 group. We aim at further examining the orientational analysis of SFG spectroscopy in other molecules in combination with MD simulation.

common input parameters, as mentioned in section 5.2. Comparing the two ratios, it is apparent that the model (purple line) generally yields negatively smaller values than the MD result (red line). We can elucidate the discrepancy by considering the effect of the cylindrical angle ψ as follows. Figure 11a shows the MD result of the population distribution of surface methanol as a function of ψ at θ = 38°, where the depth distribution is averaged with the weighting factor w(Ẑ ). We note that ψ = 0° indicates a molecular orientation with the OH pointing downward to the bulk liquid while ψ = 180° indicates a molecular orientation with the OH pointing upward to the vapor, as illustrated in the inset of Figure 11a. Figure 11a indicates that the population distribution around ψ is not uniform, but the population of ψ ≃ 0° is larger than that of ψ ≃ 180°. This is quite reasonable since the OH bond of methanol tends to form a hydrogen bond toward the bulk liquid. We further investigated the ψ dependence of the ratio (2) χ(2) eff,PPP/χeff,SSP. For that purpose, we calculated the hypothetical ratio with an assumption of given fixed molecular orientation of θ and ψ using eq 3. Thus, we assumed the rotational matrix + in eq 3 with the fixed values of θ and ψ and with the uniform ϕ distribution. Using the rotational matrix + , the hyperpolarizability tensor elements βijk in the molecule-fixed coordinates (cf. Table 1) were transformed into the tensor components of χ(2) IJK in the space-fixed coordinates. These tensor elements were further converted to the ratio of the effective (2) (2) nonlinear susceptibilities χeff,PPP /χeff,SSP using eq 1. The obtained ratio predicts the hypothetical value if the surface methanol molecules pose an orientation of the assumed angles of θ and ψ. The results thus obtained are shown in Figure 11b as a function of ψ at a fixed θ = 38°. Figure 11b indicates that the ratio certainly depends on the cylindrical angle ψ. In fact, the ratio at about ψ ≃ 0° could be negatively larger than that at about ψ ≃ 180°. Therefore, if we simply averaged out the ψ dependence and did not consider the preferential distribution at ψ ≃ 0° than at ψ ≃ 180°, the χ(2) model of eq 4 would lead (2) to a negatively underestimated ratio of χ(2) eff,PPP/χeff,SSP. The cylindrical distribution around ψ plays a nonnegligible role in the polarization analysis of the CH3 group of methanol.

6. CONCLUDING REMARKS Molecular orientation at the surface is one of the fundamental properties to characterize the surface structure, and detecting the molecular orientation is often an important purpose of many SFG studies. SFG spectroscopy can provide information on the polarization dependence of the SFG signals, from which the microscopic orientation has been estimated. Though such analysis is routinely carried out by many experimental studies, its accuracy largely remains to be examined. Therefore, in the present work we thoroughly examined the conventional orientational analysis method in SFG spectroscopy with the help of MD simulation. Quantitative examination of the orientational analysis is in fact a challenging issue, mainly because the analysis depends on a number of experimental conditions and assumed parameters of molecules. Many of them often involve significant uncertainties. To minimize the uncertainties, we carried out the present work in two steps. First, we calculated the SFG signals and their polarization dependence by MD simulation and compared them with the experimental results. This stage allows us to examine the MD calculation of SFG signals and to

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Prof. Doseok Kim for helpful comments. This work was supported by Grants-in-Aid for Scientific Research (Nos. 21245002, 25104003, 26288003), MEXT, Japan. The numerical calculations were performed using the supercomputers at the Research Center for Computational Science, Okazaki, Japan.

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REFERENCES

(1) Jungwirth, P.; Finlayson-Pitts, B. J.; Tobias, D. J. Structure and Chemistry at Aqueous Interfaces. Chem. Rev. 2006, 106, 1137−1539.

9887


Article

The Journal of Physical Chemistry C (2) Miranda, P. B.; Shen, Y. R. Liquid Interfaces: A Study by SumFrequency Vibrational Spectroscopy. J. Phys. Chem. B 1999, 103, 3292−3307. (3) Richmond, G. L. Molecular Bonding and Interactions at Aqueous Surfaces as Probed by Vibrational Sum Frequency Spectroscopy. Chem. Rev. 2002, 102, 2693−2724. (4) Gopalakrishnan, S.; Liu, D.; Allen, H. C.; Kuo, M.; Shultz, M. J. Vibrational Spectroscopic Studies of Aqueous Interfaces: Salts, Acids, Bases, and Nanodrops. Chem. Rev. 2006, 106, 1155−1175. (5) Wang, H. F.; Gan, W.; Lu, R.; Rao, Y.; Wu, B. H. Quantitative Spectral and Oreintational Analysis in Surface Sum Frequency Generation Vibrational Spectroscopy (SFG-VS). Int. Rev. Phys. Chem. 2005, 24, 191−256. (6) Ishiyama, T.; Imamura, T.; Morita, A. Theoretical Studies of Structures and Vibrational Sum Frequency Generation Spectra at Aqueous Interfaces. Chem. Rev. 2014, 114, 8447−8470. (7) 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. (8) Gan, W.; Wu, B. H.; Zhang, Z.; Guo, Y.; Wang, H. F. Vibrational Spectra and Molecular Orientation with Experimental Configuration Analysis in Surface Sum Frequency Generation (SFG). J. Phys. Chem. C 2007, 111, 8716−8725. (9) Shultz, M. J. Sum Frequency Generation: An Introduction with Recent Developments and Current Issues,. Adv. Multi-Photon Processes Spectrosc. 2008, 18, 133−200. (10) Superfine, R.; Huang, J. Y.; Shen, Y. R. Nonlinear Optical Studies of the Pure Liquid/Vapor Interface: Vibrational Spectra and Polar Ordering. Phys. Rev. Lett. 1991, 66, 1066−1069. (11) Du, Q.; Superfine, R.; Freysz, E.; Shen, Y. R. Vibrational Spectroscopy of Water at the Vapor/Water Interface. Phys. Rev. Lett. 1993, 70, 2313−2316. (12) Wolfrum, K.; Graener, H.; Laubereau, A. Sum-Frequency Vibrational Spectroscopy at the Liquid-Air Interface of Methanol. Water Solutions. Chem. Phys. Lett. 1993, 213, 41−46. (13) Huang, J. Y.; Wu, M. H. Nonlinear Optical Studies of Binary Mixtures of Hydrogen Bonded Liquids. Phys. Rev. E 1994, 50, 3737− 3746. (14) Ma, G.; Allen, H. C. Surface Studies of Aqueous Methanol Solutions by Vibrational Broad Bandwidth Sum Frequency Generation Spectroscopy. J. Phys. Chem. B 2003, 107, 6343−6349. (15) Chen, H.; Gan, W.; Lu, R.; Guo, Y.; Wang, H. F. Determination of Structure and Energetics for Gibbs Surface Adsorption Layers of Binary Liquid Mixture 2. Methanol + Water. J. Phys. Chem. B 2005, 109, 8064−8075. (16) Sung, J.; Park, K.; Kim, D. Surfaces of Alcohol-Water Mixtures Studied by Sum-Frequency Generation Vibrational Spectroscopy. J. Phys. Chem. B 2005, 109, 18507−18514. (17) Jubb, A. M.; Hua, W.; Allen, H. C. Environmental Chemistry at Vapor/Water Interfaces: Insights from Vibrational Sum Frequency Generation Spectroscopy. Annu. Rev. Phys. Chem. 2012, 63, 107−130. (18) Vazquez, G.; Alvarez, E.; Navaza, J. M. Surface Tension of Alcohol + Water from 20 to 50°C. J. Chem. Eng. Data 1995, 40, 611− 614. (19) Paul, S.; Chandra, A. Hydrogen Bond Properties and Dynamics of Liquid-Vapor Interfaces of Aqueous Methanol Solutions. J. Chem. Theory Comput. 2005, 1, 1221−1231. (20) Pártay, L. B.; Jedlovszky, P.; Vincze, Á .; Horvai, G. Structure of the Liquid-Vapor Interface of Water-Methanol Mixtures as Seen from Monte Carlo Simulations. J. Phys. Chem. B 2005, 109, 20493−20503. (21) Pártay, L. B.; Jedlovszky, P.; Vincze, Á .; Horvai, G. Properties of Free Surface of Water-Methanol Mixtures. Analysis of the Truly Interfacial Molecular Layer in Computer Simulation. J. Phys. Chem. B 2008, 112, 5428−5438. (22) Matsumoto, M.; Takaoka, Y.; Kataoka, Y. Liquid-Vapor Interface of Water-Methanol Mixture. I. Computer Simulation. J. Chem. Phys. 1993, 98, 1464−1472.

(23) Morita, A. Molecular Dynamics Study of Mass Accommodation of Methanol at Liquid-Vapor Interfaces of Methanol/Water Binary Solutions of Various Concentrations. Chem. Phys. Lett. 2003, 375, 1−8. (24) Walker, D. S.; Hore, D. K.; Richmond, G. L. Understanding the Population, Coordination, and Orientation of Water Species Contributing to the Nonlinear Optical Spectroscopy of the VaporWater Interface through Molecular Dynamics Simulations. J. Phys. Chem. B 2006, 110, 20451−20459. (25) Perry, A.; Neipert, C.; Space, B.; Moore, P. B. Theoretical Modeling of Interface Specific Vibrational Spectroscopy: Methods and Applications to Aqueous Interfaces. Chem. Rev. 2006, 106, 1234−1258. (26) Morita, A.; Ishiyama, T. Recent Progress in Theoretical Analysis of Vibrational Sum Frequency Generation Spectroscopy. Phys. Chem. Chem. Phys. 2008, 10, 5801−5816. (27) Nagata, Y.; Mukamel, S. Vibrational Sum-Frequency Generation Spectroscopy at the Water/Lipid Interface: Molecular Dynamics Simulation Study. J. Am. Chem. Soc. 2010, 132, 6434−6442. (28) Skinner, J. L.; Pieniazek, P. A.; Gruenbaum, S. M. Vibrational Spectroscopy of Water at Interfaces. Acc. Chem. Res. 2012, 45, 93−100. (29) Sulpizi, M.; Salanne, M.; Sprik, M.; Gaigeot, M.-P. Vibrational Sum Frequency Generation Spectroscopy of the Water Liquid-Vapor Interface from Density Functional Theory-Based Molecular Dynamics Simulations. J. Phys. Chem. Lett. 2013, 4, 83−87. (30) Ishiyama, T.; Morita, A. Analysis of Anisotropic Local Field in Sum Frequency Generation Spectroscopy with the Charge Response Kernel Water Model. J. Chem. Phys. 2009, 131, 244714. (31) Ishiyama, T.; Sokolov, V. V.; Morita, A. Molecular Dynamics Simulation of Liquid Methanol. I. Molecular Modeling Including C-H Vibration and Fermi Resonance. J. Chem. Phys. 2011, 134, 024509. (32) Ishiyama, T.; Sokolov, V. V.; Morita, A. Molecular Dynamics Simulation of Liquid Methanol. II. Unified Assignments of Infrared, Raman, and Sum Frequency Generation Vibrational Spectra in Methyl C-H Stretching Region. J. Chem. Phys. 2011, 134, 024510. (33) Morita, A.; Hynes, J. T. A Theoretical Analysis of the Sum Frequency Generation Spectrum of the Water Surface II. TimeDependent Approach. J. Phys. Chem. B 2002, 106, 673−685. (34) Goldstein, H., Poole, C., Safko, J. Classical Mechanics, 3rd ed.; Pearson: San Francisco, 2002. (35) Hirose, C.; Akamatsu, N.; Domen, K. Formulas for the Analysis of Surface Sum-Frequency Generation Spectrum by CH Stretching Modes of Methyl and Methylene Groups. J. Chem. Phys. 1992, 96, 997−1004. (36) Hirose, C.; Yamamoto, H.; Akamatsu, N.; Domen, K. Orientation Analysis by Simulation of Vibrational Sum Frequency Generation Spectrum: CH Stretching Bands of the Methyl Group. J. Phys. Chem. 1993, 97, 10064−10069. (37) Morita, A.; Kato, S. Ab Initio Molecular Orbital Theory on Intramolecular Charge Polarization: Effect of Hydrogen Abstraction on the Charge Sensitivity of Aromatic and Nonaromatic Species. J. Am. Chem. Soc. 1997, 119, 4021−4032. (38) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. Molecular Dynamics with Coupling to an External Bath. J. Chem. Phys. 1984, 81, 3684−3690. (39) Allen, M. P., Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, 1987. (40) Patel, S.; Zhong, Y.; Bauer, B. A.; Davis, J. E. Interfacial Structure, Thermodynamics, and Electrostatics of Aqueous Methanol Solutions via Molecular Dynamics Simulations Using Charge Equilibration Models. J. Phys. Chem. B 2009, 113, 9241−9254. (41) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; Wiley: New York, 1997. (42) Kagaku Binran, 5th ed.; Maruzen: Tokyo, 2004. (43) Bertie, J. E.; Zhang, S. L.; Eysel, H. H.; Baluja, S.; Ahmed, M. K. Infrared Intensities of Liquids XI: Infrared Refractive Indices from 8000 to 2 cm−1, Absolute Integrated Intensities, and Dipole Moment Derivatives of Methanol at 25°C. Appl. Spectrosc. 1993, 47, 1100− 1114. 9888


Article

The Journal of Physical Chemistry C (44) Bertie, J. E.; Lan, Z. Infrared Intensities of Liquids XX: The Intensity of the OH Stretching Band of Liquid Water Revisited. Appl. Spectrosc. 1996, 50, 1047−1057. (45) Shiratori, K.; Morita, A. Molecular Theory on Dielectric Constant at Interfaces: A Molecular Dynamics Study of the Water/ Vapor Interface. J. Chem. Phys. 2011, 134, 234705. (46) Wang, C. Y.; Groenzin, H.; Shultz, M. J. Surface Characterization of Nanoscale TiO2 Film by Sum Frequency Generation using Methanol as a Molecular Probe. J. Phys. Chem. B 2004, 108, 265−272. (47) Yu, Y.; Wang, Y.; Lin, K.; Hu, N.; Zhou, X.; Liu, S. Complete Raman Spectral Assignment of Methanol in the C-H Stretching Region. J. Phys. Chem. A 2013, 117, 4377−4384. (48) Morita, A.; Hynes, J. T. A Theoretical Analysis of the Sum Frequency Generation Spectrum of the Water Surface. Chem. Phys. 2000, 258, 371−390. (49) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (50) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (51) Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (52) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96, 6796−6806. (53) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2010. (54) We note that the amplitudes of different concentrations are comparable to each other, though they are given in arbitrary units. All the variables were commonly treated in atomic units by our MD program. The same argument is also applied to Figure 7.

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