Surface Structure of Organic Carbonate Liquids Investigated by

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Surface Structure of Organic Carbonate Liquids Investigated by Molecular Dynamics Simulation and Sum Frequency Generation Spectroscopy Lin Wang, Qiling Peng, Shen Ye, and Akihiro Morita J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03935 • Publication Date (Web): 28 Jun 2016 Downloaded from http://pubs.acs.org on June 29, 2016

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The Journal of Physical Chemistry

Surface Structure of Organic Carbonate Liquids Investigated by Molecular Dynamics Simulation and Sum Frequency Generation Spectroscopy Lin Wang,†,‡ Qiling Peng,¶ Shen Ye,¶,‡ and Akihiro Morita∗,†,‡ Department of Chemistry, Graduate School of Science, Tohoku University, Aoba-ku, Sendai 980-8578, Japan, Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-8520, Japan, and Institute for Catalysis, Hokkaido University, Kita-ku, Sapporo 001-0021, Japan E-mail: [email protected] Phone: +81-22-795-7717.

Abstract The vapor-liquid interface structures of two typical organic carbonates, propylene carbonate (PC) and dimethyl carbonate (DMC), are investigated in collaboration of sum frequency generation (SFG) spectroscopy and molecular dynamics (MD) simulation. The present general molecular model for organic carbonates well reproduces various liquid properties, including density, heat of vaporization, infrared, Raman and SFG spectra. The MD simulation revealed contrasting interface structures between PC and DMC. The PC interface exhibits layered structure of oscillatory orientation, while the DMC interface is quite random. The structural feature of the PC interface is ∗

To whom correspondence should be addressed Tohoku University ‡ Kyoto University ¶ Hokkaido University †

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mainly attributed to dimer formation of PC molecules. We elucidated that the different surface structures are manifested in their Im[χ(2) ] SFG spectra in the C=O stretching band, showing opposite signs of bipolar peaks between the two liquids.

1

Introduction

In the modern battery technology, organic solvents such as propylene carbonate (PC) and dimethyl carbonate (DMC) are widely employed. Those solvents have an advantage over aqueous solvent due to a wide electrochemical window, and thus they are particularly preferred for the lithium ion battery. These organic carbonates have relatively high dielectric constant, ion mobility and stability in organic solvents. 1 The performance of the solvents is largely related to the interface of the electrodes, where the solvation/desolvation and transport of the ions take place in connection to the intercalation. 2–5 Therefore, microscopic structure of the interfaces between electrodes and electrolyte organic solutions has been investigated by various means, such as infrared (IR) absorption, 6,7 X-ray, 8,9 Raman scattering, 10,11 and theoretical calculations. 12,13 However, it is generally a challenging task to reveal detailed solvation structure at the electrode-electrolyte interfaces. The probe technique must have sufficient selectivity to the interfacial molecules which have to be distinguished from chemically identical molecules in the bulk solution. Many surface probe techniques developed mainly for solid surfaces are hard to be applied to detect the solution at the buried interfaces. Sum frequency generation (SFG) spectroscopy is a useful technique for these purposes. It is applicable to such buried interfaces as long as they are accessible by lights, and is capable of detecting the molecules at the interfaces with excellent interface selectivity. 14–16 Recently, several experimental SFG studies of electrode/electrolyte interface have been reported. 17–21 The analysis of SFG suggests that there are two adsorption modes of PC with opposite orientation on PC/LiCoO2 interface. 17 However, observed SFG spectra are often not amenable to intuitive interpretation, and reliable theoretical support is strongly desirable to fully ex2 ACS Paragon Plus Environment

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tract microscopic information from SFG spectra. Recently, computational methods for SFG analysis have been greatly developed 16,22–31 since the first report by Morita and Hynes. 32 These methods can predict SFG spectra of given interfaces using molecular dynamics (MD) simulation, and thereby allow for detailed interpretation of observed spectra in terms of microscopic interfacial structure. These analysis methods have been intensively applied to water and aqueous surfaces 16,22,23,26–28,30–32 besides some simple organic molecules 33,34 to date. The present paper reports our attempt to study PC and DMC surfaces, two typical organic solvents used in the lithium ion battery. As a first attempt toward understanding the electrode interfaces, here we deal with their vapor-liquid interfaces in collaboration of the SFG spectroscopy and MD simulation. In the MD calculation of SFG spectra, molecular modeling is of key importance. The SFG calculation using time correlation function 22,25 requires a flexible and polarizable model which is capable of providing instantaneous values of dipole moment vector and polarizability tensor. The instantaneous description of the dipole and polarizability is beyond conventional force fields of MD simulation. Therefore, we proposed a molecular modeling based on the Charge Response Kernel (CRK) theory 35,36 for these purposes. The CRK describes electronic polarization based on the interaction site model of molecules in a quite general manner. Since the calculation of CRK is non-empirical by ab initio molecular orbital or the density functional theory (DFT), it is readily applicable to a variety of molecules at their arbitrary conformations. So far we have applied the CRK modeling to some simple molecules, such as water, 37 sulfate ion, 38 methanol 39 and benzene. 34 In the present work we extend the modeling to the organic carbonate molecules. The PC molecule is a suitable example for the modeling because it has various moieties of organic molecules, such as carbonyl group, five-membered ring, methyl and methylene groups. The procedure of molecular modeling is straightforwardly applied to DMC. This modeling procedure will be useful to other organic interfaces such as self-assemble monolayer, polymer surfaces, and the electrode-liquid interfaces.



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The remainder of this paper is constructed as follows. Section 2 presents the MD procedures, while Sec. 3 the experimental conditions of spectroscopic measurements. Then we describe the analysis methods of the SFG spectra in Sec. 4. Section 5 is devoted to the results and discussion about the surface structure and SFG spectra of PC and DMC liquids. Brief summary and conclusion follow in Sec. 6.

2

Molecular Dynamics Simulation

2.1

Molecular Modeling

Here we explain the molecular modeling of PC as an example. The modeling procedure is transferable to DMC and other organic species.

2.1.1

Flexible Model

The structure of PC molecule is schematically shown in Figure 1. We note that PC has chiral isomers, (S)-PC and (R)-PC, though the parameters of molecular model are common. The PC molecule has Natom = 12 atoms and thus a total of 3Natom − 6 = 33 internal degrees of freedom. These are defined by the natural internal coordinates 40 (NICs). The NICs for the PC molecule, S1 ∼ S33 , are listed in Table 1. The intramolecular potential of a PC molecule uintra is given in the following function: √ 1 ∑∑ ki,j ∆Si ∆Sj + c33 cos( 3S33 ) + D(1 − e−α∆S1 )2 + unonbond = 2 i=1 j=1 32

uintra

32

(1)

In the right side of Eq. (1), the first term represents harmonic potential, where ∆Si denotes the displacement of Si from its equilibrium value, and ki,j is a symmetric matrix of the harmonic force constants. The potential along the large amplitude motion of C-CH3 rotation S33 is treated in the second term. The third term is a Morse potential to describe the anharmonic C=O stretching along S1 . The anharmonicity along S1 is important in re4 ACS Paragon Plus Environment

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producing the vibrational spectra for the C=O stretching, and accordingly the harmonic potential of the S1 coordinate in the first term is excluded, k1,1 = 0. The fourth term describes non-bond interactions inside the molecule between 1-4 and further sites. It consists of Lennard-Jones (LJ) and Coulomb potentials, where the intramolecular 1-4 interactions are scaled by 0.5. Their functional forms are common to those used for the intermolecular interactions in Sec. 2.1.3. The parameters in the intramolecular potential are obtained with quantum chemical calculations in the following procedure. The values of ki,j are determined so as to be consistent to the Hessian of the quantum chemical calculation, and we further set k1,1 = 0. c33 is obtained by least square fitting of the scanned potential surface along S33 by the quantum calculation. D and α are obtained by the second and third derivatives of the quantum chemical energy with respect to S1 . The quantum chemical calculations are performed by B3LYP 41,42 and aug-cc-pVTZ basis set 43 using Gaussian09 package. 44 The non-bond parameters are the same with intermolecular potential described in Sec. 2.1.3. All the parameters thus obtained are summarized in Supporting Information (SI). In the DMC case, its molecular structure is also schematically shown in Figure 1. The intramolecular potential function and the parameters were determined in the analogous manner, and the obtained parameters are also given in SI.

2.1.2

Polarizable Model

The present polarizable models of PC and DMC are constructed with the partial charges and CRK on the basis of interaction sites, which are placed at all atoms of the PC molecule. The partial charge at site a, Qa , is determined via the electrostatic potential (ESP) fitting, and the CRK is defined as Kab = (∂Qa /∂Vb ), where Vb is the electrostatic potential at site b. The ESP fitting procedure was performed by ChelpG method, 45 with employing the damping treatment 46 to avoid ill-defined behavior of ESP charges at buried sites. We optimized the damping parameter to be λ = 0.25, as described in SI.



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In the presented model, the conformational dependence of charge distribution is also taken into account. The partial charge and CRK of an isolated molecule, Q0a and Kab , are represented as a function of the NICs as:

Q0a (S)

=

Qeq a

+

eq Kab (S) = Kab +

NICs ∑ i=1 NICs ∑ i=1

∂Qa ∆Si ∂Si

(2)

∂Kab ∆Si ∂Si

(3)

eq where Qeq a and Kab are the partial charge and CRK at the equilibrium conformation {∆Si =

0}. The first-order Taylor expansion around the equilibrium conformation in Eqs. (2) and (3) is applied to i = 1 ∼ 32, while the large-amplitude motion along S33 is not taken into account in these equations. This treatment is valid in the subsequent discussion on the surface structure and SFG spectra. In condense phase, charge distribution is also influenced by intermolecular interactions. These effects are represented with the electrostatic potential Vb as:

Qa (S, V ) =

Q0a (S)

+

sites ∑

Kab (S)Vb

(4)

b

Equation (4) expresses the fluctuating charge distribution in response to the vibration and intermolecular electrostatic potential. eq All the ingredient parameters in Eqs. (2)-(3), Qeq a , Kab , (∂Qa /∂Si ) and (∂Kab /∂Si ), are

calculated with B3LYP/aug-cc-pVTZ level of theory using Gaussian09 package 44 with our extension to incorporate the CRK calculation. These parameters obtained as such are given in SI.

2.1.3

Intermolecular Interaction

The total potential energy Utotal of a condensed system is written as Utotal = Uintra +ULJ +UC , where Uintra is the sum of intramolecular potentials in Eq. (1) over all constituent molecules. 6 ACS Paragon Plus Environment

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ULJ is the sum of intermolecular site-site LJ potentials,

ULJ =

molecules sites ∑ ∑ i>j

[( 4εab

a,b

σab rai,bj

)12

( −

σab rai,bj

)6 ] (5)

where rai,bj is the distance between the site a of molecule i and the site b of molecule j. The LJ parameters of PC are taken from the OPLS force field. 47 The LJ parameters for distinct √ atom species are give by the Lorentz-Berthelot rule: σab = (σa + σb )/2, εab = εa εb . All the LJ parameters for PC and DMC are listed in Table 2. UC is the electrostatic interaction given as

UC =

1 ∑∑ 1 ∑∑ Kabi Vai Vbi Qai Vai − 2 i a 2 i a,b

(6)

The first term of the right-hand side of Eq. (6) indicates the intermolecular site-site Coulombic interactions, and the second term the electronic reorganization energy. The electrostatic potential at the site a of molecule i is written by

Vai =

∑ ∑ Qbj fai,bj rai,bj b

(7)

j(̸=i)

fai,bj is introduced in Eq. (7) as a damping factor of short-range Coulomb interaction. 39 In the polarizable MD simulation using the CRK model, Eq. (4) for each molecule i and Eq. (7) are solved self-consistently at every time step. We note in Eq. (7) that fai,bj should be unity in ordinary Coulomb interaction. The damping is often invoked in polarizable MD simulation to avoid polarization catastrophe. 48,49 and particularly necessary for hydrogen bonding liquids to make the polarizable MD trajectories stable. In the present work, however, it is set to unity as the MD simulation of PC or DMC liquid is stable without the short-range damping. We also confirmed that the binding energy of PC dimer is adequately described with the present model in Sec. 5.5.



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2.2

MD Conditions

MD simulations to investigate bulk liquid and vapor-liquid interface were carried out separately both for liquid PC and liquid DMC. The liquid PC consists of a racemic mixture of (S)-PC and (R)-PC. For bulk simulations, 256 PC or DMC molecules were placed in a cubic cell of 33 ˚ A × 33 ˚ A × 33 ˚ A. The simulations were carried out under isothermal-isobaric (N P T ) ensemble with three-dimensional periodic boundary conditions. Initial configuration was prepared by the Packmol package 50 and then equilibrated by MD simulation for 0.3 ns. Further MD simulation for 1.8 ns was carried out for production. For interface simulations, 256 PC or DMC molecules were placed in a rectangular cell of Lx × Ly × Lz = 33 ˚ A × 33 ˚ A × 165 ˚ A. The liquid forms a slab with two vapor-liquid interfaces normal to the z axis. The simulations were carried out under canonical (N V T ) ensemble with three-dimensional periodic boundary conditions. The MD simulation was performed for 0.3 ns of equilibration and for 0.6 ns of production. We prepared 48 independent initial configurations for interface simulations so that the total production time is 0.6 ns × 48 = 28.8 ns for each species. For all simulations, the temperature is set to 298.15 K using the Nosè-Hoover thermostat 51,52 with a coupling constant of 0.4 ps. The pressure in the bulk simulations is set to 1 bar using the Hoover barostat 53 with a coupling constant of 2 ps. The equations of motion are integrated using the velocity Verlet algorithm with a time step of 0.61 fs. The Ewald summation method 54,55 with a separation parameter of 0.242 ˚ A−1 is used for long range electrostatic interactions. The cutoff distance for the LJ and real-space Coulomb interactions is set to be 14 ˚ A.

3

Experimental Conditions

Materials: Special grade regents of PC and DMC were purchased from Kanto Chemical Co., Inc. (Tokyo, Japan). The chemicals were used without further purification.


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Infrared Measurements: A Fourier transform infrared (FTIR) spectrometer, JASCO 6100 with a DTGS detector was used in the study. The IR spectra were obtained using an ATR accessory with a ZnSe crystal (PR0450-S, JASCO). Typically, 8 interferograms were accumulated for one spectrum with a resolution of 4 cm−1 . All IR spectra shown in the study were after the ATR correction.

Raman Measurements: The Raman spectra were recorded using a Renishaw inVia microscope. A thin-layer liquid cell was used for the ex situ Raman measurement. The excitation light (Nd:YAG laser at 532 nm, 5% of intensity) was focused on the liquid surface through a 20× objective and the acquisition time was extended to 15 s. The spectral resolution of the Raman spectra in the study was ca. 1.0 cm−1 . Details were described elsewhere. 56

SFG Measurements: The details about our femtosecond broadband SFG system were described elsewhere. 57–59 Briefly, a Ti:sapphire oscillator (MaiTai, Spectra Physics) provides an 800 nm seed beam with pulse duration of ca. 100 fs. The seed beam is amplified by a 1 kHz, 2 W Ti:sapphire regenerative amplifier (Spitfire Pro, Spectra Physics) pumped by a Nd: YLF laser (EMPower, Spectra Physics) to produces 120 fs pulses at 800 nm. Half of the amplifier’s output is directed into an optical parametric amplifier (OPA) followed by difference frequency generation (DFG) to generate mid-IR pulses (TOPAS, Light Conversion Inc.). The IR pulses are tunable from 2.5 to 10 µm with a spectral width of ∼ 200 cm−1 . The other half of the amplifier’s output is directed into a homemade pulse shaper to generate picosecond pulse at 800 nm (an FWHM of ∼ 10 cm−1 ) as the visible beam. The SFG signal was recorded by a CCD detector (DU420-BV, Andor Technology) attached to a spectrograph (MS3504, Solar-TII). A specially designed cell used for the SFG measurement on the liquid/air interface. The cell was covered by a thin CaF2 window plate. To avoid the influences of the evaporated molecules (especially for DMC, which has a lower boiling point) on the window surface, a sheet heater of silicone rubber (SBH2113, Hakko Electric Co., Japan) was used to heat the 9 ACS Paragon Plus Environment


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window plate to a temperature of ca. 40◦ C The SFG spectra were recorded by spatially and temporally overlapping the IR and visible pulses on the surface of PC or DMC liquid under the ssp (i.e., s-SFG, s-visible, p-IR) and sps (s-SFG, p-visible, s-IR) polarization combinations. The angles of incidence of IR and visible beams were 50◦ and 70◦ , respectively. All the SFG spectra of the liquid surface were normalized by a SFG spectrum of a GaAs. Typically, SFG signals of ca. 0.3 photon/s were obtained from the liquid/air interface. SFG spectra were necessary to integrate for longer period to improve the S/N ratio. In the present study, the SFG spectra with integration period of 60 min were used. All the measurements were carried out at room temperature (23◦ C).

4 4.1

Analysis of SFG Spectra χ(2) formula

The vibrational SFG spectroscopy is governed by the second-order susceptibility χ(2) , which consists of vibrational resonant term χ(2),res and nonresonant term χ(2),nonres : χ(2) = χ(2),res + χ(2),nonres . The resonant term is calculated with the time correlation function between the polarizability A and the dipole moment M of the entire system, 25

χ(2),res pqr

iω = kB T

∫

∞

dt⟨Apq (t)Mr (0)⟩eiωt

(8)

0

where the suffixes p, q, r denote the space-fixed coordinates x ∼ z, ω the infrared frequency, kB the Boltzmann constant, and T the temperature. The nonresonant term χ(2),nonres is real and constant over the vibrational frequency range in electronically off-resonant conditions. We assumed χ(2),nonres to be consistent to the experimental spectra in the present SFG calculations. The lineshapes of the SFG intensity spectra of ssp and sps polarizations are (2)

(2)

SFG SFG ∝ ∝ |χyyz |2 and Isps given with the square of pertinent χpqr tensor elements, i.e. Issp


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(2)

|χyzy |2 . We also deal with the imaginary part of nonlinear susceptibility, Im[χ(2) ], which carries phase information in relation to the molecular orientation. 32 Note that the imaginary part is determined by its resonant term, Im[χ(2) ] = Im[χ(2),res ], since the nonresonant term is real. Decomposition of χ(2) : Equation (8) allows for various decomposition analyses of SFG spectra. The polarizability A and the dipole moment M of the entire system in Eq. (8) are formally decomposed into those of the constituent molecules, 22,60

Apq =

molecules ∑

αpq,j ,

j

Mr =

molecules ∑

µr,j

(9)

j

where αpq,j and µr,j denote the polarizability and dipole moment of the molecule j, respectively, which include the local field effect. 37 Eq. (9) can be decomposed along the depth coordinate zˆ to investigate the surface sensitivity of SFG. The depth coordinate zˆ near the surface is defined so that zˆ = 0 refers to the Gibbs dividing surface, and zˆ > 0 (ˆ z < 0) indicates the vapor (liquid) side. Then we assume a certain threshold z thres , and evaluate A and M in spatially restricted region z thres < zˆ as Apq {z thres < zˆ} =

∑

αpq,j ,

Mr {z thres < zˆ} =

j∈R

∑

µr,j

(10)

j∈R

where the summation is taken over the molecules j whose centers of mass are located in the vapor side of the threshold. Using the restricted values of A and M in Eq. (10), we accordingly evaluate χ(2),res {z thres < zˆ} by Eq. (8). By gradually expanding the surface region with lowering the threshold z thres , we obtain the convergence behavior of χ(2),res . The convergence behavior reveals the SFG active region of interface in its depth profile. (2)

Another decomposition of χpqr in Eq. (8) into self and cross parts is possible in the



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following manner. Substituting Eq. (9) into (8), we obtain

χ(2),res pqr

iω = kB T

∫

∞

dt 0

molecules ∑

⟨αpq,j (t)µr,k (0)⟩ eiωt

j,k

∑ iω ∫ ∞ ∑ ∑ iω ∫ ∞ iωt = dt⟨αpq,j (t)µr,j (0)⟩e + dt⟨αpq,j (t)µr,k (0)⟩eiωt k T k T B B 0 0 j j̸=k =χ(2),self + χ(2),cross pqr pqr (2),self

where χpqr

(11) (2),cross

refers to the self correlations, whereas χpqr

to the correlations between

different molecules. 60,61 The self part is represented by a sum of molecular contributions,

= χ(2),self pqr

∑

res βpqr (j)

(12)

j

res where βpqr (j) is assigned as the vibrationally resonant component of the molecular hyperpo-

larizability, res βpqr (j)

4.2

iω = kB T

∫

∞

dt⟨αpq,j (t)µr,j (0)⟩eiωt

(13)

0

Relation to C=O orientation

Next we discuss the C=O stretching band of PC and DMC molecules to investigate their orientation. Suppose the time correlation function in Eq. (13) is driven by the damped oscillator of C=O stretching vibration, (

)( ) ∂αpq ∂µr ⟨αpq,j (t)µr,j (0)⟩ ≈ ⟨Q(t)Q(0)⟩ ∂Q ∂Q ( )( ) ∂αpq ∂µr kB T −Γt e cos ωCO t = 2 ∂Q ∂Q 2mωCO

(14)

where Q is the normal mode of C=O stretching, ωCO the harmonic frequency of Q, m the res (j) of Eq. (13) reduced mass for the oscillator, and Γ the damping factor. Using Eq. (14), βpqr


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is converted to 25 res βpqr (j)

1 ≈ 2mωCO

(

∂αpq ∂Q

)(

∂µr ∂Q

)

1 ωCO − ω − iΓ

(15)

Equation (15) is often used for qualitative interpretation of SFG spectra. Then we discuss (∂αpq /∂Q) and (∂µr /∂Q) in the space-fixed coordinate in relation to molecular orientation. Transition dipole and polarizability: The molecular orientation is described with relation of the space-fixed coordinates (x, y, z) to the molecule-fixed ones (ξ, η, ζ). Here we give the molecule-fixed coordinates (ξ, η, ζ) of PC and DMC as illustrated in Figure 1. We define the ζ axis along the carbonyl C1 =O1 bond, and introduce an auxiliary η ′ axis normal to the carbonate O2 -C1 -O3 plane. We note that the η ′ axis may not be orthogonal to ζ when the C=O bond is deformed in out-of-plane manner. In case that the η ′ is not orthogonal to ζ, the η axis is defined by orthogonalizing η ′ to the ζ axis with the Gram-Schmidt method. The direction of η is defined so that the non-planar C4 of (S)-PC is in the positive side and that of (R)-PC in negative. The remaining ξ axis is given to be orthogonal to the other two. Table 3 summarizes the calculated values of (∂αpq /∂Q) and (∂µr /∂Q) of (R)-PC and DMC molecules at the B3LYP/aug-cc-pVTZ level of theory in their molecule-fixed coordinates (ξ, η, ζ). It is known that the sign of Im[χyyz ], which corresponds to the ssp-polarized SFG spectra, is particularly informative about polar orientation of molecules, since it involves the transition dipole along the surface normal (∂µz /∂Q). As shown in each case of PC and DMC in Table 3, the transition dipole is dominated by the ζ component of the molecule-fixed coordinate, and the transition polarizability is dominated by the diagonal, isotropic components. Therefore, the sign of Im[βyyz ] is mainly determined by the orientation of the C=O bond. We note that the (∂µζ /∂Q) component is negative in Table 3, implying that the upward C=O bonds have negative Im[χyyz ] and the downward C=O bonds have positive Im[χyyz ].



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Up-down analysis: In the analysis of C=O orientation, one can readily decompose χ(2),self of Eq. (11) into the contributions of molecules having C=O bonds pointing upward and those pointing downward,

χ(2),self pqr

∑ iω ∫ ∞ dt⟨αpq,j (t)µr,j (0)⟩eiωt = k T B 0 j ∫ Tshort up down ∑ ∑ iω ∫ Tshort iω iωt ≈ dt⟨αpq,j (t)µr,j (0)⟩e + dt⟨αpq,j (t)µr,j (0)⟩eiωt k T k T B B 0 0 j j =χ(2),up + χ(2),down pqr pqr

(16)

The criterion of upward/downward orientation is given with the tilt angle of C=O bond from the surface normal θCO ; the molecules with 0◦ < θCO < 90◦ are assigned to upward (pointing to the vapor phase) and those with 90◦ < θCO < 180◦ to downward (pointing to the liquid phase). The molecular orientation is determined at t = 0 of the time correlation function. In the practical calculation of Eq. (16), the upper bound of the time correlation function is set to Tshort = 3.1 ps. This value is chosen so as to be shorter than the calculated rotational relaxation times of 5.83 ps and 3.51 ps for liquid PC and DMC, respectively, while it is long enough to decay the tail of the time correlation. Therefore, the molecular orientation is nearly invariant within this period and thus fairly well defined. These contributions are (2),up

labeled by χpqr

5 5.1

(2),down

and χpqr

, and will be utilized in the analysis of Sec. 5.4.

Results and Discussion Thermodynamic Properties

In order to evaluate the force fields of PC and DMC, we calculated several thermodynamic properties of these liquids, such as density, heat of vaporization, and surface tension by MD simulation. The calculated results are summarized in Table 4 in comparison to experimental data. 14 ACS Paragon Plus Environment

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The heat of vaporization ∆Hv was calculated from the bulk MD simulation with the following equation: 47

⟨ ∆Hv = −

ULJ + UC N

⟩ + kB T

(17)

where ULJ + UC is defined in Eqs. (5) and (6), and N is the number of molecules. The first term indicates the intermolecular potential per molecule in liquid phase, and the second term the pV contribution. The surface tension γ was calculated from the slab MD simulation by the difference of normal and tangential pressure tensors: 62 [ ] 1 Lz ⟨Pzz ⟩ − (⟨Pxx ⟩ + ⟨Pyy ⟩) γ= 2 2

(18)

where Pxx , Pyy , and Pzz is the xx, yy, and zz components of the pressure tensor, respectively. The calculation of the pressure tensor does not take account of the effect of long-range Lennard-Jones tail beyond the cutoff. The estimation of the long-range LJ correction 63,64 was performed in SI. We also note in passing that the surface tension is rather insensitive to the details of the short-range electrostatic interaction. 65 As shown in Table 4, the calculated results show reasonable agreement with experimental values. 66–70 We also find that the calculated results of density, heat of vaporization and surface tension are slightly overestimated for both PC and DMC. The surface tension may be more overestimated by considering the long-range LJ correction, as the contribution is roughly estimated to 3 ∼ 4 mN/m in the SI. Such slight but systematic deviation is arguably due to the LJ parameters we employed. The general OPLS parameters have been optimized for non-polarizable force field, and thus may tend to overestimate intermolecular interaction in combination of our polarizable model. Yet the present parameters are useful enough to elucidate the different interface structures between PC and DMC, as will be discussed below. We are planning to systematically reoptimize the general LJ parameters to the polarizable CRK model.



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5.2

Infrared and Raman Spectra

Next we examine the vibrational infrared (IR) and Raman spectra of these liquids by comparing the experimental and computational results. The experimental conditions of measurement are summarized in Sec. 3. The calculation of IR and Raman spectra was performed by the MD simulation of bulk liquids in Sec. 2.2 using the time correlation function formalism. 39,71 Figure 2 shows the IR and total Raman spectra of liquid PC, and Figure 3 shows those of liquid DMC. These figures also show the results of harmonic analysis of isolated molecules by B3LYP/aug-cc-pVTZ. While the calculated spectra reproduce overall spectral features, we notice large deviations particularly below 1600 cm−1 , as we further discuss below. In the present paper, we mainly deal with the analysis of the C=O stretching band in relation to the surface structure. The red shift of C=O stretching mode is properly described in either system by the anharmonic potential in Eq. (1). The peak position of the experimental IR spectra of PC shifts from 1860 cm−1 in the gas phase 72 to 1780 cm−1 in liquid (by 80 cm−1 ), while that of the MD calculation shifts from 1884 cm−1 to 1798 cm−1 (86 cm−1 ). In DMC, the experimental IR spectra show a shift from 1782 cm−1 in the gas phase 72 to 1749 cm−1 in liquid (33 cm−1 ), while the MD simulation from 1784 cm−1 to 1742 cm−1 (42 cm−1 ). The relative intensity of the C=O stretching band to the C-H stretching is reasonably well reproduced in both IR and Raman spectra. Comparing the calculation with the experimental spectra of both PC and DMC liquids, we notice that the calculated Raman spectra particularly overestimate the band intensities in 1000 ∼ 1600 cm−1 . We found that the overestimated Raman bands are attributed to the C-H deformation modes in methyl and methylene groups. Further refinement of the modeling of deformation will be necessary when we deal with these modes.


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5.3

Molecular Orientation at Interface

Density profiles: The calculated density profiles at vapor-liquid interface of liquid PC and DMC are shown in Figures 4 (a) and (b), respectively. The density profiles along the depth coordinate zˆ were least-square fitted with the following formula, 73 [ ( )] ρ0 zˆ ρ(ˆ z) = 1 − tanh 2 0.455 z10-90

(19)

where ρ0 indicates the bulk density of the liquid, and z10-90 the 10-90 thickness of the surface. The optimized parameters in Eq. (19) are ρ0 = 1.252 g/cm3 , z10-90 = 3.42 ˚ A for PC, and ρ0 = 1.077 g/cm3 , z10-90 = 5.15 ˚ A for DMC. Density and orientation: The orientation of PC and DMC molecules at interface is represented with the tilt angle θCO of the C=O bond, as illustrated in Figures 4. We calculated the ensemble average of ρ⟨cos θCO ⟩ as a function of zˆ, ∫ ρ⟨cos θCO ⟩(ˆ z) =

1 −1

d(cos θCO ) cos θCO ρ(cos θCO , zˆ)

(20)

where ρ(cos θCO , zˆ) is the density distribution as a function of cos θCO and zˆ. The results of ρ⟨cos θCO ⟩(ˆ z ) are plotted in Figures 4 (c) and (d) for PC and DMC, respectively. In either panel, ρ⟨cos θCO ⟩(ˆ z ) → 0 is realized in sufficiently deep region of liquid (e.g. zˆ < −10 ˚ A), implying random orientation in the bulk liquid. In the PC liquid (Panel (c)), ρ⟨cos θCO ⟩(ˆ z) < 0 is observed at the topmost layer of the surface, −5 ˚ A < zˆ, indicating C=O bonds slightly pointing to the bulk. It is interesting to note in the PC liquid that the sign of ρ⟨cos θCO ⟩(ˆ z) oscillates in the surface region (e.g. −10 ˚ A < zˆ) until it decays to zero in the interior of the bulk. On the other hand, Panel (d) shows that ρ⟨cos θCO ⟩(ˆ z ) is close to zero over the zˆ coordinate in the DMC liquid, even at the topmost layer of the surface. No oscillation is observed in the DMC surface, in contrast to the PC surface.



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Orientational conformation: Molecular orientation at interface is uniquely characterized by θCO and θnor , where θnor is the angle between the surface normal and a unit vector along the η axis, as illustrated in Figure 5. The direction of the unit vector for PC is taken to be parallel to the η axis in (S)-PC and anti-parallel in (R)-PC, so that the out-of-plane methyl (C4 ) group is always in the positive side of the unit vector. In the DMC molecule, no distinction is made about the direction of the unit vector. The molecular orientation at interface is further investigated by probability distribution of these orientational angles. The probability distribution of cos θ = cos θCO in a segmented surface layer between zˆ = z1 and z2 is defined by ∫ P (cos θ, {z1 < zˆ < z2 }) =

1 2

∫

z2

dˆ z ρ(cos θ, zˆ) ∫ z2 d(cos θ) dˆ z ρ(cos θ, zˆ) z1

1

−1

(21)

z1

We calculated the probability distributions in segmented layers such as the first layer (−5 ˚ A< zˆ), second layer (−10 ˚ A < zˆ < −5 ˚ A), and the bulk (ˆ z < −10 ˚ A), and display the results in Figure 5 (a) for PC and in Figure 5 (b) for DMC. We also calculate the probability distributions along cos θ = cos θnor in the segmented layers using Eq. (21) in the same manner. The results of P (cos θnor , {z1 < zˆ < z2 }) are displayed in Figures 5 (c) and (d) for PC and DMC, respectively. In both liquids, the probability distributions in the bulk layer are flat over cos θCO and cos θnor , indicative of random orientation in the bulk. In the PC liquid (Panels (a) and (c)), the deviation from the uniform distribution is conspicuous in the first layer. In Panel (a), the probability in the first layer, P (cos θCO , {−5 ˚ A < zˆ}), is larger than unity at cos θCO ≈ 0 while smaller than unity at cos θCO ≈ −1 or 1, which means that the C=O bonds of PC tend to lie in parallel to the interface. The location of maximum in this curve somewhat shifts toward the negative side of cos θCO , indicating that the C=O bonds of PC slightly point toward the bulk. This feature is consistent to the negative ρ⟨cos θCO ⟩(ˆ z ) in the first


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layer (−5 ˚ A < zˆ) of PC liquid in Figure 4 (c), as we argued in the preceding subsection. In the cos θnor distribution of Figure 5 (c), the first layer of PC liquid preferentially takes the orientation of cos θnor ≈ 1. This feature indicates that the PC molecules in the first layer tend to orient their methyl groups toward the vapor, as illustrated in the top left panel of Figure 5. The preference of cos θnor ≈ 1 over cos θnor ≈ −1 essentially originates from the fact that the out-of-plane methyl group of a PC molecule breaks the reflection symmetry with respect to the pseudo-plane of the five-membered ring. Briefly speaking, the preferential orientation of PC molecule at the first layer of the surface is characterized with slightly downward C=O (cos θCO < 0 in Panel (a)) and upright orientation of the methyl group (cos θnor ≈ 1 in Panel (c)). On the other hand, the second layer of PC liquid shows nearly uniform distribution over both the cos θCO (Panel (a)) and cos θnor (Panel (c)). In the DMC liquid (Panels (b) and (d)), even the first layer shows nearly uniform distribution over both coordinates, indicating that the orientation of DMC molecules is almost random even in the first layer. This result is consistent to the previous argument of Figure 4 (d) that ρ⟨cos θCO ⟩(ˆ z ) is close to zero over the zˆ coordinate. As such, the above discussion clearly illustrates the quite different interfacial structure of PC and DMC liquids. In the following we examine the difference in relation to the SFG spectra, and discuss the mechanism of the difference.

5.4

SFG Spectra

Experiment and simulation: Figure 6 shows the experimental and calculated SFG spectra for liquid PC and DMC. The SFG spectra for PC and DMC in different polarization combinations were obtained under the exactly same experimental conditions. Although the SFG signals in the sps polarized spectra were much weaker in comparison with those in the ssp polarized spectra, one was still able to distinguish them from the original SFG spectra before the normalization (see Figure S2 in SI). The calculated spectra of both ssp and sps polarizations reproduce the experimental spectra quite well, including their lineshapes, peak 19 ACS Paragon Plus Environment


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frequencies, and relative intensities between ssp and sps. The peak frequencies of the calculated spectra of PC surface are 1818 cm−1 for ssp and 1825 cm−1 for sps, and those of DMC are 1745 cm−1 for ssp and 1758 cm−1 for sps. These frequencies are in good agreement with the experimental ones. In both PC and DMC, the sps spectra have significantly smaller intensity than the ssp and the sps bands are located in the higher frequency side. These results also validate the performance of our model to analyze the SFG spectra. We further analyzed the sps band in SI, and found that the apparent blue shift of the sps band is due to the interference with the nonresonant background, indicating that the ssp and sps bands originate from the same C=O stretching vibration.

(2)

(2)

Im[χyyz ] spectra: We further investigate the Im[χyyz ] spectra of PC and DMC. (The (2)

(2)

results of Im[χyzy ] are given in SI) Figure 7 shows the calculated Im[χyyz ] spectra of PC and DMC liquids, including their convergence behavior with expanding interfacial region (2) ˚) show in Eq. (10). In both liquids, the converged Im[χyyz ] spectra (blue lines, zˆ > −15 A

bipolar peaks in the C=O stretching region. It is remarkable, however, that the band shapes (2)

of the bipolar peaks are contrasting between PC and DMC; in Panel (a) the Im[χyyz ] band of PC consists of negative low-frequency and positive high-frequency components, while (b) that of DMC vice versa. This qualitative difference in the band shapes implies significant difference in the interfacial structure between PC and DMC, as elucidated below. The convergence behavior with expanding interface region is also quite distinct in Figure 7. The PC liquid shows a nearly converged amplitude with the interface region of zˆ > −10 ˚ A. On the other hand, DMC exhibits faster convergence. Even the first layer (2) (ˆ z > −5 ˚ A) is enough to reach the converged Im[χyyz ] spectrum. It is also remarkable that

the convergence behavior of PC is more complicated than that of DMC. In particular, the low-frequency component of PC has a positive sign at zˆ > −5 ˚ A while it becomes negative at zˆ > −10 ˚ A to reach the convergence. In the following we elucidate these remarkable differences between PC and DMC. 20 ACS Paragon Plus Environment

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(2)

Decomposition Analysis of Im[χyyz ]: Before analyzing the differences, we examine the ] [ (2) self and cross parts in Im χyyz of these liquids by Eq. (11). Figure 8 displays the self [ ] [ ] (2),self (2) ) and total (Im χyyz ) spectra of PC and DMC interfaces. The difference be(Im χyzz [ ] [ ] (2),cross (2) (2),self tween the two lines is attributed to the cross part, Im χyyz = Im χyyz − χyyz . The [ ] (2),self results indicate that self-part Im χyyz spectra of PC and DMC reproduce the bipolar [ ] (2) feature of the respective Im χyyz spectra and the reversed signs between PC and DMC correctly. Therefore, these mechanisms should be explained qualitatively through analyzing the self-part spectra, using the decompositions discussed in Sec. 4. First we discuss the DMC liquid, which apparently exhibits faster convergence. The fact [ ] (2) (2) (2) that the Im[χyyz ] spectrum of DMC is determined in the first layer (Im[χyyz ] ≈ Im χyyz {−5 ˚ A < zˆ} ) in Figure 7 is in full accord with the previous discussion in Sec. 5.3 that the orientation of DMC molecules is well randomized near the interface. Therefore, we focus our analysis on the first layer (−5 ˚ A < zˆ) of the DMC liquid, and perform the decomposition into up(2),up

ward/downward C=O by Eq. (16). Figure 9 shows the decomposed results into χyyz (2),down

χyyz

and

(2),up

for the first layer of DMC liquid. The results clearly show that the Im[χyyz ] com(2),down

ponent is negative while Im[χyyz

(2)

] is positive. These relation between the sign of Im[χyyz ]

and the orientation of C=O is readily understandable from the calculated molecular hyperpolarizability tensors in Table 3. However, the peak frequencies of the two components are apparently different; the peak of Im[χyyz ] is located at 1762 cm−1 while that of Im[χyyz

(2),down

(2),up

]

at 1748 cm−1 . The downward C=O bond shows a lower frequency than the upward C=O, since the downward vibration tends to be more influenced by solvation effect than the upward one. As illustrated in Figure 9, the upward C=O bond at the topmost surface have a vibration frequency close to that in the gas phase at 1785 cm−1 , 72 whereas the downward C=O bond has a frequency close to that in the liquid phase at 1742 cm−1 (Figure 3). There(2),up

fore, the summation of χyyz

(2),down

and χyyz

leads to the bipolar band in Figure 9, which

consists of negative high-frequency and positive low-frequency components. Although the orientation of DMC molecules is nearly random at the interface, the anisotropic environment



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of solvation causes the bipolar shape in the SFG spectrum. Next, PC interface is analyzed. As we discussed the convergence behavior in Figure 7, (2)

the Im[χyyz ] amplitude of PC does not converge in the topmost layer, but the contribution of the second layer is significant. Thus we separate the contributions of the first layer L1 = {−5 ˚ A < zˆ} and the second layer L2 = {−10 ˚ A < zˆ < −5 ˚ A}, and calculated the self-part (2),self

Im[χyyz

(2),L1

] spectrum of each layer. Figure 10 displays the self-part spectra of the two layers, (2),L2

(2),L1

Im[χyyz ] and Im[χyyz ], and the total system. In the first layer, the Im[χyyz ] spectrum shows positive amplitude over the C=O stretching band with a peak at 1825 cm−1 . The positive amplitude is consistent to the net downward C=O orientation in the first layer of (2),L2

PC, where ρ⟨cos θCO ⟩ < 0 is observed in Figure 4 (c). On the other hand, the Imχyyz

spectrum of the second layer shows a negative peak at 1790 cm−1 . This is again consistent to the ρ⟨cos θCO ⟩ > 0 for the second layer in Figure 4 (c), indicating net upward C=O (2),L1

(2),L2

orientation. The difference in the peak frequencies between Im[χyyz ] and Im[χyyz ] comes from the different solvation environment. The peak frequency of the first layer is higher as it is close to the vapor phase, while the solvent environment of the second layer generates a larger red shift of C=O stretching frequency. As illustrated in Figure 10, the high-frequency (2)

positive component and the low-frequency negative component of the bipolar Im[χyyz ] band are attributed to the first and second layers of the PC interface, respectively. This mechanism also elucidates the reverse signs of the bipolar bands between PC and DMC.

5.5

PC Dimer Structure

We investigated the mechanism of the second layer formation at the PC interface, which shows the opposite orientation to that in the first layer. A previous study in the supersonic jet 74 reported dimer formation of PC molecules with anti-parallel C=O bonds. The present model supports the stable PC dimer formation in the gas phase, and the binding energy of (S)-PC and (R)-PC is calculated to be 46.9 kJ/mol with the present model. This binding energy is comparable to previous results of quantum 22 ACS Paragon Plus Environment

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chemical calculations, 29.5 kJ/mol by B3LYP, 48.0 by B97D, 58.1 by MP2 with the 6311++G(d,p) basis set. 74 We notice that the result of the present CRK model shows better agreement with the latter two including the dispersion interaction. Such dimer formation is further examined in the liquid phase. 75,76 We performed preliminary quantum chemical calculations of the PC dimer with incorporating the solvent effect by Gaussian09 package. 44 The calculations were done at the MP2/aug-cc-pVTZ level with the polarizable continuum model (PCM) 77 with a dielectric constant of 64.9. 68 Owing to the chirality of PC, three kinds of dimer structures can be formed, between (S)-PC and (R)-PC (SR dimer), (R)-PC and (R)-PC (RR dimer), and (S)-PC and (S)-PC (SS dimer). The optimized structures of these dimers are similar and we show the structure of the SR dimer in Figures 11 (a) and (b) as an example. The dimer structure is represented by two coordinates r and θ, where r is the distance between two carbonyl carbon atoms and θ is the angle between the two C=O bond vectors. The optimized structure has r = 3.4 ˚ A and θ = 180◦ . We also investigated the dimer formation of PC at the surface by the present MD simulation. The calculated probability distribution of r and cos θ between the adjacent PC molecules at the surface of liquid PC is shown in Figure 11 (c). The probability distribution P (r, cos θ) was calculated by sampling the pairs of nearest neighbor PC molecules whose centers of mass are located in the interface region of zˆ > −10 ˚ A, and it is normalized by ρ 2

∫

∫

∞

dr 4πr 0

1

2

d(cos θ)P (r, cos θ) = 1

(22)

−1

where ρ is the number density of bulk PC liquid. Equation (22) indicates that P (r, cos θ) is dimensionless and the number of the nearest PC molecule is unity. The two-dimensional map of P (r, cos θ) in Figure 11 (c) clearly shows particularly dense region at around r = 3.75 ˚ A and cos θ = −1 (θ = 180◦ ). Such preferential structure is consistent to that of the optimized dimer mentioned above, though r is slightly larger than that in the optimized dimer. These



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results indicate that the PC molecules tend to form anti-parallel dimer at interface. The tendency of forming the PC dimer elucidates the formation of the second layer with opposite orientation. As we have argued in Sec. 5.3, the PC molecules in the first layer tend to point the C=O moieties downward. Thus the dimer formation between the first and second layers induces slightly upward preference of the C=O bonds in the second layer. This mechanism could also elucidate the oscillating structure of ρ⟨cos θCO ⟩(ˆ z ) at the surface of liquid PC in Figure 4 (c).

6

Conclusion

In this paper, we presented a collaborative work of MD simulation and SFG measurement to investigate the vapor/liquid interfaces of PC and DMC, typical organic carbonate solvents used in batteries. To perform the MD calculation of the SFG spectra, we developed flexible and polarizable models of these organic molecules on the basis of the CRK theory. We also report experimental IR, Raman and SFG (ssp and sps) vibrational spectra of these liquids, which provide useful test of the performance of the proposed models. The molecular models are carefully validated through calculating various thermodynamic properties and vibrational spectra of the bulk liquids and interfaces. The molecular models generally well reproduce these experimental properties, and in particular reliably describe the C=O stretching vibration, including the red shift in condensed phase as well as the experimental ssp and sps SFG spectra (Figure 6). However, the critical examination also showed some rooms for improvement about general LJ parameters and deformation modes of Raman spectra, as mentioned in Secs. 5.1 and 5.2. These issues will be addressed in our forthcoming works. The present paper focuses on the SFG spectra in the C=O stretching region in relation to the surface structure of liquid PC and DMC. The MD simulation revealed that the PC and DMC interfaces show quite different orientational structure. The PC interface shows alternating downward and upward C=O moieties


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along the depth profile (Figure 4 (c)), while the DMC shows nearly random orientation even at the topmost layer (Figure 4 (d)). The Im[χ(2) ] spectra in the C=O stretching region shows bipolar band for both PC and DMC, though the sign of the bipolar band is opposite (Figure 7), which reflects significantly different surface structures of PC and DMC. The bipolar band of DMC is attributed to the splitting of upward and downward C=O moieties of DMC at the topmost layer. On the other hand, the bipolar band of PC is attributed to the anti-parallel dimer formation of PC molecules, which induces opposite orientation of C=O between the first and second layers. The mechanism of the dimer formation also elucidates the alternating C=O orientations near the PC surface mentioned above. The ultimate goal of the present study is to extend our MD analysis method of SFG spectroscopy to general interface systems including organic molecules. For these purposes we demonstrated the validity of the general molecular modeling to analyze the interface structures and SFG spectra. Further work to refine and extend the molecular models based on the CRK theory is in progress.

Acknowledgement This work was supported by Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Cooperative Research Program of Institute for Catalysis, Hokkaido University, and the Grants-in-Aids (Nos. JP25104003, JP26288003) by the Japan Society for the Promotion of Science (JSPS) and Ministry of Education, Culture, Sports and Technology (MEXT), Japan. The numerical computations were performed with the supercomputers in Research Center for Computational Science, Okazaki, Japan.

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Adsorption of Solvents on the Cathode Surface of Lithium Ion Batteries. Angew. Chem. Int. Ed. 2013, 52, 5753–5756. (19) Horowitz, Y.; Han, H.-L.; Ross, P. N.; Somorjai, G. A. In Situ Potentiodynamic Analysis of the Electrolyte/Silicon Electrodes Interface Reactions - A Sum Frequency Generation Vibrational Spectroscopy Study. J. Am. Chem. Soc. 2016, 138, 726–729. (20) Nicolau, B. G.; Garca-Rey, N.; Dryzhakov, B.; Dlott, D. D. Interfacial Processes of a Model Lithium Ion Battery Anode Observed, in Situ, with Vibrational Sum-Frequency Generation Spectroscopy. J. Phys. Chem. C 2015, 119, 10227–10233. (21) Mukherjee, P.; Lagutchev, A.; Dlott, D. D. In Situ Probing of Solid-Electrolyte Interfaces with Nonlinear Coherent Vibrational Spectroscopy. J. Electrochem. Soc. 2012, 159, A244–A252. (22) Morita, A.; Hynes, J. T. A Theoretical Analysis of the Sum Frequency Generation Spectrum of the Water Surface II. Time-Dependent Approach. J. Phys. Chem. B 2002, 106, 673–685. (23) Perry, A.; Ahlborn, H.; Moore, P.; Space, B. A Combined Time Correlation Function and Instantaneous Normal Mode Study of the Sum Frequency Generation Spectroscopy of the Water/Vapor Interface. J. Chem. Phys. 2003, 118, 8411–8419. (24) Walker, D. S.; Hore, D. K.; Richmond, G. L. Understanding the Population, Coordinatino, and Orientation of Water Species Contributing to the Nonlinear Optical Spectroscopy of the Vapor-Water Interface through Molecular Dynamics Simulations. J. Phys. Chem. B 2006, 110, 20451–20459. (25) Morita, A.; Ishiyama, T. Recent Progress in Theoretical Analysis of Vibrational Sum Frequency Generation Spectroscopy. Phys. Chem. Chem. Phys. 2008, 10, 5801–5816.


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Table 1: Natural internal coordinates S1 ∼ S33 of PC. Description = rC=O C=O str C=O in-plane = √12 (θ1 − θ2 ) bend C=O = ω1 out-of-plane bend is the wagging angle of C=O bond from the O-C-O plane NIC

Carbonyl group:

S1 S2 S3 ω1

Five-membered ring:

Methylene group:

Methine group:

Methyl group:

S4 =

√1 (r1 2

+ r5 )

skeletal(1)

S5 = √12 (r1 − r5 ) skeletal(2) 1 S6 = √2 (r2 + r4 ) skeletal(3) 1 S7 = √2 (r2 − r4 ) skeletal(4) S8 = r 3 skeletal(5) S9 = 0.6324[α1 + a(α2 + α5 ) + b(α3 + α4 )] skeletal(6) S10 = 0.3325[(a − b)(α2 − α5 ) + (1 − a)(α3 − α4 )] skeletal(7) S11 = 0.6324[b(τ1 + τ5 ) + a(τ2 + τ4 ) + τ3 ] skeletal(8) S12 = 0.3325[(a − b)(τ4 − τ2 ) + (1 − a)(τ5 − τ1 )] skeletal(9) r1 , e.g., is the bond 1-2. α2 , e.g., is the angle 1-2-3, and τ2 , e.g., is the dihedral angle 1-2-3-4. a = cos 144◦ , b = cos 72◦ . S13 = √12 (r1 + r2 ) C-H sym str 1 S14 = √2 (r1 − r2 ) C-H asym str S15 = α CH2 bend 1 S16 = 2 (β1 − β2 + β3 − β4 ) CH2 rock S17 = 12 (β1 + β2 − β3 − β4 ) CH2 wag 1 S18 = 2 (β1 − β2 − β3 + β4 ) CH2 twist r1 , r2 are the bond of C-H1 and C-H2 , respectively. S19 = r1 C-H str S20 = r2 C-C str S21 = α HCC bend S22 = √12 (β1 − β3 ) C-H def 1 S23 = 2 (β1 − β2 + β3 − β4 ) HCC rock 1 √ S24 = 2 (β2 − β4 ) C-C def r1 , r2 are the bond of C-H and C-C, respectively. S25 = √13 (r1 + r2 + r3 ) C-H sym str 1 √ S26 = 6 (2r1 − r2 − r3 ) C-H asym str 1 1 √ S27 = 2 (r2 − r3 ) C-H asym str 2 1 √ S28 = 6 (α1 + α2 + α3 − β1 − β2 − β3 ) CH3 sym def 1 √ S29 = 6 (2α1 − α2 − α3 ) CH3 asym def 1 1 √ S30 = 2 (α2 − α3 ) CH3 asym def 2 1 √ S31 = 6 (2β1 − β2 − β3 ) CH3 rock 1 1 S32 = √2 (β2 − β3 ) CH3 rock 2 1 S33 = √3 (τ1 + τ2 + τ335 ) torsion Paragon Plus Environment r1 , e.g.,ACS is the bond of C-H 1 and τ1 , e.g., is the dihedral angle of H1 -C-C-H.


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table 2: ESP charges and LJ parameters, σ and ε, of PC and DMC. The numbering of atoms is denoted in Figure 1. H(Cn ) denotes the hydrogen atom(s) attached to the Cn atom. Atom C1 O1 O2 O3 C2 H(C2 ) C3 H(C3 ) C4 H(C4 )

charge [e] PC DMC 0.726 0.789 -0.517 -0.527 -0.344 -0.358 -0.343 -0.358 0.157 0.045 0.058 0.059 0.148 0.045 0.041 0.059 -0.077 0.037

σ [˚ A] 3.75 2.96 3.00 3.00 3.50 2.42 3.50 2.42 3.50 2.42


ε [J/mol] 439.32 878.64 711.28 711.28 276.14 62.76 276.14 62.76 276.14 62.76

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3: Derivatives of dipole moment (∂µ/∂Q) and polarizability (∂α/∂Q) with respect to C=O stretching normal mode Q of (R)-PC and DMC. The molecule-fixed coordinates (ξ, η, ζ) are shown in Figure 1. Calculations were performed by B3LYP/aug-cc-pVTZ with the reduced mass of Q being unity. The table shows only the lower left elements of the polarizability derivative ∂αpq /∂Q, as it is a symmetric tensor. Units: atomic units. (R)-PC ∂µr ∂Q ∂αpq ∂Q

ξ η ζ

DMC ∂µr ∂Q ∂αpq ∂Q

ξ η ζ

ξ η -0.0004 -0.0003 0.0031 -0.0002 0.0088 0.0037 0.0011

ζ -0.0199

ξ 0 0.0133 0 0

η 0

ζ -0.0135

0.0283 0

0.0391

0.1022



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 4: Calculated and experimental results of density (ρ), heat of vaporization (∆Hv ), and surface tension (γ) of liquid PC and DMC. Error bars are shown in brackets. PC ρ (g/mL) ∆Hv (kcal/mol) γ (mN/m)

Cal. 1.246 (0.002) 18.24 (0.09) 50.39 (4.29)

Exp. 1.205 66 15.60 67 45.0 68

DMC Cal. Exp. 1.075 (0.002) 1.064 69 10.83 (0.06) 9.09 70 36.40 (1.43) 31.9 68


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1: Molecular structure of (S)-PC, (R)-PC and DMC. The red vectors illustrate the definition of molecule-fixed coordinates (ξ, η, ζ).



(b) Exp.

IR

(c) Cal.

Intensity (arb. unit)

(a) Cal. 1798

Absorbance (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1780

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Raman

1792 (d) Exp.

1780 1000 2000 3000 -1 Wavenumber(cm )

1000 2000 3000 -1 Wavenumber(cm )

Figure 2: IR (a, b) and total Raman (c, d) spectra of liquid PC by the present calculation (a, c) and experiment (b, d). Each spectrum is normalized by the integrated intensity of the C-H stretching band. The peak frequencies of C=O stretching are labeled inside the figure. The black perpendicular lines in (a) and (c) indicate the results (frequency and intensity) of the harmonic analysis of an isolated molecule by B3LYP/cc-aug-pVTZ.


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IR

(a) Cal.

(c) Cal.

Raman

Intensity (arb. unit)

1742

Absorbance (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(b) Exp. 1749

1742 (d) Exp.

1755 1000 2000 3000 -1 Wavenumber(cm )

1000 2000 3000 -1 Wavenumber(cm )

Figure 3: IR (a, b) and total Raman (c, d) spectra of liquid DMC by the present calculation (a, c) and experiment (b, d). Other conditions are same as those in Figure 2.



Density(g/mL)

1.5

1.5

(a)

1

0.2

(b)

1

Cal. Fit

0.5 0

ρ(g/mL)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 50

0

(c)

0.2

0

0

−0.2

−0.2

−15

−10

Cal. Fit

0.5

−5

0

5

10

(d)

−15

−10

^

−5

0

5

10

^

z (Å)

z (Å)

Figure 4: Calculated surface structures of liquid PC (left) and DMC (right). (Top panels) Definition of the tilt angle θCO . (a, b) Density profiles as a function of zˆ, where the red circles denote MD results and blue lines the fitted curves by Eq. (19). (c, d) Product of density ρ and cos θCO by Eq. (20) as a function of zˆ.


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P(cosθ)

3

(a)θCO

2

3 Bulk 1st layer 2nd layer

(b)θCO

Bulk interface

2

1

1

0

P(cosθ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

(c)θnor

2

2

1

1

0

(d)θnor

0 −1

−0.5

0 cosθ

0.5

1

−1

−0.5

0 cosθ

0.5

1

Figure 5: Calculated orientational distributions of PC (left) and DMC (right). (Top panels) Definition of θnor . (a-d) Orientational distributions of cos θCO and cos θnor by Eq. (21) at different regions.



(a) Cal.

(c) Cal.

PC

ssp sps

SFG Intensity (arb. unit)

SFG Intensity (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(b) Exp.

1700

1750 1800 1850 Wavenumber(cm-1)

Page 44 of 50

DMC ssp sps

(d) Exp.

1900 1700

1750 1800 1850 Wavenumber(cm-1)

1900

Figure 6: Calculated (a, c) and experimental (b, d) SFG intensity spectra of PC (a, b) and DMC (c, d) vapor-liquid interfaces. The ssp-polarized spectra are shown in red, and sps in blue.


Page 45 of 50

Im[χ(2) yyz](a.u.)

0.6

(a)

0

z>−5Å ^

z>−10Å z>−15Å ^

−0.6 0.6

Im[χ(2) yyz](a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


^

(b)

0

−0.6 1700

1750

1800

1850

1900

Wavenumber(cm−1) (2)

Figure 7: Calculated imaginary χyyz spectra of (a) PC and (b) DMC interfaces. The convergence behavior with expanding the threshold in Eq. (10) is also shown in different colors.



Im[χ(2) yyz](a.u.)

1.2

(a)

0.6 0 self part total

−0.6 1.2

Im[χ(2) yyz](a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 50

(b)

0.6 0

−0.6 1700

1750

1800

1850

1900

Wavenumber(cm−1) (2)

Figure 8: Calculated self (red) and total (black) imaginary χyyz spectra of (a) PC and (b) DMC interfaces.


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2

Amplitude(a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 (2),up

Im[χyyz ] Im[χ(2),down ] yyz Im[χ(2),self yyz ]

−2 1700

1750

1800

1850

1900

−1

Wavenumber(cm ) (2),self

Figure 9: Decomposed Im[χyyz ] spectra into upward (blue) and downward (green) molecules of the first layer of DMC interface by Eq. (16). The red line is identical to that in Figure 8 (b). Typical corresponding orientations of DMC molecules are illustrated in the top panel.



2

Amplitude(a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0 Im[χ(2),L1 yyz ] Im[χ(2),L2 yyz ] Im[χ(2),self yyz ]

−2 1700

1750

1800

1850

1900

−1

Wavenumber(cm ) (2),self

Figure 10: Decomposed Im[χyyz ] spectra into the first (green) and second (blue) layers of PC interface. The red line is identical to that in Figure 8 (a). Typical orientations of PC molecules in these layers are illustrated in the top panel.


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(a)

(b)

(c) 1

2

0.5

cosθ

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

1

−0.5 −1

3

4

r(Å)

5

6

0

Figure 11: (a, b) Dimer structure of (S)-PC and (R)-PC optimized by the quantum chemical calculation. Its side and top views are shown in (a) and (b), respectively, and the definition of the coordinates r and θ are illustrated. (c) Probability distribution P (r, cos θ) between the nearest neighbor PC molecules at the interface by MD simulation.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 12: TOC graphic. 6.5 cm × 4.75 cm.


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Surface Structure of Organic Carbonate Liquids Investigated by

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