An ab initio molecular dynamics study of the liquid-vapor interface of an aqueous NaCl solution: Inhomogeneous density, polarity, hydrogen bonds, and frequency fluctuations of interfacial molecules Jyoti Roy Choudhuri and Amalendu Chandra Citation: The Journal of Chemical Physics 141, 194705 (2014); doi: 10.1063/1.4901118 View online: http://dx.doi.org/10.1063/1.4901118 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/141/19?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hydrogen bonded structure, polarity, molecular motion and frequency fluctuations at liquid-vapor interface of a water-methanol mixture: An ab initio molecular dynamics study J. Chem. Phys. 141, 134703 (2014); 10.1063/1.4896233 Hydrogen bonded structure and dynamics of liquid-vapor interface of water-ammonia mixture: An ab initio molecular dynamics study J. Chem. Phys. 135, 114510 (2011); 10.1063/1.3637499 Dissociation of NaCl in water from ab initio molecular dynamics simulations J. Chem. Phys. 132, 114510 (2010); 10.1063/1.3360310 Molecular dynamics simulations of aqueous NaCl and KCl solutions: Effects of ion concentration on the singleparticle, pair, and collective dynamical properties of ions and water molecules J. Chem. Phys. 115, 3732 (2001); 10.1063/1.1387447 Large ionic clusters in concentrated aqueous NaCl solution J. Chem. Phys. 111, 5150 (1999); 10.1063/1.479783

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THE JOURNAL OF CHEMICAL PHYSICS 141, 194705 (2014)

An ab initio molecular dynamics study of the liquid-vapor interface of an aqueous NaCl solution: Inhomogeneous density, polarity, hydrogen bonds, and frequency fluctuations of interfacial molecules Jyoti Roy Choudhuri and Amalendu Chandraa) Department of Chemistry, Indian Institute of Technology, Kanpur 208016, India

(Received 28 May 2014; accepted 24 October 2014; published online 19 November 2014) We have presented a first principles simulation study of the structural and dynamical properties of a liquid-vapor interfacial system of a concentrated (5.3 M) aqueous NaCl solution. We have used ab initio molecular dynamics to examine the structural and dynamical properties of the bulk and interfacial regions. The structural aspects of the system that have been considered here include the inhomogeneous density profiles of ions and water molecules, hydrogen bond distributions, orientational profiles, and also vibrational frequency distributions in the bulk and interfacial regions. It is found that the sodium ions are mostly located in the interior, while the chloride anions occupy a significant portion of the interface of the slab. The water dipoles at the interface prefer to orient parallel to the surface. The dynamical aspects of the interfaces are investigated in terms of diffusion, orientational relaxation, hydrogen bond dynamics, and vibrational spectral diffusion. The results of the interfacial dynamics are compared with those of the corresponding bulk region. It is observed that the interfacial molecules exhibit faster diffusion and orientational relaxation with respect to the bulk. However, the interfacial molecules are found to have longer hydrogen bond lifetimes than those of the bulk. We have also investigated the correlations of hydrogen bond relaxation with the vibrational frequency fluctuations of interfacial water molecules. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4901118] I. INTRODUCTION

Studies of aqueous interfaces are of fundamental interest in a wide variety of scientific areas such as chemistry, biology, materials science, and also environmental and atmospheric sciences and engineering. Such studies have great significance in the field of heterogeneous atmospheric chemistry. It has also been found that aqueous salt aerosols perform crucial roles in marine boundary layers in the atmosphere.1–9 The atmospheric processes of bromine activation in sea salt aerosols, seawater spray deposited on the surface of polar ice packs, and halide anions on the surface of aerosol particles functioning as scavengers of reactive gases such as ozone or hydroxyl radical1, 10 are eminent examples of processes at aqueous solution/air interfaces. It was also suggested that at polar sunrise in the Arctic, the photochemical release of Br2 and BrCl helps in destruction of the surface layer of ozone.11, 12 In view of this well recognized importance, a large number of experimental and theoretical studies have been carried out to understand the interfacial structure of aqueous solutions at molecular level.13–46 Experimental techniques such as surface second harmonic21 and sum frequency generation22–24 methods have provided a more detailed molecular level picture of the structure and dynamics of liquid-vapor interfaces. Vibrational sum-frequency spectroscopy (VSFS) on sodium halide solutions13 reported that anions are present in the surface

a) E-mail: [email protected]

0021-9606/2014/141(19)/194705/10/$30.00

region but not necessarily with enhanced concentration. Allen and co-workers14 reported that the depth of the interfacial region that contributes to the VSFS signal is larger for the bromide and iodide solutions than for neat water. The isotopic dilution studies revealed a small VSFS intensity observed due to the presence of Cl− and Br− ions. The alteration of water hydrogen bonding was reflected deeper in the interfacial region where water hydrogen bonding is stronger.13 It was concluded that the ions in air-water interface leads to widening of the interfacial region further into the aqueous bulk water which results in an increase of VSF spectral intensity.13–15 The conventional picture of the interface of simple aqueous salt solutions is based mainly on thermodynamic quantities such as surface tension and surface potential. Molecular dynamics simulations based on non-polarizable force-fields25, 26 reported that the changes in free energy to move anions (Cl− and F− ) to the surface are less than that for moving a cation like Na+ . The orientation of water molecules around the ion was found to be only slightly affected by transition to the surface. Hu et al. reported that the chloride and bromide ions could be present at the air/water interface27 and explained the uptake of Cl2 and Br2 gases by aqueous salt solutions. Reaction based studies of oxidants with concentrated aqueous NaCl solution also supported this view.1, 28 Simulation studies using polarizable force fields16–18 reported that, with increase in size and polarizability of the halide ions, their surface concentration increases. The additional stabilization of polarizable ions at the interface was explained on the basis of solvation property.17, 19 At the interface, due to

141, 194705-1

© 2014 AIP Publishing LLC

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asymmetric solvation, the ions are subjected to non-zero net dipole arising from the vector sum of the individual dipoles of the surrounding water molecules. The net water dipole polarizes large anions at the surface leading to an energy gain which can balance (or even overcome) the energy due to incomplete solvation. On the other hand, less polarizable Na+ ions prefer the homogeneous bulk environment as they are not stabilized through asymmetric solvation structures near the interface. A recent molecular dynamics simulation study looked at the liquid-vapor interfaces20 of aqueous NaCl solutions of varying concentration and reported the variation of structural and dynamical properties of interfacial water molecules with ion concentration. All the above simulation studies related to liquid-vapor interface of aqueous ionic solutions are based on empirical potential models. In the present study, we have used the method of ab initio molecular dynamics which involves a quantum mechanical many-body treatment of the energies and forces without employing any model potentials. In this method, forces on the nuclei are obtained directly from quantum electronic structure calculations performed “on the fly” via an adiabatic dynamics principle.47, 48 This method has already been employed in studying liquid-vapor interfaces of pure water29–31 and water-ammonia32 systems. Here, we have made a detailed investigation of the structural and dynamical aspects of liquid-vapor interface of an aqueous NaCl solution. One of the objectives of our study is to examine the structural and dynamical aspects of interfacial hydrogen bonds and their relation to vibrational frequency fluctuations, the so-called vibrational spectral diffusion of interfacial molecules. In recent times, the correlations between hydrogen bond fluctuations and spectral diffusion of aqueous systems have gained immense interest both experimentally33–37 and theoretically.31, 32, 38–41 In addition to hydrogen bond and vibrational frequency fluctuations, we have also looked at the density and orientational profiles, distributions of hydrogen bonds, diffusion and orientational relaxation of both bulk and interfacial molecules. The organization of the rest of the paper is as follows. In Sec. II, we have presented the details of ab initio molecular dynamics simulation for trajectory generation and time series analysis for frequency calculations. The results of various equilibrium and dynamical properties are presented in Secs. III–V. Our conclusions are briefly summarized in Sec. VI. II. DETAILS OF SIMULATIONS AND TIME SERIES ANALYSIS

We have carried out ab initio molecular dynamics simulations of the liquid-vapor interface of an aqueous ionic solution at room temperature. The initial configuration of the system was generated by classical molecular dynamics simulations using classical models of water and ions.49–51 We first carried out a bulk simulation in a cubic box of the present system containing 24 Na+ , 24 Cl− , and 208 water molecules, periodically replicated in all three dimensions.20 The dimension of the box is 19.32 Å which corresponds to the experimental density of the aqueous solution.52 After proper equi-

J. Chem. Phys. 141, 194705 (2014)

libration of the bulk liquid, the central simulation box was elongated along z-direction by adding empty cubic boxes on both sides. For the next stage of the simulation run, this rectangular box was taken as the simulation box, having sides of 19.32 Å along the x and y directions and 57.96 Å along the z direction. Again by imposing periodic boundary conditions in all three dimensions, the system was re-equilibrated at the room temperature. Two interfacial regions were generated on both sides of the liquid slab along the z direction with a liquid slab of width of about 25 Å separated by vacuum layers of approximately equal width. The final configuration of the classical runs was taken as the initial configuration for the ab initio molecular dynamics simulations. Then the ab initio molecular dynamic simulations were carried out by employing the Car-Parrinello47, 48 method and the CPMD code.53 The electronic structure of the extended system was represented by the Kohn-Sham (KS) formulation54 of density functional theory within a plane wave basis. The core electrons were treated via atomic pseudopotentials of Vanderbilt ultrasoft pseudopotentials55 which allow for a lower value of the energy cut-off in the basis set expansion. The plane wave expansion of the KS orbitals was truncated at a kinetic energy cut-off of 25 Ry as used in earlier studies.31, 32 We used the well-known BLYP56 functional in the present simulations as was also used in earlier simulations of interfacial systems.46 A fictitious mass of μ = 800 a.u. was assigned to the electronic orbitals and the coupled equations of motion describing the system dynamics both nuclei and orbitals were integrated by using a time step of 5 a.u. The hydrogen atoms were assigned the mass of deuterium which ensured that electronic adiabaticity and energy conservation were maintained throughout the simulations. Then, we equilibrated the system for a time span of 10 ps in a canonical ensemble at 298 K by using the Nosé-Hoover chain method.57 Then we continued the run in a microcanonical ensemble for another 25 ps for calculations of various equilibrium and dynamical quantities. We have also carried out two classical simulations for the bulk and interfacial systems of same dimension for the calculations of various structural and dynamical quantities classically following the methodology used in earlier studies.20 Another ab initio molecular dynamics trajectory of 25 ps is generated containing 10 Na+ , 10 Cl− , and 88 water molecules in a cubic box of length 13.5 Å to compare the structural properties of the bulk solution with the ab initio molecular dynamics results of the bulk part of the interfacial system considered here. Thereafter, we carried out a time series analysis of the ab initio molecular dynamics trajectories using the wavelet method.58 This method allows the calculation of time dependent frequencies of the OD modes through a continuous wavelet transform of the trajectories. First, a time dependent function f(t) is expressed in terms of basis functions which are constructed as translations and dilations of a mother wavelet φ,58–60

φa,b (t) = a −1/2 φ



t −b a

 ,

(1)

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J. Roy Choudhuri and A. Chandra

A. Density and hydrogen bond profiles

The variation of inhomogeneous density profile across the interface characterizes the structural property of an interfacial system. The density profile is obtained by calculating the average number of molecules of a given species in the slabs of thickness z where the z coordinate is along the surface normal and the center of the simulation system is located at z = 0. The thickness of each slab is taken to be 0.05 Å in the present calculations. Expectedly, there is a sharp decrease in the density of water molecules and ions as we move from the bulk to the interfacial region. The difference between the behavior of the two ions is that the sodium ions are practically absent from the surface and chloride ions occupy a sizable fraction of the interface which is in agreement with the earlier classical results using polarizable models.16, 17 The difference in the polarizabilities between the “hard” sodium ions with no valence electrons and the “soft” polarizable chloride anions play the crucial role here. Clearly, sodium ions have more preference toward the interior solvation. For the chloride ions, an enhancement of density at the surface is observed relative to the sodium ions. So a “double layer” is set up at the liquidvapor interfacial region of the ionic solution. The results of the density profiles from ab initio molecular dynamics are shown in Fig. 1(a) and the results of the corresponding classical simulation are shown in Fig. 1(b). We note that the classical simulations involved nonpolarizable force fields which produce similar density profiles for the positive and negative ions at the interface. Following previous work,20, 29, 46, 64–68 we define the interfacial region as the one over which the number density varies from 90% to 10% of the bulk liquid density. Using the above definition, we have calculated interfacial thickness which is found to be 3.2 Å. It is notable that the interfacial thickness is lower than the pure liquid-vapor29, 31, 64 system. The reason is that for liquid-vapor interface of a highly concentrated ionic solution, ions in the liquid region exert attractive forces on the interfacial water molecules leading to a decrease in the interfacial width.20 The surface excess of the solutes in water considered by Tobias69 is calculated here and found out to be −0.6 nm−2 for both the ions, which is in good

AIMD

-3

sodium chloride water

0.6 0.4 0.2 0

0

1

3

6

9

12

(b)

15

18

Classical

0.8

sodium chloride water

0.6 0.4 0.2 0

III. STRUCTURAL PROPERTIES

(a)

0.8 ρ(z) (g cm )

for a > 0 and b real. For the mother wavelet, we have used the so-called Morlet-Grossman wavelet.61 Following our previous work on water and aqueous ionic solutions,41, 62, 63 the time dependent function f(t) for a given OD bond is constructed to be a complex function with its real and imaginary parts corresponding to the fluctuations in instantaneous OD distance and the corresponding momentum along the OD bond and the stretch frequency at a given time t = b is then determined from the scale a that gives the maximum modulus of the corresponding wavelet transform at b. The process is then performed for all the OD modes and for the entire trajectory.

1

-3

and the coefficients of the expansion are represented by the wavelet transform of f(t) which is defined as    ∞ t −b dt , (2) Lψ f (a, b) = a −1/2 f (t)ψ¯ a −∞

J. Chem. Phys. 141, 194705 (2014)

ρ(z) (g cm )

194705-3

0

3

6

9 Z (Å)

12

15

18

FIG. 1. Density profiles (g cm−3 ) of different species in the bulk and liquidvapor interfacial regions from (a) ab initio and (b) classical simulation trajectories.

agreement with the experimental value calculated from the activity dependence of experimental surface tension data.70 We have also calculated the fraction of existing Na+ and Cl− ion pair and the values obtained classically and quantum mechanically are 0.15 and 0.14. We also note in this context that there are existing studies available in the literature where solvation of a single Na+ or Cl− in bulk water can be compared for different classical models and density functional theory.51, 71–73 In addition to the density profiles, we have also calculated the hydrogen bonds per species in the bulk and interfacial regions. Here, two types of hydrogen bonds are possible: Waterwater and water-chloride ion hydrogen bonds. We have used a set of geometric criteria to define these hydrogen bonds. Two water molecules are taken to be hydrogen bonded if their hydrogen-oxygen distance is less than 2.5 Å and for chloride ion-water, the hydrogen and chloride ion distance is taken to be less than 3.0 Å. The distance criteria are taken from radial distribution plots which are shown in Figs. 2–4. The radial distribution plot of chloride ion-oxygen pair is compared with the experiment result,74 which shows a good agreement. In Fig. 5, we have shown the hydrogen bond profiles of the system. As we move from bulk to interface, the number of molecules is decreased which means a decrease in the number of hydrogen bonds. We have also calculated the average number of hydrogen bonds per water molecule in the bulk and interface which are found to be 3.1 and 2.2, respectively. The average water coordination (number of water molecules in the first solvation shell) is calculated and it is found out to be 3.1 at the bulk and 2.1 at the interface. B. Molecular orientation

The orientation of a water molecule is studied in terms of the angle (θ ) that its molecular dipole vector makes with the surface normal along the z-axis. In Fig. 6, we have shown the

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4

3

(a) bulk_classical interface_AIMD experimental_data bulk_AIMD

2

(a) bulk_classical interface_AIMD bulk_AIMD

2.5 2 gOO(r)

3 gClO(r)

J. Chem. Phys. 141, 194705 (2014)

1.5 1

1 0

0.5 0

3

1

2

3

4

0

7

6

0

6

(b) bulk_classical interface_AIMD bulk_AIMD

2.5

1

2

3

5

6

7

(b) bulk_classical interface_AIMD bulk_AIMD

4

1.5

3 2

1 0.5

1

0

0

0

1

2

3

4

5

7

6

0

1

2

3

FIG. 2. Radial distribution functions (rdf’s) for (a) chloride ion-oxygen and (b) chloride ion-hydrogen pair. The blue solid and red dashed lines indicate results from the bulk classical and interface ab initio molecular dynamics (AIMD) trajectories (for only the bulk slab). The green dashed lines indicate plots for bulk AIMD trajectories. The results of chloride ion-oxygen rdf are compared with the experimental result (maroon).74

orientational distribution of dipole vectors of water molecules at the interface. The figure shows the probability distribution of cos θ of water molecules. A uniform distribution is found for bulk water (picture not shown) which means that there is no preferred orientation in the bulk phase as expected. However, in the interfacial region, a maximum is found at around cos θ = −0.17 for dipole orientation which shows a preference toward a particular orientation of the dipole at the 7

4

5

6

7

r (Å)

r (Å)

FIG. 4. Radial distribution functions (rdf’s) for (a) oxygen-oxygen and (b) oxygen-hydrogen pair. The blue solid and red dashed lines indicate results from the bulk classical and interface AIMD trajectories (for only the bulk slab). The green dashed lines indicate plots for bulk AIMD trajectories.

interface. The molecules orient their dipoles at an angle of about 95◦ with the surface normal, i.e., almost parallel to the surface. We have also examined the distribution of the OD vectors with the surface normal and the results reveal two maxima at around θ = 65◦ and 120◦ . The former angle corresponds to the dangling bonds and the latter corresponds to the OD modes which point inward to form hydrogen bonds. This orientational structure is in agreement with earlier watervapor studies.31, 64 Also the distribution is quite broad which means that other orientations of the OD groups are also possible in the interfacial region but with a lower probability.

(a)

6

bulk_classical interface_AIMD bulk_AIMD

5 gNaO(r)

4

5 gOH(r)

2 gClH(r)

5

C. Average frequencies and hydrogen bonds

We have calculated the average frequencies of the OD groups in the bulk region and also of free OD groups for the interfacial molecules. The OD groups of bulk water which

4 3 2 1 0

4

1

2

3

4

(b)

6

7

bulk_classical interface_AIMD bulk_AIMD

3 gNaH(r)

5

2 1 0

0

1

2

3

4

5

6

7

r (Å) FIG. 3. Radial distribution functions (rdf’s) for (a) sodium ion-oxygen and (b) sodium ion-hydrogen pair. The blue solid and red dashed lines indicates results from the bulk classical and interface AIMD trajectories (for only the bulk slab). The green dashed lines indicate plots for bulk AIMD trajectories.

6 Number of hydrogen bond per species

0

water--water Cl --water

5 4 3 2 1 0

0

3

6

9 Z (Å)

12

15

18

FIG. 5. Number of water-water hydrogen bonds per water and chloride ionwater hydrogen bonds per chloride ion in the bulk and interfacial regions.

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J. Chem. Phys. 141, 194705 (2014)

0.8

P(cos θ)

0.003

Population distribution

OD vector dipole vector

0.002

0.001

(a) Bulk 0.6

0.4

0.2

0

0 -1

0

-0.5

0.6 Hydrogen bonded (interface) Hydrogen bonded (bulk) Dangling (interface) Dangling (bulk)

0.3

0.15

Population distribution

are mostly hydrogen bonded, are found to be red shifted in comparison to free OD modes at the interface. The hydrogen bonding states of OD groups largely influence the frequency shift of the molecules. The stronger the hydrogen bond, higher will be the redshift in OD stretching frequency. The average frequency of the OD modes in the bulk phase is found to be 2395 cm−1 which is very close to the corresponding result for pure water (2380 cm−1 ) found in earlier studies.41 The small difference may be attributed to the influence of ionwater hydrogen bonds. The average frequency of the dangling OD modes at the interface is found to be 2570 cm−1 . The calculated frequency shift of 175 cm−1 between the hydrogen bonded bulk and dangling interfacial OD modes is comparable with the corresponding experimental value of about 220– 250 cm−1 for OD modes of HOD and D2 O.75–79 The calculated frequencies are somewhat smaller than the experimental frequencies which could be attributed to various factors such as the BLYP density functional, electronic fictitious mass, finite basis set cut-offs,80–82 and also the thermostat of the simulation system. The main focus here is to study the frequency fluctuations and their correlations to hydrogen bond dynamics. The normalized dynamics of frequency fluctuations is not expected to be critically influenced by these discrepancies in our calculated average frequencies. In Fig. 7, we have shown

P (ω)

DD

SD

DD

0.8

FIG. 6. Probability distributions of the orientation of water dipole (blue dashed) and OD vectors (red solid) in the interfacial region.

0

SD

1

0.5

cos θ

0.45

ND

(b) Interface 0.6

0.4

0.2

0

ND

Hydrogen bonding state FIG. 8. Population distribution of water molecules in different hydrogen bonding states in the (a) bulk and (b) at interface.

the frequency distribution of water molecules in the bulk and at interface. It can be seen that the OD modes which are hydrogen bonded at the interface are slightly blue shifted than the hydrogen bonded bulk molecules which is in agreement with the experimental findings.79 The hydrogen bonding state of the hydrogen atoms of interfacial water molecules can be of three types: (i) water with no donor hydrogen bonds (ND or non-donor), (ii) water with one OD bond dangling and other one hydrogen bonded (SD or single-donor), and (iii) water with both OD groups hydrogen bonded (DD or double-donor). At the interface, maximum water molecules (77%) are found as SD, 18% of the molecules exist in DD hydrogen bonding state and very few water molecules (5%) are found with both OD modes dangling. The probabilities for SD, DD, and ND in the bulk phase are 0.29, 0.70, and 0.01, respectively. In Fig. 8, we have shown three different types of hydrogen bonds in the bulk and at interface. The distributions of the hydrogen bonding environment of water clearly show that the interfacial region is markedly different from bulk region. The overall trends of the SD, DD, and ND populations in the bulk and the interfacial region are qualitatively similar to the earlier work on liquidvapor interface of pure water.31 IV. ELECTRONIC PROPERTIES

2000

2500

3000

3500

Frequency (cm-1 ) FIG. 7. Probability distributions of stretch frequencies of hydrogen bonded and dangling OD modes in bulk and interfacial regions.

We have calculated the molecular dipole moments of water molecules as one moves from bulk to the interfacial region. The molecular charge distribution is quantified using the method of maximally localized Wannier functions.83, 84

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J. Chem. Phys. 141, 194705 (2014)

3

2

2

2

(Å )

Bulk Interface

1

0

0

1

2

3

4

Time (ps) FIG. 10. Variation of the mean square displacement with time for bulk and interfacial water molecules.

MSD along the x-direction of the particles that remain in the interfacial region over the time interval t = 0 to t. Thus, the long time limit of MSD of the interfacial molecules is given by85 x(t)2 i = 2Pc (t)Dx (I )t .

FIG. 9. Variation of the average dipole moments of (a) water molecules and (b) chloride ions with position along z-direction.

Each water molecule has four Wannier centers for electronic charges. The electronic and nuclear charge centers are used to calculate the dipole moment of each water molecule. In Fig. 9(a), the average molecular dipole moment is shown as a function of interfacial depth. It is observed that the average molecular dipole moment for water is around 2.85 D in the bulk region and it decreases to a value around 1.9 D at the surface region. A similar qualitative behavior was also found in an earlier study of liquid-vapor interface of pure water using first principles simulations.46 The dipole moment for pure bulk water46, 83 was found to be 3.0 D. Thus, there is not much variation in the dipole moment of water in the bulk region due to the presence of ions. The variation of dipole moment of chloride ion along z-direction is shown in Fig. 9(b), which shows a slight increase in the dipole moment at the interface. This can be explained by the unsymmetrical solvation of chloride ion at the interface. Thus, the net water dipole surrounding the chloride ion polarizes the ion and causes a slight increase in the dipole moment at the interface with respect to homogeneously solvated chloride ion in the bulk. The average bulk dipole moment of chloride ion is 0.8 D, which is in accordance with earlier result.72 V. DYNAMICAL PROPERTIES A. Diffusion

The diffusion coefficients of interfacial molecules are obtained by calculating the time dependence of mean square displacements (MSD). It may be noted that the probability of an interfacial molecule to remain continuously at the interface is not unity. We define Pc (t) as the survival probability85 for a molecule to reside continuously in the interfacial region over the time interval from t = 0 to t.  x(t)2 i is defined as the

(3)

Hence, the parallel diffusion coefficient of the interfacial molecules along the x- and y-directions can be calculated from the following equation: x(t)2 i + y(t)2 i . t→∞ 4tPc (t)

Dx,y (I ) = lim

(4)

For the bulk molecules, the survival probability is unity and the above equation reduces to the more familiar MSD expression for the bulk diffusion. Fig. 10 shows the time dependence of MSD of bulk and interfacial water molecules. The diffusion coefficients are calculated from the slope of the curves in the long time region for bulk and interfacial regions and the respective values are 0.42 × 10−5 cm2 s−1 and 1.62 × 10−5 cm2 s−1 . From classical simulations, these values are found out to be 3.83 × 10−5 cm2 s−1 and 4.92 × 10−5 cm2 s−1 which is much faster with respect to ab initio calculations. The results are included in Table I. We have also calculated the diffusion coefficients for the ions from ab initio trajectories. The values for chloride ion are 0.20 × 10−5 cm2 s−1 and 0.35 × 10−5 cm2 s−1 at the bulk and interface, respectively. Thus, a diversity in the value of chloride ion exists in both the regions. The diffusion coefficient of sodium ion at the bulk is 0.12 × 10−5 cm2 s−1 . Clearly, the interfacial molecules are more diffusive than the bulk molecules. This is due to lower density and reduced collisional effects of water at the interface compared to those of the bulk. Thus, the present calculations reveal a significant anisotropy at the interface. TABLE I. Values of diffusion coefficients (× 10−5 cm2 s−1 ) of water. Molecular dynamics

Bulk

Interface

Ab initio Classical

0.42 3.83

1.62 4.92

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J. Chem. Phys. 141, 194705 (2014) TABLE II. Values of orientational relaxation times (τ μ ) of water in ps.

1 Bulk Interface

(a) Dipole vector

C2(t)

0.8 0.6 0.4 0.2

0

1

2

3

Interface

Ab initio Classical

4.6 2.61

2.5 1.32

4

C. Hydrogen bond dynamics (b) OD vector

Bulk Interface

0.8

C2(t)

Bulk

ter molecules at the interface much more free compared to the bulk molecules.

1

0.6 0.4 0.2

Molecular dynamics

0

1

2

3

4

Time (ps) FIG. 11. Variation of the (a) dipole and (b) OD vector orientational correlation functions with time for the bulk and interfacial water molecules.

B. Orientational relaxation

Rotational dynamics of water is one of the key factors that leads to the formation and deformation of hydrogen bonds during thermal fluctuations. So, we investigated the rotational dynamics of bulk and interfacial molecules through the orientational relaxation of their dipole and OD vectors. The orientational time correlation function Cl (t) is given by Cl (t) =

ˆ · e(t)) ˆ Pl (e(0) , ˆ · e(0)) ˆ Pl (e(0)

(5)

ˆ dewhere Pl is the Legendre Polynomial of rank l and e(t) notes the unit vector along the dipole or the OD vectors. The experimentally measured rotational anisotropy is directly related to the second-rank rotational function C2 (t). We have estimated the reorientational relaxation of the molecular dipole μ (C2 (t)) and OD vectors (COD 2 (t)) for the bulk and interfacial molecules. The time dependence of the second-rank orientational correlation function of the dipole and OD vectors of the bulk and interfacial region water molecules are shown in Fig. 11. The second-rank orientational relaxation times for the bulk and interfacial water molecules as obtained by integratμ ing C2 (t) are found to be 4.6 and 2.5 ps, respectively. From classical simulations, theses values are found out to be 2.61 and 1.32 ps which is much faster with respect to ab initio calculations. The results are included in Table II. The corresponding values for OD rotation from ab initio calculation are 4.40 and 2.4 ps, respectively. We observe a faster rotational relaxation at the interface compared to that in the bulk. This is due to less number of molecules at the interface, hence less number of hydrogen bonds compared to that in the bulk. The reduced number of hydrogen bonds makes the rotation of wa-

We have used the so-called population correlation function approach86–92 to study the dynamics of ion-water and water-water hydrogen bonds in the bulk and interfacial regions. The geometric criterion used for defining these hydrogen bonds have been discussed in Sec. III A. In the population correlation function approach, we define two hydrogen bond population variables h(t) and H(t). The variable h(t) is equal to unity when a water-water or ion-water pair is hydrogen bonded at time t and is zero otherwise. If two molecules remain continuously hydrogen bonded from time t = 0 to t, then H(t) = 1 or it is zero otherwise. We have calculated the continuous hydrogen bond time correlation function SHB (t) which is defined as86–92 h(0)H (t) , (6) SH B (t) = h(0)2  where . . .  denotes an average over all pairs of a given type. SHB (t) describes the probability that an initially hydrogen bonded ion-water pair remains bonded at all times up to t. The associated integrated relaxation time τ HB gives the average lifetime of a hydrogen bond of that particular pair type. We have shown the time dependence of SHB (t) of different types of hydrogen bonds in the bulk and interfacial regions in Fig. 12. It is observed that chloride ion-water hydrogen bonds (Fig. 12(a)) have a longer lifetime than water-water hydrogen bonds (Fig. 12(b)). The values of all the relaxation times are included in Table III. In the bulk phase, the calculated lifetime of chloride ion-water hydrogen bond is 4.69 ps which is greater than the corresponding value of 2.75 ps for waterwater hydrogen bonds. The lifetimes of these hydrogen bonds are found to increase in the interfacial region. This is due to reduced density at the interface which decreases the cooperativity effect among the molecules. The classical results are also included in Table III, which shows faster dynamics with respect to ab initio relaxation times. We have also calculated the dangling OD correlation function SDH (t) which is shown in Fig. 12(c). This correlation gives the probability that an initially non-hydrogen-bonded OD group remains dangling at all times from t = 0 to time t and also gives information on hydrogen bond reformation dynamics. The lifetime of dangling OD modes in bulk phase is found to be 0.22 ps but it increases to 2.28 ps at the interface. This is due to reduced density at the interface which forces an initially dangling OD bond to remain dangling for a longer time. In the bulk region, due to strong cooperative effects, hydrogen bond breaking and reformation occur at a faster rate, hence the lifetime of dangling OD modes is very short. At the interface, due to less

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194705-8

J. Roy Choudhuri and A. Chandra

1

J. Chem. Phys. 141, 194705 (2014)

1

(a)

Bulk Interface

0.8

Bulk Fitted curve (Bulk)

0.8

Interface

0.6

Cω(t)

SHB(t)

Fitted curve (Interface)

0.4 0.2 0

0.4 0.2

0

1

2

4

(b)

0

6

0

1

Bulk Interface

0.8

SHB(t)

0.6

2

3 4 Time (ps)

5

6

FIG. 13. Variation of time correlation function of OD fluctuating frequencies of water molecules with time in bulk (blue dashed) and interface (red dashed) regions. The smooth grey lines represent the fits by a tri-exponential function. The resulting plots are averaged over the OD modes which are present in a given region.

0.6 0.4 0.2 0

0

1

1

2

(c)

Cω (t) =

Bulk Interface

0.8

SDH (t)

correlation function defined by

3

0.6 0.4 0.2 0

0

0.5

1

1.5

2

Time (ps) FIG. 12. Time dependence of the (a) continuous hydrogen bond correlation function SHB (t) between chloride ion and water molecules, (b) continuous hydrogen bond correlation function SHB (t) between two water molecules, and (c) continuous dangling correlation function SDH (t) of OD bond in the bulk and interfacial regions.

number of particles, an initially hydrogen bonded molecule takes more time to find a new hydrogen bonding partner. As a result, both the lifetimes of hydrogen bonds and dangling OD modes are longer at the interface than the corresponding values in the bulk phase.

D. Dynamics of vibrational frequency fluctuations at the interface

The vibrational frequencies of water molecules in an aqueous solution fluctuate due to fluctuations in the local solvation environment. The central dynamical quantity of interest in the context of vibrational frequency fluctuations, the so-called vibrational spectral diffusion, is the frequency time

δω(t)δω(0) , δω(0)2

(7)

where δω (t) is the fluctuation from the average frequency at time t. The average of this equation is over those modes which are present in a given region. In the vibration spectral diffusion studies, the time dependence of the fluctuations in vibration frequencies which takes place due to fluctuations in the surrounding environment is explored.31–41 In an aqueous ionic solution, hydrogen bonds exist between the anions and water molecules and also between the water molecules themselves. Thus, the changes in solvation environment particularly modify the nature of hydrogen bonds. Hence, the dynamics of vibrational spectral diffusion essentially captures the dynamics of hydrogen bond fluctuations that spontaneously take place in the system due to thermal effects. In the present work, we have calculated the frequency correlation for the OD bonds of the water molecules in the bulk and interfacial regions. The results of the frequency correlation function are shown in Fig. 13 for both bulk and interfacial water molecules. The decay of the function shows that there is a fast decay at short times which is followed by a slower decay extending up to few picoseconds. We have fitted a tri-exponential curve to this decay curve and the values of the relaxation times and their weights are included in Table IV. The oscillation in the short time is likely due to the underdamped motion of intact hydrogen-bonded pairs. The long time decay captures the hydrogen bond dynamics as these time scales agree reasonably well with our calculated lifetimes of water-water and chloride ion-water hydrogen bonds. So, it can be concluded that the frequencies of the OD modes are modulated by the waterwater and ion-water hydrogen bonds both at the bulk and TABLE IV. Relaxation times and weights of the vibrational frequency correlations of OD modes in bulk and interfacial regions. The results are averaged over those OD modes which are present in a given region.

TABLE III. Values of hydrogen bond lifetimes (τ HB ) in ps. Type of hydrogen bond

Bulk (ab initio)

Interface (ab initio)

Bulk (classical)

Interface (classical)

Water−water Chloride−water

2.75 4.69

3.15 5.23

1.50 2.60

1.75 2.80

Region Bulk Interface

τ 1 (ps)

τ 2 (ps)

τ 3 (ps)

a1

a2

a3

0.08 0.05

2.5 2.7

5.35 5.85

0.61 0.41

0.10 0.21

0.29 0.38

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194705-9

J. Roy Choudhuri and A. Chandra

interface. In case of interfacial molecules, the reformation dynamics of hydrogen bonds can also contribute to the long time part of the frequency correlation as the dangling lifetime of OD modes is rather long. VI. SUMMARY AND CONCLUSIONS

We have presented a theoretical study of the structural, dynamical and electronic properties of liquid-vapor interface of a 5.3 M aqueous solution of NaCl from first principles simulations without employing any empirical potential models. The present work provides a detailed picture of the difference in behavior of the bulk and interfacial molecules in presence of ions. The structural aspects have been studied by calculating the inhomogeneous density, hydrogen bond distribution, orientational structure, and frequency-structure correlations of the system. From the density profiles, it is found that there is a decrease in density at the interface and the more polarizable chloride ions have higher propensity for the interface compared to the sodium ions. The higher propensity can be explained in terms of the asymmetric solvation of the more polarizable chloride ions experienced at the liquidvapor interface. Due to decreased density, water molecules at the interface possess less number of hydrogen bonds, hence they rotate more freely. At the interface, the water molecules have a preferred orientation at an angle 95◦ to the surface normal, i.e., almost parallel to the surface. This orientation means that one OD bond points toward the vapor side and the other bond points toward the inner side to form hydrogen bond with other water molecules and anions. We have also examined the distributions of OD stretch frequencies which are calculated from time series analysis. It is found that the strength of the associated hydrogen bonds can alter the frequency of an OD bond. The stretching frequencies of the nonhydrogen-bonded OD modes of the interfacial molecules are found to fall in the higher side of the frequency distributions. The most red shifted frequencies are found for the hydrogen bonded molecules in the bulk region. The study of electronic properties reveals a significant decrease of molecular dipole moments near the surface compared to that of the bulk water molecules. The dynamical aspects of the interfacial system are investigated by calculating the diffusion, orientational relaxation, hydrogen bond dynamics, and spectral diffusion. The interfacial molecules exhibit a faster diffusion with respect to the bulk. This can be explained on the basis of lower density and reduced collisional effects at the interface. A hydrogen bonded molecule at the interface takes more time to find a new partner for hydrogen bonding due to the reduced density. But in the bulk, due to higher cooperative effects, the breaking and reformation of hydrogen bonds occur more frequently. Hence, we found a slower relaxation of hydrogen bonds and also of the dangling bonds for the interfacial water molecules. We have also analyzed the dynamics of vibrational frequency fluctuations of interfacial and bulk molecules through frequency time correlation function calculations. It is found that the long-time decay components of the frequency correlations in the interfacial and bulk regions are close to the lifetimes of water-water and chloride ion-water hydrogen

J. Chem. Phys. 141, 194705 (2014)

bonds in their respective regions. Our investigation of electronic properties reveals a significant decrease of molecular dipole moments near the surface compared to that of the bulk water molecules. Surface specific experimental techniques such as second harmonic or sum frequency generation79, 93–98 methods have been employed to investigate the vibrational spectra of surface molecules. In recent years, a number of theoretical studies have also been performed to calculate the sum frequency spectroscopy of aqueous surface and these studies have provided a lot of information regarding the molecular details of surface water molecules.65, 99–101 Majority of existing theoretical studies of sum frequency spectrum are based on model potentials. A very recent study has reported calculations of sum frequency spectrum of water surfaces from ab initio simulations.102 However, no such first principles calculations have yet been reported for liquid-vapor interfaces of ionic solutions. Clearly, it would be interesting to calculate the surface nonlinear spectroscopy of aqueous interfaces of ionic solutions from first principles simulations without using any model potentials. We note that the present ab initio simulations were performed using the BLYP functional without any dispersion corrections. Recent studies on liquid-vapor interfaces of pure water have shown that inclusion of such dispersion interactions gives better bulk density.64, 103 The effects of such dispersion interactions on liquid-vapor interfaces of aqueous NaCl solution will be addressed in a future publication.

ACKNOWLEDGMENTS

Financial support from the Department of Science and Technology (DST) and Council of Scientific and Industrial Research (CSIR), Government of India, are gratefully acknowledged. Part of the calculations were done at the DSTsupported High Performance Computing Facility at Computer Center, IIT Kanpur. 1 E.

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