An Ab Initio Molecular Dynamics Study

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Structural and Dynamical Nature of Hydration Shells of the Carbonate Ion in Water: An Ab Initio Molecular Dynamics Study Sushma Yadav, and Amalendu Chandra J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b11636 • Publication Date (Web): 05 Jan 2018 Downloaded from http://pubs.acs.org on January 7, 2018

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The Journal of Physical Chemistry

Structural and Dynamical Nature of Hydration Shells of the Carbonate Ion in Water: An Ab Initio Molecular Dynamics Study

Sushma Yadav1 and Amalendu Chandra1,2,∗ 1

Department of Chemistry, Indian Institute of Technology Kanpur, India 208016. 2

Department of Theoretical and Computational Molecular Science, Institute of Molecular Science, Myodaiji, Okazaki 444-8585, Aichi, Japan

————————— ∗

Corresponding author. E-mail: [email protected], Tel: +91 512 2597241

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Abstract Structural and dynamical nature of hydration shells of the carbonate ion in water is investigated through ab initio molecular dynamics simulation. The anisotropic solvation shell structure of the ion is resolved by calculating conically restricted pair distribution and radial/angular correlation functions. The vibrational frequency of OD modes hydrogen bonded to the ion is found to be smaller than that of bulk water which means the carbonate ion-water hydrogen bonds are stronger than that between water molecules. Calculations of the orientational and residence dynamics and translational diffusion reveal retarded mobility of hydration shell water molecules compared to the bulk water due to stronger ion-water interactions. It is shown that the rotation of hydration shell water takes place through dual routes of hydrogen bond switching where an OD bond initially hydrogen bonded to a carbonate oxygen switches its hydrogen bond to another carbonate oxygen or to a water oxygen. The carbonate ion is found to have a non-zero dipole moment of 1.0 D in water which can be attributed to its interactions with the fluctuating environment of the surrounding water. The carbonate ion is also found to have a long range effect on neighboring water molecules which goes beyond the first solvation shell.

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Introduction Studies of aqueous solutions of simple monatomic ions have been reported rather

extensively in the literature 1–5 . However, the solvation shell structure and dynamics of polyoxy ions with multiple atoms have not been studied with equal vigor because of many associated difficulties in such studies. The carbonate ion (CO2− 3 ) is one such doubly charged polyoxy-anion which is ubiquitous and encompasses all of the environmental compartments of the atmosphere, hydrosphere, biosphere, and, as CaCO3 forms major part of the lithosphere 6,7 . It is the major source of buffering in ocean 6 . The propensity of carbonate ion to make complexes with aqueous metal cations greatly affects their environmental behavior 8 . The carbonate ion has a planar geometry with D3h symmetry in the gas phase. However, Raman spectral studies of aqueous carbonate solutions have reported a breaking of 9 the D3h symmetry due to asymmetrical hydration of CO2− 3 ions in aqueous solutions . Re-

cent neutron diffraction studies with isotopic substitution for aqueous CsNO3 and CsCO3 solutions have shown that the hydrogen bonds between water molecules and carbonate ions are stronger than those formed with the nitrate ions 10 . There have also been a number of theoretical studies on aqueous carbonate systems using methods of quantum chemical calculations and dynamical simulations 11–20 . The quantum chemical studies of Ref. 11,12 have reported the effects of water molecules on the hydrated clusters of the carbonate ion of varying size through calculations of their structural and vibrational properties. Calculations based on reference interaction site model self-consistent field spatial electron density distribution (RISM-SCF-SEDD) have also shown that the symmetry of the anion in aqueous solution is inherently broken due to the effects of the surrounding solvent molecules 13 . We note the recent molecular dynamics study of K2 CO3 in water which employed electronic continuum corrections (ECC) for the ionic charges to take into account the polarization effects and found good agreement between the simulation and experimental neutron scattering structure factors 17 . This study also showed the inadequacy of nonpolarizable models in describing solvation of high charge density solutes like the carbonate ion in water. In another study 18 , classical molecular dynamics simulations of calcium carbonate in water using polarizable force fields provided a molecular-level picture of the solvation properties of ions involved in calcium carbonate mineral nucle-

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ation. It was reported that the carbonate ion possesses an amphiphilic character with the regions perpendicular and in the plane of the ion behaving very differently toward hydration by the surrounding water 18 . The importance of polarization effects prompted us to study the carbonate ion solvation in water through ab initio molecular dynamics where such polarization effects are naturally taken into account without involving any empirical models. Also, the presence of anisotropic solvation led us to deconvolute the hydration region around the ion into various conical shells so that one could study the structure of the hydration shells that are resolved in both distance and angular variables. Clearly, such calculations require more elaborate means of analysis such as the calculations of conically restricted pair distributions and radial/angular correlations to resolve the spatial and angular arrangement of solvent molecules in vicinity of the anion. Such conical regions have been employed earlier to characterize the asymmetric solvation shells of other planar solutes like the benzene 21 and nitrate ion 22 and here we extend such calculations to the case of asymmetric solvation of the carbonate ion. It may be noted that the carbonate ion is located on the opposite end of the Hofmeister series compared to the previously studied isoelectronic nitrate anion 22 , and the important differences in the solvation of these two ions can be gleaned through the current study. The carbonate ion affects the vibrational frequencies of its surrounding water 11,23,24 . The symmetric and asymmetric stretch bands of water get shifted to lower frequencies in presence of the ion compared to the corresponding spectra of pure water 11 . Our calculations of the frequencies of OD modes and hydrogen bonds of water in the hydration shells of this anionic solute provide a comprehensive picture of the changes in hydrogen bond characteristics of surrounding water molecules. In the current study, we have investigated the structure and dynamics of hydration shells of the carbonate ion by means of Car-Parrinello molecular dynamics (CPMD) simulation using a dispersion corrected density functional. In order to look at the possible long range effects of this anion beyond the first hydration shell, we have considered a simulation system which is large enough to support two full solvation shells around the ion in all directions and have also performed the simulation for a rather long time (from the perspective of ab initio simulations). We note that the system size and run-length of the current simulation are much higher than those of an earlier ab initio simulation of the carbonate ion-water system 19 . Besides,

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the effects of dispersion interactions were not included in the earlier work 19 unlike the current study. We also note in this context that while an earlier simulation study 20 considered only the carbonate ion and its immediate solvation shell quantum mechanically and the rest of the solvent classically, we have considered the entire system quantum mechanically for calculations of the electronic structure and forces. We have also calculated the spatial distribution functions (SDF) in addition to the angle-resolved radial distribution functions which provide detailed information on the three-dimensional anisotropic arrangement of water molecules around the carbonate ion. Furthermore, the calculations of various dynamical properties of the solvation shell such as the orientational relaxation, escape dynamics, hydrogen bond dynamics and diffusion reveal a significant retardation of the dynamics since the solvation shell water molecules are bound rather strongly under the influence of the electric field of this doubly charged anion. We have also investigated the reorientational dynamics from the perspective of angular jumps 22,25 . We have looked at the nature of such angular jumps associated with switching of a carbonate oxygen-water hydrogen bond to either another carbonate oxygen-water or a water-water hydrogen bond.

The rest of the Paper is organized as follows. In Section 2, we have described the simulation details of the aqueous carbonate solution considered here. In Section 3, we have presented the pair distribution functions to describe the angular and spatially resolved solvation structure of the carbonate ion. In Section 4, the results are presented for the orientational jumps during hydrogen bond switching and also other dynamical properties such as the hydrogen bond relaxation and residence dynamics. Finally, our conclusions are briefly summarized in Section 5.

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Computational Details

In the present work, we have carried out ab initio molecular dynamics simulation of an aqueous solution of a carbonate ion by using the Car-Parrinello method 26,27 and the CPMD Code 28 . We considered a single carbonate ion in a cubic box of 107 water molecules. We note that 107 water molecules are sufficient to accommodate two solvation shells around the carbonate ion. The edge length of the cubic simulation box, which was determined from the corresponding experimental density, is 14.88 ˚ A. Periodic boundary conditions were applied in all three directions. Kohn-Sham (KS) formulation 29 5



of the density functional theory was employed for calculation of the electronic structure of the extended system. The Troullier-Martin 30 pseudopotentials were used to treat the core electrons. For the plane wave expansion of the KS orbitals, a kinetic energy cutoff of 80 Ry was used. We used a simulation time step of 5 a.u. for integration of the dynamical equations and the fictitious electronic orbital mass (µ) was taken to be 800 a.u. We assigned the deuterium mass to all the hydrogen atoms 31 . The choices of the parameters ensured that electronic adiabaticity and energy conservation were maintained during the simulation. In the current simulation, we employed the BLYP-D2 functional which includes dispersion corrections at D2 level 32,33 into the BLYP functional 34,35 . In recent years, there have been a number of ab initio simulation studies on aqueous solutions and other hydrogen-bonded liquids 36–42 which have shown the importance of dispersion interactions in correct description of the structure, dynamics and phase diagram of these liquids. We have used the Grimme-D2 version of the dispersion correction scheme in which the damped atom-pairwise dispersion correction of the form C6 r−6 was incorporated for the dispersion interactions in the system where r represents the distance between two atoms and C6 is the prefactor determining the strength of the dispersion interaction. The initial configuration of the system was generated using force-field based molecular dynamics simulation. The ab initio simulation was then run for ∼15 ps for equilibration in the canonical ensemble at 298 K and then for another 100 ps in the micro-canonical ensemble. In order to calculate the time dependent vibrational frequencies of OD stretch modes of all the D2 O molecules, a time series analysis was performed using the wavelet method 43–45 . The details of this method have been described in Ref. 46,47 for calculations of the time dependent OD stretch frequencies of aqueous systems.

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Structural Properties of the Hydration Shells and Dipole Moments

We first discuss the results of different radial distribution functions (RDFs) shown in Figs.1(a) and 1(b). The hydrogen atom is represented by D as the deuterium mass has been used in place of H. We have shown gOc Ow (r), gOc Dw (r), gOw Ow (r), gOw Dw (r) distributions in Fig.1(a) and gCOw (r) and gCDw (r) distributions in Fig.1(b), where Oc denotes the oxygens of the carbonate ion, Ow and Dw stand for the oxygen and deuterium atoms of a water molecule and C stands for carbon atom of the carbonate ion. Considering 6


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first the Oc -Ow RDF shown in Fig.1(a), one recognizes that the height of its first peak is smaller and the corresponding first minimum is deeper than that of the Ow -Ow RDF. The carbonate ion-water hydrogen bonds are considerably shorter and somewhat stronger than those between solvent molecules as evident from the first peak of the Oc -Dw RDF which is located at a shorter distance than that of the Ow -Dw RDF. It is also seen that the height of the first (intermolecular) peak of Ow -Dw RDF is less than that of the ionwater hydrogen bond peak. For further investigation of the ion-water interactions, we have calculated the coordination numbers from the first peaks of the ion-water (gOc Dw (r)) and water-water (gOw Dw (r)) RDFs. It is found that one Oc forms roughly three hydrogen bonds while the first peak of the Ow -Dw RDF integrates to two meaning two acceptor hydrogen bonds by a water molecule. These results are in reasonably good agreement with X-ray diffraction and neutron scattering experiments as well as with previous ab initio and mixed quantum/classical simulations 19,48 . The CO2− 3 ion exhibits a total coordination number of 8.7 which is in accordance with the results of previous studies 49,50 .

It has been reported that the carbonate ion shows an amphiphilic character in which water molecules are expelled from the region close to the perpendicular axis of the carbonate plane 18,19 . In order to better understand the amphiphilic nature of the ion, the asymmetric hydration structure is now investigated by employing the deconvolution of the entire solvation shell into conical regions of different angles. The pair distribution functions are now calculated for different conical segments to obtain the angle resolved picture around the carbonate ion. The surrounding solvation structure is now studied through different conical shells around the carbonate ion. The region between the two coaxial cones around the same principal axis (C3 axis) with conical angles θ1 and θ2 is defined as the conical shell of thickness △θ as shown in the panel on the left side of Figs.2(a) and 2(b). The volume of such a conical shell of angular thickness △θ = (θ2 − θ1 ) is given by Vθ2 −θ1 = (4/3)π(cos θ2 − cos θ1 )r3 ,

(1)

where θ1 is the smaller angle and r is the radial distance from the center of mass of the carbonate ion. For a symmetrically solvated ion, the simple RDFs can be calculated by using the spherical shells around the ion and normalizing them by the uniform bulk density. However, simple RDFs only provide an angle-averaged picture. In order to

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capture the anisotropy in the solvation shell, we have divided the entire solvation shell into different conical regions by taking the carbonate center of mass as the reference point and then calculated the carbonate center of mass-oxygen (gCO3 Ow (r)) and carbonate center of mass-deuterium (gCO3 Dw (r)) RDFs separately for different values of the corresponding conical angles. The results are shown in Figs.2(a) and 2(b) where CO3 represents the center of mass of the carbonate ion.

Due to its planar symmetry, the contributions of the associated cones above and below the plane of the ion are averaged out. The angularly resolved RDFs reveal major differences at different conical angles. It may also be noted that the 0−90 ◦ conical regions, shown in Figs.2(a) and 2(b) by black curves, represent the total solvation region around the carbonate ion. It is found from Fig.2(a) that, for the conical shell of 0−30 ◦ , the gCO3 Ow (r) shows a small shoulder meaning a small probability of oxygen to stay in this region which is likely because of the interaction of the positively charged carbon with the negatively charged oxygen of water. However, this peak is smaller due to delocalization of electrons over the plane of carbonate ion and this electron density repels more oxygens to come closer. It is interesting to note that with the increase of angle of the conical shell, the peak minimum in the 60−90 ◦ region becomes deeper than other regions which means a stronger interaction in this region. This is due to the hydrogen bonded interaction which is more prominent in the 60−90 ◦ region. For the CO3 -Dw pair distributions, the deconvolution of the pair correlation functions provides a noticeable difference in the three different conical shell regions. Here again, the overall solvation shell structure (0−90 ◦ ) (black curve) around the carbonate ion shown in Fig.2(b) is resolved in three different conical shells. The water which gives rise to the small shoulder of oxygen density around the carbonate ion in CO3 -Ow 0−30 ◦ conical shell RDF shows almost negligible density of deuterium in the same region. This is because there exists a competitive strong solvation by water molecules at the oxygen sites of the carbonate anion. Such feature is necessary to understand why the two carbonate ions species stacked over each other to minimize the water interactions as found in cluster calculations of CaCO3 hydration 18 . The typical pattern associated with these hydrogen bonds can be identified from the density of the conical shells of 30−60 ◦ and 60−90 ◦ angles. Such restricted density distribution predominant at approximately −60 ◦ , 0 ◦ , and 60 ◦ with respect to the carbonate ion molecular plane has already been reported

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by an earlier neutron diffraction study. 10 We emphasize that the conically restricted pair distribution functions of the current work have captured the asymmetric hydration of CO3 2− rather than the angle-averaged hydration shell captured by the regular RDFs. The calculation of these distributions enables us to look at the changes in the hydration structure as the angle with respect to the principal axis of the carbonate ion is changed. In order to capture the orientational preference of water molecules around the carbonate ion, we have also calculated the radial/angular distribution functions which represent the probability distributions resolved in both radial and tilt angle coordinates in various conical shells. These distributions are calculated for two tilt angles: water dipole tilt angle ω and the OD bond vector tilt angle α which are defined as the angles that the water dipole and OD vectors, respectively, make with the vector connecting water oxygen to the carbonate center of mass. These tilt angles are illustrated in Fig.3(a)-(b). Due to negligible density of water in 0−30 ◦ conical shell region, the plots of the water dipole (gCO3 −Ow (r,cosω) ) and O-D (gCO3 −Ow (r,cosα) ) radial/angular distribution functions for the conical shell region of 30−60 ◦ are shown in Figs.3(c) and 3(d) and those for the 60−90 ◦ region are shown in Figs.3(e) and 3(f). The dipole orientational correlations (Figs.3(c) and 3(e)) show a peak below 4.0 ˚ A which evolves in the range of cos ω = 1.0 to 0.0, and corresponds to the value of ω from 0 ◦ to 90 ◦ . These peaks can also be linked to the OD vector tilt angle α. The OD bond vector orientation shows an interesting feature with relatively higher density in few regions as shown in Figs.3(d) and 3(f). It is found to have a maximum probability at around 3.4 ˚ A and the OD vectors are found to maintain one distinct peak around cos α value of 0.75 and another broad peak between 0.0 to -0.75. These locations correspond to α = 45 ◦ and α = 90 to 140 ◦ , respectively (Figs.3(d) and 3(f)). This shows that the water molecules prefer to orient with one of their OD bonds pointing toward ~r (α=45 ◦ ). This angle also shows that there is a slight deviation from linearity of hydrogen bonds. The separation of the first and second solvation shells is clearly seen in color codes. This can be attributed to rather strong hydrogen bonding which prevents the exchange of water between the two shells during the simulation time. The density distribution in the 60−90 ◦ (Figs.3(e) and 3(f)) conical shell becomes more pronounced due to stronger hydrogen bonding interactions of surrounding water with oxygen atoms of the carbonate ion. 9



The three dimensional picture of the solvation shell is obtained through calculations of the spatial distribution functions (SDFs). The TRAVIS 51 software is used in the SDF calculations. The regions covered by the deuterium and oxygen atoms of water molecules are shown by grey and red isosurfaces, respectively. Both side and top views of these SDFs are shown in Figs.4(a) and 4(b). Due to ion-water hydrogen bonding interactions, the deuterium lobes are found to be closer to the ion than the oxygen atoms. Each oxygen atom of the carbonate ion is found to be surrounded by a ring-like lobe of higher probability of deuterium atoms of water arising from the strong hydrogen bonding interactions. The densities of oxygen and deuterium atoms are found to lie above and below the carbonate oxygen and not exactly in the direction of the CO line as determined by the preferred orientation of hydrogen bond interactions. It shows that the hydrogen bonds deviate slightly from the perfect linearity which was also seen in the radial/angular distribution functions discussed above. It is also interesting to see that there is almost zero or very small probability of finding a water right on top or below the carbonate carbon in the perpendicular direction within the cut-off distance of the solvation shell. Since there is a preferential solvation toward the oxygen sites, the solvation shell is found to exhibit characteristics of hydrophobic environment along the perpendicular axis of the carbonate ion 18 .

The presence of ions alters the local environment of water molecules which, in turn, can alter the vibrational frequencies of water molecules. Here, we have calculated the fluctuating stretch frequencies of water molecules by using the method of wavelet analysis 43–45 to capture the strength of the water molecules. Clearly, it is found that water molecules which are hydrogen bonded to the carbonate ion (Oc Dw 1st ) have red shifted stretch frequencies than bulk water molecules (Fig.5 and Table 1). Whereas, the OD modes of water in the first solvation shell which are bonded with other water molecules (Ow Dw 1st ) appear at the blue side in the frequency distribution as shown with red dashed curve in the Fig.5. This reflects the difference in the strength of ion-water and waterwater hydrogen bonds. The red shift of OD modes with ion-water hydrogen bonds is in accord with the results of an earlier IR study 11 which showed a red shift of 250-300 cm−1 in the stretch frequency of water in a solution of carbonate ions. An earlier Raman spectral study 24 also showed a new band in the red region of the OH stretch band

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corresponding to the strongly hydrogen bonded water molecules in the hydration shell of the bivalent CO2− anion. We note that such red shifts in water stretch frequencies 3 due to strong ion-water hydrogen bonding interactions were also found earlier for water near charged lipid surfaces 52,53 . Because of such strong hydrogen bond formation with 13,54 water, the CO2− Also, 3 ion was designated as a ”structure maker” in the literature.

the weakening of Ow Dw 1st can be interpreted as a result of the stronger hydrogen bond of a water making the other bond of the same water weaker which was also observed in an earlier study 55 . Another issue of interest is whether the effect of the ion is long ranged and extends beyond the first hydration shell. To address this issue, we have calculated the frequency distribution of the OD modes of water molecules in the second solvation shell of the ion. The average frequency in the second solvation shell (2348 cm−1 ) is also found to be red-shifted than the bulk frequency (2380 cm−1 ) which means the effect of the ion goes over a longer distance beyond the first hydration shell.

We have calculated the dipole moments of the carbonate ion and water molecules through calculations of the Wannier centers 56 for time-equispaced configurations from the simulation trajectory. The dipole moment of the carbonate ion in the aqueous solution is found to be 1.0 D. It may be noted that the dipole moment of CO2− 3 is zero in the gas phase. This finite value of the dipole moment of CO2− 3 in the solution can be attributed to the symmetry breaking of the ion because of its interactions with the fluctuating environment of surrounding water. The average dipole moment of water is found to be 3.05 D for the first hydration shell, 3.04 D for the second hydration shell and 3.01 D for the bulk phase. The bulk value is in agreement with earlier experimental and theoretical results 57–59 for pure liquid water.

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Dynamics of Water in the Solvation Shells

The orientational relaxation of OD vectors of water in the solvation shells of the carbonate ion and in the bulk region are investigated through calculations of the orientational correlation function defined as ClOD (t) =

< Pl (uOD (t) · uOD (0)) > , < Pl (uOD (0) · uOD (0)) >

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(2)


where Pl is the Legendre polynomial of rank l and uOD is the unit vector which points along an OD bond of a water molecule. In this work, we have calculated the time dependence of ClOD (t) for l=1 and 2. In Fig.6, we have plotted the second-rank rotational function (C2OD (t)) which is directly related to experimentally measured time dependent rotational anisotropy of water molecules. We have calculated the orientational correlation time from the fitted exponential functions. The results show that the OD rotational relaxation of the first solvation shell water (τ2OD =8.30 ps) is slower than that of bulk water molecules (τ2OD =5.45 ps). The fast short-time decay of C2 (t) captures the inertial and non-Markovian effects 60 . The long range effect of CO2− 3 ion on water molecules is also seen in the slower reorientational decay of the second solvation shell water molecules (τ2OD =7.92 ps) than bulk water (Fig.6 and Table 1). The orientational relaxation time (τ2OD ) of bulk water is in accord with the earlier results of Bankura et al 39 . The orientational motion of water was earlier ascribed to reorientation pathways involving large amplitude angular jumps 61 . The extended jump model was also found to be valid for ion-water hydrogen bond switching in the anionic hydration shells 25 . Here we have employed the jump model to analyze the reorientational motion of solvation shell water around the CO2− ion. We have considered all the events in which a water OD 3 bond, which was initially hydrogen bonded to one carbonate oxygen, switches its hydrogen bond to a different acceptor which can either be another oxygen of the carbonate ion (Route I) or the oxygen of a water (Route II) 22,62 . Several key quantities are calculated to characterize the hydrogen bond switches such as the distances RO*Oa and RO*Ow where O* is the oxygen of the reorienting solvation shell water and Oa and Ow represent the hydrogen bond acceptor oxygens in the carbonate and water molecules, respectively. The results of these calculations are shown in Figs.7(a) and 7(b). The D* is found to flip between the two carbonate oxygen atoms (Oa1 and Oa2 ) with a jump of θ = -18 ◦ to 18 ◦ and a comparatively larger jump angle of θ = -20 ◦ to 20 ◦ from Oa to Ow . These angles are found to be smaller than the corresponding values found earlier for the isoelectronic nitrate ion of similar molecular structure 22 , and which lies on the opposite side of the Hofmeister series. This is likely due to the denser surrounding of the carbonate ion due to its higher charge compared to the nitrate ion where one finds the partner quickly at a closer distance to switch its hydrogen bond, and thus requiring smaller angular jumps for such switching events.

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The lifetime of a hydrogen-bond is an important dynamical quantity that largely depends on the strength of the hydrogen bonds and also on other characteristics such as cooperativity in the network. Following earlier work 63,64 , we have calculated the continuous hydrogen bond correlation function which is defined as SHB (t) =

< h(0)H(t) > , < h(0)h(0) >

(3)

where H(t) = 1 if a water-water (or ion-water) hydrogen bond remains intact continuously from time 0 to t, otherwise H(t) = 0. The population variable h(t) = 1 if a tagged pair of water molecules (or an ion-water pair) is hydrogen bonded at time t, and it is zero otherwise. Clearly, SHB (t) gives the probability that a water-water or carbonate ion-water pair remains continuously hydrogen bonded from time t = 0 to t. The integral of SHB (t) gives the average hydrogen bond lifetime τHB . The hydrogen bond correlation function was calculated earlier to investigate the hydrogen bond dynamics in bulk water, aqueous ionic solutions and also in other hydrogen bonded media 63–69 . Fig.8 shows the decay of hydrogen bond correlations of water−water pairs around the carbonate ion and in the bulk. The existence of hydrogen bonds between ion-water and water-water is determined by taking the cutoff distances obtained from corresponding RDFs. The corresponding cutoff distances for ion-water and water-water hydrogen bonds are taken to be 2.30 and 2.45 ˚ A(first minimum of intermolecular oxygen-deuterium of RDFs), respectively. It is found that the average hydrogen bond lifetime of water molecules making hydrogen bonds with the carbonate ion (3.7 ps) is longer than that of water-water hydrogen bonds (2.32 ps) in the solvation shell (Fig.8). The lifetime of water-water hydrogen bonds in the hydration shell (2.32 ps) is found to be negligibly shorter than that of bulk water (2.43 ps) reported in Table 1 and Fig.8. This may be due to the stronger ion-water hydrogen bonding which in turn, makes the dynamics of water-water hydrogen bonds in the solvation shell little faster. The slower dynamics of ion-water hydrogen bonds is consistent with the higher strength of these hydrogen bonds as discussed in Sec.3. The increase in the lifetime of hydrogen bonds involving the carbonate species is in accord with the results of an earlier ab initio simulation study 19 and can be attributed to the higher charge density of the carbonate oxygens than that of water molecules.

We have also calculated the continuous residence correlation function SR (t) by following the method of Ref. 70 . Here, we consider the population variable g(t) which is 13



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equal to 1 when a water molecule is found in the hydration shell of the ion (or another water molecule) at time t, and it is zero otherwise. We also define another population variable g ′ (t; t∗ ) which is 1 if a water molecule, which was in the solvation shell of the ion (or another water molecule) at time t=0, remains continuously in the same solvation shell up to time t subject to an allowance time t*. That is, if the water molecule leaves the hydration shell for a period less than t* between the time 0 and t, it is assumed that it has not left the solvation shell at all. The continuous residence time correlation function is defined as SR (t; t∗ ) =

< g(0)g ′ (t, t∗ ) > . < g(0)g(0) >

(4)

The results of the continuous residence correlation functions are shown in Fig.9. We have used an allowance time of 2 ps 70 for calculations of the continuous residence function and found values of 12.70 ps and 9.49 ps for the integrated residence time (τr ) of water molecules in the solvation shell around C and in bulk, respectively. It is found that a water resides in the solvation shell of the carbonate ion for a longer period than the lifetime of carbonate ion-water hydrogen bonds. This is because the water in the ion hydration shell can switch its ion-water hydrogen bond to another oxygen of the carbonate ion while continuing to stay in the hydration shell. Also, the longer residence time gives rise to a slower mobility of the solvation shell water molecules than bulk. This trend is confirmed by the self-diffusion coefficients calculated from the mean square displacement of oxygens of water 62 . The diffusion coefficients (Table 1) are found to be 1.42 × 10−5 cm2 s−1 , 1.60 × 10−5 cm2 s−1 and 1.62 × 10−5 cm2 s−1 for water molecules in the first and second hydration shells of the carbonate ion, and in the bulk water, respectively. Clearly, the carbonate ion retards the translational mobility of water molecules in the solvation shells than bulk water. Finally, we note that this slower solvent dynamics in the neighborhood of the carbonate ion, compared to that of pure water, reflects the structure making ability of the CO2− 3 ion in water.

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Summary and Conclusions

We have presented an ab initio molecular dynamics study of the structure, dynamics and vibrational spectral properties of water in the solvation shells of a carbonate ion by using a dispersion corrected density functional. The carbonate ion is known to have

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anisotropic arrangement of water molecules around it. The complexity of the hydration shells around the ion could be properly addressed through calculations of the correlation functions beyond the regular one-dimensional pair distribution functions. In particular, we have calculated the conically restricted pair distributions around the carbonate ion which greatly helped in resolving the spatial arrangement of water molecules in the vicinity of the ion. It is found that, in the first solvation shell, there are about three water molecules hydrogen bonded to each oxygen of the carbonate ion whereas almost negligible density of water molecules is found towards the perpendicular axis of the carbonate ion within the cut-off distance of the first solvation shell. This is likely due to the hydrophobic-like environment that the water molecules feel along the perpendicular axis of the carbonate ion as it was also noted in an earlier study 18 . The radial/angular distribution functions yielded an even more detailed hydrogen bonding picture of the hydration shell and showed that there is a slight angular deviation from the linearity for the ion-water hydrogen bonds. The spatial distribution functions also revealed the three dimensional anisotropic arrangement of water around the carbonate ion. We believe such a combined approach to look at the structural properties would prove to be a useful means to investigate the asymmetric solvation of complex solutes. Distinct vibrational frequencies are found for OD modes of the same water molecule depending on whether a chosen OD mode is hydrogen bonded to the carbonate ion or to another water. The stronger ion-water hydrogen bonding interactions are found to give rise to a red-shift in the frequencies of OD modes which are hydrogen bonded to the CO2− 3 ion compared to that of the bulk water. Formation of such strong hydrogen bonds makes carbonate a ”structure maker”, which is also evident from the significant slowing down of the orientational relaxation, diffusion and also of residence and hydrogen bond dynamics of water in the vicinity of the solute. The carbonate ion is also found to have significant long range effect on neighboring water structure and dynamics beyond the first solvation shell. The nature of angular jumps for switching of hydrogen bonds from the carbonate oxygen to another oxygen of the carbonate ion or a water molecule is also investigated in the current study. The associated amplitude of angular jumps of the OD bond from oxygen of the carbonate ion to an oxygen of water found to be smaller than the angular jumps reported earlier for the nitrate ion which has a similar planar structure 22 . This is likely due to the more structured surroundings of water around the carbonate ion

15



unlike nitrate ions. We note that in the current study, we have probed the structure and dynamics of the anisotropic solvation shell of the carbonate ion through calculations of various structural and dynamical correlation functions. Very recently, it has been shown that the coordination number can also be used as a good probe for examining solvation structure and kinetics around ions and the asymmetry of solvation structure 71,72 . It would be interesting to use such approach to probe the solvation shells of carbonate and other polyoxy-anions. Finally, although the dipole moment of a carbonate ion is zero in the gas phase, it is found to be 1.0 D in water due to asymmetric interactions of the ion with fluctuating environment of the surrounding water molecules.

Acknowledgment Financial support through a J.C. Bose Fellowship to A.C. from the Science and Engineering Research Board, a statutory body of the Department of Science and Technology and University Grants Commission (through a Junior/Senior Research Fellowship to S.Y.), Government of India, is gratefully acknowledged. Part of the calculations were done at the High Performance Computing Facility at Computer Centre, IIT Kanpur.

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TABLE 1. Orientational Relaxation, Hydrogen Bond and Residence Times, Diffusion Coefficient and Vibrational Frequency of Water Molecules in Solvation Shells of the Carbonate Ion and in the Bulk Regiona .

Quantity

Ion-Water

1st Solvation Shell

2nd Solvation Shell

Bulk

τ2OD

−

8.30

7.92

5.45

τHB

3.7

2.32

−

2.43

τr

−

12.70

−

9.49

D

−

1.42

1.60

1.62

ω

2243

2424

2348

2380

a. Diffusion coefficient (D) and the vibrational frequency (ω) are expressed in 105 cm2 /s and cm−1 , respectively. All time constants are expressed in ps.

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FIGURES Fig.1. Radial distribution functions of (a) gOc Ow (r), gOc Dw (r), gOw Ow (r) and gOw Dw (r), and (b) gCOw (r) and gCDw (r), where Oc and C denote the oxygen atoms and carbon of the carbonate ion. Ow and Dw stand for water oxygen and deuterium atoms.

Fig.2. The left panel represents the definition of conical shells around the carbonate ion. The angles θ1 and θ2 are the angles with the principal axis of C3 symmetry. The radial distribution functions (RDFs) between center of mass of the carbonate ion (CO3 ) and oxygen atoms of water (Ow ) are plotted in (a) of the right panel for 0−30 ◦ (red), 30−60 ◦ (green), 60−90 ◦ (blue) and 0−90 ◦ (black) conical shells of the carbonate solvation shell, respectively. The corresponding plots for CO3 -Dw RDFs are shown in (b).

Fig.3. Top panel defines the molecular vectors and tilt angles of a water molecule in the carbonate solvation shell. The carbonate ion center of mass is taken as the origin. The vector ~r is defined as the vector joining the carbonate ion center of mass to the water oxygen and ~µ is the unit vector along the DOD angle bisector originating from oxygen. (a) The tilt angle ω is the angle between ~r and dipole vector ~µ; (b) The tilt angle α is the angle between ~r and OD bond vector. The radial/angular distribution functions of water position and dipole tilt angle, gCO3 −Ow (r,cos ω), in different conical shells of 30−60 ◦ , 60−90 ◦ angles are shown in figures (c), (e) respectively; Figs.(d) and (f) show the radial/angular distribution functions of water position and OD tilt angle, gCO3 −Ow (r,cos α), in different conical shells of 30−60 ◦ and 60−90 ◦ angles, respectively.

Fig.4. Spatial distribution functions of hydration shell water in the Cartesian space. (a) Top view (b) Side view. The deuterium atoms are shown in grey and the oxygens are plotted in red color.

Fig.5. Distributions of the stretch frequency for OD modes hydrogen bonded with Oc of the carbonate ion (Oc D1st w ) shown in red, hydrogen bonded with water in first solvation 2nd shell (Oc D1st w ) shown in red dashed, OD modes in the second solvation shell (Ow Dw )

shown in green dashed, dangling OD shown in blue color and bulk OD modes shown in 26


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black color.

Fig.6. Time correlation functions of OD orientation for the first solvation shell water (red), second solvation shell water (blue) and bulk water (black).

Fig.7. Time evolution of the hydrogen bond switching events as described in the text. (a) Route I, (b) Route II.

Fig.8. Time dependence of the continuous hydrogen bond correlation function (SHB (t)). The results for the solvation shell water-water hydrogen bonds are shown in red, bulk water-water hydrogen bonds shown in black color and the green dashed curve shows the relaxation of carbonate ion-water hydrogen bonds.

Fig.9. Time dependence of the continuous residence correlation function (SR (t)). The dynamics of the solvation shell water molecules is shown in red, and that of bulk water is in black color.

27



Figure 1.

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Figure 2.

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Figure 3.

Figure 4.

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Figure 5.

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Figure 6.

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Figure 7.

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Figure 8.

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Figure 9.

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TOC Graphic.

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An Ab Initio Molecular Dynamics Study

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