A First-Principles Molecular Dynamics Study of the Solvation Shell

Article pubs.acs.org/JPCB

A First-Principles Molecular Dynamics Study of the Solvation Shell Structure, Vibrational Spectra, Polarity, and Dynamics around a Nitrate Ion in Aqueous Solution Sushma Yadav, Ashu Choudhary, and Amalendu Chandra* Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur, India 208016 ABSTRACT: A first-principles molecular dynamics study is presented for the structural, dynamical, vibrational, and dipolar properties of the solvation shell of a nitrate ion in deuterated water. A detailed description of the anisotropic structure of the solvation shell is presented through calculations of various structural distributions in different conical shells around the perpendicular axis of the ion. The nitrate ion−water dimer potential energies are also calculated for many different orientations of water. The average vibrational stretch frequency of OD modes in the solvation shell is found to be higher than that of other OD modes in the bulk, which signifies a weakening of hydrogen bonds in the hydration shell. A splitting of the NO stretch frequencies and an associated fast spectral diffusion of the solute are also observed in the current study. The dynamics of rotation and hydrogen bond relaxation are found to be faster in the hydration shell than that in the bulk water. The residence time of water in the hydration shell is, however, found to be rather long. The nitrate ion is found to have a dipole moment of 0.9 D in water which can be attributed to its fluctuating interactions with the surrounding water. and molecular dynamics methods.20 The solvation structure of a nitrate anion has also been studied extensively by means of quantum chemical methods25−28 and molecular simulations.15,29−33 The main focus of these studies was on the hydrogen bond structure and energetics of the solvation shell water around the anion. However, to achieve a full characterization of the anisotropic solvation shell around a nitrate ion, it is necessary to deconvolute its hydration shell into smaller spatial and angular shells and investigate the nature of each of those individual shells around the ion. In the current work, we have presented such a study of the angle resolved structure of the anisotropic solvation shell of a nitrate ion in water by means of ab initio molecular dynamics simulation with a dispersion corrected density functional. On the vibrational spectral and dynamical side, a recent study of polarization anisotropic decay through two-dimensional infrared (2D-IR) spectroscopy combined with molecular simulation16 looked at the orientational dynamics of a nitrate ion in water. It was found that the rotational motion of the nitrate ion is faster than water. Thus, the breaking and reformation of hydrogen bonds of the surrounding water with oxygens of the nitrate ion can also be faster than that in bulk water. A very recent ultrafast 2D-IR spectroscopic study34 of molecular anions confirmed a weaker hydration shell for the

1. INTRODUCTION An understanding of the structure and dynamics of water in solutions containing inorganic ions is essential to explain different processes occurring in diverse systems like electrochemical cells, atmospheric aerosols, land water masses, and living organisms. However, in spite of exhaustive studies on the behavior of water in the presence of ions,1−8 the role of water still remains a mystery in many areas of science.9 In the case of poly-oxyanions, relative positions of the oxygen atoms may alter the hydration properties of the solutes when compared with those of simple monatomic anions. The nitrate ion, being the major player in atmospheric chemistry, is the most abundant and important species among all poly-oxyanions in a variety of chemical and biological processes. It is considered to be the terminal ion in the reactions involving nitrogen in inorganic compounds.10 This ion could also be formed from atmospheric N2 and O2 under ultraviolet or sunlight radiation.11,12 There have been many experimental and theoretical studies on the solvation structure of nitrate ions in liquid water and also at interfaces and clusters.1,13−33 The diffraction studies of aqueous nitrate solutions have revealed that this flat ion interacts differently with water in the axial and equatorial positions.23 The presence of such varying nitrate−water interactions has also been inferred from the broad distribution of OD stretch band around the nitrate ion.24 A recent study on NaNO3 solutions has explored the hydration and contact ion pairing of the sodium and nitrate ions for a range of salt concentrations by extracting their structural correlations using both experimental © XXXX American Chemical Society

Received: July 11, 2017 Revised: August 30, 2017

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DOI: 10.1021/acs.jpcb.7b06809 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B nitrate ion. Another experimental study based on a low field nuclear magnetic resonance (NMR) relaxometry approach35 also looked at the nature of interactions of simple and complex ions with water and revealed the kosmotropic/chaotropic duality of nitrate ions. The dual behavior was attributed to the asymmetric distribution of water in the hydration shell. The presence of an asymmetric solvation environment of NO3− ion leading to a splitting of the NO vibrational frequency band was also found in the experimental study of ref 34. It has been shown in recent molecular dynamics simulations36−38 that there can be two reorientational routes of water molecules around a nitrate ion. In the first case, the switching of hydrogen bonds takes place between two oxygens of the same nitrate ion. In the second case, a water initially hydrogen bonded to a nitrate ion switches its hydrogen bond to another water molecule. The nature of nitrate rotation was shown to be different for the two mechanisms of hydrogen bond switching.37 In the current study, we have further examined the molecular details of these hydrogen bond switching processes and their connections to other dynamical and spectral properties of the solute and hydration shell water from ab initio molecular dynamics. The aim of the present study is to explore the microscopic structure, dynamics, vibrational spectra, and polarity of the hydration shell of a nitrate ion through Car−Parrinello molecular dynamics simulations39,40 using a dispersion corrected density functional. To the best of our knowledge, such an ab initio simulation study with a dispersion corrected density functional is presented here for the first time for a nitrate ion−water system. First, we have looked at the angle resolved anisotropic structure of the solvation shell around the nitrate ion through deconvolution of various spatial and orientational structural distributions into different angular conical regions around the perpendicular axis of the nitrate ion. We have calculated the radial and radial/angular distribution functions in different axial conical regions around the solute which provide detailed information on the anisotropic arrangement of water molecules around a nitrate ion. The spatial distribution functions are also calculated to explore the changes in spatially resolved angular preferences of water molecules around the nitrate ion. We have also performed ab initio calculations of the nitrate ion−water dimer potential energies for many different orientations of the water molecule in the plane of the nitrate ion and also in perpendicular positions. The simulation results of the hydration shell structure having preferable ion−water interactions in the plane of the nitrate ion are discussed on the basis of the differences in the nitrate ion−water potential energies for different relative orientations of water and the solute ion. Subsequently, we have looked at the vibrational spectral and dipolar properties of the solute and solvation shell water and also examined how the nitrate ion affects the orientational relaxation of water OD groups and water dipoles. Specifically, we have looked at the changes in the dynamics of the solvation shell as compared to that of the bulk. We have calculated the angular jumps of the solvation shell water and also the hydrogen bond and escape dynamics of hydration shell water molecules around the nitrate ion. Apart from the dynamics of the surrounding water, we have also looked at the rotational relaxation and vibrational spectral diffusion of the NO modes of the nitrate ion in water. The organization of the rest of the paper is as follows. In section 2, we have described the simulation details of the

aqueous nitrate solution that is considered in this study. In section 3, the results of the angle resolved anisotropic structure of the solvation shell in different axial conical regions around the solute, quantum calculations of the nitrate−water dimer, and also vibrational spectral properties of the solvation shell water in the aqueous solution are discussed. The results of our dipole moment calculations are presented in section 4. In section 5, the dynamical results are presented for the rotational relaxation, hydrogen bond, and escape dynamics of solvation shell water and also the orientational jumps during hydrogen bond switching processes in the solvation shell. Finally, our conclusions are briefly summarized in section 6.

2. COMPUTATIONAL DETAILS In the present work, we carried out ab initio molecular dynamics simulation of an aqueous solution of a nitrate ion by using the Car−Parrinello method39,40 and the CPMD code.41 We considered a single nitrate ion in a cubic box of 107 water molecules. The edge length of the simulation box (14.84 Å) was determined from the corresponding experimental density of the solution.42 Periodic boundary conditions were applied in all three directions. The Kohn−Sham (KS) formulation43 of the density functional theory was employed for calculation of the electronic structure of the extended system. The core electrons were treated via Troullier−Martin44 pseudopotentials. The plane wave expansion of the KS orbitals was truncated at a kinetic energy cutoff of 80 Ry. We used a fictitious electronic orbital mass of μ = 800 au and a simulation time step of 5 au for integration of the dynamical equations. We considered D2O in place of H2O by assigning the deuterium mass to all of the hydrogen atoms which ensured that the electronic adiabaticity and energy conservation were maintained throughout the simulation45 for the chosen time step and electronic orbital mass. We note that the proper choice of the fictitious orbital mass parameter and time step are important issues in carrying out Car−Parrinello simulations. While a value of 800 au for the fictitious orbital mass is not expected to reliably maintain electronic adiabaticity for H2O,46 it was found to be acceptable for the current D2O system, as no significant drift in the orbital kinetic energy was observed during the simulations. Thus, it is noted that the dynamical properties that are discussed in the following sections are those of a nitrate ion in liquid D2O rather than liquid H2O. In the current simulation, we employed the BLYP-D2 functional where the dispersion corrections are incorporated into the BLYP functional47,48 by using the scheme of Grimme.49,50 In recent years, there have been a number of ab initio simulation studies on ionic solutions and other hydrogenbonded liquids which have shown the importance of dispersion interactions in an accurate description of the structure, dynamics, and phase diagram of these liquids.51−56 In the present study, we have used the Grimme-D2 version50 of the dispersion correction scheme in which the damped atompairwise dispersion correction of the form C6r−6 is 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 between a pair of atoms. The initial configuration of the system was generated using classical molecular dynamics simulation with empirical interaction potentials. The ab initio simulation was run for ∼15 ps for equilibration in the canonical ensemble at 298 K and then for another 80 ps in the microcanonical ensemble. After the trajectories were generated, we performed a B


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also note that the first peak of the OnDw correlation is found to be of significantly lower height, thus showing a weaker and less structured hydration shell, than that predicted by classical simulations with fixed-charge force fields.16,32,37 The overprediction of the hydration structure of the nitrate ion by classical nonpolarizable force fields was also noted in ref 16. The weaker hydration shell of the nitrate ion is also supported by our vibrational frequency calculations of solvation shell water molecules which are discussed later in this section. In Figure 1b, it is interesting to note that the first peak of the NDw correlation is located closer to the nitrogen atom than the NOw peak. The two peaks are located at 2.6 and 3.6 Å, respectively. The neutron diffraction measurements63 have also determined the locations of the gNH and gNO maxima to be at 2.8 and 3.78 Å, respectively. Since the N atom is positively charged, the peak of NDw correlation can be expected farther from N in comparison to that of the NOw peak around the nitrogen atom. Hence, the location of this first peak of the NDw correlation needs to be understood in greater resolution. It was also found in the experimental study of ref 22 that the axial hydrogens are closer to the nitrogen than the oxygens. It was also inferred that the oxygen atoms of the nearest-neighbor water molecules are axially above or below the nitrogen atom. In view of these findings and also in order to capture the anisotropic nature of the solvation shell, we have performed a deconvolution of the pair correlation functions which gives the angle resolved picture around the nitrate ion. The solvation shell structure of the nitrate ion is studied through different conical shells around the nitrate ion. These conical shells of thickness Δθ are defined as the region between two coaxial cones around the same principal axis with conical angles θ1 and θ2, as shown in Figure 2. The volume of such a conical shell of angular thickness Δθ = (θ2 − θ1) is

time series analysis using the wavelet method57−59 to calculate the time dependent vibrational frequencies of OD stretch modes of all of the water molecules. The methodological details of the calculation of time dependent OD stretch frequencies from ab initio simulation trajectories have already been described elsewhere.60,61

3. STRUCTURAL AND VIBRATIONAL SPECTRAL PROPERTIES OF THE HYDRATION SHELL 3.1. Radial Distribution Functions. We first investigate the overall structure of the nitrate ion solvation shell through calculations of the radial distribution functions which are shown in Figure 1. Note that the hydrogen atoms are represented by D

Figure 1. Radial distribution functions of (a) gOnOw(r), gOnDw(r), gOwOw(r), and gOwDw(r) and (b) gNOw(r) and gNDw(r), where On and N denote the oxygen and nitrogen atoms of the nitrate ion and Ow and Dw stand for water oxygen and deuterium atoms.

Vθ2 − θ1 = (4/3)π(cos θ2 − cos θ1)r 3

as we have used the deuterium mass for H. We have shown the radial distribution functions gOnOw(r), gOnDw(r), gOwOw(r), gOwDw(r), gNOw(r), and gNDw(r) in Figure 1, where On denotes the oxygens of the nitrate ion and Ow and Dw stand for the oxygen and deuterium atoms of water. Our results of the nitrate ion−water structural correlations are in good agreement with those of a recent ab initio simulation study which used a smaller system size and different values for other simulation parameters like the time step and fictitious orbital mass.16 In Figure 1a, pronounced peaks are found at 2.76 Å for OwOw and at 1.80 Å for OwDw RDFs. For comparison, the peaks of the experimental OwOw and OwDw RDFs for pure water are located at 2.88 and 1.85 Å, respectively.62 The OwOw and OwDw RDFs for the nitrate solution simulated here (Figure 1a) resemble those of pure water, indicating that the nitrate ion does not significantly affect the water−water structure. In contrast, for the OnDw (red curve in Figure 1a), the considerably smaller peak at 1.89 Å shows a more diffuse and weaker first hydration shell of the NO3− ion, whereas a pronounced peak at 1.80 Å and lower first minimum of OwDw correlation (blue curve in Figure 1a) mean a highly structured first solvation shell of water in bulk around a “solute” water. The OnOw peak maximum at 2.8 Å followed by a flat minimum means exchange of water molecules between the two solvation shells. Similar results for RDFs were also found in previous mixed quantum/classical simulations.33 We

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Figure 2. Definition of conical shells around the nitrate ion. The angles θ1 and θ2 are the angles with the principal axis of C3 symmetry. θ2 − θ1 (=Δθ) is the angular thickness of the conical shell of interest. C


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The Journal of Physical Chemistry B where θ1 is the smaller angle and r is the radial distance from the center of mass of the nitrate solute, as shown in Figure 3.

again because there exists no well-defined structural feature in this region. A more pronounced peak at 2.6 Å and a welldefined structure appear in the 30−60° conical shell region which increases in the 60−90° conical shell region. This can be attributed to the interaction of the deuterium of water in the first solvation shell with oxygens of the nitrate ion which are located in the larger conical shell regions. 3.2. Radial/Angular Distribution Functions. The radial/ angular distribution functions represent the structural probability distributions resolved in both radial and tilt angle coordinates, and hence provide further insights into the orientational preference of water molecules around the nitrate ion. These distributions are calculated for the water dipole tilt angle ω and the OD bond vector tilt angle α which are defined as the angles that the dipole and OD vectors of a water molecule make, respectively, with the vector connecting the water oxygen to the nitrate center of mass. These tilt angle definitions are illustrated in Figure 4. The results of water dipole (gNit−Ow(r, cos ω)) and O−D (gNit−Ow(r, cos α)) radial/ angular distribution functions for different conical shell regions are shown in Figure 5.

Figure 3. (a) Radial distribution functions (RDFs) between the center of mass of the nitrate ion (Nit) and oxygen atoms of water (Ow) plotted for 0−30° (red), 30−60° (green), 60−90° (blue), and 0−90° (black) conical shells of the nitrate ion solvation shell. The corresponding plots for Nit−Dw RDFs are shown in part b.

For a symmetrically solvated ion, the RDFs can be calculated by considering the spherical shells around the ion and normalizing those by the uniform bulk density. However, for an oxyanion like nitrate which has an asymmetric solvation shell, we have divided the overall solvation shell into different conical regions by taking the nitrate center of mass as the reference point and then calculated the nitrate center of mass-oxygen (gNit−Ow(r)) and nitrate center of mass-deuterium (gNit−Dw(r)) RDFs separately for different values of the corresponding conical angles, as shown in Figure 3, where Nit represents the center of mass of the nitrate ion. The angularly resolved RDFs reveal major differences at different conical angles. It is to be noted that the 0−90° conical region represents the total solvation shell around the nitrate ion in Figure 3a and b. It is found from Figure 3a that, for the conical shell of 0−30°, all gNit−Ow(r) correlations show a broad first peak which is likely because the weak structural features are averaged out by other water molecules. Moreover, this peak is closer toward the center of mass in comparison to that in other conical regions. This can be seen from the RDFs (Figure 3a) where it started to evolve from 2.5 Å for the 0−30° conical shell, whereas it starts from 2.8 Å in other conical regions. This is in accordance with the neutron diffraction results22 where the nearest neighbor oxygens were found to be in the axial positions. It is interesting to note that, with an increase of the angle of the conical shell, the positions of the peaks remain unchanged. However, the peaks become prominent as they appear because of structural arrangements due to hydrogen bonding interactions in the larger conical shell regions. For the Nit−Dw pair distributions, the deconvolution of the pair correlation functions provides a noticeable difference in the three different conical shell regions. The overall solvation shell structure (0−90°) around the nitrate ion in Figure 3b is resolved in different conical shells. A small shoulder followed by a broad peak appear in the small conical shell (0−30°) which is

Figure 4. Definition of molecular vectors and tilt angles of a water molecule in the nitrate solvation shell. The center of mass of the nitrate ion is taken as the origin. The vector r⃗ is defined as the vector joining the nitrate ion center of mass to the water oxygen, and μ⃗ is the unit vector along the DOD angle bisector originating from oxygen. (a) The tilt angle ω is the angle between r ⃗ and the dipole vector μ⃗ . (b) The tilt angle α is the angle between r⃗ and the OD bond vector.

The dipole orientational correlations provide information on the preferred orientation of water dipoles near the nitrate ion in different conical shells (Figure 5a−c). For the 0−30° conical shell shown in Figure 5a, a broad distribution of the dipole tilt angle is found which shows that water molecules are arranged with no clear preference of the tilt angle. This result is consistent with the 0−30° RDF shown in Figure 3a. As we move from smaller to larger conical shells (Figure 5a and b), the peak below 4.0 Å evolves in the range of cos ω = 1.0 to 0.0. This corresponds to the value of ω from 0 to 90°. The peak becomes more prominent in the 60−90° conical region shown in Figure 5c. An interesting feature appears from the OD bond vector orientation in Figure 5d where the two broad peaks in the 0−30° conical shell region mean no clear preferential alignment of water molecules in this region. However, water molecules show higher angular preference in the 30−60 and 60−90° conical shells, as can be seen from Figure 5e and f. The 30−60° conical shell (Figure 5e) is found to have a maximum probability at around 3.4 Å, and the OD vectors are found to maintain one distinct peak around cos α = 0.75 and another broad peak between 0.0 to −0.75. The first peak corresponds to α = 45°, and the broad peak falls in the range of α = 90−140° (Figure 5b). The peaks become more prominent for the larger conical shells (Figure 5f). The water molecules in larger conical D


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Figure 5. Radial/angular distribution functions of water position and dipole tilt angle, gNit−Ow(r, cos ω), in different conical shells of 0−30, 30−60, and 60−90° angles arranged from top to bottom in parts a−c. Parts d−f represent the radial/angular distribution functions of water position and OD tilt angle, gNit−Ow(r, cos α), in different conical shells of 0−30, 30−60, and 60−90° angles.

Figure 6. Nitrate ion−water binding energy (kcal mol−1) curves for different orientations of water along the (a) axial and (b−d) equatorial directions. The angle along the X-axis is that of the OD bond (with circled D) with respect to the C3 (perpendicular) axis of the nitrate ion for (a) axial nitrate−water dimer and (b) with respect to an NOn bond of the nitrate ion in the equatorial plane for equatorial nitrate−water dimers. The angle corresponds to the clockwise rotation of the OD bond with the circled D. (a) The oxygen of water is placed at 3.4 Å (NOw peak maximum) from the center of mass of the nitrate ion along the C3 axis, and (b) the water oxygen is placed at 2.9 Å from On along an NOn axis. The water oxygen is placed in the equatorial plane, and (c) the tagged OD is rotated out of the plane or (d) the tagged OD is rotated in the equatorial plane.

shells prefer to orient with one of their OD bonds pointing toward r ⃗ (α = 45°) and the second OD pointing away from r.⃗ The second broad peak is due to the other deuterium of the hydrogen bonded water and is averaged out with the bulk water molecules. This is also expected from the dipole orientational picture discussed above for the same regions. Thus, the water molecules in these regions show preferred orientation for hydrogen bonding. The maximum probability region shifts to larger distances and becomes broader for smaller conical regions (Figure 5d) which means a weakening of the solvation shell and no clear preference for any particular OD vector orientation in the smaller conical shell region of the solvation shell. Therefore, the radial/angular distribution functions reveal the presence of nitrate ion−water hydrogen bonding interactions at larger conical shell regions. One can clearly

connect the angular preference of water dipoles and OD vectors to the peaks observed in the Nit−Ow and Nit−Dw RDFs. In Figure 6, we have presented further analysis of different parts of the Nit−Ow radial/angular distribution functions for the axial (toward the C3 axis) and equatorial (in the plane of the nitrate ion) conical regions around the nitrate ion using separate calculations of a nitrate−water dimer. This is done following our earlier work on the anisotropic environment of benzene in water.64 Here, the objective is to explore the nature of axial and equatorial nitrate−water dimeric configurations that contribute to the maxima and minima of the nitrate−water radial/angular distribution functions in the respective regions. The Nit−Ow distances are kept fixed at 4.2 Å. In Figure 6a, the water molecule initially kept at the top of the nitrate (in the E


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ion and deuterium atoms of water in the plane of the nitrate ion, as it was also seen from the radial-angular distribution functions of Figure 5. 3.4. Vibrational Frequencies of Water and the Nitrate Ion. The local environment of water molecules can be affected by the presence of ions which, in turn, can alter the vibrational frequencies of water molecules. We have used the method of wavelet analysis57−59 to calculate the fluctuating stretch frequencies of water molecules inside the solvation shell of the nitrate ion with an On−Ow distance cutoff of 3.3 Å. The stretch frequencies of the solvation shell water are found to be higher on average than the bulk water molecules. This implies a shift to the lower vibrational frequency when a water molecule leaves the solvation shell of the nitrate ion and enters the bulk water. In Figure 8a, we have shown such a change in the instantaneous stretch frequency of a water molecule which was initially hydrogen bonded to On of NO3− ion and then leaves its solvation shell. The results shown in Figure 8a and b are for a particular OD bond. In order to have a better understanding of the average frequency of OD modes that are hydrogen bonded to the nitrate oxygens and also of OD modes in the bulk, we have calculated the frequency distributions, as shown in Figure 8c. The frequency of an OD mode hydrogen bonded to an oxygen of the nitrate ion is found to be greater (blue-shifted) than that of an OD mode in the bulk water. The shift toward higher frequency for a water near the nitrate ion means the nitrate ion−water hydrogen bonds are weaker than water− water hydrogen bonds. The power spectra from the velocity autocorrelation function of deuterium atoms of the hydration shell and bulk water molecules are shown in Figure 8d. The power spectrum also shows a blue shift of about 25 cm−1 for the stretch frequencies of hydration shell water compared to the corresponding spectrum of bulk water. This is in accord with the results of the earlier QM/MM study33 of hydrated NO3− which showed that the nitrate ion can break the water structure of the hydration shell in its vicinity. Also, the recent ultrafast infrared spectroscopic study34 showed a weaker hydrogen bonding between the nitrate ion and water with a blue-shifted (15 cm−1) OH stretch in the nitrate solution than that of pure water. It may, however, be noted that in the current work we have considered deuterated water, hence the calculated stretch frequency is that of an OD mode rather than the OH stretch measured experimentally in ref 34. Moreover, we have also looked at the frequency distribution of NO modes of NO3− ion which is shown in Figure 9a. Interestingly, we see a splitting of the N−On stretch into two features with frequencies centering around 1087 and 1150 cm−1. This splitting was also found in experiments and interpreted in terms of an asymmetric distribution of water around the nitrate ions.34 The current results are also in agreement with the findings of an NMR study35 which revealed an asymmetry in terms of strongly and weakly bound water molecules around a nitrate ion. We have also looked at the frequency−frequency time correlation function61 to capture the time dependence of vibrational frequency changes of the NO modes due to fluctuations in the surrounding environment. The associated time scale is found to be 140 fs, as shown in Figure 9b which is faster than the recently found time constant of 490 fs for the nitrate ion stretch lifetime from 2D-IR spectroscopic study.34 This difference may be attributed to the difference in concentration or the simulation conditions from that of the experimental systems.

axial position) is rotated so as to vary its OD orientation with respect to the C3 axis of the nitrate ion from −180 to +180°. Here, the two minima are found at 0 and 180°, while a maximum is present at 120°. These results can be correlated with the radial/angular distribution function (Figure 5d) where the probability is found to be maximum at around 30 and 180°. At 0°, it is relatively less probable because an OD mode oriented directly toward Nit (center of mass of the nitrate ion) will minimize the hydrogen bonds. Also, with water−water hydrogen bonds being more stable than the nitrate−water hydrogen bonds, the orientational angle is somewhat increased to maximize the number of hydrogen bonds, and therefore one finds a probability maximum peak at around 30° in the radialangular distribution function. In Figure 6b, where the correlation in the equatorial region is shown, the minimum is found at 0° which means the linear arrangement is favorable for On−Dw for hydrogen bonding. We have also rotated the equatorial OD mode in and out of the plane in Figure 6c and d, respectively. These calculations confirm that the region around 25° is more stable and it shows up as a strong peak in Figure 5e and f. Moreover, it is important to note that the nitrate ion−water interaction energies for water in the equatorial positions are stronger than those in the axial positions. Thus, the equatorial positions are found to provide more stable and preferred interaction for the nitrate ion−water pairs. 3.3. Spatial Distribution Functions in Cartesian Space. The spatial distribution functions (SDFs) provide a threedimensional picture of the arrangement of water molecules in the solvation shell. In the present study, the SDFs65 are calculated in the Cartesian space by considering the positions of oxygens in a body fixed frame centered at the center of mass of the nitrate ion. The calculations are done by using the TRAVIS66 software. The yellow and red isosurfaces in Figure 7

Figure 7. Spatial distribution functions of the hydration shell water in the Cartesian space: (a) side view; (b) top view. The deuterium atoms are shown in yellow, and the oxygens are shown in red color.

describe the regions covered by the deuterium and oxygen atoms of water molecules, respectively. The side view is shown in Figure 7a, and the corresponding top view of the SDFs is shown in Figure 7b. It is seen that the Dw atoms of water reside preferentially closer to the nitrate ion than the Ow atoms of water due to hydrogen bonding and electrostatic interactions. The six lobes of higher probability of the deuterium atoms, represented by the yellow color in Figure 7, are distributed around the nitrate plane and along the bisector On−N−On angles. This is consistent with the higher probability of finding hydrogen bonding interactions between oxygens of the nitrate F


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Figure 8. Time dependence of the fluctuating frequency of an OD bond of water as it leaves the solvation shell of On to which it was hydrogen bonded initially. The time when the escape occurs, i.e., when the On−Ow distance exceeds 3.3 Å, is taken to be t = 0, and the frequency and distance fluctuations are shown for ±2 ps before and after the escape event. (a) Time dependence of the stretch frequency of the OD bond and (b) the corresponding On−Ow distance. (c) Distribution of the OD frequency for all OD modes hydrogen bonded to an On of the nitrate ion (red) and bulk (black). (d) Power spectra of the velocity time correlation of deuterium atoms of heavy water in the nitrate hydration shell (red dashed) and in the bulk region (solid black).

Figure 10. Although there is a substantial width in the probability distributions, on average, the frequency is seen to increase with an increase of the On−Dw distance, as can be seen from Figure 10a. A similar conditional probability distribution of observing an N−On frequency for a given On−Dw distance is shown in Figure 10b. The N−On frequency shows a broader distribution, implying the presence of varying environments of the surrounding water molecules. In Figure 10c, we have shown the cross correlation distribution of N−On and Ow−Dw frequencies. This distribution shows a slightly diagonal relationship, meaning a rather weak correlation in the changes of N−On and Ow−Dw frequencies. We note that such a cross correlation distribution was also looked at in the recent experimental study of aqueous solutions of nitrate and carbonate ions.34 A weaker hydration shell and less mixing of the N−On and Ow−Dw frequencies in the nitrate solution were found compared to that of the carbonate solutions.

4. ELECTRONIC PROPERTIES: DIPOLE MOMENT OF WATER AND THE NITRATE ION The interactions of the nitrate ion with the surrounding water have also been analyzed through calculations of the electronic properties. In particular, it is known that the electronic polarization effects affect the molecular dipole moments. The dipole moments of the nitrate ion and water molecules have been calculated through calculations of the maximally localized Wannier function (MLWF) centers67 for a series of timeequispaced configurations from the simulation trajectory. The average dipole moment of the nitrate ion is zero in the gas phase, but it is found to have a finite nonzero value of 0.9 D in water. This can be attributed to the breaking of symmetry of the ion because of its fluctuating interactions with the surrounding water. The dipole moments of water molecules show a distribution centered at 2.9 D. The results of water

Figure 9. (a) Frequency distribution of NO modes of the nitrate ion. (b) Frequency time correlation function of the fluctuating frequencies of NO modes of the nitrate ion.

We have also calculated the conditional probability distributions of observing a particular Ow−Dw frequency for a given On−Dw distance for water molecules in the nitrate solvation shell of the nitrate ion, and the results are shown in G


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Figure 10. Joint probability distribution of On−Dw distance and (a) Ow−Dw frequency and (b) N−On frequency, respectively. The contour levels of different fractions of the maximum value are shown in different color codes. (c) Cross correlation probability distribution of the aforementioned Ow−Dw and N−On frequencies.

dipole distribution are found to be in general agreement with earlier results for pure liquid water68−70 (figure not shown).

Table 1. Orientational Relaxation Times of the Nitrate Ion and Water Molecules inside the Solvation Shell and in the Bulk Regiona

5. DYNAMICS OF THE HYDRATION SHELL 5.1. Rotational Dynamics and Angular Jumps. The rotational motion of water molecules is closely related to the formation and breaking of hydrogen bonds. The orientational motion of water molecules is investigated by calculating the OD vector orientational time correlation function, COD l (t), for water in the solvation shell of the nitrate ion and also for bulk water molecules. The orientational correlation function is defined as ClOD(t ) =

⟨Pl(uOD(t ) ·uOD(0))⟩ ⟨Pl(uOD(0)·uOD(0))⟩

∫0

∞

dt ClOD(t )

ion

τNO l τOD l

1.23

τHB

0.40

solvation shell

bulk

1.79 1.50

2.85 1.95

a

Results for average lifetimes of the nitrate ion−water HBs and also water−water HBs in the solvation shell and bulk water are also included. All time constants are expressed in picoseconds.

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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 COD l (t) for l = 1 and 2. We have shown only the second-rank rotational function (COD 2 (t)) which is directly related to the experimentally measured time dependent rotational anisotropy of water molecules. The orientational correlation time, τOD l , is defined as the time integral of the orientational correlation function τlOD =

quantity

Figure 11. Time correlation functions of water OD orientation for solvation shell water (red), bulk water (black), and the nitrate ion (green dashed).

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We have calculated τOD by explicit integration of COD l l (t) from simulation and by calculating the integral for the tail part from fitted exponential functions. The orientational relaxation times for the solvation shell OD vectors and also for the other OD vectors of bulk water molecules are included in Table 1. The results show that the OD rotational relaxation of the hydrated water (τOD = 1.79 ps) is faster than that of bulk water molecules l (τOD = 2.85 ps). The short-time decay of C2(t) is usually l nonexponential due to inertial effects,71 as can be seen from Figure 11. The slower reorientational component was shown to

arise from reorientational pathways which involve large amplitude angular jumps.72 The jump model was found to be equally valid for ion−water hydrogen bond switching events in the anionic hydration shells.73 The overall faster dynamics in the solvation shell can be linked to the structure breaking ability of the nitrate ion which accelerates the orientational relaxation of the hydration shell water.33,36 This structure breaking ability was also seen in the previous section where a blue shift in the frequency was found for the hydration shell water compared to that of the bulk water. We have also looked at the rotational H


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The Journal of Physical Chemistry B dynamics of the nitrate anion itself, as shown by the green dashed line (Figure 11), and compared it with that of the bulk water. The orientational relaxation of the nitrate ion is faster (τNO = 1.23 ps) than water molecules, which is in qualitative l agreement with the experimental findings of ref 74 which dealt with NO3− in H2O and can be linked to the weak and shortlived character of the hydrogen bonds formed by the nitrate ion with the surrounding water. The time scales are included in Table 1. We have also looked at the rotational dynamics of OD bonds in the solvation shell of the nitrate ion from the perspective of the angular jump mechanism. Following earlier work,36,37 we have considered all of the events in which a water OD bond, that was initially hydrogen bonded to an oxygen of the nitrate ion, switches its hydrogen bond to a different acceptor that can either be another oxygen of the nitrate ion (route I) or the oxygen of a water (route II). The two relaxation routes are shown in Figure 12. Several key quantities which are calculated

Figure 13. Time evolution of different distances and angles during the hydrogen bond switching event as described in the text and in ref 36: (a) route I; (b) route II.

hydrogen bond time correlation function, SHB(t),75−78 which gives the probability that a water−water or a nitrate ion−water pair remains continuously hydrogen bonded from time t = 0 to t. The average hydrogen bond lifetime τHB is defined as the integral of SHB(t). Figure 14 shows the decay of hydrogen bond

Figure 12. Successive steps of the concerted process of breaking of a nitrate ion−water hydrogen bond and formation of a new H-bond of the same water with another oxygen of the nitrate ion (route I) or with the oxygen of a water (route II). (a) Route I: Initially, H-bonded water jumps from one oxygen (Oa1) to another (Oa2) of the nitrate anion. RO*Oa1 and RO*Oa2 are the oxygen−oxygen distances between the water and its starting and ending H-bond acceptors, respectively. θ is the angle between the O*D* vector and the Oa1O*Oa2 bisector plane. (b) Route II is the same as route I, except that the water jumps from one nitrate oxygen (Oa) to another water oxygen (Ow).

to characterize the hydrogen bond switch, in particular the distances RO*Oa and RO*Ow, where O* is the reorienting hydration shell water and Oa and Ow are the hydrogen bond acceptor oxygens in the nitrate ion and water molecules, respectively, are shown in Figure 12. The notations used here are similar to those used for ion−water switches in ref 36. The D* is seen to flip between the two nitrate oxygen atoms (Oa1 and Oa2) with a jump of θ = −18 to 18° and with a larger jump angle of θ = −35 to 35° from Oa to Ow, which is consistent with the earlier results by Xie et al.36 The smaller jump angle in route 1 can be attributed to the closeness of the two oxygens of the nitrate ion, while the larger jump in route II is likely due to the search for a suitable water (Ow) by D*, as shown in Figure 13. The current ab initio results of the jump dynamics are also consistent with the findings of a recent molecular dynamics study37 of an aqueous solution of KNO3 which used empirical force fields and a much larger simulation system. We also note that the smaller angular jumps as required by route 1 of hydrogen bond switching than the other route in the solvation shell or in the bulk facilitate the breaking of hydrogen bonds and thus contribute to the faster hydrogen bond and rotational relaxation of solvation shell water. 5.2. Dynamics of Hydrogen Bond Breaking and Escape of Water. We have calculated the continuous

Figure 14. 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, those for the bulk water−water hydrogen bonds are shown in black, and the green dashed curve shows the nitrate ion−water hydrogen bonds.

correlations of water−water pairs around the nitrate ion and also of ion−water pairs. The integrated relaxation times of the nitrate ion−water and water−water hydrogen bonds are included in Table 1. It is found that the average lifetime of hydrogen bonds between the nitrate ion and water is less than that of water−water hydrogen bonds in the solvation shell. The lifetime of water−water hydrogen bonds in the hydration shell is, in turn, shorter than that of bulk water. The ion−water hydrogen bond dynamics is found to be much faster than the water−water pairs which can be attributed to the weaker nature of the ion−water hydrogen bonds in the hydration shell of the nitrate ion. I


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ion and also in perpendicular positions. The simulation results of the hydration shell structure of ion−water RDFs having preferable interactions in the plane of the nitrate ion are discussed on the basis of the differences in the nitrate ion− water potential energies for different orientations. The spatial distributions of water molecules around the nitrate ion provide distinct density lobes of deuterium atoms of water around the nitrate plane which again reveal the presence of hydrogen bonding in the plane of the ion. It is shown that the ion−water interactions have a noticeable influence on the vibrational stretch frequencies of the hydration shell water. A rather wide distribution of the vibrational frequencies is found for both the hydration shell and bulk water. The average vibrational stretch frequency of OD modes in the solvation shell of the nitrate ion is found to be higher than that of other OD modes in the bulk which signifies a weakening of hydrogen bonds in the solvation shell. It is found that the contributions to the blue side of the frequency distribution originate from weakly hydrogen bonded OD oscillators in the solvation shell, while the bulk molecules essentially behave like the pure water OD oscillators. The asymmetric nature of the hydration shell is also captured in the N−On frequency distribution with a splitting of the peak which is in good agreement with recent IR experiments.34,35 Results are also presented for the dipole moments of the nitrate ion and water molecules in the solution. On the dynamical side, we have first looked at the orientational relaxation of OD vectors of water molecules that are in the hydration shell of the NO3− ion and also of other OD bonds. Our calculations show a significantly faster rotational relaxation of water in the hydration shell of the nitrate ion which is in agreement with earlier experimental results.16,34,74 As the hydrogen bonds get weaker, the OD frequency is blue-shifted and the reorientation of water molecules becomes faster in the solvation shell than that in the bulk. The nitrate ion−water hydrogen bond lifetime is also found to be shorter than that of water−water hydrogen bonds. The shorter ion−water hydrogen bond lifetime also leads to a rather fast spectral diffusion of the solute NO modes in water. Further, the solvent residence time in the hydration shell is found to be intimately linked to the molecular structure of the nitrate ion. While for a chosen nitrate oxygen the calculated residence time of water in its hydration shell is found to be shorter than that around a “solute” water in the bulk, the overall residence time of a water molecule in the entire solvation shell of the nitrate ion is found to be significantly longer. Calculations of the angular jumps reveal that the availability of two routes of hydrogen bond switching, which were also identified in earlier studies,36,37 from an oxygen of the nitrate ion to another oxygen of the same ion or to the oxygen of a water molecule in the solvation shell makes the escape of a water from the entire solvation shell a rather slow process. As a result, the residence time of solvation shell water is found to be longer than that of bulk water even though the rotational relaxation and hydrogen bond breaking of the solvation shell water take place at a significantly faster rate than that in the bulk. We have further examined the angular jump processes associated with the two routes in the solvation shell. Overall, the present study provides a detailed picture of the anisotropic structural distribution, vibrational spectra, polarity, and also the associated dynamics of water around the nitrate ion. In the current study, we have considered a single nitrate ion in water. It would be worthwhile to study the effects of

In order to study the escape dynamics of water from the hydration shell, we have calculated the continuous residence correlation function, SR(t), for water in the hydration shell of the nitrate ion by following the method of ref 79. The associated integrated relaxation time, τr, determines the residence time of water in the hydration shell. For our calculations of the residence dynamics, we have used an allowance time of 2 ps79 for the continuous residence function and found a value of 5.07 ps for the residence time of water molecules in the On solvation shell and 9.65 ps for the entire hydration shell of the nitrate ion (around N). The residence time of bulk water is 8.70 ps. A water molecule in the solvation shell of the nitrate ion resides for longer time due to route 1 in the jump mechanism (discussed in subsection 5.1), where a water molecule performs orientational jumps between different oxygen sites of the same nitrate ion. It is found that the hydrogen bond and orientational dynamics of OD modes are faster for the solvation shell OD modes than that of bulk water. The water molecules rotate in the solvation shell itself but move out of the solvation shell in a much longer time scale. The current results are consistent with those of an earlier study;36 however, the dynamics found in the current study is somewhat faster due to the inclusion of dispersion corrections in the density functional used in the current work. We finally note that the dynamics of the hydration shell water is strongly coupled with that of the nitrate ion.37 The rotation and angular jumps of both the nitrate ion and water molecules contribute to the hydrogen bond breaking and subsequent escape of water from the hydration shell. This coupling of the solute and solvent motion makes the hydration shell dynamics rather complex and difficult to explain only in terms of motion of individual components.

6. SUMMARY AND CONCLUSIONS We have presented a first-principles molecular dynamics study of the anisotropic structure and dynamics of deuterated water in the hydration shell of a nitrate ion. The structural properties of the anisotropic hydration shell are investigated by calculating a variety of correlation functions such as the radial and radial/ angular distribution functions for different axial conical shells and also spatial distribution functions around the nitrate ion. The angle resolved radial and spatial distribution functions reveal the details of the anisotropic nature of the solvation shell of the NO3− ion. A change in the hydration pattern is found with an increase in the conical angle with respect to the perpendicular axis of the nitrate ion. The conically resolved pair distribution functions not only enable a qualitative assessment but also provide a quantification of the extent of hydration in different directions around the solute. Additionally, calculations of the radial-angular distribution functions provide a more explicit resolution of the structure of the hydration shell water in these conically restricted regions. The typical structural features associated with hydrogen bonding are observed in conical regions of larger angles which are oriented more toward the plane of the nitrate ion. It is found that, although the axial water oxygens can come closer to the nitrogen of the nitrate ion than the equatorial water oxygens, the density of water in the plane of the nitrate ion is higher due to hydrogen bonded interactions between the oxygens of the nitrate ion and deuterium atoms of the surrounding D2O molecules. We have also presented ab initio quantum chemical calculations of the nitrate ion−water dimer potential energies for many different orientations of the water molecule in the plane of the nitrate J


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Composition (Δ17O) of Atmospheric Nitrate. Atmos. Chem. Phys. 2009, 9, 5043−5056. (12) Yuan, S. J.; Chen, J. J.; Lin, Z. Q.; Li, W. W.; Sheng, G. P.; Yu, H. Q. Nitrate Formation from Atmospheric Nitrogen and Oxygen Photocatalysed by Nano-Sized Titanium Dioxide. Nat. Commun. 2013, 4, 2249. (13) Waterland, M. R.; Kelley, A. M. Far-Ultraviolet Resonance Raman Spectroscopy of Nitrate Ion in Solution. J. Chem. Phys. 2000, 113, 6760−6773. (14) Hudson, P. K.; Schwarz, J.; Baltrusaitis, J.; Gibson, E. R.; Grassian, V. H. A Spectroscopic Study of Atmospherically Relevant Concentrated Aqueous Nitrate Solutions. J. Phys. Chem. A 2007, 111, 544−548. (15) Xu, M.; Larentzos, J. P.; Roshdy, M.; Criscenti, L. J.; Allen, H. C. Aqueous Divalent Metal-Nitrate Interactions: Hydration versus Ion Pairing. Phys. Chem. Chem. Phys. 2008, 10, 4793−4801. (16) Thogersen, J.; Rehault, J.; Odelius, M.; Ogden, T.; Jena, N. K.; Jensen, S. J. K.; Keiding, S. R.; Helbing, J. Hydration Dynamics of Aqueous Nitrate. J. Phys. Chem. B 2013, 117, 3376−3388. (17) Wren, S. N.; Donaldson, D. J. Glancing-angle Raman Study of Nitrate and Nitric Acid at the Air-Aqueous Interface. Chem. Phys. Lett. 2012, 522, 1−10. (18) Brown, M. A.; Winter, B.; Faubel, M.; Hemminger, J. C. Spatial Distribution of Nitrate and Nitrite Anions at the Liquid/Vapor Interface of Aqueous Solutions. J. Am. Chem. Soc. 2009, 131, 8354− 8355. (19) Hua, W.; Verreault, D.; Allen, H. C. Surface Electric Fields of Aqueous Solutions of NH4NO3, Mg(NO3)2, NaNO3, and LiNO3: Implications for Atmospheric Aerosol Chemistry. J. Phys. Chem. C 2014, 118, 24941−24949. (20) Megyes, T.; Bálint, S.; Peter, E.; Grósz, T.; Bakó, I.; Krienke, H.; Bellisent-Funel, M. C. Solution Structure of NaNO3 in Water: Diffraction and Molecular Dynamics Simulation Study. J. Phys. Chem. B 2009, 113, 4054−4064. (21) Caminiti, R.; Licheri, G.; Paschina, G.; Piccaluga, G.; Pinna, G. Interactions and Structure in Aqueous NaNO3 Solutions. J. Chem. Phys. 1980, 72, 4522−4528. (22) Neilson, G. W.; Enderby, J. E. The Structure Around Nitrate Ions in Concentrated Aqueous Solutions. J. Phys. C: Solid State Phys. 1982, 15, 2347−2352. (23) Marcus, Y. Ionic Radii in Aqueous Solutions. Chem. Rev. 1988, 88, 1475−1498. (24) Bergström, P. A.; Lindgren, J.; Kristiansson, O. An IR Study of the Hydration of Perchlorate, Nitrate, Iodide, Bromide, Chloride and Sulfate Anions in Aqueous Solution. J. Phys. Chem. 1991, 95, 8575− 8580. (25) Pathak, A. K. Theoretical Study on Microhydration of NO−3 ion: Structure and Polarizability. Chem. Phys. 2011, 384, 52−56. (26) Pathak, A. K. Normal Modes for Probing the Local Solvation Environment of Nitrate Anion during Step wise Hydration: A Theoretical Study. Chem. Phys. 2012, 400, 86−92. (27) Pathak, A. K.; Samanta, A. K.; Maity, D. K.; Mukherjee, T.; Ghosh, S. K. Instability Range of Microsolvated Multiply Charged Negative Ions:Prediction from Detachment Energy of Stable Hydrated Clusters. Phys. Rev. E 2011, 83, 021112. (28) Ramesh, S. G.; Re, S. Y.; Hynes, J. T. Charge Transfer and OH Vibrational Frequency Red Shifts in Nitrate-Water Clusters. J. Phys. Chem. A 2008, 112, 3391−3398. (29) González Lebrero, M. C.; Bikiel, D. E.; Elola, M. D.; Estrin, D. A.; Roitberg, A. E. Solvent-induced Symmetry Breaking of Nitrate Ion in Aqueous Clusters: A Quantum-Classical Simulation Study. J. Chem. Phys. 2002, 117, 2718−2725. (30) Miller, Y.; Thomas, J. L.; Kemp, D. D.; Finlayson-Pitts, B. J.; Gordon, M. S.; Tobias, D. J.; Gerber, R. B. Structure of Large NitrateWater Clusters at Ambient Temperatures: Simulations with Effective Fragment Potentials and Force Fields with Implications for Atmospheric Chemistry. J. Phys. Chem. A 2009, 113, 12805−12814. (31) Chialvo, A. A.; Vlcek, L. NO−3 Coordination in Aqueous Solutions by 15N/14N and 18O/natO Isotopic Substitution: What Can

counterions and salt concentration on the structural and dynamical behavior of aqueous metal nitrate solutions from ab initio simulations. Also, in the current study, we have employed the dispersion corrected BLYP-D2 functional.49,50 This particular functional was used in many earlier ab initio simulations of aqueous systems51−56 and was found to provide a significantly improved description of the structure, dynamics, and phase diagram of aqueous systems than the corresponding BLYP functional47,48 without any dispersion correction. We also note in this context that other dispersion corrected functionals such as B97-D250 and BLYP-D380 have also been used in ab initio simulations of water and other hydrogen bonded systems such as methanol.54,81 Hence, it would be worthwhile to carry out a study of the comparative performance of these different dispersion corrected functionals for aqueous solutions of nitrate and other poly-oxyanions. We hope to address such issues in our future work.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91 512 2597241. ORCID

Amalendu Chandra: 0000-0003-1223-8326 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS 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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A First-Principles Molecular Dynamics Study of the Solvation Shell

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