Charge and Electric Field Fluctuations in Aqueous NaCl Electrolytes

Article pubs.acs.org/JPCB

Charge and Electric Field Fluctuations in Aqueous NaCl Electrolytes Bernhard Sellner,† Marat Valiev,‡ and Shawn M. Kathmann*,† †

Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, Washington 99352, United States

‡

S Supporting Information *

ABSTRACT: Crystalloluminescence, the long-lived emission of visible light during the crystallization of certain salts, was first observed over 200 years ago; however, the origin of this luminescence is still not well understood. The observations suggest that the process of crystallization may not be purely classical but also involves an essential electronic structure component. Strong electric field fluctuations may play an important role in this process by providing the necessary driving force for the observed electronic structure changes. The main objective of this work is to provide a basic understanding of the fluctuations in charge, electric potentials, and electric fields for concentrated aqueous NaCl electrolytes. Our charge analysis reveals that the water molecules in the first solvation shell of the ions serve as a sink for electron density originating on Cl−. We find that the electric fields inside aqueous electrolytes are extremely large (up to several V/Å) and thus may alter the ground and excited electronic states in the condensed phase. Furthermore, our results show that the potential and field distributions are largely independent of concentration. We also find the field component distributions to be Gaussian for the ions and non-Gaussian for the O and H sites (computed in the lab frame of reference), however, these non-Gaussian distributions are readily modeled via an orientationally averaged nonzero mean Gaussian plus a zero mean Gaussian. These calculations and analyses provide the first steps toward understanding the magnitude and fluctuations of charge, electric potentials, and fields in aqueous electrolytes and what role these fields may play in driving charge redistribution/transfer during crystalloluminescence.

I. INTRODUCTION Concentrated electrolytes are important in several areas of fundamental chemical physics research, biology, geology, and many technological applications. Our particular interest is aimed toward understanding concentrated aqueous electrolytes leading to crystallization. Conventional wisdom concerning crystallization assumes that when NaCl crystallizes from a supersaturated solution the solvated ions retain their ionic character and simply relocate from their hydration spheres to their most stable positions in the crystal lattice. However, this conventional picture is at odds with observations over 200 years ago reporting the emission of long-lived light resulting from the crystallization of certain salts (e.g., NaCl, KCl, etc.), appropriately referred to as crystalloluminescence1,2 (the interested reader will find the Barsanti and Maccarrone crystalloluminescence comprehensive review article helpful). This observation of crystalloluminescence suggests that electronic structure plays an essential role in crystallization. Strong electric field fluctuations in the gas or condensed phases can drive changes in electronic structure. The importance of electric field fluctuations driving electron transfer has been a topic of intense research since the seminal work of Marcus.3−5 To understand and accurately quantify the detailed mechanisms underlying crystallization and any associated luminescence, several challenging aspects of condensed phase chemical physics must be confronted: concentration effects, charge redistribution/transfer, electric potential and field fluctuations, © 2013 American Chemical Society

internal stark shifts (i.e., solvatochromism), electronic transitions, spin−orbit coupling, and nonadiabatic dynamics. In condensed phase systems the internal electric fields and potentials evaluated at either the positions of nuclei or throughout the space between nuclei are extremely strong (i.e., 10 GV/m = 10 V/nm = 1 V/Å), similar to those generated in high-energy laser pulses, inertial confinement fusion implosions, and particle accelerators.6−8 Characterization of these electric fields and potentials within the condensed phase, their interfaces or within cavities have recently been used to understand mean inner potentials/surface potentials9−14 and ion free energies of solvation,15−17 vibrational spectroscopic response in deuterated mixtures of water,18−23 water around ions,22,24 Stark effect hole-burning spectroscopy,25 and autoionization in pure water.26,27 In the electric field vibrational and hole-burning studies referenced, the reported fields are about 1 V/Å. In the case of evaluation of the surface potential or mean inner potential, a distinction must be made concerning the classical versus quantum mechanical charge density as well as the choice of which regions of space to evaluate and average the electric fields or potentials. In the vibrational and electronic spectral response (e.g., solvatochromatic and electrochromatic shifts), the central concept is that spectral blue- or redshifts are linked to the field evaluation sites which act as variable Received: June 5, 2013 Revised: July 31, 2013 Published: August 1, 2013 10869

dx.doi.org/10.1021/jp405578w | J. Phys. Chem. B 2013, 117, 10869−10882

The Journal of Physical Chemistry B

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Figure 1. Pair distribution functions for all pairs occurring in NaCl solutions for all concentrations. Furthermore, the results for pure water are included in the relevant plots.

antennas to sense the local electric fields and potentials with and without application of external electric fields.22,28 In these spectral response measurements, it is the sensitivity of the transition energies to the local electric field strengths that is manifested in photon absorption or emission frequency shifts. The importance of electric field fluctuations were underscored by Parrinelo et al.,29 who used metadynamics to show that a combination of electric potential and coordinate distributions provided a more complete description of the free energetics of dissociation of NaCl in water. Here we focus our attention on calculating the charge (on the ground state singlet electronic surface) and electric potential and field (using point charges as field sources) fluctuations as functions of NaCl concentration in aqueous electrolytes. In this way we can begin to understand the magnitude and fluctuations of electric potentials and fields in aqueous electrolytes and what role these fields may play in driving charge redistribution/transfer during crystalloluminescence.

II. METHODS AND COMPUTATIONAL DETAILS The various NaCl aqueous electrolytes were modeled classically using the simulation package CP2K30 via a bulk configuration containing 512 ions/molecules of Na+, Cl−, and H2O species. Our simulation cells where chosen as a result of current standard practices in large-scale MD simulations. Classical simulations were performed as opposed to direct quantum mechanical simulations as a matter of practicality and conceptual simplicity. The water interactions were described classically using the SPC/E31 model, whereas the Na+ and Cl− interactions were described using the Smith−Dang model.32 Five concentrations were considered: 1, 2, 4, 5.2, and 6.7 M. These correspond to NaCl/H2O molecular ratios of 9/494, 17/ 478, 33/446, 46/420, and 58/396, respectively. All simulations were pre-equilibrated starting from random initial configurations where each species was placed at the center of one of 512 equivalent cells making up the entire cubic simulation box. The simulation boxes of side L (Lx = Ly = Lz = L) corresponding to the various concentrations (in parentheses) were 24.690 (1 M), 24.557 (2 M), 24.303 (4 M), 24.447 (5.2 M), and 24.346 Å (6.7 M). The simulation volumes were 10870



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calculated from the experimental densities. For the case where the electrolyte is supersaturated (6.7 M), we choose a box size consistent with the sum of the pure water volume plus the pure crystal volume. NVT simulations were performed at a temperature T = 298 K using a Nosé-Hoover thermostat and the molecular dynamics generated with a time step of 2.5 fs. A total of 1 ns, after 1 ns of equilibration to erase all history of the starting structures, was used for the production runs and subsequent analysis of the simulation data. The PBE DFT functional was used, as implemented in CP2K,30 in resampling the classical trajectory to obtain the electron densities. These electron densities were then analyzed using Bader analysis to obtain charges for each species via the code from Henkelman and co-workers.33 We briefly mention here that some care must be taken in choosing the computational grid on which the electron density is computed and the use of pseudopotentials versus all electron calculations. In all electron calculations an extremely fine grid is necessary to capture the steep electron densities associated with the core electrons such that the resulting total electron count is accurate. The use of pseudopotentials allows the use of a coarser grid (0.095 Å) so as to obtain the total valence electron count to be accurate within 0.001 e. More details about the electronic structure aspects of the simulation can be found in our recent study13 on the surface potential (or mean inner potential) of water. Electric fields and potentials at each species were computed from point charges using 3D periodic Ewald summation. For the case of H2O, the internal fields within each water molecule were not included so that the electric fields and potentials are due only to those charges outside of the molecule and hence can be considered “far-field”. The values for pure salt were obtained from a single configuration of a 4 × 4 × 4 cube with a lattice constant of 5.64 Å. For all concentrations and pure water 101 snapshots out of a single trajectory were analyzed where the time between two snapshots was 250 fs for pure water and 10 ps for all other concentrations. Bader analysis was performed on snapshots resampled with DFT out of trajectories with concentrations ranging from 1 to 6.7 M using 80 snapshots separated by 10 ps.

Figure 2. Illustration of the “charge cloud” oscillations around a central Na+ ion (blue). The coloring is as follows: O (red), Cl− (green), and H (white).

inherently classical in the sense that we considered the atoms as point charges. In the charge analysis comparison below, we show that the actual quantum charge is significantly different and thus requires a more careful comparison. The Na−Cl and O−O RDFs show the largest changes with NaCl concentration with significant alterations in the first, second, and third coordination shells. These results are quantitatively consistent with other simulations of aqueous NaCl.40−46 For the Na−Cl RDFs, these changes mirror the increasing stability of the contact-ion pairs (CIPs) at the expense of the destabilized solvent-separated ion pairs (SSIPs). This can be seen by inversion47 of the RDFs using the relation Wij(r) = −kBTln[gij(r)], where Wij(r) is the potential of mean force between atom types i and j, and kB is Boltzmann’s constant. This leads to a lowering of the SSIP → CIP free energy barrier and an increase in the CIP→SSIP barrier consistent with the intuitive picture that as the concentration increases the ions tend to come into contact. However, it is important to be aware that NaCl clustering occurs even in subsaturated aqueous NaCl electrolytes (i.e., clusters occur that are larger than NaCl pairs).41,48 For example, dynamic light scattering49,50 measurements of aqueous NaCl show NaCl clusters about 1 nm in size for concentrations ranging from 0.68 to 5.32M. Within the context of NaCl crystallization from solution, the approach toward the supersaturated state is accompanied by the evolution of subcritical NaCl cluster populations. These subcritical clusters are not required to occur stoichiometrically, i.e., there can be excesses of Na+ or Cl− ions and thus these clusters may not be neutral. Moreover, these subcritical clusters are generally not tiny cubic fragments of salt. From our preliminary cluster analysis, the subcritical clusters evolve via a qualitative sequence from “1D → 2D → 3D” structures, i.e., from distorted chains, distorted planes, and distorted polyhedral structures. This is consistent with the observations from early research in the field of model concentrated electrolytes concerning the importance of higher-order correlation functions34,36,37 as well as more recent metadynamics studies on transient polymorphism in NaCl.51 This makes the interpretation of aqueous electrolyte structure more complicated and hence requires greater sophistication and quantification beyond simple pair RDFs and will be the

III. RESULTS AND DISCUSSION Liquid Structure. In order to understand the influence of Na+ and Cl− ion concentration on the aqueous NaCl electrolyte structure we have computed ten radial distribution functions gij(r) (RDFs), between atom types i and j, shown in Figure 1 for pure water and at concentrations 1, 2, 4, 5.2, and 6.7 M. These results are presented to structurally characterize the system and to ensure the fidelity of our statistical mechanical sampling generated during the molecular dynamics simulations. From Figure 1, it is seen that the Cl−Cl, O−O, Cl−O, Na−Na, and Na−Cl RDFs change the most with increasing NaCl concentration, leaving the other five RDFs (H−H, Cl−H, O− H, Na−H, and Na−O) rather insensitive to concentration. Taken together, the Na−O, Na−Cl, Na−H, and Na−Na RDFs (similarly for Cl−H, Cl−Na, Cl−O, and Cl−Cl with the charge ordering reversed) in Figure 1 display “charge cloud” oscillations (illustrated in Figure 2) as a result of electric charge screening analogous to those described by Stillinger and Lovett 34,35 (also seen in modified Poisson−Boltzmann studies36,37 and can be thought of as classical analogs to quantum Friedel oscillations38,39). We note here that it is important to realize that this interpretation leading to solvation charge oscillations, corresponding to the RDF data, is 10871



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increases. The pure water 1.0 bar (black circles in upper part of Figure 3) X-ray O−O RDF does not quite match the simulated pure water or other X-ray scattering data in the 3−5 Å range and was attributed by Skinner et al.61 to both systematic and statistical errors arising from the inherently small fraction of coherent scattering signal compared to the total measured scattering intensity. Our concentration dependent O−O RDF results are consistent with the picture that water undergoes a continuous conversion from low-density liquid (LDL) water to high-density liquid (HDL) water, i.e., LDL water being “crushed” into a HDL structure. Thus, the “pressure effect” of ions on the structure of water is in some ways similar to water under high-pressure. However, there are important quantitative differences due to the specific ion’s presence consistent with other studies on aqueous electrolytes.54−56 We note that a preliminary extended X-ray absorption fine structure (EXAFS) spectroscopic analysis of our trajectories (not shown here) indicates that the local structure around the ions (within 5 Å of the ions) is not as well described by the classical force field employed in these studies. This is in contrast to the excellent agreement we find with the neutron diffraction data. EXAFS probes local atom-specific (i.e., electron density) short-range structural motifs and symmetries around the outgoing photoelectron source via interference with the surrounding liquid scattering whereas neutron diffraction probes the medium to long-range structure via scattering off of nuclei and hence is sensitive to various isotopes. We are currently working toward direct ab initio dynamics simulations (as opposed to classical force fields) and this work will be the subject of a future publication. These studies should capture the subtle differences in local structure arising from a better description of the ions and water molecules as well as the local quantum fields. Charge. As a first step toward understanding the electrical properties of aqueous electrolytes and how they change as the solution becomes more saturated, we consider the fluctuations in the system’s charge distribution. Here, we simply use Bader analysis from quantum resampling our classical trajectories. We partition the total system’s charge into the charge on the ions and water molecules. Bader analysis divides the total electron density of the system based on the existence of electron density “necks”, however, the H2O molecule is not in all instances reliably partitioned into O and H atomic regions. This makes an atom resolved head-to-head comparison with the effective charges used in empirical water potentials difficult. Consequently, we compare only the total charge on each H2O molecule. The distribution of charges P(qi) = ⟨δ[qi − qi(Γ)]⟩ where i = H2O, Na+, and Cl− for all five simulated concentrations of aqueous NaCl are shown in Figure 4. Here qi(Γ) denotes the charge on species i at the system configuration Γ. An ion charge of exactly ±1 is by necessity an oversimplification and will not be belabored at this point; our use of the plus (+) and minus (-) superscripts on Na+ and Cl− is simply for convention and convenience. The P(qi) on the H2O molecules for the lowest concentration in Figure 4 (top panel) shows a peak close to zero and slightly negative (−0.007 e). This Gaussian-shaped distribution for H2O clearly shifts toward more negative charges with increasing concentration with the width being about the same for all of them. Figure 4 (middle panel) shows the charge distribution on Na+ is Gaussian and very narrow with a width of about 2/100s electrons and a peak at ∼0.950 e and shows no concentration dependence. Figure 4 (bottom panel) for Cl−

focus of a future publication where we employ a cluster-based analysis of concentrated aqueous NaCl electrolytes. We now turn to the O−O RDFs as they provide insight into the influence of ions on the structure of water. Several studies have employed the concepts of ions in aqueous electrolytes as “structure makers” and “structure breakers” a.k.a. “kosmotropes” and “chaotropes”, respectively.52−56 This influence of ions on the structure of water is often referred to as the “Hofmeister Effect”.57 An important issue recently proposed is the similarity between the structural effects of ions on water versus the structural effect of high-pressure on pure water.52−56,58 The key concept is this: ions in aqueous electrolytes “crush” the intervening water molecules as the ion concentration increases (∼5 M) in a manner similar to how the structure of pure water changes when it is “crushed” by an external pressure (∼8000 atm). This may alternatively be thought of as an electrostriction effect where the compression arises from a breakdown of the hydrogen bonding network and a simultaneous decrease in void spaces.59 The structural characterization of pure water under high-pressure and aqueous electrolytes at various concentrations has been measured using X-ray58,60,61 and neutron diffraction52,53 techniques, respectively. The comparison of the simulated O−O RDFs from the present work is compared to the measured X-ray (pure water under increasing pressure) and neutron diffraction (aqueous NaCl electrolyte with increasing concentration) is shown in Figure 3. First, note the excellent agreement between our

Figure 3. Comparison of O−O RDFs at various pressures (open circles: 1.0 bar in black; 1.0, red; 2.0, orange; 3.0, light green; 4.0, green; 5.0, light blue; 5.8, blue; 6.5, magenta; 7.7 kbar, purple) using experimental X-ray diffraction for pure H2O and simulated (NaCl)aq (curves: pure H2O, black and NaCl:H2O (salt to water molecular ratio) = 1:55, red; 1:28, orange; 1:14, green; 1:9, blue; 1:7, purple) and experimental neutron diffraction for (NaCl)aq (pure H2O, black, NaCl:H2O = 1:83, red; 1:40, orange; 1:17, green; 1:10, blue).

simulated O−O RDFs and those from the neutron diffraction. This gives us confidence that the molecular dynamics simulation is sampling the relevant regions of configuration space. Second, note the similarities and differences between the X-ray and neutron O−O RDFs. In both measurements, the second peak in the O−O RDFs (which is considered as a telltale sign of water’s tetrahedrality) shifts toward shorter distances and becomes a broad shoulder on the right-hand side of the first peak in the O−O RDFs. However, the first peak of the X-ray high-pressure pure water O−O RDFs is independent of pressure whereas the first peak of the neutron O−O RDFs shows a strong reduction in height as the concentration of ions 10872



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Figure 5. (Top) Correlation between the qCl and the number of Na+ ions in the 1st solvation shell. (Bottom) Correlation between the qCl and the number of H atoms in the 1st solvation shell.

6, we find a clear linear trend that levels off only for large numbers of H atoms in the shell. Again, this correlation is independent of concentration and an increase in coordination number by one reduces the total charge by +0.024e. The contour plots of histograms as a function of the charge on Cl− and the minimal distance to the next Na+ reveal that the distributions shown in Figure 6 can be decomposed into two components: (1) a symmetric (Gaussian) distribution arising from solvent separated ion pairs (peak at ∼4.5 Å; also the peak at ∼7 Å only clearly present for the lowest concentration) and (2) an asymmetric distribution due to Cl− which have at least one counterion in the first solvation shell. Figure 7 shows how the average charge on H2O behaves when decomposed into three sets: first solvation shell, second solvation shell, and bulk, defined by all other H2O that do not fit into the previous sets. The results indicate that there are only two distinct sets: H2O in a first solvation shell of an ion and all other H2O molecules. For those in the first solvation shell, it is shown that they carry a negative charge that increases, on average, with concentration. For all other waters (2nd solvation shell and bulk), the average charge is zero for all concentrations. The correlation of the charge on H2O with the number of ions surrounding it is shown in Figure S1 (in the Supporting Information). The total ion coordination number was evaluated as the sum of all Na+ within the first solvation shell of the O atom and the sum of all Cl− within the first solvation shell of the two H atoms of the molecule for each H2O. This correlation can be well described by a linear fit showing the most negative H2O coordinated to 4 ions. To further resolve the concentration dependence of the negative charge on the H2O in the first solvation shell, a two-dimensional correlation function was evaluated where the coordination of either the two H with Cl− or the O with Na+ is resolved. The H2O charge as a function of these variables can be seen in Figure S2. It reveals, as in Figure 7, that bulk H2O has zero charge (bottom left) and an H2O coordinated to 4 ions is most negative (top right) but

Figure 4. Distribution of charges P(q) on water (top), Na+(middle), and Cl− (bottom) obtained from Bader analysis for different concentrations.

shows a Gaussian distribution only for the lowest concentration (1 M) and is centered at a lower magnitude (−0.700 e) with a wider distribution compared to Na+. When going to higher concentrations the distributions widens into the more negatively charged region and clearly displays non-Gaussian behavior, however without reaching the equal and opposite charge compared to Na+, as one would find in the reference bulk NaCl crystal. In order to explore correlations of the charge distributions with respect to concentration, the coordination numbers of single atoms where used. In the following analysis the coordination number was evaluated by counting the number of atoms within a given distance interval specified by extremal values taken from the RDFs displayed in Figure 1. The first solvation shell is defined by the distance interval ranging from 0 (with the exception of the first peak in the O−H distribution which is due to the intramolecular structure of H2O) to the minimum after the first peaks of the RDFs. The increase in negative charge on Cl− correlates extremely well with the number of Na+ ions within the first solvation shell as shown in Figure 5 (top panel). This behavior is independent of concentration and a linear fit yields a charge of −0.698e for the Cl− not surrounded by Na+. Each additional counterion within the first solvation shell adds about −0.032e to the total charge. Since the two atoms most likely to be found next to Cl− are Na+ and H, the charge on Cl− also correlates with the number of H atoms in the first solvation shell shown in Figure 5 (bottom panel). For coordination numbers ranging from 0 to 10873



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Figure 6. Contour plots of histograms for all concentrations as a function of Cl− charge and minimum distance to the next Na+ ion.

in addition shows that each Cl− coordinated to H adds about −0.01e of negative charge whereas the first Na+ in the first solvation shell of O adds −0.0239e but the second one only −0.015e since they share the same O atom. For a general discussion of the total system charge distribution, it is worthwhile examining the total charge carried by the distinct “molecular” species (Na+, Cl−, and H2O) as functions of concentration shown in Figure 8. This plot shows that Na+ carries more overall positive charge than all of the Cl−, resulting in a net positive charge on the ions in total. Furthermore, the magnitude of charge on Cl− is always smaller that for Na+. Since the total system charge is neutral, H2O must

carry the negative charge to compensate for this charge imbalance. As a consequence, H2O molecules carry on average more and more negative charge the higher the concentration because the total number of ions increases. This charge is redistributed, independent of concentration, to the first solvation shell H2O molecules while the number of these H2O molecules increases with concentration. Given that the charge on Na+ is concentration independent, both charge distributions of Cl− and H2O have to shift toward more negative values with increasing concentration. In summary, the charge distribution on Cl− can be decomposed into (a) symmetric and (b) asymmetric 10874



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aqueous electrolytes as they become supersaturated. The charge distributions computed here provide a baseline from which the system can begin to show much larger changes associated with crystalloluminescence. Electric Potentials. Here we quantify the distribution P(ϕi) = ⟨δ[ϕi − ϕi(Γ)]⟩ of the scalar electric potential in aqueous NaCl to provide a basis from which to better understand the scalar field fluctuations. Here, i denotes the Na+, Cl−, O, and H sites at which we evaluate the electric potentials (and vector electric fields below). As mentioned previously, the internal (intramolecular) fields (scalar and vector) within each water molecule were not included so that the fields and potentials are due only to those charges outside of the molecules and ions and hence considered to be “far-field” intermolecular contributions within the condensed phase. This is an essential distinction since the inclusion of the intramolecular fields arising from a point charge description of water is unphysical. For example, the electric field at the O site arising from only the other two H atoms within the H2O molecule is 7.0 V/Å (along the C2v axis in the same direction as water’s dipole moment) and those on the H atoms are 10.4 V/Å each (this fields point toward the O atom but are off the OH bond by about 7.3 degrees). Furthermore, one can readily discern the differences in the “near-fields” by visual inspection of the quantum (MP2/aug-cc-pvdz) versus classical (SPC/E) electric potential isosurfaces (red = +1.63 V, green = −1.36 V) as shown in the top and bottom of Figure 9, respectively. The H2O molecule (middle) is shown for reference at the same scale as the isosurfaces. In the quantum case, the positive red isosurface encloses all of the H2O nuclei and the negative green isosurface lies outside the molecule (this isosurface is due to the lone pairs of electrons). In the classical case, the negative and positive isosurfaces “cut” H2O along the OH bond and the positive red isosurface encloses the H nuclei and the negative green isosurface encloses the O nucleus. Clearly, the quantum and classical “near-fields” are qualitatively and quantitatively very different, and it is a current research topic in chemical physics to understand in what regions of space these differences arise, under what circumstances these differences are significant, and how the differences can be reconciled. For an accurate description of the intramolecular fields, one must use a quantum mechanical description and compute the quantum electric potential (i.e., Hartree potential) that is probed by high-energy electron diffraction and holography. The distribution of electrostatic potentials at atomic sites of Na+, Cl−, O, and H for all concentrations can be found in Figure 10a−d. Figure 10a shows the distribution for Na+ and is peaked around −8.5 V for all concentrations with a slight shift toward higher potentials for higher concentrations. These distributions are consistent with the Madelung potential in the crystal at −8.9 V (using ±1 charges); however, the peak lies below it. Recall that the Madelung potential is the electric potential at an ion in a crystal arising from all other point charges in the crystal. The results for the distribution of potentials at Cl− can be found in Figure 10b. Again, the peaks for all concentrations are below the Madelung potential. In the case of H2O, the potentials on O (Figure 10c) range from 0 to about 2.5 V peaking at about 1.2 V. The potentials on H (Figure 10d) vary from −2.0 to 1.5 V peaked at −0.1 V. A slight deviation can be found comparing pure water with the concentrated aqueous electrolyte, however, there is almost no concentration dependence in these two distributions.

Figure 7. Average qwater resolved for different solvation shells as a function of concentration.

Figure 8. Sum of charges on the distinct species Na+, Cl−, and H2O as a function of concentration.

contributions, as follows: (a) at the less negative end, arising from solvent separated ions, and (b) an asymmetric contribution which arises from Cl− within ionic salt clusters which carry more negative charge. An asymmetric distribution of cluster sizes is the most likely explanation for the shape of this distribution. The H2O molecules within the first solvation shell of an ion are negatively charged independent of the sign of the charge of the ion, whereas the second solvation shell water bears no positive charge, and is uncharged on average just like bulk H2O in agreement with Soniat and Rick.62 We define the reference state, using Bader analysis, as the salt crystal [| q(Na,Cl)| = 0.9e] and liquid water [q(H2O) = 0] for the following conclusions. Na+ is largely unaffected by charge redistribution and bears approximately the same charge in the crystal and solution independent of the concentration. In contrast, Cl− is less negative in solution than it is in the crystal and looses ca. −0.200e in dilute solutions. In the case of ionic clustering at higher concentrations the negative charge increases close to the value of the crystal using the extrapolated value for octahedral coordination by Na+ from Figure 5 (top panel), which yields 0.881e. As mentioned previously, there is a redistribution of charge from Cl− to H2O, and thus, the H2O molecules generally act as a sink for electronic charge. This charge is relocated in the first solvation shells of the ions leaving all other H2O molecules unaffected. This holds true for both cations and anions, however, the average charge stored on an H2O around the cation (excluding clusters of ions) is more than twice as large (−0.024e) than the charge that can be accommodated when this H2O molecule surrounds the anion (−0.010e). This is in contrast to the charge oscillations discussed within the context of the (classical point charge) structural analysis discussed above, which by definition has only neutral H 2 O molecules. Our charge analysis provides interesting insights into the charge state of concentrated 10875



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For the analysis of correlations between potentials and structure the same definitions of coordination numbers are used here as were used for the charge analysis. The correlation of averaged potentials at Cl− sites with the average Cl−H distance resolved for different coordination number scenarios was analyzed for the case where no counterion is present in the first solvation shell and is presented in Figure S3 (top panel). Figure S3 shows that the potential depends linearly on the average distance of Cl− to its surrounding H atoms when resolved by coordination number and depends (nearly) linearly on the number of H atoms inside the first solvation shell for a given average Cl−H distance. The situation gets much more complicated when a more general case including Na+ ions is considered. For this case two-dimensional correlation plots showing the potential as a function of both average Cl−H distance and average Cl−Na distance within the first solvation shell are presented for selected pairs of coordination numbers in the Figure S4. It can be seen that the potential is highest when both the average Cl−H and Cl−Na distances are small and the potential lowest when the distances are large indicating that the behavior for multicomponent first solvation shells is similar to the simpler case presented in Figure S3 (top panel). The averaged potentials at Na+ sites that have no Cl− ions within the first solvation shell show a linear increase with the average distance to O atoms within the first solvation shell when resolved by coordination number Figure S3 (bottom panel). When both Cl− and O are present in the first solvation shell the potential is lowest if both average distances Na−Cl and Na−O are small and highest when they are both large as can be seen from the two-dimensional correlation plots for selected coordination numbers in Figure S5. For the potentials on the atomic sites in H2O, the averaged potentials at the H sites without Cl− ions present in the first solvation shell, the inverse distance to the next O atom dominates the correlation for all coordination numbers shown in Figure S6. If the next O atom is far away, the potential becomes positive, and if it is close then the potential is negative.

Figure 9. Isosurfaces of the electric potentials of the quantum (top, MP2/aug-cc-pvdz) versus classical (bottom, SPC/E). The corresponding colors red = +1.63 V and green = −1.36 V. The H2O molecule is shown for reference with the same scale as the isosurfaces. In quantum case, the positive red isosurface encloses all the H2O nuclei and the negative green isosurface lies outside the molecule (this isosurface is due to the lone pairs of electrons). In the classical case, the negative and positive isosurfaces “cut” H2O along the OH bond and the positive red isosurface encloses the H nuclei and the negative green isosurface encloses the O nucleus.

Figure 10. Distribution of electrostatic potentials P(ϕ) at (a) Na+, (b) Cl−, (c) O, and (d) H for all concentrations (including pure water for O and H). The Madelung potential in the crystal is indicated as the vertical black bar in the plots for Na+ and Cl+, respectively. 10876



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Figure 11. Adiabatic potential energy curves for the NaCl dimer in vacuum without (left) and with (right) an external electric field of 0.5 V/Å pointing from Na+ toward Cl− (top). The electric field moves the zero field avoided crossing from ca. 9 to 4 Å, and the first excited singlet (A1∑+) and triplet (3Π) states are stabilized by about 30 kcal/mol relative to the ground singlet state (X1∑+) minimum.

In the more general case when Cl− ions are present, a similar situation is observed as shown in the two-dimensional correlation plot in Figure S7. The potential is negative when either a Cl− or an O atom is close to the H and positive when neither of them is close to the H atom. In case of O, the averaged potentials at sites where no Na+ is present in the first solvation shell correlate with the inverse distance to the next lying H neighbor when resolved by coordination number as shown in Figure S8. The case where also Na+ is present is displayed in the two-dimensional correlation plot in Figure S9 showing the potential at O sites as a function of the distance to the closest Na+ ion and the sum over distances to all H atoms within the first solvation shell. This automatically resolves the distribution by coordination number. If the distance between both O−Na and all O−H is small, the potential is large, and if both are far away it is small. Furthermore, it increases with the O−H coordination number. In summary, the distributions of potentials at the ion sites show a similar picture with inverted sign. Differences between them can be found in the location of the peak that is about 8.2 V in the case of Cl− vs 8.5 V in the case of Na+, the width that is smaller for Cl− and the distribution of Cl− does not show the small concentration effect that the one of Na+ does. In both cases the correlation plots show that the potentials that are high in magnitude arise from a stressed environment in the first solvation shell whereas the magnitude of the potentials is low if the first solvation shell is loose/large. This is largely independent of the identity of the atoms in the first solvation shell, which is suspected to be the origin of the small differences found in the two distributions. In contrast to the ions, the potentials at both the H and the O atoms are mainly a measure for the distance to the closest neighbor. This is in good agreement with the character of H bonds that depend on angle and also in good agreement with the nonspherical shape of the water molecules. The correlation plot shown in Figure S6 indicates that a second O in the first solvation shell is “screening” (as defined by the slope) the potential that is

caused by the closest O to the H site, whereas in case of the O sites (see Figure S8) the cases of more than one H atom in the first solvation shell are characterized by a linear dependence with the distance to the closest H atom plus a constant additional potential for every auxiliary H atom. This difference arises most likely from the fact that H atoms typically have a single H bonding partner whereas O atoms can have more than one. Electric Fields. As mentioned previously, electric field fluctuations play an essential role in the solute vibrational response as well as in Marcus’s theory of electron transfer. Part of this paper’s objective is to explore the magnitudes and distributions of electric fields that occur in aqueous NaCl electrolytes. Here we also provide an initial benchmark field analysis to understand the field influence on ground and excited electronic states as referenced to the NaCl dimer. From highlevel electronic structure calculations using MOLPRO63 (MRCI/aug-cc-pvtz) on the NaCl dimer in vacuum, we find that an electric field of 0.5 V/Å pointing from Na+ toward Cl− moves the zero field avoided crossing from ca. 9 to 4 Å; see Figure 11. Additionally, the first excited singlet and triplet states are stabilized by about 1.3 eV (30 kcal/mol) relative to the ground singlet state minimum (i.e., an energy gap reduction). These results are in excellent agreement with other studies on the influence of electric fields on alkali halide dimers.64,65 However, further details concerning these high-level gas-phase calculations as well as condensed phase QM/MM calculations on concentrated aqueous NaCl electrolytes are beyond the scope of the present work and will be the focus of future publications. Clearly, electric fields of about 0.5 V/Å are sufficient to dramatically alter electronic energy gaps as well as avoided crossing points. This opens the possibility that if these types of fields occur in condensed phase aqueous NaCl electrolytes, and then similar effects in the energy gaps and crossings may occur. The question is: What are the electric field magnitudes and distributions in the condensed phase? In previous studies, various test sites at certain locations are 10877



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Figure 12. Distributions of the magnitude of the electric field P(E) (left panel, top to bottom, respectively) at the Na+, Cl−, O, and H sites. Distributions of the electric field vector P(E) = P(E)/4πE2 (right panel, same order as left).

order as left). These distributions for Na+ and Cl− are qualitatively different from the distributions for O and H due to the asymmetry of the solvation of the O and H sites on water compared to more symmetric solvation environment around Na+ and Cl−.66 If the electric field component distributions are independent, then the total distribution is P(E) = P(Ex)P(Ey)P(Ez). Figure 13 (top left and right panels) shows the x-component distributions (the y and z components are not shown but are similar to x) for Na+ and Cl−, showing Gaussian behavior. Subsequently, it can easily be shown that if these component distributions are equivalent and independent Gaussians, then the most probable electric field magnitude (the peak value) E* and average E̅ electric field magnitudes are E* = √2σE and E̅ = (8/π)1/2σE, respectively, where σE is the standard deviation. For example, in the case of the components of the electric field distributions on Na+, the distributions look quite normal and thus, after a Gaussian fitting of the x component of the 6.7 M data, one obtains σE = 0.32 V/Å (fitted) and thus E* = 0.45 V/ Å and E̅ = 0.51 V/Å which are in excellent agreement with the corresponding P(E) data for Na+ in Figure 13. However, the

chosen to evaluate the fields (e.g., at the atomic sites, the center of charge, or bond midpoint sites). Here, the distributions P(Ei) = ⟨δ[Ei − Ei(Γ)]⟩ of electric fields (of magnitude E = |E|) are analyzed at the Na+, Cl−, O, and H sites using the lab frame of reference instead of in the water molecule’s body frame of reference (which does make a difference in the resulting distributions and will be discussed shortly). Figure 12 (left panel, top to bottom) shows the distributions, P(Ei), of the magnitude of the electric field at the Na+, Cl−, O, and H sites, respectively. Figure 12 (left panel) shows that the electric field distributions on Na+ and Cl− are nearly concentration independent with the distributions for O and H showing a slight concentration dependence and having larger fields (by a factor of 4) and broader distributions (factor of 2) than those on Na+ and Cl−. The most important feature is the large fields that occur in these concentrated aqueous NaCl electrolytes − clearly these fields are large enough to potentially influence excited electronic states. P(E) is related to the distribution of the electric field vector, P(E), by P(E) = 4πE2P(E) and these distributions, as a function of the electric field magnitude, are shown in Figure 12 (right panel, same 10878



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Figure 13. Distributions of the electric field x components in the lab frame on Na+ (upper left), Cl− (upper right), O (lower left), and H (lower right) for all concentrations and pure water.

component distributions for the O and H atoms shown in Figure 13 (bottom left and right panels) are non-Gaussian. This non-Gaussianity is also manifested in the P(E) data. However, as mentioned previously, these field distributions were calculated in the lab frame, in contrast to field distributions calculated in the body frame. Other studies21,27 on the vibrational properties of deuterated water and water in dilute electrolytes found the electric field component distributions in body frame to be remarkably Gaussian! In these studies the authors found that the Gaussian distributions of x, y, and z components of the electric field in a body frame of reference had two components with nonzero mean and the other component had a zero mean or vice versa. In the current study we were not specifically interested in the electric field in a body frame of the water molecule. Thus, how do we reconcile this apparent discrepancy between electric field distributions computed in a body versus lab frames? Let us consider a general Gaussian distribution with nonzero mean given by P(E) =

2 2 1 e−1/2σ [E − Eμ] 3/2 σ (2π )

3

PΩtot(E) =

∫

dΩ P(E)

⎡ EμE ⎤ 2 2 2 1 sinh⎢ 2 ⎥e−1/2σ [E + Eμ ] 3/2 ⎣σ ⎦ EμEσ(2π )

⎡ EμE ⎤ 2 2 2 sinh⎢ 2 ⎥e−1/2σ1 [E + Eμ ] ⎣ σ1 ⎦

EμEσ1(2π ) 2 2 c + 3 2 3/2 e−E /2σ2 σ2 (2π )

(4)

(1)

Figure 14. This plot shows that the non-Gaussian distribution of the electric field components (averaged x, y, and z at 6.7 M) in the lab frame on O can be fitted (smooth curve in green) by an orientationally averaged Gaussian distribution with nonzero mean (eq 3) plus a Gaussian with zero mean.

(2)

where dΩ = sin θ dθ dφ, then we obtain the distribution PΩ(E) =

3/2

Here, the distribution (fitting) parameters are as follows: c1 and c2 and σ1 and σ2 are the standard deviations and nonzero mean Eμ. This total distribution, Ptot Ω (E), can be fitted to the electric field distribution on the O site (averaged x, y, and z distributions) calculated in the lab frame as shown in Figure 14 where the raw data are plotted along with the fitted Ptot Ω (E).

where σ2 is the variance and Eμ is the mean. If we orientationally average P(E) via 1 PΩ(E) = 4π

c1

Thus, what may appear as non-Gaussian behavior in the lab frame can simply arise from orientationally averaging a body frame Gaussian electric field distribution. We note that in the work of Noah-Vanhoucke et al.,67 toward understanding sum frequency generation (SFG) spectroscopy at the liquid−vapor interface, they emphasize the importance of orientational averaging the projections of a body frame components onto

(3)

This, the orientationally averaged Gaussian with nonzero mean distribution, PΩ(E), can be augmented with a Gaussian with zero mean, to yield the total distribution 10879



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the lab frame components to connect the electric field distributions to the average molecular hyperpolarizabilities. This in turn is used to determine the absorptive part of the SFG susceptibility. A full analysis of these issues is beyond the current objective of this paper, however, we note that our electric field distributions P(E) are consistent with those reported in the literature for pure water and dilute aqueous electrolytes. In order to find a possible correlation between the magnitude of the field and local asymmetry, the field values at the ion positions were analyzed in the following way. First any ion that has a counterion in its first solvation shell was rejected in this analysis because there are not enough samples of this kind for good statistics and the concept of local asymmetry gets more complicated. For the remaining ions the field magnitude was paired with an asymmetry metric. In the case of sodium, this is given by asymmetry = ||

∑∀ O ∈ 1st SS rO ∑∀ O ∈ 1st SS 1

− rNa+ ||

more complicated and requires additional study to fully address the charge oscillations and screening lengths. The analysis of the system’s quantum charge distributions P(q) provides interesting insights into the charge state of concentrated aqueous electrolytes. We find, consistent with previous studies, that the charges on the ions are not unity and they are not equal and opposite to each other. Also, we find that the charge redistribution almost exclusively occurs between the solvated Cl− and the H2O molecules in the first solvation shells of either of the ions with the H2O surrounding Na+ to be more negatively charged than those around Cl−. Thus, the H2O molecules act as an electronic sink for the electrons originating on Cl−. The distribution of charges on Cl− is concentration dependent and arises from ion clustering and shows the greatest variability, followed by H2O, with Na+ showing the least dependence. The analysis of the system’s electric potential distributions P(ϕ) at the Na+ and Cl− sites shows similar trends and magnitudes but opposite in sign. In general, the magnitudes of the electric potentials are much larger on the ions compared to those on water. We also find potentials that are larger in aqueous NaCl than the Madelung potential of the NaCl crystal. Large magnitudes of the potentials on the ions arise from stressed/compact first solvation shells, whereas small potentials occur when the first solvation shell is loose/large. In contrast, the potentials at both the H and the O sites are mainly a measure for the distance to the closest neighbor. The electric potential analysis shows that the distributions are essentially concentration independent. The analysis of the electric field distributions P(E) provides an initial benchmark for future calculations of the field influence on ground and excited electronic states. The field magnitudes on the Na+ and Cl− sites range from 0 to 1 V/Å with a peak value at 0.5 V/Å. Local asymmetry is one important contribution to a high field magnitude in the case of solvent separated ions. Our MRCI gas-phase calculations on the NaCl dimer show that fields of this magnitude can dramatically alter the ground and excited states as well as the location of crossing points. The field magnitudes on the O and H sites are even larger than those on the ions! With the values for O ranging from 1 to 3 V/Å with a peak at 2 V/Å and for H ranging from 0.5 to 4 V/Å with a peak at 2 V/Å. The electric field analysis shows that the distributions are essentially concentration independent. We also find that the field component distributions to be Gaussian for the ions and non-Gaussian for the O and H sites (computed in the lab frame as opposed to the body frame of the molecule); however, these non-Gaussian distributions are readily modeled via orientationally averaging. These calculations and analyses provide the first steps toward understanding the magnitude and fluctuations of electric fields in aqueous electrolytes and what role these fields may play during crystallization and crystalloluminescence. Future studies will address the time dependence of these field fluctuations (how long they survive and what types of configurations lead to these fields), the evaluation of the ab initio mean inner potentials as functions of concentration, and the differences between the charge redistribution and structural effects arising from ab initio resampling classical trajectories versus direct ab initio dynamics.

(5)

and calculated in the same way for the Cl−H pair. The set of pairs was then collected into bins with a stride of 0.21 Å, and the field values were averaged within that bin. The results for Cl− and Na+ analyzed for all concentrations are shown in Figure S10. These results show an increase of the average field when going to higher asymmetry; however, they do not span the whole range of field values. In summary, we find that the magnitudes of the electric fields in both pure water and concentrated aqueous electrolytes are large. Both of the electric field distributions [P(E) and P(E)] for Na+, Cl−, O, and H were found to be quantitatively and qualitatively different with the field magnitudes generally being about four times larger on the O and H sites compared to the Na+ and Cl− sites. Interestingly, all show little, if any, variation with concentration. The distributions of the electric field components (in the lab frame of reference) on the Na+ and Cl− are Gaussian, however, non-Gaussianity is found for the O and H sites. However, we found that an orientationally averaged sum of Gaussians (one distribution with zero mean plus another with nonzero mean) could model the data extremely well. Hence, Gaussian distributions of electric fields in the body frame can appear non-Gaussian in the lab frame. We also find that the magnitude of the electric field on the Na+ and Cl− sites is linked to the asymmetry of the first solvation shell; as the asymmetry increases the magnitude of the field increases.

IV. CONCLUSIONS We have presented an analysis of the charge and scalar and vector field fluctuations in concentrated aqueous NaCl electrolytes. To benchmark the structural features and ensure fidelity of our sampling, we compared and contrasted our results to high-pressure X-ray diffraction on pure water versus neutron diffraction on aqueous NaCl. This analysis addressed recent studies pointing out the similarities between ions exerting equivalent pressures on the structure of water in aqueous electrolytes to the influence of high-pressure on pure water. We find excellent agreement when comparing our simulated structures to those from neutron diffraction. The structural analysis, when the atoms are considered as point charges, displays the conventional classical view of charge oscillations. However, this classical interpretation is very likely at odds with the quantum analysis of the charges which is much 10880



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ASSOCIATED CONTENT

S Supporting Information *

Additional material as discussed in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We gratefully acknowledge helpful discussions with Christopher J. Mundy and Gregory K. Schenter. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

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Charge and Electric Field Fluctuations in Aqueous NaCl Electrolytes

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