Solution Chemistry Effects on the Solvation Shell of Metal Ions

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Solution chemistry effects on the solvation shell of metal ions Xiangwen Wang,† Dimitrios Toroz,† Seonmyeong Kim,‡ Simon Clegg,§ and Gun-Sik Park,‡ and Devis Di Tommaso,*,†

† Thomas Young Centre, Materials Research Institute, and Department of Chemistry, Queen Mary University of London, Mile End Road, London, E1 4NS, United Kingdom ‡ Center for THz-driven Biomedical Systems, Seoul National University, Department of Physics and Astronomy, Seoul Na- tional University, Seoul, 08826, Republic of Korea § School of Environmental Sciences, University of East Anglia, Norwich, NR4 7TJ, United Kingdom

KEYWORDS. Electrolyte solutions. Molecular dynamics. Ion solvation. Water exchange dynamic. Hydrogen bonding.

ABSTRACT: As natural aqueous solutions are far from being pure water, being rich in ions, the properties of solvated ions are of relevance for a wide range of systems, including biological and geochemical environments. We conducted ab initio and classical MD simulations of the alkaline earth metal ions Mg2+ and Ca2+ and of the alkali metal ions Li+, Na+, K+ and Cs+ in pure water and – 2– electrolyte solutions containing the counterions Cl and SO4 . Through a detailed analysis of these simulations, this study reports on the effect of solution chemistry (composition and concentration of the solution) to the ion–water structural properties and interaction strength, and to the dynamics, hydrogen bond network, and low-frequency dynamics of the ionic solvation shell. Except for the ion– water radial distribution function, which is weakly dependent on the counter-ions and concentrations, we found that all other properties can be significantly influenced by the chemical characteristics of the solution. Calculation of the velocity autocorrelation function 2+ 2+ of magnesium ions, for example, shows that chlorine ions located in the second coordination shell of Mg weaken the Mg(H2O)6 hydration ‘cage’ of the cation. The result reported in this study suggest that ionic solvation shell can be significantly influenced by the interactions between other ions present in solution ions, especially those of opposite charge. In more general terms, the chemical characteristics of the solution, including the balance between ion-solvent and ion-ion interactions, could result in significant differences in behavior and function of the ionic solvation shell.

INTRODUCTION as free ions only in dilute solutions. Otherwise, cations and 10 A fundamental understanding of the processes controlling the anions form contact or solvent-shared ion pairs. The struc- hydration of ions is of importance to low-temperature geo- ture and dynamics of the ionic solvation shell can, therefore, chemistry. Natural aqueous solutions are far from pure water, be significantly affected by the subtle interplay between the being rich in ions, making solution environments highly influ- level of hydration of the ions, and the interactions between ential on the macroscopic properties of aqueous solutions — ions, especially those of opposite charge. In more general e.g., their viscosity1 or heat capacity2— or to processes involv- terms, the chemical characteristics of the solution, including ing other solutes in those solutions — e.g., crystal nucleation the balance between ion-solvent and ion-ion interactions, and growth.3 In the hydration model proposed by Frank and could result in significant differences in behavior and function Wen to explain deviations of ionic solution behavior relative of the FSS. to pure water, the insertion of an ion in solution radially aligns The effects of solution composition on the structure and dy- water molecules in concentric regions characterized by differ- namics of the FSS is important to characterize the reactivity ent levels of interaction between water and ion.4 The water of solvated metal ions.8,11,12 For example, in aqueous environ- molecules in the innermost region, also known as the first ments the processes of nucleation and growth of ionic crystals solvation shell (FSS), are tightly bound to the centric ion and such as calcite (CaCO3) or magnesite (MgCO3), are controlled exhibit translational and rotational entropy loss compared by the dynamics of hydration–dehydration around the cat- with pure water.5 Several classical and ab initio molecular dy- ion.13–15 Consequently, an accurate characterization of the ef- namics (MD) simulations of hydrated metal ions (single Mn+, fect of solution chemistry (composition and concentration of no counterions) have been conducted to characterize the struc- the solution) on the FSS of solvated metal ions is of funda- ture and dynamics of the ionic FSS, with the results confirm- mental importance to understand and control the nucleation of ing what anticipated by the Frank and Wen hydration model.6– minerals, as well as other reactive processes involving ions in 9 However, ions in aqueous electrolyte solutions are present solution. 1

Here, we report ab initio and classical MD simulations of the pseudopotentials were used to describe the core–valence in- alkaline earth metal ions Mg2+ and Ca2+, and of the alkali teractions.30 All atomic species were represented using a dou- metal ions Li+, Na+, K+ and Cs+ in pure water and electrolyte ble-zeta valence polarized (DZVP) basis set. The plane wave – 2– solutions containing the counterions Cl and SO4 . We have kinetic energy cut off was set to 1000 Ry. The k-sampling was chosen the above combination of ions because they are com- restricted to the Γ point of the Brillouin zone. Simulations monly found in nature, including in the composition of the sea were carried out with a wave function optimization tolerance and groundwater.16 Salt concentrations ranging from 0.9 to 3.8 of 10–6 au that allows for 1 fs time steps with reasonable en- mol.kg–1 were considered to quantify the effect of solution ergy conservation. Periodic boundary conditions were applied composition on the strength of ion–water interaction and to throughout. AIMD simulations were carried out in the canon- characterize the structure and low-frequency dynamics of the ical ensemble (constant number of particles N, volume V, FSS. The interatomic forces in ab initio MD are derived from temperature T) using a Nosé-Hoover chain thermostat to the electronic structure,17,18 usually in the framework of den- maintain the average temperature at 300 K. Periodic boundary sity functional theory,19 providing the capability of studying conditions were applied throughout. non-additivity effects in the dynamics of ions solvation shells, Classical molecular dynamics which is important when simulating ionic solutions.20 How- Classical molecular dynamics (CMD) simulations were per- ever, the computational cost of ab initio MD limits the size of formed using the GROMACS molecular dynamics package.31 simulated aqueous solutions (few hundreds of water mole- The leapfrog algorithm with a time step of 2 fs was used to cules) and the time of the simulation (<100 ps). These re- integrate the equations of motion. Simulations were constraints can limit the characterization of the dynamics of sol- ducted in the isothermal (NVT) and isothermal-isobaric vent exchange in the first hydration shell of metal ions such (NPT) ensembles at the target temperature T = 300 K and as Mg2+, which mean residence time in the first hydration shell pressure P = 1 bar. The velocity rescale thermostat and is of the order of microseconds.21,22 We have therefore com- the isotropic Parrinello-Rahman barostat were used with plemented the results from AIMD with metadynamics-biased 0.4 ps and 2.0 ps as the thermostat and barostat relaxation classical MD simulations, which have been used to elucidate times, respectively. The electrostatic forces were calcu- the water exchange reaction pathways around metal ions. lated utilizing the particle-mesh Edwald approach. Free After having introduced the computational models employed energy calculations were conducted computed using the and the details of the simulations, we next report on the effect well-tempered metadynamics-biased MD (CMμD) of the solution composition on the structure and dynamics of method,32 using GROMACS 2016.3 equipped with the the ionic solvation shell. These results are rationalized in PLUMED 2.4.1 plugin.33 CMμD simulations were con- terms of the mechanism of water exchange around cations and ducted to quantify the thermodynamics and kinetics of the wa- the strength of ion–water interaction. The distribution of hy- ter exchange around the metal ion using as the collective var- drogen bonds and the reorientation dynamics of water mole- iable the ion–water coordination number (CN). The reaction cules, in the bulk solution and the first solvation shell, are fi- coordinate for rare events can be a multidimensional function nally presented. of several geometric parameters. Exploring the dynamical aspects of the CN reaction coordinate allows one to examine the COMPUTATIONAL DETAILS ability of a hydrated ion to explore the transition mechanism Ab initio molecular dynamics between under- and over-coordinated states during the dy- Ab initio (Born-Oppenheimer) molecular dynamics (AIMD) namics of ion solvation.34 The CN was defined using the con- simulations were conducted with the electronic structure code tinuously differentiable function: 23 CP2K/Quickstep code, version 4.1. CP2K implements den- 푟 − 푑 푛 1 − ( 푖 0) sity functional theory (DFT) based on a hybrid Gaussian plane 푟0 24 퐶푁 = ∑ 푚 (1) wave. The Perdew–Burke–Ernzerhof (PBE) generalized- 푟푖 − 푑0 푖 1 − ( ) gradient approximations (GGA) for the exchange and correla- 푟0 tion terms were used, together with the general dispersion cor- where r0 = 1.1 Å, d0 = 1.9 Å, n = 4, m = 8, ri is the distance rection termed D3, to provide a more accurate description of between the magnesium and the oxygen of i-th water mole- the structure of liquid water.25,26 The effect of the DFT method cule.35 The free energy profiles were constructed by running was also considered by conducting simulations using the classical well-tempered metadynamics-biased MD (CMμD) BLYP27,28 and revPBE29 functionals, with and without the simulations with Gaussians laid every 1 ps and with an initial DFT-D3 correction term. The Goedecker-Teter-Hutter (GTH) height equal to kBT. The Gaussian widths were 0.2 and 0.1 2 along with the distance and coordination number (CN), re- oxygen atom at a distance r from the metal ion. In general, the spectively. We have used the interatomic potential model de- average metal–water distance of the first coordination shell veloped by Zeron et al.36 (denoted as Madrid-2019 forcefield) increases when moving down the alkali and alkali earth group. + + + 2+ 2+ − 2− Li , Na , K , Mg , Ca , Cl , and SO4 in aqueous solu- The lithium, magnesium, calcium and, to a lesser extent, so- tion.36 In the Madrid-2019 forcefield, the water molecules are dium ions are characterized by a rigid and well defined first represented by the TIP4P/2005 model,37 which provides an solvation structure. As to the hydration structure of the K+ and excellent description of several properties of liquid water.38 Cs+, the intensities of the first peaks are lower and their pro- Monovalent and divalent ions are modelled using charges of files are much less defined. In aqueous electrolyte solutions, – 2– 0.85 and 1.7, respectively (in electron units). The non-electro- the presence of the Cl and SO4 counterions does not have a + + 2+ static ion–water and ion-ion interactions are described by pair- significant effect on the gMO(r) profiles of Li , Na , Mg and wise Lennard-Jones potentials. Ca2+. On the other hand, the chlorine ions broaden the RDFs of the K+ and Cs+ cations, indicating a perturbation of their Simulation protocol coordination shells and a more labile hydration structure. CMD simulation of 64 water molecules in the NPT ensemble (1 ns) have been conducted to generate an equilibrated aqueous solution. The last configuration was used to create the initial configuration of the hydrated metal ions (single Mn+, no counterions, Mn+: Mg2+, Ca2+, Cs+, Na+, K+) by replacing one n+ H2O with one M . Aqueous electrolyte solutions with concentrations ranging from 0.9 to 3.8 mol.kg–1, were generated by randomly replacing water molecules with Mn+ and Xm– (Cl– 2– and SO4 ) ions, by making sure that the initial configuration did not contain contact ion pairs. Details of the solutions considered in this study (number of ions and water molecules, average cell lengths and system concentrations) are reported in Table S1 of ESI. 39 For comparison purposes, we have also conducted AIMD simulations of pure liquid water (64 H2O, 1 –3 – g.cml ) and a chlorine ion (Cl ) in 63 H2O molecules. For each system, we first conducted 6 ns of CMD (NPT) to equil- ibrate the cell volume and the last configuration was used to conduct at least 50 ps of AIMD. Trajectories were analyzed to characterize the properties of the FSS of the metal ions in terms of the radial distribution function (RDF) and orientation of the solvent molecules in the ionic hydration shell, the strength of the cation–water interaction in terms the velocity- autocorrelation functions of Mn+, the dynamics of first hydration shell in terms of the mean residence time (MRT) of water, and the low-frequency dynamics associated with the reorientation behavior of the water molecules in solution.

RESULTS AND DISCUSSION Figure 1. Ion-water radial distribution functions, gMO(r), obtained Solvation structure from AIMD (PBE-D3) simulations of hydrated metal ions (single Ion-water radial distribution function. Information regard- Mn+, no counterions) and of aqueous electrolyte solution (1.9 mol.kg–1). (A) Solutions containing Li+, Na+, K+, Cs+. (B) Solutions ing the structural properties of the coordination sphere of the containing Mg2+ and Ca2+. alkali metal ions (M = Li+, Na+, K+ and Cs+) and alkaline earth Ion-water coordination shell distribution and ion pairing. metal ions (M = Mg2+ and Ca2+) in pure liquid water and in the – 2– We report in Fig. 2 the probability distribution of the number presence of chlorine (Cl ) and sulphate (SO4 ) counterions, of water molecules in the first coordination shell of the metal can be deducted from the radial distribution functions (RDFs) ions, obtained from the analysis of the AIMD trajectories of of the M-O pairs, gMO(r), in Fig. 1, which represent the prob- single cations Mn+ in pure water and of the 1.9 kg.mol–1 aque- ability, relative to a random distribution, of finding a water ous electrolyte solutions. 3

Table 1. The speciation (%) of the cations M (Li+, Na+, K+, Cs+, 2+ 2+ – 2– Mg and Ca ) and anions X (Cl , SO4 ) ion pairs as a function of concentration determined in terms of the following ion pairing criteria: contact ion pair (CIP) when M and X are in direct physical contact; solvent-shared ion pairs (SSHIP) when M and X are separated by one water molecule; solvent-separated ion pairs (SSIP) when M and X are separated by at least two water molecules. Re- sults obtained from the analysis of AIMD (PBE-D3) simulations. Concentration (b) in mol.kg–1.

System b CIP SSHIP SSIP LiCl 0.9 85.6 14.4 0.0 NaCl 1.9 0.0 68.9 31.1 KCl 1.9 3.3 51.4 45.3 CsCl 0.9 72.8 27.2 0.0

MgCl2 1.9 0.0 55.5 44.5

CaCl2 1.9 0.7 97.1 2.2

MgSO4 1.9 100.0 0.0 0.0

CaSO4 1.9 0.0 99.6 0.4

For the aqueous LiCl solutions, the analysis of the ion-water coordination shell distribution shows that in the presence of chlorine ions, the number of water molecules coordinated to Li+ reduces from four to three as a result of the formation of Li+∙∙∙Cl– contact ion pairs (Table 1). In the 1.9 mol.kg–1 NaCl solution, Na+ and Cl– form mostly SSHIPs (69%), where the chlorine ions are in the second shell of Na+. Despite not being coordinated to Na+, chlorine ions induce a significant contrac- tion of the sodium hydration shell: in NaCl(aq) the sodium ions are in the five-coordinated state for 90% of the simulation period, compared to approximately 50% of the simulation pe- Figure 2. Probability distributions of the number of water mole- riod of hydrated Na+ (isolated Na+, no counterions). Conse- cules in the first coordination shells of the metal ions Li+, Na+, K+, quently, counterions such as Cl– can stabilize under-coordi- Cs+, Mg2+ and Ca2+. Results obtained from the analysis of AIMD (PBE-D3) trajectories of hydrated metal ions (single Mn+, no coun- nated metal-water complexes even when they are not part of terions) and of aqueous electrolyte solution (1.9 mol.kg–1). the first coordination shell of Mn+. On the other hand, Cs+ and Cl– are for most of the simulation period present as CIPs The results for hydrated Mn+ show that the average size of the (72%). However, because of the high flexibility of the FSS of FSS, as well as the number of accessible hydration states, in- Cs+, the coordination number distribution is only marginally creases as we move down the periodic table. The tetrahydrated affected by the presence of chlorine ions (Fig. 2). In + lithium complex [Li(H2O)4] , and the hexahydrated magne- 2+ MgCl2(aq) the hexahydrated [Mg(H2O)6] is the only hy- 2+ 2+ sium and calcium complexes [Mg(H2O)6] and [Ca(H2O)6] drated complex present in solution, and in MgSO4(aq) only were the only species detected for these ions. On the other four water molecules are directly coordinated to Mg2+ because + + + hand, hydrated Na , K and Cs can access multiple hydration the magnesium and sulphate ions form very stable contact ion states; the cesium ion, for example, can coordinate between pairs (Table 1). DFT calculations of the free energy of for- four and nine water molecules. In aqueous electrolyte solu- 2+ 2– 2+ – mation (ΔG) of the Mg /SO4 and Mg /Cl contact ion pairs tions, metal ions are not purely hydrated, but they tend to 2– confirm the much higher propensity of SO4 to form very sta- form, with the anions in solution, contact ion pairs (CIPs), sol- 2+ – 2+ 2– ble CIPs with Mg compared with Cl : Mg(H2O)6 + SO4 vent-shared ion pairs (SSHIPs), and solvent-separated ion –1 2+ → MgSO4(H2O)4 + 2H2O, ΔG = –160 kJ.mol ; (Mg(H2O)6 pairs (SSIPs). The percentages of CIPs, SSHIPs and SSIPs in – – –1 + Cl → MgCl(H2O)5 + H2O, ΔG = –25 kJ.mol the 1.9 mol.kg solutions are listed in Table 1, while the results (wB97XD/aug-cc-pdvz level of theory in the CPCM solvation –1 for the more dilute (0.9 mol.kg ) and concentrated (3.8 model). The coordination shell distribution of the calcium ion –1 kg.mol ) solutions are reported in ESI (Table S2). displays a counterintuitive behaviour, with the coordination number (CN) of Ca2+ increasing from six in pure water to 4 around seven in CaCl2(aq) (Fig. 2). The chlorine ions are Table 2. Probability (%) distributions of the number of water mol- 2+ hardly ever coordinated to the calcium ions, with which they ecules in the first coordination shells of hydrated Ca (no counterions) obtained using different DFT based AIMD methods. predominantly form SSHIPs (Table 1). Therefore, the chlo- 2+ NH2O/Ca is the number of water molecules per calcium in the sim- rine ions located in the second coordination shell of Ca2+ sta- ulation cell; tsim is the simulation period used to compute the co- 2+ 2+ bilize the seven-coordinated Ca(H2O)7 complex over the six- ordination number (CN) distribution around Ca . 2+ coordinated Ca(H2O)6 species. The same behavior is ob- Method NH2O / tsim CN 2+ 2– served in CaSO4(aq), where Ca and SO4 form almost ex- Ca2+ (ps) clusively SSHIPs (99.6%) and the epta-hydrated calcium 6 7 8 Avg. complexes are stabilized by the sulphate ions located in the PBE 63 50 100.0 0.0 0.0 6.0 second hydration shell of metal ion. PBE-D3 63 50 95.1 4.9 0.0 6.0 100 96.6 3.4 0.0 6.0 The average CN of for the first hydration shell of Ca2+ has 500 98.7 1.3 0.0 6.0 been a controversial issue for AIMD simulations.40 Several 124 200 47.6 51.6 0.8 6.5 DFT based MD simulations, using the Car-Parrinello and revPBE 63 50 38.2 61.7 0.1 6.6 revPBE- 63 50 86.9 12.1 1.0 6.1 Born-Oppenheimer schemes, of the hydrated calcium ion (sin- D3 2+ gle Ca , no counterions) reported six water molecules in the BLYP 63 50 32.7 17.3 0.0 6.3 first hydration shell of Ca2+,41 which agrees with the result re- BLYP-D3 63 500 15.0 80.7 4.3 6.9 ported in this study (Fig. 2). However, experimental results Dynamics of the ionic solvation shell from extended X-ray absorption fine structure (EXAFS) Water exchange around metal ions. The frequency of water measurements in CaCl2 solutions, with concentrations rang- exchange around cations is generally considered as the rate –1 ing from 0.12 to 6 mol.kg , resulted in CNs between 6.8 and determining for the reactions involving these ions in aqueous 42,43 8. As previously discussed, the presence of counterions solutions.44–47 We have characterized the dynamics of the first – 2– (Cl and SO4 ), which are normally present in experiments, and second hydration shells of the alkali metal ions (Li+, Na+, 2+ stabilizes the higher coordination states of Ca , yielding a K+ and Cs+) and alkaline earth metal ions (Mg2+ and Ca2+) in 2+ computed CN of Ca in CaCl2(aq) and CaSO4(aq) (CN=6.9) pure liquid water and electrolyte solutions using the “direct” in much better agreement with EXAFS measurements of method proposed by Hofer and co-workers.48 This methodol- CaCl2 solutions. Therefore, one simple reason for the disa- ogy has been previously applied for, among others, the char- greement between theory and experiment could be the com- acterization of ligand exchange between coordination shells position of the solution used to conduct the simulations. Other of hydrated alkaline earth metal ions and their carbonate and factors such as the size of the simulation box, the length of the bicarbonate complexes,49–51 as well as the quantification of the simulation period, and the choice of the density functional water exchange frequency around calcium sites in calcite-wa- method have also been considered by conducting AIMD sim- ter interface 52,53 and hydroxyapatite nanopores.54 In the “di- 2+ ulations of hydrated Ca (no counterions) in a box containing rect” method, the MD trajectories are analyzed for water mol- 63 and 124 water molecules using the PBE, rev-PBE and ecule movements and whenever a water molecule crosses the BLYP functionals with and without the D3 dispersion correc- boundary of the cation coordination shell its path is followed; tion. The results in Table 2 show that: a simulation period of if its new position outside or inside this shell lasts for more 50 ps is sufficiently long to get a convergent distribution of than τ* = 0.5 ps then the event is accounted as a real exchange the calcium-water coordination shell; Ca2+ in 63 and 124 water event (Nex). The choice of τ* = 0.5 ps is based on the average molecules yield CNs of 6.0 and 6.5; BLYP-D3 gives a CN of lifetime of a hydrogen bond between the solvent molecules, 6.9 and a coordination distribution that is shifted to higher co- obtained experimentally using femtosecond spectroscopy,55 ordination states compared the average CN obtained with and is the standard value used in the applications of the “direct PBE-D3 (6.0) and revPBE-D3 (6.1). Both the system size and method”. Setting τ* = 5 ps gives only minor differences to the the DFT method can, therefore, influence the coordination dis- statistics of water exchange frequency around the metal ion tribution and average coordination size. This analysis suggests (Table S3.2 of ESI). Table 3 reports Nex in the first and sec- that solution composition, system size and level of theory ond coordination shell of the metal ions, together with the should all be considered when comparing AIMD simulations number of exchange events normalized to 10 ps, Nex / 10 ps, and experimental determinations of ionic coordination num- which represents a measure of the “lability” of the hydration bers. shell of the metal. From the number of water exchange events, the mean residence times (MRT) of the water molecules in the first and second hydration shell of the ion can be computed as

MRT = (CN × tsim) / Nex, where CN is the average number of water molecules in the first or second coordination shell and 39 tsim is the duration time of the simulation. For the alkali metal ions, the first shell solvent exchange dynamics increases sub- stantially on going from Li+ (MRT=11.8 ps) to the other alkali metal ions Na+ (1.1 ps), K+ (0.4 ps) and Cs+ (0.2 ps). The mean – residence time of solvent around H2O and Cl is approximately 0.5 ps, which is comparable to the values obtained for K+ and Cs+, confirming the high lability of these ions. As reported in Table 3, AIMD simulations of hydrated magnesium ion (single Mg2+, no counterions) showed no exchanges around Mg2+, compared with compared to ~50 of such exchanges (more facile dehydration) in 500 ps around aqueous Ca2+ (MRT=61.2 ps). The reactivity of the cations varies, therefore, as follow: Mg2+ << Ca2+ < Li+ << Na+ < K+ ≈ Cs+. We can rationalize Figure 3. Free energy as a function of the ion-water coordination this behavior by comparing, in Fig. 3, the free energy profiles obtained from CMμD simulations. The ion–water interaction for + + 2+ as a function of the metal–water coordination number (CN) Li , Na and Mg was described by the Lennard-Jones ion models from the Amber database.56 For Ca2+ the ion – water interaction + + 2+ 2+ for Li , Na , Mg and Ca , from which we can extract ther- was described by the Buckingham potentials parameterized by de modynamic information on the accessible coordination states Leeuw57 and Kerisit and Parker.58 Water molecules were described 59 for these cations. The ion–water CN is defined as the number using the SPC/E model. of water molecules in the FSS of the cations. Using the CN as As to the dynamics of the second hydration shell, for all ions, collective variable allows us to explore the transition mecha- the MRTs is less than 1 ps and close to the MRT of solvent nism between under- and over-coordinated states during the around H2O (0.5 ps). This result contrasts with results from ab dynamics of ion solvation.34 The hydrated ions Ca2+, Li+ and initio MD simulations of the alkaline earth metal ions Mg2+, Na+ have several coordination states corresponding to a mini- Ca2+ and Sr2+, which reported MRT values between 3.3 and mum on the free energy profile and particularly for Na+ the 6.8 ps. These simulations, however, used smaller simulation transition between these states is almost barrierless. For Mg2+ boxes than the one used in this study and did not employ dis- the only coordination state accessible at room temperature is persion corrected DFT functionals.49 Simulations of hydrated 6 and the free energy barrier to reach the 5-coordinated meta- Na+, K+ and Ca2+ using different functionals, simulation peri- 2+ 2+ stable state is about six times higher than for Ca . As Mg is ods and number of H2O molecules confirm the fast solvent strongly hydrated, water exchange is drastically retarded in its exchange in the second coordination shell of the metal ions FSS. A further comment concerns the effect of DFT methods and the absence of long-range effects (Table S3.2 in ESI). density functional on the MRTs values of the FSS of hydrated Regarding the effect of counterions in solution to water ex- 2+ calcium (isolated Ca , no counterions). We tested different change dynamics of the cations, in LiCl(aq) the formation of DFT methods with (PBE-D3, revPBE-D3, BLYP-D3) and Li+/Cl– CIPs increases significantly the MRT around Li+ to 20 without (PBE, BLYP, revPBE) Grimme’s D3 correction. No ps. The other, very labile, alkali ions Na+, K+ and Cs+ are sub- exchanges were accounted with the PBE method, while for the stantially unaffected by the presence of counter-ions in solu- 2+ other methods the MRT in the FSS of Ca varies from 14 ps tion and the dynamics of water exchange around Na+, K+ and (revPBE-D3) to 61 ps (PBE-D3) (Table S3.2 in ESI). Recent + Cs remain very fast. AIMD simulations of MgCl2(aq) and estimates using different interatomic potential models and 2+ MgSO4(aq) show no exchanges around Mg . However, notice techniques to characterize the dynamics of water produced the contrasting behavior of the chloride and sulphate ions on values lying in the range of 60-80 ps, in good agreement with 2+ the solvent exchange dynamics around Ca : in CaCl2(aq), the value of 61 ps obtained in this work using the PBE-D3 where the Cl– ion is located in the second coordination shell 51 functional. of Ca2+, the MRT is 10.6 ps (faster dynamics) compared with

61.2 ps (slower dynamics) in pure liquid water; in CaSO4(aq), 2– 2+ where SO4 forms very stable CIPs with Ca , there were no accounted water exchange events around the first solvation shell of the calcium ion.

푯ퟐ푶 + + + + Table 3. Number of accounted water exchange events (푵풆풙 ) in the first and second coordination shells of the metal ions Li , Na , K , Cs , Mg2+ and Ca2+, with a duration of more than τ* = 0.5 ps, obtained from the analysis of AIMD (PBE-D3) simulations of hydrated metal ions (single Mn+, no counterions), aqueous electrolyte solution, pure water and hydrated chlorine ion. Mean residence time (MRT) of water molecules in the first hydration shell computed using the relation MRT = (tsim×CN)/Nex, where tsim is the period of simulation and CN is the average ion-water coordination number of the first and second coordination shell, which was obtained from the integration of the ion-water radial distribution function up to the first and second minimum, respectively. Concentration (b) in mol.kg-1.

First Shell Second Shell 푯ퟐ푶 푯ퟐ푶 푯ퟐ푶 푯ퟐ푶 System b tsim CN 푵풆풙 푵풆풙 /ퟏퟎ ps MRT (ps) CN 푵풆풙 푵풆풙 /ퟏퟎ ps MRT (ps) Li+ 0.9 50 4.0 17 3.4 11.8 15.3 2066 413.2 0.4 LiCl 1.9 50 3.0 7.5 1.5 20.0 13.9 3760 752.0 0.2 Na+ 0.9 50 5.1 233 46.6 1.1 20.0 1852 370.4 0.5 NaCl 0.9 50 5.1 178 35.6 1.4 21.4 2022 404.4 0.5 1.9 50 5.0 195.5 39.1 1.3 20.9 3152 630.4 0.3 3.8 50 4.7 186.5 37.3 1.3 19.3 7205 1441.0 0.1 K+ 0.9 50 6.2 750 150.0 0.4 21.1 1675 335.0 0.6 KCl 0.9 50 4.8 536 107.2 0.4 21.9 1852 370.4 0.6 1.9 50 5.5 693.5 138.7 0.4 20.4 3832 766.4 0.3 3.9 50 3.9 694 138.8 0.3 19.5 6964 1392.8 0.1 Cs+ 0.9 50 8.3 1299 259.8 0.3 21.5 1556 311.2 0.7 CsCl 1.9 50 6.3 983 196.6 0.3 25.0 3726 745.2 0.3 Mg2+ 0.9 40 6.0 0 0.0 – 20.0 1057 264.3 0.8 MgCl2 1.9 50 6.0 0 0.0 – 18.9 1266 253.2 0.7 MgSO4 1.9 50 4.5 0 0.0 – 14.8 3223 644.6 0.2 Ca2+ 0.9 500 6.0 49 1.0 61.2 21.0 15694 313.9 0.7 CaCl2 1.9 50 6.8 32 6.4 10.6 19.1 2429 485.8 0.4 CaSO4 1.9 50 6.9 0 0.0 – 21.0 3121 624.2 0.3 H2O – 50 3.9 536 107.3 0.4 23.0 2316 463.3 0.5 Cl– 0.9 40 6.2 502 125.5 0.5 26.4 1702 425.5 0.6

Caging effect in the hydration shell of ions minimum (t0), can be used as descriptors of the strength Towards resolving the origin of the different local ion–water of ion interaction with the surrounding water molecules 22 interaction, the velocity-autocorrelation functions (VACFs) of and of the rigidity of the interatomic vibration. The + + + the metal ions (M) were computed.60 VACF is defined as fol- VACFs of Na (t0 = 0.1 ps), K (t0 = 0.16 ps), and Cs (t0 = lows: 0.5 ps) in particular, display a smooth decay, which suggests a weak caging effect by the solvent; this explains the facile 푁푂 푁푀 kinetics of dehydration of these cations. The lithium ion 1 푉퐴퐶퐹푀(푡) = ∑ ∑ 풗푖(푡푗) ∙ 풗푖(푡푗 + 푡) (2) shows a much sharper first minimum (t0 = 0.04 ps) followed 푁푂푁푀 푗=1 푖=1 by a marked oscillatory behavior because of the more rigid + where vi is the velocity vector of atom i, NO and NM are interatomic vibration between the smaller Li with the sur- 2+ the number of time origins spaced by t and number of rounding hydration cage. The comparison of the Ca and metal ions respectively. Fig. 4 displays the VACF profiles Mg2+ VACFs (Fig. 4B) shows a very different oscillatory 2+ 2+ obtained from AIMD (PBE-D3) simulations of the hydrated behaviour (t0 = 0.01 ps for Mg and t0 = 0.06 ps for Ca ), cation (single Mn+, no counter-ions) and aqueous electrolyte which is indicative of the strengthening of ion-interaction solutions (1.9 mol.kg–1). Comparison of the VACF profiles with the surrounding water molecules and increased ri- 2+ obtained from the full set of NaCl, KCl and CaSO4 solutions gidity of the interatomic vibrations ongoing from Ca to are reported in ESI (Fig. S4). In general, the occurrence of Mg2+. The presence of chlorine counterions has no signif- a dip to negative values in the VACF profile results from icant effect on the VACF profiles of the alkali metal ions the so-called “cage effect” for the tagged particle, that is, and of the calcium ion. On the other hand, the inset of Fig. it takes some time for the particle to escape from the cage 4B shows a smoother decay of the VACF of Mg2+ in 61 formed by its surrounding water molecules. The VACF MgCl2(aq), which is a clear indication of a looser inter-hexa- is very sensitive to the local ion hydration environment hedral vibration. Therefore, the chlorine ions located in the 2+ 2+ and changes in the profiles of this time correlation func- second coordination shell of Mg weaken the Mg(H2O)6 tion, such as oscillatory behaviour and position of the first water ‘cage’ of the ion.

existence of a hydrogen bond between two water molecules:62,63 (i) the oxygen–oxygen distance is less than 3.5 Å; (ii) the intermolecular hydrogen-oxygen distance is less than 2.45 Å; (iii) the oxygen-oxygen-hydrogen angle is less than 30 degrees. The average number of HBs in bulk water computed from AIMD (PBE-D3) simulations is 3.75, which is in the range of experimental values (3.5-3.9) obtained using several techniques.64 In comparison, the revPBE-D3 and BLYP-

D3 functionals give nHB values of 3.40 and 3.61, respectively. The average number of HBs reported in Table S5 decreases with the increase of salt concentration, a result in agreement with previous MD studies of aqueous alkali halide salt solutions.50,62,65 However, the extent on the HB network is specific to the metal ion. In the 1.9 mol.kg–1 electrolyte solutions containing the doubly charged Mg2+ and Ca2+ ions, the average number of HBs is three, which is significantly lower than the 1.90 mol.kg–1 solutions of LiCl (3.53), NaCl (3.40), KCl (3.37) and CsCl (3.50). Fig. 6 compares the percentage of water molecules that engage in n HBs for the solutions considered in this study. In pure liquid water, molecules are mostly engaged in four (70%) and three (20%) HBs, with a similar distribution being observed in LiCl(aq), NaCl(aq), KCl(aq)

and CsCl(aq). On the other hand, in MgCl2(aq) and CaCl2(aq), the distribution of HBs is significantly shifted to lower n, with

an almost equal proportion of molecules forming two, three Figure 4. Velocity autocorrelation functions (VACF) of the metal and four HBs. ions obtained from AIMD (PBE-D3) simulations of the hydrated cation (single M, no counterions) and of aqueous electrolyte solu- Hydrogen bond statistics in ionic solvation shell. Guàrdia tions (1.9 mol.kg–1). (A) Solutions containing Li+, Na+, K+, Cs+. et al. revealed significant modifications in the hydrogen bond- 2+ 2+ (B) Solutions containing Mg and Ca . ing architecture for the water the first ionic solvation, which This dynamic flexibility further highlights the effect of coun- do not persist beyond the second shells.66 To investigate terions on the dynamics of water molecules around Mg2+. A the origin of the ion-specific effects to the hydrogen bond final comment concerns the sensitivity of the VACF on the structure, we have therefore computed the distribution of HBs density functional method used in the AIMD simulations. The for the water molecules that, at each step of the AIMD simu- VACF profiles of hydrated Ca2+ obtained from AIMD simulation, are coordinated to the metal ion. Table 4 compares the lations using PBE, revPBE, and BLYP, with and without D3 percentage of molecules having n water–water HBs (fn) and correction, shows noticeable differences (Fig. S4.2 in ESI). the average number of HBs (nHB) in the first solvation shell of The PBE method generates the more marked oscillatory be- the monovalent (Li+, K+, Na+, and Cs+) and the divalent (Mg2+ havior, to which corresponds a more rigid Ca-water coordina- and Ca2+) cations, together with the HB statistics for pure wa- tion environment compared to the other DFT methods, ex- ter and the water molecules coordinated to Cl–, with the latter plaining the absence of water exchange events around Ca2+ obtained from AIMD of hydrated Cl–. For the hydrated metal during the AIMD (PBE) simulation (Table 3). ions (single Mn+, no counterions), water molecules coordi- 2+ 2+ Hydrogen bond statistics nated Mg (nHB = 2.20) and Ca (2.30) display very large deviations from the HB distribution of the bulk (3.75), com- Distribution of hydrogen bonds in bulk solution. The pared with the first solvation shell of the more labile K+ (3.06) AIMD trajectories of pure liquid water and the aqueous elec- and Cs+ (3.24). The water molecules coordinated to Cl– (3.61) trolyte solutions were scanned to determine the effect of ions display only minor deviations from H O. Fig. 6 highlights, on the hydrogen bond (HB) structure, in terms of the percent- 2 however, that the average numbers of HBs in the FSS of metal age of molecules having n water–water HBs and the average ions consistently reduces in chloride-bearing solutions com- number of HBs (nHB) per molecule (Table S5 of ESI). We pared to hydrated metal ions (single M, no counterions). adopted the following geometrical criteria to determine the

〈흁(0) ∙ 흁(t)〉 푃 (푡) = (3) 1 흁(0)2 where μ(0) and μ(t) are the unit vectors defining the orientation of the dipole moment at times 0 and t, respectively. The averages were computed using several time origins and over- lapping intervals, each of length t = 16 ps. (Figs. S5.1–S5.4 in ESI). Fig. 7 reports the concentration-dependent time correla-

tion P1(t) profiles of the water molecules, obtained from the AIMD (PBE-D3) simulations of the hydrated cation (single M, no counter-ions) and aqueous electrolyte solutions. In gen-

eral, the P1(t) function starts at 1 and then decays asymptoti- cally to zero because of the random and isotropic reorientation of the water molecules in solution. The early stages of fast loss of correlation are caused by librational motion, whereas the Figure 5. Percentage of water molecules that engage in n hydrogen bonds (HBs) in pure water and electrolyte solutions. Values ob- long term decay is due to reorientational motion and can be fit 68 tained from AIMD (PBE-D3) trajectories. by a bi-exponential model, exp(−t/τ1) + b exp(−t/τ2). The The interaction between ions of opposite charge results, there- overall time associated with this process is given by the sum fore, insignificant differences in the distribution of HBs for of the fitting parameters τ1 and τ2. The value of τreor for pure the water molecules in the ionic FSS. However, speciation liquid water, computed at the PBE-D3 level of theory is 5.3, 69 analysis of the aqueous electrolyte solutions has shown that is in good agreement with the experimental value of 4.8 ps. metal ions are present as free ions only in very dilute electro- Table 4. The distribution of the number of hydrogen-bonds (HBs) lyte solutions.67 Otherwise, ions tend to form contact and sol- per water molecule in pure water and in the first solvation shell (FSS) of Li+, Na+, K+, Cs+, Mg2+ and Ca2+ obtained from AIMD vent shared pairs with the anions present in solution (Table (PBE-D3) simulations of hydrated ions and electrolyte solution. 1). In electrolyte solutions, we can, therefore, consider that The values are percentages of H2O with the given number of HBs. water molecules exist in different hydration states, depending Concentration (b) in mol.kg-1. on their relative position (coordination) to the cations and an- Number of HBs (%) in the FSS ions in solution. Classical MD simulations of MgCl2 solutions System b f0 f1 f2 f3 f4 f5 Avg. with concentrations ranging from 0.3 to 2.8 mol.kg–1 were also Li+ 0.9 0.3 7. 3 31.1 60.9 0.5 0.0 2.54 conducted to determine the fraction of water molecules that LiCl 1.9 0.3 11.1 26.8 61.0 0.8 0.0 2.51 are in the bulk (or free water), coordinated to one single ion, Na+ 0.9 0.2 4.7 26.1 66.6 2.4 0.0 2.66 2+ – or coordinated to both Mg and Cl . Fig. 6B shows that about NaCl 0.9 0.6 1.7 26.8 62.5 2.4 0.0 2.58 2+ – 20% of water molecules are coordinated to both Mg and Cl , 1.9 0.7 5.9 25.9 65.8 1.6 0.0 2.62 making cooperative ionic effects important for most concen- 3.8 1.3 14.1 35.0 47.3 2.2 0.0 2.35 trations but very dilute solutions. Despite the influence to the K+ 0.9 0.2 1.5 13.5 61.3 23.4 0.1 3.06 2+ HB network should be mainly ascribed to the specific Mg – KCl 0.9 0.5 4.0 27.3 57.6 10.5 0.0 2.74 water interaction, this confirms that the HB structure of the 1.9 0.5 4.2 26.0 60.7 8.5 0.1 2.73 first hydration shell is governed by the subtle interplay be- 3.9 2.0 11.9 33.3 47.0 5.5 0.2 2.43 tween the level of hydration of the ions, and the interactions Cs+ 0.9 0.0 0.6 10.4 53.3 35.0 0.6 3.24 between ions, especially those of opposite charge. In more CsCl 1.9 0.9 4.2 20.5 52.6 21.7 0.2 2.91 general terms, the cooperative effect of cations and anions in Mg2+ 0.9 0.5 12.2 53.7 33.6 0.0 0.5 2.20 solution reflect a balance between solute-solvent and solute- MgCl2 1.9 0.3 14.3 69.4 15.9 0.0 0.0 2.01 solute interactions since relatively minor changes to the chem- MgSO4 1.9 6.0 32.4 41.1 20.6 0.0 0.0 1.76 ical characteristics result in dramatic changes to the HB dis- Ca2+ 0.9 0.2 8.4 52.2 39.1 0.0 0.0 2.30 tribution. CaCl2 1.9 1.4 26.7 51.2 20.2 0.1 0.0 1.91 CaSO4 1.9 3.8 25.0 41.3 29.9 0.0 0.0 1.96 Water reorientation dynamics H2O – 0.0 0.3 4.6 19.8 70.7 4.6 3.75 The rotational dynamics of the water dipole, P1(t), was com- Cl– 0.9 0.0 0.5 5.5 25.4 65.8 2.8 3.61 puted from the first order Legendre polynomial time correlation function:68

Chowdhuri and Chandra showed that in the vicinity of ions A the diffusion coefficients are reduced and the orientational relaxation times are increased compared with pure water.70 We have therefore computed the reorientation dynamics of the water molecules that are in the first and second coordination shells of the metal ions, and that is in the bulk (beyond second coordination shells of all ions in solution). Fig. 8 compares the correlation profiles obtained from the analysis of the AIMD trajectories of the hydrated metal ions K+ and Mg2+ and –1 of 1.9 mol.kg aqueous KCl(aq) and MgCl2(aq). For hydrated K+, the reorientation dynamics of water dipoles in the hydration shells is similar to bulk behavior. The reorientation dynamics of water dipoles is faster in chloride-containing solutions compared to that observed for the hydrated single metal

ion: the P1(t) profiles of the water molecules in the first shell + B of K in KCl(aq) are drastically accelerated compared to the behavior around hydrated K+ (single ion, no counterions).

Conversely, the decay of the P1(t) profiles of the water molecules directly coordinated to Mg2+ are drastically slower than in the bulk, but the effect of solution composition (presence of other Mg2+ and Cl– in solution) is not significant. This can be explained by the much stronger ion-water interaction of 2+ + Mg compared to K . The correlation function P1(t) is, therefore, sensitive to solution speciation and provide insights into the combined effect of metal ions and Cl– ions on the water reorientation dynamics. Conclusions We have conducted molecular dynamics simulations of the alkaline earth metal ions Mg2+ and Ca2+, and of the alkali metal

ions Li+, Na+, K+ and Cs+ in pure water and aqueous solutions – 2– Figure 6. (A) Average number of hydrogen bonds (HBs) in the first containing Cl and SO4 , with salt concentrations ranging hydration shell of metal ions obtained from AIMD (PBE-D3) sim- from 0.9 to 3.8 mol.kg–1, to determine the effect of solution ulations of hydrated metal ions (single M, no counterions) and of aqueous electrolyte solutions (1.9 mol.kg–1). (B) Distribution of the composition on the structural and dynamic properties of meta number of molecules among the water subpopulations, obtained ion first solvation shell. In aqueous electrolyte solutions, the from classical MD simulations of MgCl2 solutions. – 2– presence of the Cl and SO4 counterions does not have a sig- In electrolyte solutions, the presence of solvated ions acceler- nificant effect on the ion-water radial distribution functions of + + 2+ 2+ ates the reorientation dynamics of water dipoles (faster P1(t) profiles of Li , Na , Mg and Ca . The presence of counter- decay) compared to pure liquid water. However, the P1(t) pro- ions in solution influences the size of the hydration shell not files of NaCl(aq) and KCl(aq) do not consistently decrease only because of the formation of contact ion pairs, which re- with the concentration as they are also influenced by the type duces the coordination sites available around the metal ion, of ion pairs present in solution. For NaCl(aq), the fastest reor- but also when cations and anions form solvent-shared ion ientation dynamics (fastest P1(t) decay) is observed for the 0.9 pairs. We found, for example, that in CaCl2(aq) and –1 + – mol.kg solution, which only contains free Na and Cl ions. CaSO4(aq), the chlorine and sulphate ions in the second coor- On the other hand, the 1.9 and 3.9 mol.kg–1 NaCl solutions, dination shell of Ca2+ stabilize the seven-coordinated 2+ 2+ which contains contact and solvent-shared pairs, have water Ca(H2O)7 complex over the six-coordinated Ca(H2O)6 spe- reorientation behavior like that of hydrated Na+ (Fig. 6). The cies. Calculation of the velocity autocorrelation function of correlation function P1(t) is, therefore, sensitive to solution the metal ions has been used to probe the strength of the local speciation and can provide insights into the combined effect ion-water interaction and the rigidity of the interatomic vi- of cations and anions on the water reorientation dynamics. bration.

(t)

1 lnP

Figure 8. Profiles of the correlation function P1(t) for the water molecules in the first and second shell of K+ and Mg2+ obtained from AIMD (PBE-D3) simulations of hydrated metal ions (single M, no counterions) and of aqueous electrolyte solutions (1.9 mol.kg–1).

ASSOCIATED CONTENT Details on simulated aqueous electrolyte solutions; analysis of ion pairing; dynamics of ionic hydration shell; velocity autocorrelation function of the metal ions; hydrogen bond statistics; protocol for the calculation of time correlation function. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author

* Email: [email protected] Figure 7. Profiles of the correlation function P1(t) for the water molecules obtained from AIMD (PBE-D3) simulations of hydrated Author Contributions metal ions (single M, no counterions) and of electrolyte solutions. The manuscript was written through contributions of all authors.

2+ All authors have given approval to the final version of the manu- We found a smoother decay of the VACF of Mg in script. MgCl2(aq), which is a clear indication of a looser inter-hexa- hedral vibration. Chlorine ions, located in the second coordi- REFERENCES 2+ 2+ nation shell of Mg weaken the Mg(H2O)6 water ‘cage’ of (1) Collins, K. D.; Washabaugh, M. W. The Hofmeister Effect and the Behaviour of Water at Interfaces. Q. Rev. Biophys. 1985, 18 the ion. This dynamic flexibility highlights the effect of coun- (4), 323–422. terions on the dynamics of H2O around ions. Analysis of the (2) Silvester, L. F.; Pitzer, K. S. Thermodynamics of Electrolytes. 8. hydrogen bond statistics in ionic solvation shell shows how High-Temperature Properties, Including Enthalpy and Heat Capacity, with Application to Sodium Chloride. J. Phys. Chem. the influence to the water network cannot only be ascribed to 1977, 81 (19), 1822–1828. 2+ the specific Mg –water interaction, but also to the subtle in- (3) Ruiz-Agudo, E.; Kowacz, M.; Putnis, C. V; Putnis, A. The Role terplay between the level of hydration of the ions, and the in- of Background Electrolytes on the Kinetics and Mechanism of Calcite Dissolution. Geochim. Cosmochim. Acta 2010, 74 (4), teractions between ions, especially those of opposite charge. 1256–1267. (4) Frank, H. S.; Wen, W. Y. Ion-Solvent Interaction. Structural ACKNOWLEDGEMENTS Aspects of Ion-Solvent Interaction in Aqueous Solutions: A Suggested Picture of Water Structure. Discuss. Faraday Soc. This project FUNMIN is funded through the ACT programme (Ac- 1957, 24, 133–140. celerating CCS Technologies, Horizon2020 Project No 294766). (5) Saha, D.; Mukherjee, A. Impact of Ions on Individual Water Financial contributions made from Department for Business, En- Entropy. J. Phys. Chem. B 2016, 120 (30), 7471–7479. ergy & Industrial Strategy (BEIS). We are grateful to the UK Ma- terials and Molecular Modelling Hub for computational resources, (6) Dang, L. X.; Schenter, G. K.; Glezakou, V.; Fulton, J. L. Molecular Simulation Analysis and X-Ray Absorption which is partially funded by EPSRC (EP/P020194/1). Via our Measurement of Ca2+, K+ and Cl- Ions in Solution. J. Phys. membership of the UK's HEC Materials Chemistry Consortium, Chem. B 2006, 110 (47), 23644–23654. which is funded by EPSRC (EP/L000202), this work used the (7) Koneshan, S.; Rasaiah, J. C.; Lynden-Bell, R. M.; Lee, S. H. ARCHER UK National Supercomputing Service Solvent Structure, Dynamics, and Ion Mobility in Aqueous (http://www.archer.ac.uk). This research utilized Queen Mary's Solutions at 25 °C. J. Phys. Chem. B 1998, 102 (98), 4193–4204. Apocrita HPC facility, supported by QMUL Research-IT. (8) Rode, B. M.; Schwenk, C. F.; Tongraar, A. Structure and http://doi.org/10.5281/zenodo.438045 11

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