Local Aqueous Solvation Structure Around Ca2+ During Ca2+middotmiddotmiddotClminus PairFormationMarcel D Baer and Christopher J Mundy

Physical Science Division Pacific Northwest National Laboratory Richland Washington 99354 United States

ABSTRACT The molecular details of single ion solvation around Ca2+ and ion-pairingof Ca2+middotmiddotmiddotClminus are investigated using ab initio molecular dynamics The use of empiricaldispersion corrections to the BLYP functional are investigated by comparison toexperimentally available extended X-ray absorption fine structure (EXAFS) measure-ments that probe the first solvation shell in great detail Besides finding differences inthe free-energy for both ion-pairing and the coordination number of ion solvationbetween the quantum and classical descriptions of interaction there were importantdifferences found between dispersion corrected and uncorrected density functionaltheory (DFT) Specifically we show significantly different free-energy landscapes forboth coordination number of Ca2+ and its ion-pairing with Clminus depending on the DFTsimulation protocol Our findings produce a self-consistent treatment of short-rangesolvent response to the ion and the intermediate to long-range collective response of the electrostatics of the ionminusion interactionto produce a detailed picture of ion-pairing that is consistent with experiment

INTRODUCTIONAlthough the importance of the free-energetics of solvation andion-pairing has been known for decades the unique molecularscale signatures that give rise to the measured free-energies ofsolvation and activity have yet to be established12 Moreoverour modern theoretical understanding of solvation comes fromtwo distinct points of view The continuum theory or Bornmodel in its simplest formulation is based in linear-responsetheory Nevertheless it is well-accepted that the subtlestructural nonlinearities and asymmetries in the solvationprocess are contained in the definition of the Born radiusAnother successful theory of solvation is the so-calledquasichemical theory (QCT)3minus6 QCT views partitioning thefree-energy of solvation as coming from two distinct lengthscales in a thermodynamic cycle the short-range where themolecular detail informs our understanding and the remaininglong-range (mean-field or linear response) that is determinedby long-range slowly varying dielectric fluctuation7 QCTdemonstrates that the details of the local hydration structureand its interaction with the solvent are decisive Thecomplexities involved in identifying those structures by usinginformation from ab initio simulations of aqueous solutionshave been examined recently8minus11 Nevertheless the subtlequestion of the relationship between the proper level ofmolecular interaction to determine both the correct populationof structures for isolated ions in the condensed phase and thecollective intermediate- to long-range response that isresponsible for ion-pairing is a subject of great interest12

Moreover it is only recently that the direct connectionbetween simulation and experiment regarding the precisemolecular structure of aqueous electrolytes has been made1314

To this end our focus is on the aqueous solvation structure ofCa2+ an ion that plays a significant role in disparate fieldsranging from biology to geology For the purposes presented

herein Ca2+ is chosen because of its stable oxidation stateunder aqueous conditions and the experimentally determinedproperty that it does not undergo ion-pairing with Clminus untilhigher concentrations15 Thus it is an excellent candidate totest the simulation protocol under nearly ideal solutionconditionsHerein we will investigate both the molecular details of

single ion solvation and ion-pairing of CaCl2 One of the mostremarkable findings will be regarding the flexible nature of thesolvation shell of Ca2+ defined as the populations ofcoordination numbers that are accessible within thermalfluctuations Earlier pioneering work by Ikeda et al addressedthe question of Ca2+ hydration using ab initio moleculardynamics simulations in conjunction with free-energy samplingof the coordination number16 The local solvation structure asmeasured by the radial pair distribution function has long beencontroversial as discussed in many experimental1517minus33 andtheoretical studies121633minus38 Although the local structurearound Ca2+ has been resolved using EXAFS in conjunctionwith ab initio molecular dynamics using density functionaltheory (DFT) as the description of molecular interactions33

there is still the need to be able to compare and contrast theflexibility of the solvation shell as defined previously asdetermined by using different simulation protocol Most abinitio studies discussing the details of the Ca2+ solvationstructure have been performed using standard generalizedgradient corrected (GGA) density functionals1634minus38 Anadditional study performed with a hybrid functional33 is in

Special Issue Bruce C Garrett Festschrift

Received September 30 2015Revised January 18 2016Published January 20 2016

Article

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good agreement with the GGA studies indicating that thestructure is not obviously affected by the description ofexchange The disparity in reported coordination numbers inthese earlier studies is likely a result of multiple minima in thecoordination number free-energy We will show below thattransitions between different coordination numbers can beconsidered rare events and therefore the starting structuresand the time-scale limitation of ab initio simulation could leadto differences between the DFT studiesNevertheless open questions remain regarding how the role

of the thermodynamic state point of water which is known tobe sensitive to DFT simulation protocol can affect the localsolvation structure around ions39 To date there has not been aDFT simulation performed at constant pressure to investigatethe influence on the solvation structure near ambient statepoints of dilute electrolytes Herein we use a robust approachby placing the ion of interest in the middle of a water slab in astandard liquidminusvapor interface geometry In previous studieswe have shown that this simulation protocol reasonablyreproduces the thermodynamic condition of mass density ofliquid water that is relevant for studies at near-ambientconditions Under bulk periodic boundary conditions for purewater in the presence of anions including waterrsquos self-ions theuse of an empirical dispersion correction introduced byGrimme40 is imperative and provides an excellent descriptionof the solvation of a variety of ions as compared to EXAFSexperiments1341minus44

An additional aspect of this study is to contrast thedifferences in the aqueous solvation structure and ion-pairingbetween different representations of molecular interaction Atthe level of single ion solvation it has been demonstrated thatthe solvent response to an ion using quantum-based potentialscan be significantly different than that obtained by classicalempirical potentials41minus4345 In fact a recent DFT study hasexamined the effects of simulation protocol on the aqueoussolvation structure of ions where significant differences inaqueous structure for Na+ and K+ were reported underconcentrated solution conditions46 Given the advances in theefficiency of DFT methods researchers are now computingpotentials of mean force (PMF) using non-Boltzmann methodsfor the ion-pairing process1347minus51

Understanding the relationship between the single ionsolvation and the ion-pairing process was clearly shown in arecent study where the free-energy of ion-pair formation Ca2+middotmiddotmiddotClminus is strongly correlated to the flexibility of the solvation shellaround the Ca2+47 The balance between ionminuswater and ion-pairing interactions for doubly charged cations has beenrecently revisited with classical empirical interaction potentialsto describe the fidelity of the aqueous structure of the firstsolvation shell as determined by EXAFS and to obtain themeasured ion-pair statistics determined by neutron scatter-ing155253 The research presented herein builds on theaforementioned empirical studies and provides a self-consistentpicture of how local solvation structure impacts solutionthermodynamics

DESCRIPTION OF METHODSHerein four different system sizes and compositions arestudied For all simulations the BornminusOppenheimer ab initiomolecular dynamics simulations within the NVT (T = 300 K)ensemble using periodic boundary conditions are performedwithin the CP2K simulation suite (httpwwwcp2korg) Abinitio calculations were performed with the QuickStep module

using density functional theory (DFT) as the theory for theelectronic structure54 We followed a similar protocol as in ref50 using a double-ζ basis set that has been optimized for thecondensed phase55 in conjunction with GTH pseudopoten-tials56 and a 400 Ry cutoff for the auxiliary plane wave basis ANoseminusHoover thermostat was attached to every degree offreedom to ensure equilibration57 The Becke exchange58 andcorrelation due to Lee Yang and Parr (LYP)59 is utilized inaddition to the dispersion correction (D2) put forth byGrimme40 with a 40 Aring cutoffThe first system is composed of a single Ca2+ solvated by 64

water molecules in a periodic cubic box of length 1256 Aring(water density of 097 gcm3) The second simulation is a largersystem containing one Ca2+ ion and 96 water molecules in aperiodic cubic box of length 143 Aring (water density of 098 gcm3) The third system closely follows the approach of hardsphere solvation in water45 where we choose to model thesystems with two buffering liquidminusvapor interfaces containing338 water molecules and one Ca2+ that is counterbalanced withtwo OHminus anions that are initially placed near the twoindependent surfaces Cell dimensions for the slab system are20 times 20 times 50 Aring3 and periodic images were screened by using atwo-dimensional wavelet Poisson solver60 During the simu-lation no ion-pair formation is observedThe fourth system was constructed to compute the free-

energy of ion-pairing between Ca2+ and Clminus under bulkperiodic boundary conditions using umbrella sampling Thissystem contains a single Ca2+ and Clminus and 110 water moleculesin a 15198 times 15198 times 15198 Aring3 supercell yielding a systemdensity of 099 gcm3 Umbrella sampling windows for theCa2+middotmiddotmiddotClminus distance ranging from 24 to 56 Aring were equallyspaced by 02 Aring employing harmonic umbrella potentials of thefrom V(r) = k(r0 minus r)2 with a force constant k of 956 kcalmolminus1 Aringminus2 To ensure sufficient sampling in the barrier regionfor the Ca2+ additional windows with stiffer force constantswere added ranging from 32 to 45 Aring equally spaced 01 Aringapart with a force constant of 3346 kcal molminus1 Aringminus2 In eachumbrella window a trajectory of at least 50 ps was collectedafter 5 ps of equilibration The weighted histogram analysismethod (WHAM) was employed to extract a free-energyprofile from these histograms61 We also compared our resultsof ion-pairing and ion solvation to two recent classical empiricalinteraction potentials a polarizable model52 and a charge scaledmodel53 The potential of mean force for Ca2+middotmiddotmiddotClminus bindingand the free-energy in coordination space around a single Ca2+

are calculated using the same system sizes and force constantsas discussed for the BLYP-D simulations outlined above Allclassical simulations are performed using CP2K suite(httpwwwcp2korg)The coordination number (n) is computed using the same

functional form as that in a previous study16

sum=minus

minusn

1 ( )

1 ( )i

Nrr

p

rr

q

i

i

O0

0 (1)

Here p and q are integers usually p = 16 and q = 32 ri is thedistance between the Ca2+ and oxygen i and r0 = 30 Aring Thefree-energy is computed using the umbrella sampling techniqueSampling windows for n ranged from 49 to 81 and wereequally spaced by 01 Aring apart employing harmonic umbrellapotentials of the from V(r) = k(r0 minus r)2 with a force constant kof 956 kcal molminus1 In each umbrella window a trajectory of atleast 50 ps was collected after 5 ps of equilibration The

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weighted histogram analysis method (WHAM) was employedto extract a free-energy profile from these histograms61

EXAFS spectra are calculated using the MD-EXAFSapproach where spectra are calculated from randomly sampledstructures along the trajectory and averaged62 To ensure thatthe subset converges to the ensemble spectra we compare theradial distribution function to the full ensemble average Thecalculations are done using the FEFF9 code63 with the samesettings as in ref 33

RESULTS AND DISCUSSIONWe start with discussing the local solvation structure around asingle Ca2+ solvated with 64 water molecules at a fixed density(water density of 095 gcm3) using DFT with the BLYPfunctional both with and without an empirical dispersioncorrection As pointed out above all DFT simulations for Ca2+

to date except for one have used standard generalized gradientcorrected functionals without an empirical dispersion correc-tion Figure 1 shows the pair distribution function (PDF) of

water oxygen atoms around the Ca2+ ion in conjunction with itsrunning coordination number The solvation structure obtainedin this study using BLYP corresponds well with structures fromother published ab initio data for single ion and CaCl2simulations using a similar box size and simulation protocolresulting in a coordination number of 61634363847 When thedispersion correction is added the so-called BLYP-D protocolthe Ca2+ ion becomes seven-fold coordinated in excellentagreement with recent EXAFS experiments that estimate acoordination number of 6733 We make an ansatz that for asystem with a single divalent cation the dispersion correctionwill be largely manifest in the important waterminuswaterinteractions This is further corroborated by studies that haveshown that the density of water at 300 K shows a significantdifference between BLYP and BLYP-D simulations It is nowaccepted that uncorrected BLYP predicts a much less denseliquid phase of water (asymp085 gcm3) than BLYP-D that isconsistent with the experimental density at 300 K446465 Theextent to which empirical dispersion corrections to DFT yield

consistently better results for ion solvation is still a matter forfuture research6667

To investigate the density effect on the coordination numberof Ca2+ we use the slab configuration that has proven to be agood proxy to the NpT ensemble446568 in conjunction withBLYP-D that is known to give the correct water density in thecenter of the slab (see Description of Methods section fordetails) The resulting PDF from a 20 ps simulation is shown inFigure 1 The salient point is that the coordination number isseven for the Ca2+ under the approximate NpT conditionsafforded by the slab geometry and is almost identical to theresults from the fixed density periodic simulation The onlynoticeable difference occurs at the onset of the second solvationshellWe further analyze the simulations by directly comparing

them to the EXAFS measurements using all three differentprotocols as is shown in Figure 2aminusc The BLYP-D simulationperformed at a water density of 095 gcm365 at 300 Kreproduces the experiment and the DFT simulations usinghybrid functionals with dispersion very well33 It can clearly beseen in Figure 2b that the experiment can distinguish betweensix- and seven-fold coordination around Ca2+ It is alsointeresting to note that the average Ca2+minusoxygen distance asmeasured by EXAFS is well-reproduced by all simulationsAs was shown for the uncorrected BLYP functional in an

earlier study16 the solvated Ca2+ has multiple coordinationnumbers that are accessible within a few kBT with six being themost probable state This finding is reconfirmed hereinalthough there are no transitions observed into the neighboringcoordinating states for a free unrestrained run On the otherhand the BLYP-D simulation only explores the seven-foldcoordinated state To understand these differences it isinstructive to compute the underlying free-energy in coordina-tion space using the umbrella sampling approach To this endsimilar to a recent study using classical empirical potentials38

we directly compare the 64 water molecule system for BLYPand BLYP-D and an additional larger BLYP-D system with 96water molecules all under bulk periodic boundary conditions toexplore the effect of system size on the free-energy landscapeFigure 3a depicts the free-energy of the Ca2+ oxygencoordination number (n) in aqueous solution as described bythe aforementioned three different simulation protocols TheBLYP results correspond well with the work of Ikeda et al16

with Ca2+ in a six-fold coordinated state and a barrier to theseven-fold state of roughly 3 kcalmol that is roughly 1 kcalmol less stable The eight- and five-fold coordinated statesreside much higher in free-energy differences of 5 and 8 kcalmol respectively The results of the BLYP-D simulations withdifferent supercell size are the same within the error bars of ourcalculations Specifically BLYP-D predicts the most stablecoordination state for Ca2+ to be seven The six-foldcoordinated state is destabilized by about 1 kcalmol andseparated with a 3 kcalmol barrier independent of the size ofthe supercell Not surprisingly the largest differences betweenall of the simulations presented are in the regions of highercoordination number The eight-fold state is 2 kcalmol morestable with the BLYP-D protocol Increasing the system sizefrom 64 to 96 water molecules has a small but statisticallydiscernible effect in reducing the barrier from 4 to 3 kcalmolAs a self-consistent check we estimated the free-energy incoordination space from an unrestrained simulation in the slabgeometry using BLYP-D The free-energy surface computed byinverting the population P(n) to obtain a free-energy defined

Figure 1 Calciumminusoxygen pair distribution function () g(r) andrunning coordination number (---) n(r) computed with BLYP andBLYP-D under periodic bulk solvation (single Ca2+ in 64 watermolecules at density 097 gcm3) shown in red and black respectivelycompared with the slab geometry in green computed with BLYP-D

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by W(n) = minuskBTln(P(n)) where kB is Boltzmannrsquos constantand at a temperature T = 300 K is shown in Figure 3a Theresult is nearly identical with the larger BLYP-D system size of96 waters Moreover a dependence on the underlying free-energy in coordination space on the system size is observed forhigher coordination numbers The good overall agreementbetween the larger BLYP-D and slab simulation namely asingle Ca2+ solvated by 96 and 338 water moleculesrespectively suggests that the finite size effects are largely

absent for the 96 water BLYP-D simulation under bulk periodicboundary conditionsInstead of only focusing on the free-energy it is also

instructive to compare the resulting population P(n) computedat 300 K as shown in Figure 3b As foreshadowed in the free-energy the populations for BLYP and BLYP-D are reversedFor the BLYP simulation at equilibrium a significant majorityof 75 of the Ca2+ ions would be solvated by six watermolecules and about 25 by seven water moleculesCoordination numbers of Ca2+ that are higher than sevenand lower than five do not show any significant population inany of the simulations Both BLYP-D simulations are inagreement with 75 of the Ca2+ in a seven-fold coordinatedstate and 25 being six-fold coordinated These computedpopulations lead to average coordination numbers of 63 and67 for BLYP and BLYP-D respectivelyThus far we have established the role of both the simulation

protocol and the necessity for a high-quality interactionpotential to describe the local solvation structure around

Figure 2 Comparison of the experimental Ca K-edge XAFS spectra(blue ---)1533 with the simulated spectra using the MD-EXAFSapproach (a) Experiment in blue BLYP (black) BLYP-D (red) andBLYP-D (both single Ca2+ in 64 water molecules at a density 097 gcm3) and in the slab configuration (green) The corresponding Fouriertransform (radial structure factor) yielding (b) the real |χ(r)| and (c)its imaginary part Im|χ(r)|

Figure 3 (a) Free-energy of the Ca2+ oxygen coordination number (n)in aqueous solution obtained from umbrella sampling for BLYP (red)BLYP-D (black) for the small system containing 64 water moleculesand BLYP-D (blue) for a system with 96 water molecules Orangecircles indicate the free-energy W(n) = minuskBT ln P(n) with P(n)estimated from the slab simulation where kB is Boltzmannrsquos constantand at a temperature T = 300 K (b) Normalized probabilitydistribution P(n) (solid curves) and the integral of P(n) (dashedcurves)

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Ca2+ We continue by pursuing and understanding the subtlebalance between the aforementioned short-range solventresponse to the ion and the collective intermediate to long-range electrostatics needed to describe the ion-pairing ofCaCl2

12 The free-energy of CaCl+ ion-pair formation was oneof the first published using DFT simulations in conjunctionwith the uncorrected BLYP functional47 This study suggestedthat the resulting free-energy is highly dependent on thecoordination number that is found around the Ca2+ As shownabove our present results show significant differences for thefree-energy in coordination space for the isolated Ca2+

depending on the use of dispersion corrected and uncorrectedBLYP We extend our studies beyond the single Ca2+ andcompute the potential of mean force (PMF) of ion-pairing forCaCl+ along the Ca2+minusClminus radial distance The supercell sizefor the ion-pairing calculation requires almost doubling thenumber of water molecules from 64 to 110 as compared to theearlier study47 Figure 4 depicts the PMF of CaCl+ ion-pairing

process The uncorrected BLYP exhibits a solvent separatedion-pair (SSIP) that is about 2 kcalmol more stable than thecontact ion-pair (CIP) and separated by a 6 kcalmol barriergoing from SSIP to CIP The addition of the dispersioncorrection (BLYP-D) reduces the stability of the CIP by 15kcalmol relative to the SSIP but more noticeably the barrierfor ion-pair formation is reduced to 3 kcalmol Our resultssuggest that the differences in simulation protocol have only aminor effect on the relative stability between the CIP and theSSIP but the change in barrier height between the two states isdramatic and will have consequences for the kinetics of ion-pairformation69

Experimentally no long-lived ion-pairing is seen for CaCl+

for concentrations as high as 6 M but clear signatures of theformation of stable SSIPs are detected15 Similarly both thechlorine K-edge and calcium K-edge EXAFS spectra show nosign of ion-pairing15 On the basis of the PMF for BLYP-Dshown in Figure 4 the formation of the CIP should be verylow likely below the detection limit of the EXAFS experimentAs a self-consistent test of our simulation protocol weinvestigate the difference in the EXAFS signatures of bothCa2+ and Clminus in both the CIP and SSIP states and compare it tothe EXAFS spectra generated from the BLYP-D calculations ofthe isolated ions in water Our findings depicted in Figure 5abare in excellent agreement with the EXAFS data Both the Ca2+

and Clminus in the SSIP behave as isolated ions However for Ca2+the CIP configuration there are clear deviations from the

isolated spectra for k gt 6 The same trend is observed for theClminus For the case of Clminus the CIP displays much largerdeviations from the isolated solvated ion This suggests that theSSIP regardless of whether it is probed through the Ca2+ andClminus K-edge is not distinguishable from the simulations of theisolated ion Therefore our results suggest that the CaCl+

system is best described as either a CIP (or bound) or isolated(not associated) ionsFinally we compare the free-energy in coordination space

and the PMF of ion-pairing between the BLYP-D case that isthe best representation to the experimental EXAFS and twoclassical empirical interaction potentials that have recentlyweighed in on the ion-pairing of CaCl+5253 Both classicalrepresentations of interaction are improvements on older forcefields where it was found that the ionminusion Lennard-Jones wasreparameterized in the case of Dang and co-workers (Dangmodel) and the charges of the ions were rescaled in line withthe electronic continuum correction (ECC model) alsoLennard-Jones values were reparameterized (ECCR model)as discussed in detail by Kohagen and co-workers53 It shouldbe noted that a recent study has also pursued the consistency ofdescribing the short-range structure and its relationship to thelong-range collective behavior of CaCl2 and MgCl2 solutions

12

Through a more complex empirical model in conjunction witha physically motived charge partitioning scheme this study alsoreports good agreement of the local structure and long-rangecollective response as determined by osmotic pressure Herewe build on these concepts and examine the ion-pairing PMFfor CaCl+ using the original and modified Dang model and

Figure 4 Comparison of Ca2+ and Clminus ion-pairing free-energy usingumbrella sampling for BLYP-D (black) and BLYP (red)

Figure 5 Comparison of the simulated Ca (a) and Cl (b) K-edgeXAFS spectra For Ca the isolated ion BLYP-D (black) ensembles ofconfigurations from the CIP (red) and SSIP (green) are shown TheCl experimental reference is taken from 25 M NaCl (black) from ref13 and compared to ensembles of configurations from the CIP (red)and SSIP (green)

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BLYP-D compared in Figure 6a The improved parametrizationaffects the PMF only for distances less than 35 Aring The effect of

changing the ionminusion Lennard-Jones parameters in themodified Dang model leads to a 10 kcalmol destabilizationof the CIP to a local minimum that is 5 kcalmol less stablethan the SSIP Moreover the position of the CIP for themodified Dang model shifts by about 02 Aring from 26 to 28 veryclose to the 27 seen for the BLYP-DWe can also test the agreement between the ECCR model

that was shown to better reproduce the long-range structure asmeasured by neutron diffraction and improved mobility ratesover the original OPLS force field53 In Figure 6b three differentmodels are compared to the BLYP-D for the PMF of CaCl+

ion-pairing the original OPLS model the ECC (charges ofCa2+ and Clminus are scaled by 075) and the ECCR which hasadditional reparametrized Lennard-Jones values for both ions53

All three PMFs are very similar to the BLYP-D as shown inFigure 6b The OPLS model estimates the CIP to be about 1kcalmol less stable than the BLYP-D prediction andoverestimates the barrier by a factor of 2 from the SSIP toCIP A straightforward scaling of the charges (ECC model)yields results that are in good agreement with the BLYP-Dnamely an identical barrier from the SSIP to the CIP and only05 kcalmol in the stability of the CIP Only the ionminusiondistance for the ECC model in the CIP is shifted by 03 Aring tolarger values than that of the BLYP-D Although additionalchanges of the Lennard-Jones values (ECCR) give animprovement for the long-range structure for the ion-pair53

there is a noticeable change for the PMF of ion-pairing TheECCR produces a barrier from SSIP to CIP that is similar tothe original OPLS model Moreover ECCR overestimates the

stability for the CIP by 05 kcalmol over the BLYP-D andproduces a shift of the CaminusCl distance to 25 AringThe underlying assumption in the modification of the

classical empirical models is that it is the ion-pair interactionthat is solely responsible for an accurate representation of thePMF of ion-pairing We can test this hypothesis by examiningthe Ca2+minusoxygen pair distribution functions depicted in Figure7a Significant differences between all models are seen in the

distribution (number and distances) of the first solvation shellwater molecules The position of the first maximum is well-reproduced by both the OPLS and Dang model (the modifedDang model and the original Dang model are the same for thisinteraction) but produce differing coordination number six forthe Dang model and seven to eight for OPLS Again the bestagreement with BLYP-D is seen for the ECC model where theECCR model is shifted almost 02 Aring to smaller distancesAdditionally in Figure 7b the free-energy in coordinationnumber space for the single solvated Ca2+ is compared The

Figure 6 Comparison of Ca2+ and Clminus ion-pairing free-energyobtained with umbrella sampling (a) BLYP-D (black) the originalDang model (red) and the modified Dang model (green) (b) BLYP-D (black) and OPLS (red) ECC model (green) and ECCR model(blue)

Figure 7 (a) Pair distribution function g(r) of oxygens aroundcalcium for BLYP-D under bulk solvation (gray shaded area) theDang model (black) OPLS (red) ECC model (green) and ECCRmodel (blue) Inset highlights the region of the first maximum (b)Free-energy in coordination number space W(n) BLYP-D is depictedas a gray shaded area the Dang model (black) OPLS (red) ECCmodel (green) and ECCR model (blue)

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Dang model overall is very close to the uncorrected BLYP inboth the free-energy in coordination number space (see Figure3a) and the pair distribution function (see Figure 1) What isclear from our study is the difficulty of getting both the correctlocal solvent response and the intermediate- to long-rangecollective response encoded in a single parametrization of anempirical model in order to be quantitative about themechanisms of ion-pairing

CONCLUSION AND OUTLOOKIn summary we have shown that the local structure aroundCa2+ is well-described using the BLYP-D functional ascompared to EXAFS experiments The empirical dispersioncorrection to DFT is needed to be able to properly describe theshort-range structure around this particular set of ions namelyCa2+ and Clminus Discrepancies in the reported number of watermolecules in the first solvation shell from different DFT studiesusing the same functional can be reconciled by consideringmultiple accessible minima in the free-energy landscape for thecoordination number around Ca2+ We find significant changesdue to dispersion correction that produces a change inpreferred coordination from six- to seven-fold in agreementwith EXAFS Our studies on finite size effects suggest that thepopulation of larger coordination states will be affected likelyleading to higher coordinated states for bigger systems Theslab geometry was tested as a good proxy to the NpT ensembleand produced results consistent with bulk periodic boundarycondition simulations Not surprisingly the effect of dispersioncorrected functionals also produces a PMF of ion-pairingbetween Ca2+ and Clminus that is distinct from uncorrectedfunctionals and leads to a large reduction in the barrier fromSSIP to the CIP of CaCl+ We have demonstrated in this workthat the intrinsic solvation properties validated by EXAFS areencoded in the PMF for ion-pairing of CaCl2 The resultingPMF in the dilute limit suggests a picture consistent withreparameterized classical point charge models fit to reproduceconcentration dependent collective properties of CaCl2 asdetermined by neutron diffraction53 Future studies will befocused on further validation of the accuracy of the BLYP-DPMF for ion-pairing in the dilute limit by using this importantshort-range molecular information to compute collectiveproperties of CaCl2 solutions using methods outlined innumerous studies70minus73 Although we cannot directly speculatethat there is a connection between the BLYP-D obtained PMFand the observed concentration dependence of ion-pairing it isinteresting to note that the relative populations of the SSIP tothe CIP computed using Figure 4 are in near quantitativeagreement to the experimental values obtained at higherconcentrations15 Future investigations will be focused on usingrigorous definitions of ion-paring in conjunction with the PMFas have recently been reviewed in ref 73 Moreover oursimulated EXAFS K-edge spectra for ensembles of structures ofCa2+ and Clminus in the SSIP state predict a solvation structureindistinguishable from the computed spectra from simulationsof the isolated ionsWe also tested our understanding of our results generated

with DFT by comparison to several modified classical empiricalmodels of the solvation and ion-paring of CaCl2 Overall thebest agreement between BLYP-D and classical models wasfound to be the ECC model The ECC charge scaling approachshows better agreement with the BLYP-D over the modifiedDang model Although the reparametrizing of the ionminusioninteraction is certain to influence the computed PMF this

assumes that the short-range local solvent response to the bareion can be viewed in more simplistic terms analogous todielectric continuum theory The research presented herein isconsistent with other theoretical findings for monovalent ions7

and has shown that indeed the local solvent response is adifficult and important quantity to ascertain Moreover we haveproduced a self-consistent picture suggesting that DFTprovides both the accurate solvent response to an isolatedion and the important intermediate- to long-range ionminusioninteraction that is needed to explain the experimental data ofCaCl2 ion-pairing

15

AUTHOR INFORMATIONCorresponding AuthorsE-mail marcelbaerpnnlgovE-mail chrismundypnnlgov Phone (509) 375-2404

NotesThe authors declare no competing financial interest

ACKNOWLEDGMENTSMDB is supported by MS3 (Materials Synthesis andSimulation Across Scales) Initiative at Pacific NorthwestNational Laboratory It was conducted under the LaboratoryDirected Research and Development Program at PNNL amultiprogram national laboratory operated by Battelle for theUS Department of Energy CJM acknowledges support fromUS Department of Energy Office of Science Office of BasicEnergy Sciences Division of Chemical Sciences Geosciences ampBiosciences This research used resources of the NationalEnergy Research Scientific Computing Center a DOE Office ofScience User Facility supported by the Office of Science of theUS Department of Energy under Contract No DE-AC02-05CH11231 Additional computing resources were generouslyallocated by PNNLrsquos Institutional Computing program Theauthors thank Tom Beck for discussions regarding QCT andJohn Fulton Tim Duignan Greg Schenter and ShawnKathmann for insightful comments

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