Journal of Molecular Liquids 153 (2010) 95–100

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Journal of Molecular Liquids

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Classical and QM/MM MD simulations of sodium(I) and potassium(I) ionsin aqueous solution

S. Sikander Azam a, Zaheer-ul-Haq b, M. Qaiser Fatmi c,⁎a National Center for Proteomics, University of Karachi, Karachi 75270, Pakistanb Dr. Panjwani Center for Molecular Medicine & Drug Research, International Center for Chemical & Biological Sciences, University of Karachi, Karachi 75270, Pakistanc 420 Chemical Sciences Buildings, University of California, Riverside, Riverside, CA-92507, USA

⁎ Corresponding author. Tel.: +1 951 827 7263; fax:E-mail addresses: Muhammad@ucr.edu, qaiser_fatm

0167-7322/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.molliq.2010.01.005

a b s t r a c t

a r t i c l e i n f o

Article history:Received 5 May 2009Received in revised form 28 December 2009Accepted 11 January 2010Available online 18 January 2010

Keywords:QM/MMMD simulationNa+

K+

Structure and dynamicsHF

The optimized energy and geometry for Na+– and K+–water complexes in gaseous phase have been studiedusing different methods such as HF, MP2, B3LYP, and CCSD. Classical and quantum mechanical/molecularmechanical (QM/MM) molecular dynamics (MD) simulations have been performed to describe structuraland dynamical properties of Na+ and K+ in water and to compare the two approaches. The first hydrationshell was treated by ab initio quantum mechanics at restricted Hartree–Fock (RHF) level using the LosAlamos LANL2DZ ECP basis set for the cations Na+ and K+ and Dunning double-ζ plus polarisation basis setfor O and H. The results obtained are in good agreement with previously published experimental andtheoretical results. In the QM/MM method, the radial distribution function (RDF) showed the maximumprobability of the Na–O and K–O bond lengths at 2.39 Å and 2.85 Å, respectively. A considerable number ofwater exchange reactions were observed within the first shell during the simulation time of 16 and 12 ps ofNa+ and K+ ions in aqueous solution, respectively. The number of exchange events in both first and secondshells is higher in the case of K+ than Na+ indicating the weaker ion-ligand strength of K+.

+1 951 827 4713.i@yahoo.com (M.Q. Fatmi).

l rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

The importance of metal ions and their numerous applications inthe field of chemistry is undeniable, and their central role in vitalprocesses of life is also widely known. Detailed information ofbehavior of alkali ions is required to understand their crucial role insolution chemistry, biochemistry and pharmacology [1,2] rangingfrom the diverse cellular regulations through enzymes to thecontrasting behavior of Na+ and K+ in aqueous solution related toionic pumps across the cell membrane [3–5]. They are the essentialelements for the existence of all known life. Recent finding shows therole of (Na+K)-ATPase activity in the pathophysiology of essentialhypertension [6]. Imbalance of these ions in the body has always beenthe cause of various disorders such as deafness, chemical imbalance[7], cardiac arrhythmia, bone disorders and other ion channel diseases[8]. The role of sodium in thyroid hormone uptake was suggested inhepatocytes and erythrocytes by Krenning et al. [9] and Holm et al.[10], respectively. In the light of all facts, the importance of these ionsis unambiguous and thus the main goal of this work is to obtaindetailed insight into the structure and dynamics in aqueous solution.Both theoretical and experimental procedures have been successfully

employed in this context [11–15]. The structural and dynamicalinformation about hydrated alkali ions have been obtained from bothcomputer simulations and experiments [13,16–29]. Unlike certainexperimental approaches, which have some technical limitations[27,28], results obtained from computer simulation yield more insightinto the structure with detailed interpretation and prediction ofexperimental observations at the molecular level especially whendynamics are extremely fast. The comparison of hydration parametersobtained from different methods can be seen in Table 1. Classicalmolecular dynamics simulation methods have been widely used, interalia to analyze solutions of alkali metal ions in water or ammonia.These classical mechanical approaches can deal with large systemsbut due to the neglect of electronic effects the accuracy of the results islimited.

Ongoing developments in computer speed and capacity open upthe way to utilize more sophisticated simulation techniques usingcombined quantummechanical and molecular mechanical (QM/MM)approach which is found to be suitable in accurate description ofhydrated systems. In this hybrid method a part of the molecularpotential which is chemically most relevant region is determined by aquantum mechanical calculation while the remainder of the molec-ular potential is determined using a much faster molecular mechanicsforce field calculation. A systematic comparison has been performedto judge the suitability of force fields for the application atphysiological salt concentrations in microscopic simulation of thesehydrated ions [15].

Table 1Comparison of hydration parameters for Na+ and K+ distances in Å. rmax and rmin

represent the maximum and minimum distances between ion–O and n indicates thecoordination number distribution for the first hydration shell.

Comparison of hydration parameters for Na+ and K+

Ion Method rmax rmin n Ref

Na+ CF2-Water MD 2.36 3.04 6.5±0.2 [30]QM/MM MD 2.33 2.94 5.6±0.3 [30]MD(QM) 2.49 3.20 5.2 [48]FPMD 2.40 3.1±0.2 5.2±0.1 [52]CPMD 2.50 3.10 5.31 [49]XD 2.44 – 6 [24]XD 2.40 – 4.9±0.1 [26]XD 2.42 – 4.7 [23]QM/MM MD 2.39 3.10 6.0 This workClassical MD 2.37 2.99 6.19 This work

K+ CF2-Water MD 2.78 3.40 7.8±0.2 [30]QM/MM MD 2.81 3.72 8.3±0.3 [30]FPMD 2.85 3.6±0.2 7.2±0.4 [52]XD 2.8 – 6 [23]ND 3.1 – – [25]QM/MM MD 2.85 3.83 8.8 This workClassical MD 2.80 3.65 7.9 This work

Table 3Average Na+–O and K+–O binding energy in kcal/mol for Na+–H2O and K+–H2Oclusters of different size obtained from HF, CCSD, MP2 and B3LYP calculations.

Ion–O binding energy in kcal/mol

Cluster n HF CCSD MP2 B3LYP

[Na(H2O)n]+ 1 −26.20 −26.32 −26.67 −26.792 −25.17 −25.39 −25.73 −25.263 −23.44 −23.86 −24.16 −24.144 −21.62 −22.13 −22.40 −22.296 −17.17 −18.11 −18.32 −17.918 −12.71 −14.07 −14.31 −13.73

[K(H2O)n]+ 1 −18.35 −18.56 −18.97 −19.382 −17.71 −17.99 −18.39 −18.763 −16.81 −17.16 −17.55 −17.864 −15.78 −16.22 −16.59 −16.846 −13.34 −14.01 −14.36 −14.368 −10.78 −11.74 −12.10 −11.77

96 S.S. Azam et al. / Journal of Molecular Liquids 153 (2010) 95–100

The target of this work is to perform the QM/MM MD simulationsby using the equilibration through classical methods. Additionally,the geometry optimization and binding energy calculations of clusters[Na(H2O)n]+ and [K(H2O)n]+ (where n=1–8) using different QMmethods were performed (Tables 2 and 3). These simulations wereanalyzed with respect to the structural parameters such as radialdistribution functions and coordination number distributions andwith respect to the dynamical parameters, for instance, the ligandexchange events in the first and the second solvation shells.

2. Methodology

One critical step of a QM/MM simulation is the choice of a properbasis set, as it will be a compromise between computational effort andaccuracy of the results. The LANL2DZ basis sets were selectedaccording to previous investigations and test calculations performedby Tongraar et al. [30]. For O and HDunning double-ζ plus polarisationbasis sets were employed [30]. Previous simulations of ionic soluteshave yielded data in good agreement with experimental measure-ments if the ab initio Hartree–Fock (HF) method utilizing the doublezeta plus polarisation basis set was employed [31–34]. Despite theircommon popularity Density Functional Methods (DFT) yielded resultssignificantly different from experimental data as well as from theresults of simulations at HF level. For the estimation of reliabilityof our method of choice, geometry optimizations of the Na+ and K+

plus 1–8 water molecules were performed by different theoretical

Table 2Average Na+–O and K+–O distances in Å for Na+–H2O and K+–H2O clusters of differentsize obtained from HF, CCSD, MP2 and B3LYP calculations.

rion–O in Å

Cluster n HF CCSD MP2 B3LYP

[Na(H2O)n]+ 1 2.28 2.29 2.29 2.272 2.29 2.30 2.30 2.823 2.32 2.32 2.32 2.304 2.35 2.35 2.35 2.356 2.46 2.45 2.45 2.448 2.66 2.61 2.61 2.61

[K(H2O)n]+ 1 2.69 2.69 2.69 2.652 2.71 2.72 2.71 2.673 2.73 2.73 2.73 2.694 2.76 2.76 2.76 2.716 2.85 2.84 2.84 2.808 2.97 2.93 2.93 2.90

methods to determine the level needed to properly describe the ion–water interaction. The corresponding ion–oxygen distances for eachof the methods HF, MP2, B3LYP and CCSD are presented in Table 2 andthe relative ion–oxygen binding energies are listed in 3, respectively.For Na+, the Na–H2O distances are found to be quite insensitive to themethod applied, although B3LYP gives a slightly shorter bonds thanthe HF and the other correlated methods. In case of K+ the valuesindicated in the table signify that there are almost identical K–H2Odistances when applying HF, CCSD and MP2 to various hydratedclusters containing water molecules from 2 to 6, however, B3LYPagain shows the shortest distances thus making this method lessfavorable in these cases. A similar trend has also been observed in thecase of Li+–H2O [35,36], Rb+–H2O [37] and Cs+–H2O [38] clusters,where B3LYP yields shorter bond distances as compared to the HF andthe other correlated methods.

The molecular dynamics simulation protocol employed for Na+–and K+–water complexes was similar to that of the conventionalQM/MMMD simulations [39]. The methods used in this study includesthe optimization of Na+– and K+–water clusters, followed by thecomputation of their interaction energies as a function of the ion–waterdistance. The hybrid QM/MM MD method combines the accuracy ofquantum mechanics with the affordability of molecular mechanics,provided that a suitable coupling scheme between both subsystems isapplied.

The total force on a particle is calculated according to the followingexpression

Ftot = FMMsys + FQMQM−FMM

QM

� �⋅S rð Þ ð1Þ

where Ftot is the total force acting on a particle, FsysMM force of the wholesystem and FQM

QM and FQMMM are QM and MM forces in the QM region. A

smoothing function S(r) is applied in a region of 0.2 Å to ensure asmooth transition of particles between QM and MM region.

S rð Þ =

1 for r≤r1

r20−r2� �2

r20 + 2r2−3r21� �

r20−r21� �3 for r1br≤r0

0 for r N r0

8>>>>><>>>>>:

ð2Þ

The feasibility of ab initio QM/MM simulations is determined bythe size of QM region, level of theory and the choice of the basis setsemployed [40].

Radial and coordination number distribution functions wereemployed to characterise the structural properties of the complexesin aqueous solution. Mean ligand residence times (MRT, τ) for thefirst/second hydration shell were calculated using the direct method[41]. The parameter t*, determining the minimum time span to

97S.S. Azam et al. / Journal of Molecular Liquids 153 (2010) 95–100

account to a ligand displacement from its original coordination shell,was set to 0.5 ps, which corresponds the life time of H-bond in thesolute [42].

3. Simulation protocol

The simulations of this work were performed for one Na+ or K+

and 499 water molecules each in a pre-equilibrated elementary cubicbox of 24.6 Å side length. The density of the system corresponds to thepure solvent at 298 K (0.997 g/cm3). Periodic boundary condition wasemployed to the simulation box with a canonical ensemble and thetemperature was kept constant by the Berendsen algorithm [43,44].The flexible BJH-CF2 water model which includes an intramoleculartermwas used. The term ensures the full flexibility of water moleculesnecessary for a suitable transition from the QM into the MM regionand vice versa [45,46]. A second order predictor–corrector algorithmof the Adams–Bashforth family [47] was used to integrate theNewtonian equation of motion. Accordingly, the length of a timestep of the simulation was set to 0.2 fs, which allows for explicitmovement of hydrogens. The cutoff distances for non-Coulombicinteractions were set to 5 Å and 3 Å, respectively, for O–H and H–Hinteractions. For the Coulombic interactions a cutoff of 12.0 Å has beenset. The reaction field method was used to correct the errorsassociated to this cutoff. The smoothing function was applied to theregion of 0.2 Å from 3.1 to 3.3 for Na+ and from 3.6 to 3.8 Å for K+,respectively. Na–H2O and K–H2 Opotentials were taken from theprevious simulation carried out by Tongraar et al. [30].

A classical molecular dynamics simulation was carried out for Na+

(60 ps after 30 ps of equilibration) and for K+ (90 ps after 20 ps ofequilibration). Subsequently, the QM/MM MD simulations wereperformed for Na+ and K+ for a period of 16 and 12 ps, respectively,after 3 ps of re-equilibration of the geometry obtained from the

Fig. 1. Na–O (a), Na–H (b), K–O (c) and K–H (d) radial distribution functions and their correand the classical MD simulation (dashed line).

classical MD simulations. In order to completely include the firsthydration shell into the QM region the QM radius for both systemswas set according to the Na–O and K–O RDF of the classicalsimulations as 3.3 Å and 3.8 Å, respectively.

4. Results and discussion

Besides the applied level of accuracy, the selection of the basis setis a crucial choice as discussed before because the QM portion is themost expensive computational part in the QM/MM simulation (morethan 95% of total CPU time). The LANL2DZ ECP basis sets were selectedfor the ions and Dunning double-ζ plus polarisation was used for H,and O since the ab initio geometry optimizations using these basis setsreproduce structural properties rather well with respect to calcula-tions using larger basis sets. Geometry optimizations of the Na+ andK+ plus 1–8 water molecules were performed for different theoreticalmethods and basis sets to determine the level needed to properlydescribe the ion–water interaction. The corresponding distancesbetween Na–O and K–O for each of the methods HF, MP2, B3LYPand CCSD are presented in Table 2. In the case of Na+ the values in thetable are almost identical for HF, CCSD andMP2methods for hydratedclusters containing 2–6 water molecules. B3LYP shows the shortestdistances thus making this method less favorable in this case. For theK+ ion distances between K and O are found be quite insensitive to theab initio methods applied but B3LYP gives again too short bonds.

Radial distribution functions (RDFs) describe the formation ofhydration shells around ions, and maxima represent distances with ahigh population and thus average bond lengths can be identified. Themetal–O and metal–H radial distribution functions and theircorresponding integration numbers obtained from simulations usingeither classical pair potentials or combined QM/MM simulationsincluding the first shell in the QM region are shown in Fig. 1(a–d) for

sponding integration numbers obtained from the QM/MM MD simulations (solid line)

Table 4Maxima rM and minima rm in Å and average coordination number CN of first andsecond hydration shell obtained from a classical and a QM/MM MD simulation of Na+

and K+ in aqueous solution.

Ion–H2O Method rM1 rm1 rM2 rm2 CN1 CN2

Na–O Classical 2.37 2.99 4.75 5.50 6.19 18.5QM/MM 2.39 3.10 4.50 5.30 6.0 15.2

K–O Classical 2.80 3.65 4.99 5.88 7.9 21.1QM/MM 2.85 3.83 4.82 5.82 8.8 18.4

Na–H Classical 3.05 3.75 5.3 6.25 13.98 51.92QM/MM 2.97 3.89 5.2 5.9 15.13 38.02

K–H Classical 3.43 4.28 5.64 6.58 21.9 54.9QM/MM 3.37 4.49 a a 22.2 a

a The RDF peak in the second shell was not distinguishable from the bulk, therefore,rM2, rm2 and CN2 were not identified for K–H in the QM/MM MD simulation.

98 S.S. Azam et al. / Journal of Molecular Liquids 153 (2010) 95–100

both Na+ and K+, and the values are given in Table 4. According to theinvestigations carried out by Petra et al. [15], the positions of Na–Opeaks are less sensitive to force fields. For Na+–H2O, the Na–O peak ofthe classical simulation exhibits a first maximum at 2.37 Å, whereasthe first maximum is observed at 2.39 Å in the QM/MM simulation.Although the first and second hydration shells are well separated fromeach other in the case of the classical and the QM/MMMD simulation,the minimum between first and second shell as well as the averagefirst shell coordination number indicate that ligand exchanges haveoccurred during the simulation time of 16 ps. Another first principlesmolecular dynamics (FPMD) simulation [48] consisting of 53 watermolecules and one Na+ ion in a cubic box of length 11.74 Å, yields anincreased value of rmax (2.49 Å) with a coordination number of5.2. While in a recent study [49] the concentration dependence ofcoordination numbers is elaborated. A slight decrease of the first peakcan be observed in the Na–O RDFs with increasing concentration andcauses a decrease in the coordination number. Comparative analysisshows the value of rmax obtained by the QM/MM MD simulation iscloser to those of experimental results (Table 1). The first shellcoordination numbers and distances obtained from classical simula-tions are generally found within the ranges provided by experiments.

The first K–O maximum peak obtained from classical simulation iscentered at 2.80 Å, a little longer distance of 2.85 Å is observed in theQM/MM simulation (Table 4). The comparison of the radial distribu-tion functions of the classical and the QM/MMMD simulation in Fig. 1shows that the values of the classical simulation differ from the results

Fig. 2. First and second shell coordination number distribution obtained from the Na+ ion (a)K+ ion (c) the QM/MM MD simulation and (d) the classical MD simulation.

obtained from the QM/MM approach and thus indicates that classicalsimulations are useful only for a preliminary equilibration. In the caseof K+ the lowered intensities of the first and second shell peaks aswellas the heightened minimum between first and second shell ascompared to the Na+ RDF indicate that the hydration of K+ issignificantly more labile than that of Na+. Structure-making effect ofNa+ in aqueous solution if compared with K+, beyond the first shellboundary can be observed and has been discussed in detail in a recentstudy [50]. An advanced analysis often referred as triplet correlationfunction or three-body distributions has been carried out for a two-shell QM/MMMD simulation of Na+ in aqueous solution and it showsa broad peak indicating the expected lability of the hydrate [51].

As shown in Fig. 2(a,b), for Na+ the coordination number of 6 ispreferred, occurring with a probability of 73% and 80% in the case ofthe QM/MM and classical MD simulation, respectively. In case of theQM/MMMD simulation the coordination numbers 5 and 7 occur witha probability of 14% and 12% whereas in the classical case only seven-fold coordination is observed with a probability of 18%. The range ofcoordination numbers obtained from the QM/MM MD simulation iscoherent with comparative studies and experimental observations. Asignificant difference is observed for the second shell although it istreated by means of classical pair potentials in both cases. Thisdifference in the coordination number indicates the influence of manybody and polarisation effect beyond the first shell QM region,therefore, suggesting that an extended QM region is mandatory toget an accurate description for the second hydration shell. The mostprobable second shell coordination number in the case of the QM/MMMD simulation is 16 (31%), whereas a value of 19 (22%) is obtainedfrom the classical simulation.

In the case of K+ (Fig. 2(c,d)) the coordination number dis-tribution is much broader ranging from 7–11 in the QM/MM simu-lation and 6–9 in the case of classical MD simulation. The maximumprobabilities of 30%, 44% and 15% for coordination numbers 8, 9 and10 are observed in the QM/MM MD simulation while in the case ofclassical MD simulation the coordination number of 7, 8 and 9 withprobabilities of 24%, 46% and 21% are observed. These variations in thefirst shell coordination numbers indicate that a considerable numberof different species is simultaneously present in the solution. Again asignificant difference is found for the distribution of the second shellthat is 18 and 21 in the case of QM/MM and classical MD simulations,respectively.

the QM/MMMD simulation and (b) the classical MD simulation, and obtained from the

Fig. 3. (a) O–Na–O and (b) O–K–O angle distributions in the first hydration shellobtained from the QM/MM MD simulations.

Table 5Mean ligand residence time τ and number of accounted ligand exchange events N for t*values of 0 and 0.5 ps, sustainability of the exchanges Sex and its inverse 1/Sex for thefirst and the second hydration shell obtained from the QM/MM MD simulation of Na+

and K+ in aqueous solution.

Ions Shell Nex0.0/10 ps τd0.0 Nex

0.5/10 ps τd0.5 Sex 1/Sex

Na+ 1st shell 64 0.94 11 7.4 0.17 5.882nd shell 394 0.38 64.7 3.2 0.16 6.25

K+ 1st shell 189 0.47 26 3.4 0.13 7.72nd shell 663 0.27 81.5 2.2 0.12 8.3

99S.S. Azam et al. / Journal of Molecular Liquids 153 (2010) 95–100

Fig. 3(a and b) correspond to the O–M–O angle distributions in thefirst shell during the course of QM/MM MD simulations of the Na+

and K+ ions in aqueous solutions, respectively. Unlike the O–K–Oangle distribution, two distinct peaks at ∼88.33° and ∼165.92° in caseof the Na+ ion clearly indicate the occurrence of well definedstructures, which is in agreement with other results. The O–K–O

Fig. 4. Snapshots of Na+ (a) and K+ (b) hydrations during the QM/MM MD simulations in ageometry of the K+ ion in aqueous solution.

angles are broadly distributed from ∼40° to ∼180° and further provethe existence of multiple structures with irregular geometries in theaqueous solution.

The mean residence times (MRTs) of water molecules in thehydration shell of a solute can be evaluated by means of differentmethods in which the direct method is preferred [41]. During the16 ps QM/MMMD simulation of Na+ and 12 ps of K+, first and secondshell exchange events have been observed as shown in Table 5. In caseof Na+, the values of the mean residence time in the QM/MM MDsimulation (7.4 and 3.2 ps) are higher than those of K+ (3.4and2.2 ps), which indicate that the hydration of potassium is more labilethan sodium. The classical simulations are found to predict a morerigid structure than the corresponding QM/MM MD simulation. Thiscan be explained due to the inclusion of many body and polarisationeffects in the QM region. The comparison of the dynamical data of theclassical and the QM/MM simulation points towards an insuitability ofthe classical approach to yield accurate results. In the classical MDsimulations the mean residence times for the first shell (17.34 ps forNa+ and 5.42 ps for K+) and for the second shell (4.31 and 3.61 ps,respectively for Na+ and K+) are significantly larger than thoseof QM/MM approach (7.4 and 3.4 ps, respectively for the first shell ofNa+ and K+ and 3.2 and 2.2 ps for the second shell of Na+ and K+,respectively). The overall difference indicates that themean residencetime for sodium is larger than that of potassium both for classical andQM/MM simulation, which signifies the weaker bond strengthbetween potassium and water. It is mandatory to mention that thedegree of lability of a hydration shell is a significant factor for thedetermination of the reactivity of ions in solution via the speed of anyligand exchange. It also plays a pivotal role in determining the abilityof ions to abandon their hydration shell in order to enter specificchannels for these ions inmembranes. Certain biological processes aredirectly or indirectly dependent on the ultrafast dynamics of ions inaqueous environment and the correct description of these processeshas only become possible due to the application of ab initio QM/MMsimulations but an improved method like Quantum MechanicalCharge Field (QMCF) is still needed to apply on these ions for amuch detailed and accurate analysis. It has been observed that Na+

still displays a well-ordered structure of its hydration shell while K+

looses first shell ligands more frequently and is not successful indisplaying any specific geometrical order of its shell (Fig. 4).Considering the shorter MRT of K+, a structure without formation ofany new order has been observed. In Fig. 5 the distance plots for a t*value of 0.5 ps are displayed. The exchange events are more frequentin case of K+, describing the higher flexibility of the ion in the QM/MMsimulation than Na+. It is obvious that simple reaction models ofassociative, dissociative and interchange mechanisms are not appli-cable in the case of these rapid exchange events.

queous solution. Notice the octahedral geometry of the Na+ hydration and an irregular

Fig. 5. Ligand exchange events at t* value of 0.5 ps for the first (colored) and the second(grey) shell ligands form the Na (a) and the K (b) ion QM/MM MD simulation.

100 S.S. Azam et al. / Journal of Molecular Liquids 153 (2010) 95–100

5. Conclusion

The importance of the combined QM/MM molecular dynamicsapproach proved once more as a suitable and economic way but stillimprovement is required to take into account the higher terms on aquantum mechanical basis in much accurate manner. The methodsand the basis sets were first evaluated for clusters containing 1–8 water molecules. The basis sets (LANL2DZ) used were found to beappropriate in well describing the behavior of Na+ and K+. It was alsoconcurred that Dunning double-ζ plus polarisation basis set wassufficient for water molecule. Geometry optimizations of the Na+ andK+ plus 1–8 water molecules were performed by different theoreticalmethods and showed no substantial difference in the correspondingdistances between Na and K ion with oxygen for each of the methods,except DFT. While a comparative study indicates that the differentforce fields predict different values for quantities having limited or noexperimental data [15]. It is found that classical simulations are onlyuseful for a preliminary equilibration and that quantum effects areessential for an accurate description while the QM/MM methodrequires construction of potentials, which is a time consuming task.Thus, this work points towards the application of an improved QMCFapproach on the same ions. The comparison of dynamical dataconfirms the insuitability of the classical approach to yield accurateresults. Mean residence time for sodium is larger than that of

potassium in both classical and QM/MM simulation proving theweaker solvation of potassium by water. The K+ hydration is moreflexible than that of Na+. Such investigations are particularlyimportant in cases where detailed energetic and structural propertiesof hydrated ions are needed, e.g. when the physiological relevance ofthese ions is to be discussed.

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