Molecular dynamics investigation of water-exchange reactions on lanthanide ions inwater/1-ethyl-3-methylimidazolium trifluoromethylsufate ([EMIm][OTf])Yi-Jung Tu, Zhijin Lin, Matthew J. Allen, and G. Andrés Cisneros

Citation: The Journal of Chemical Physics 148, 024503 (2018);View online: https://doi.org/10.1063/1.4997008View Table of Contents: http://aip.scitation.org/toc/jcp/148/2Published by the American Institute of Physics

THE JOURNAL OF CHEMICAL PHYSICS 148, 024503 (2018)

Molecular dynamics investigation of water-exchange reactionson lanthanide ions in water/1-ethyl-3-methylimidazoliumtrifluoromethylsufate ([EMIm][OTf])

Yi-Jung Tu,1 Zhijin Lin,1 Matthew J. Allen,1 and G. Andres Cisneros2,a)1Department of Chemistry, Wayne State University, Detroit, Michigan 48202, USA2Department of Chemistry, University of North Texas, Denton, Texas 76201, USA

(Received 20 July 2017; accepted 18 December 2017; published online 9 January 2018)

We report a kinetic study of the water exchange on lanthanide ions in water/[1-ethyl-3-methylimidazolium][trifluoromethylsufate] (water/[EMIm][OTf]). The results from 17O-NMR mea-surements show that the water-exchange rates in water/[EMIm][OTf] increase with decreasing size ofthe lanthanide ions. This trend for water-exchange is similar to the previously reported trend in water/1-ethyl-3-methylimidazolium ethyl sulfate (water/[EMIm][EtSO4]) but opposite to that in water. Togain atomic-level insight into these water-exchange reactions, molecular dynamics simulations forlanthanide ions in water/[EMIm][OTf] have been performed using the atomic-multipole-optimized-energetics-for-biomolecular-application polarizable force field. Our molecular dynamics simulationsreproduce the experimental water-exchange rates in terms of the trend and provide possible expla-nations for the observed experimental behavior. The smaller lanthanide ions in water/[EMIm][OTf]undergo faster water exchange because the smaller lanthanide ions coordinate to the first shell [OTf]�

anions more tightly, resulting in a stronger screening effect for the second-shell water. The screeningeffect weakens the interaction of the lanthanide ions with the second-shell water molecules, facili-tating the dissociation of water from the second-shell and subsequent association of water moleculesfrom the outer solvation shells. Published by AIP Publishing. https://doi.org/10.1063/1.4997008

I. INTRODUCTION

Room-temperature ionic liquids are salts that are generallycomposed of organic cations and inorganic or organic anions.Ionic liquids have attracted attention for a broad range of appli-cations in catalysis,1–4 organic synthesis,5,6 separations,7 andelectrochemistry8,9 because of their unique properties such aslow vapor pressure, non-flammability, and high thermal, chem-ical, and electrochemical stabilities. These properties can betuned by choosing an appropriate combination of cations andanions, making ionic liquids task-specific solvents.

Many ionic liquids have been used as solvents for lan-thanide solutes because the luminescent,10–14 magnetic,15–18

and catalytic19–22 properties of lanthanides have been exten-sively exploited for the development of lighting devices, med-ical diagnosis, catalysis, and organic synthesis. A variety ofthese properties and applications can be modulated throughvariation of the lanthanide ions and the coordination envi-ronments. Moreover, water-exchange rates influenced by thecoordination chemistry of lanthanides are important param-eters for characterizing the efficiency of contrast agents forbiomedical imaging and diagnosis and catalysts in organicreactions.23,24 Recently, ionic liquids have become importantfor the coordination chemistry of lanthanides because lan-thanide ions in ionic liquids often exhibit unique propertiescompared to conventional organic solvents.14,16,22 A number

a)Author to whom correspondence should be addressed: andres@unt.edu

of properties and behaviors of lanthanides in ionic liquidshave been studied experimentally14,16,22 and theoretically.25,26

However, to our knowledge, water-exchange kinetics of lan-thanide ions in ionic liquids are scarcely discussed, and morecomprehensive structural and dynamics studies of these pro-cesses in ionic liquids will be helpful for the development oflanthanide-based catalysts for diverse applications in both thechemical and biomedical fields.

Molecular dynamics (MD) simulations can explicitly rep-resent solvents and, therefore, have become powerful tools tostudy solvation characteristics and the water-exchange pro-cesses.25–33 However, rates of water exchange are influencedby metal–water and water–solvent interactions, so an accu-rate force field is required for appropriately modeling theseintermolecular interactions. The atomic-multipole-optimized-energetics-for-biomolecular-application (AMOEBA)34 forcefield has been used to simulate water-exchange dynamics forvarious metal ions because it can accurately describe the inter-actions between metal ions and water molecules. Recently,our group has developed a protocol to incorporate Gaus-sian electrostatic model-distributed multipoles (GEM-DMs)35

into the AMOEBA force field and was able to successfullyestimate the bulk properties for several ionic liquids.36 Inaddition, our previous MD study based on the AMOEBAforce field was able to reproduce the experimental water-exchange behaviors that revealed that the trend of water-exchange rates in water/[EMIm][EtSO4] for different lan-thanide ions is opposite to that observed in water.33,37 Oursimulation results demonstrated that the dissociation of a water

0021-9606/2018/148(2)/024503/9/$30.00 148, 024503-1 Published by AIP Publishing.

024503-2 Tu et al. J. Chem. Phys. 148, 024503 (2018)

from the first shell is a key step for water-exchange eventsin water/[EMIm][EtSO4]. Smaller lanthanide ions undergofaster water exchange in water/[EMIm][EtSO4] because theybind to the first shell [EtSO4]� anions more tightly thanlarger lanthanide ions, resulting in more steric effects on thefirst shell water molecules and facilitating the dissociation ofwater.

Lanthanide trifluoromethylsufates (or triflates) have beenextensively used as Lewis acids in a wide range of organic-synthesis and catalysis applications in aqueous solutionbecause these acids are tolerant of water.38–40 In addition,because of the high thermal and electrochemical stability oftriflate ionic liquids, they are of interest as the heat transfermaterials and the electrolytes in the electrochemical cells.41,42

However, water-exchange reactions of lanthanide ions in tri-flate ionic liquids have not been studied, and more comprehen-sive studies will be important for further applications of theseionic liquids. In this paper, we explore the water exchange pro-cesses for different lanthanide ions in water/[EMIm][OTf]. Wefollow our previous methodology36 to develop the AMOEBAforce field parameters for [OTf]�, which are not available inthe current AMOEBA force field. With the optimized forcefields, we can simulate rates of water-exchange reactions inwater/[EMIm][OTf]. The solvation characteristics, transportproperties, and solvated structures from the MD trajecto-ries were further examined to understand the water-exchangebehaviors of lanthanide ions in water/[EMIm][OTf].

II. METHODSA. Parameterization of the [OTf]− anion

The force-field parameters for lanthanide ions and the[EMIm]+ cation have been developed previously,33 and theseoptimized parameters were used for simulation of water-exchange reactions on lanthanide ions in water/[EMIm][OTf].Here, we employed the same computational procedures todevelop the required AMOEBA force-field parameters for[OTf]�.36 Briefly, we optimized the structure for a [OTf]�–water dimer at the MP2 level43–47 with a 6-311G(d,p) basisset using the Gaussian software package.48 The relaxed one-electron density from the optimized structure was employedto calculate the distributed multipoles via the Gaussian elec-trostatic model-distributed multipole (GEM-DM) method.35

At the optimized geometry, second-order symmetry-adaptedperturbation theory (SAPT2)49–51 energy decomposition anal-ysis was performed using the Psi4 package52 to determineindividual components of intermolecular interactions for dif-ferent [OTf]�–water dimers as a reference. All parame-ters were optimized by comparison to different quantum-mechanical calculations including optimized structures, inter-molecular interactions, and energy decomposition analysesas previously described.35 MD simulations were performedwith 216 ion pairs of [EMIm][OTf] to test the accuracyof the developed force field for [EMIm][OTf]. The sim-ulated densities and heats of vaporization were comparedwith reported experimental values.53,54 The parameters forthe [EMIm][OTf] ion pair are provided in the supplementarymaterial.

B. MD simulation procedure

Simulations for three lanthanide ions—Gd3+, Dy3+,and Ho3+—were performed with a mixture of water and[EMIm][OTf]. To match the experimental NMR conditions(the volume ratio 1:19 of water to [EMIm][OTf]), 99 watermolecules were placed randomly in a box of 180 [EMIm][OTf]ion pairs. Three [EMIm]+ cations were replaced with a lan-thanide ion for each simulation studied to keep the sys-tems electroneutral. All simulations were performed with theAMBER14 package55 and the AMOEBA polarizable forcefield with the above-determined parameters. The simulationswere carried out in an isothermal isobaric ensemble (NPT) at298 K and 1 bar with a 1 fs time step using an 8.5 Å cutoff fornon-bonded interactions and an 8.0 Å cutoff for the smoothparticle mesh Ewald (PME) method56 for long-range electro-statics. The Berendsen thermostat and barostat57 were used tocontrol temperature and pressure with relaxation times of 1 and3 ps, respectively. All production trajectories were generatedfor at least 20 ns, and snapshots were recorded every 100 fs.All properties—such as radial distribution function, moleculardiffusion coefficient, and mean residence time—were calcu-lated from three independent MD trajectories with the standarddeviation used as the uncertainty.

C. Experimental methods

The experimental method and procedures used to measurewater-coordination numbers and water-exchange rates of lan-thanides in water/ionic liquids have been reported,37 and thedata collection in this work followed those procedures with thechange of [EtSO4]� from that report being replaced by [OTf]�

in this study. The luminescence-decay measurements ofEu(OTf)3 and Tb(OTf)3 (Table S9 of the supplementary mate-rial) were used to determine an average water-coordinationnumber of 1.0 for Eu3+ or Tb3+ in water/[EMIm][OTf](1:19, v/v). Data from variable-temperature 17O-NMR mea-surements of lanthanide triflates [Gd(OTf)3, Dy(OTf)3, andHo(OTf)3] and their diamagnetic reference [Y(OTf)3] col-lected in the experimental determination of water-exchangerates are provided in the supplementary material (TablesS9–S14 and Figs. S10–S12).

III. RESULTS AND DISCUSSIONA. 17O-NMR water-exchange rates

Water-exchange rates of three lanthanide ions inwater/[EMIm][OTf] were determined using 17O-NMRrelaxation-rate measurements. The results show that water-exchange rates of lanthanide ions in water/[EMIm][OTf]increase as a function of charge density (the ratio of chargeto ionic radius). The increase of water exchange rates fromGd3+ to Ho3+ was also observed in water/[EMIm][EtSO4].However, the exchange rate increases more rapidly with theincreasing size of metal ions in water/[EMIm][OTf] thanin water/[EMIm][EtSO4]. To understand the water-exchangereactions in this solvent, we started with the developmentof force-field parameters for [EMIm][OTf]. To validate theforce field for [EMIm][OTf], the density, the heat of vapor-ization, and the self-diffusion coefficient for [EMIm][OTf]

024503-3 Tu et al. J. Chem. Phys. 148, 024503 (2018)

TABLE I. Density (ρ, g/cm3) and heat of vaporization (∆Hvap,a kJ/mol) of [EMIm][OTf].b

MD with original vdW MD with the scaling of vdW Experiment

Temperature (K) ρ ∆Hvap ρ ∆Hvap ρ ∆Hvap

298 1.413(2.1%) 97.5(29.3%) 1.394(0.8%) 136.6(0.9%) 1.384c 137.9d

308 1.392(1.2%) 1.375c

318 1.388(1.6%) 1.367c

328 1.384(1.8%) 1.359c

aThe heat of vaporization (∆Hvap) is also calculated using the equation: ∆Hvap = ∆E + RT, where ∆E is the difference of thepotential energies in the gas and liquid phases, R is the gas constant and T is at 298 K.60

bThe values in parentheses are the percent error in the simulation results compared to the experimental measurements.cReference 53.dReference 54.

were simulated. With the optimized force-field parameters,we simulated the water-exchange dynamics of lanthanides inwater/[EMIm][OTf].

B. Thermodynamic properties of [EMIm][OTf]ionic liquid

Table I lists the experimental and simulated densitiesand heat of vaporization for [EMIm][OTf] for four differenttemperatures. A density of 1.413 g/cm3 predicted from simu-lation at 298 K is 2.1% higher than the experimental values of1.384 g/cm3 using the original van der Waals (vdW) parameterfrom the AMOEBA potential. In addition, the calculated heatof vaporization (97.5 kJ/mol) is underestimated by 29.3% com-pared to the experimental ∆Hvap of 137.9 kJ/mol. Therefore,the van der Waals parameters for [OTf]� were optimized bycomparing the calculated density and ∆Hvap with their experi-mental counterparts at a single temperature (298 K) to improveagreement with the experimental data. After the van der Waalsparameters for [OTf]� were optimized, the calculated den-sity (1.394 g/cm3) and heat of vaporization (136.6 kJ/mol)at 298 K show errors below 1% with respect to the experi-mental counterparts. The calculated density slightly decreaseswith increasing temperature (Table I) and is in good agreementwith experimentally reported data, with errors below 2% forall temperatures.

C. Solvation characteristics of lanthanide ionsin water/[EMIm][OTf]

Radial distribution functions, g(r), were calculated foreach lanthanide ion (Gd3+, Dy3+, and Ho3+) with varioussolvent molecules (water, [OTf]�, and [EMIm]+) to examine

TABLE II. The lanthanide–water (Ln–Owater, Å) and lanthanide–triflate(Ln–OOTf, Å) distances for the first and second coordination shells oflanthanide ions in water/[EMIm][OTf].

Gd3+ Dy3+ Ho3+

g(r) CN g(r) CN g(r) CN

1st shell Ln–Owater 2.23 1.0 2.23 1.0 2.23 1.0Ln–Hwater 2.85 2.0 2.87 2.0 2.91 2.0Ln–OOTf 2.79 9.0 2.77 9.0 2.75 8.9

2nd shell Ln–Owater 4.47 1.2 4.51 1.5 4.55 2.0Ln–Hwater 4.97 2.4 5.03 3.1 5.05 4.1Ln–OOTf 4.11; 4.51 6.4a 4.07; 4.49 6.2a 3.99; 4.45 5.5a

aThe integration of two Ln–OOTf g(r) peaks in the second shells.

the coordination environment of lanthanide ions in water/[EMIm][OTf]. The peak positions of g(r) indicate the locationof solvent coordination shells around the lanthanide ions, andthe corresponding integral values of g(r) peaks, CN(r), repre-sent the average coordination numbers of solvent molecules.The peak positions and the corresponding integrated valuesare summarized in Table II.

FIG. 1. Radial distribution functions g(r) and the corresponding g(r) integra-tion of water molecules (O atoms in solid line and H atoms in dashed line)around (a) Gd3+, (b) Dy3+, and (c) Ho3+ in water/[EMIm][OTf].

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The g(r) for the lanthanide ion with inner-sphere waterare displayed in Fig. 1 and are given by water O (Ln–Owater

g(r), solid line) and H atoms (Ln–Hwater g(r), dashed line).In Fig. 1, Ln–Owater g(r) display two well-resolved peaks,indicating the population of water in the first and second coor-dination spheres of the lanthanide ion. The first sharp peakappears at 2.23 ± 0.01 Å, indicating a population of water inthe first coordination sphere of the lanthanide ion. The peakposition of Ln–Owater g(r) for all lanthanide ions is locatedat almost the same distance and shows no dependence on thesize of the lanthanide ions. However, the maxima of thesepeaks are centered at shorter distances compared to the pre-viously reported distances of 2.35–2.38 Å in water and 2.40–2.43 Å in water/[EMIm][EtSO4].33 This difference indicatesthat the binding strength between the lanthanide ions and waterin water/[EMIm][OTf] is stronger compared to only wateror water/[EMIm][EtSO4], possibly resulting from less stericrepulsion between water and [OTf]� than water–[EtSO4]� andwater–water in the first coordination shell.

The first and second peaks of Ln–Owater g(r) are wellseparated by a minimum, and the minimum reaches zero. Inaddition, integration of the first Ln–Owater g(r) gives an inte-ger of 1.0. These results indicate that only one water moleculestays in the first shell and no water-exchange processes occurbetween the first and second shells during the simulations.

The second Ln–Owater g(r) peak is broader than the firstone and appears at 4.47 Å for Gd3+, 4.51 Å for Dy3+, and4.55 Å for Ho3+. The second and third solvation shells are also

separated by a minimum, but the minimum after the secondpeak does not reach the x-axis, indicating that second-shellwater exchanges with outer-sphere water. The integral valuesof the second Ln–Owater g(r) peaks show that the number ofwater molecules in the second coordination shell is betweenone and two due to water-exchange events between the secondshell and the bulk.

Similar to Ln–Owater g(r), Ln–Hwater g(r) display two well-defined peaks corresponding to the first and second solvationshells. The first peak of Ln–Hwater g(r) has zero overlap withthe first one of Ln–Owater g(r), indicating that the water dipolein the first coordination shell is strongly oriented toward thelanthanide ion. The second Ln–Hwater g(r) peak appears at 5.0–5.1 Å and is partially overlapped with the second Ln–Owater

g(r) peak, indicating that the second shell water molecules arealso strongly oriented by the lanthanide ion but have moreflexibility compared to the first shell water molecules. Thehigher flexibility of the second shell water is consistent withwater-exchange with the bulk.

The Ln–OOTf g(r) for the lanthanide ions and the O atomsof [OTf]� anions for the distribution of [OTf]� anions werealso calculated (Fig. 2, left panel). For all lanthanide ions, theLn–OOTf g(r) patterns are similar, and a well-resolved peak atthe distance of 2.7–2.8 Å indicates the location of the first coor-dination shell formed by the O atoms of [OTf]� anions. Thefirst peak of Ln3+–OOTf g(r) appears at 2.79 Å for Gd3+, 2.77 Åfor Dy3+, and 2.75 Å for Ho3+. Integration of the first Ln–OOTf

g(r) peaks show that the lanthanide ions are coordinated with

FIG. 2. Radial distribution functionsg(r) and the corresponding g(r) inte-gration of [OTf]� and [EMIm]+ around(a) Gd3+, (b) Dy3+, and (c) Ho3+ inwater/[EMIm][OTf].

024503-5 Tu et al. J. Chem. Phys. 148, 024503 (2018)

TABLE III. Self-diffusion coefficients (cm2/s) for water (DH2O) and lanthanide ions (DLn) inwater/[EMIm][OTf].a

Solvent Metal ions DH2O DLn Danionb

Water/[EMIm][OTf] Gd3+ 1.94× 10�8 1.53× 10�10 2.39× 10�9

(1.51× 10�8) (2.99× 10�11) (1.58× 10�9)Water/[EMIm][OTf] Dy3+ 1.80× 10�8 2.88× 10�10 2.06× 10�9

(4.25× 10�9) (2.24× 10�10) (2.11× 10�10)Water/[EMIm][OTf] Ho3+ 1.33× 10�8 2.35× 10�10 1.45× 10�9

(1.47× 10�9) (2.67× 10�10) (6.28× 10�10)Water/[EMIm][EtSO4]c Gd3+ 1.40× 10�8 1.65× 10�10 4.28× 10�9

Water/[EMIm][EtSO4]c Dy3+ 8.64× 10�9 1.80× 10�10 3.10× 10�9

Water/[EMIm][EtSO4]c Ho3+ 7.86× 10�9 3.37× 10�10 2.99× 10�9

aThe standard deviation from three independent MD simulations are listed in parentheses.bSubscript anion refers to [OTf]� anions in water/[EMIm][OTf] and [EtSO4]� anions in water/[EMIm][EtSO4].cReference 33.

nine O atoms from six [OTf]� anions in the first shell. In addi-tion, the first peak of Ln–OOTf g(r) is broad compared to thatof Ln–Owater g(r), and the broader peak for Ln–OOTf g(r) ispartly due to interconversion of coordination modes of [OTf]�

between bidentate and monodentate during the simulation.The Ln–[EMIm]+ g(r) show zero population of [EMIm]+

cations in the first coordination shell because of the repul-sion between the lanthanide and [EMIm]+ cations (Fig. 2,right panel). When the distance of the lanthanide ions and[EMIm]+ is longer than 4 Å, the Ln–[EMIm]+ g(r) becomenon-zero, indicating that [EMIm]+ cations occupy the secondcoordination shell of lanthanide ions.

D. Molecular diffusion in water/[EMIm][OTf]

Determination of diffusion coefficients can provide use-ful information about the molecular mobility and kinetics of

water-exchange reactions in a given solvent environment. Themolecular diffusion coefficients (D) can be determined byusing Einstein’s relation61

6Dt = limt→∞

MSD(t),

where MSD is the mean-square displacement of moleculesover a period of time (t). In the diffusive regime, the MSDgrows linearly with time, which enables calculation of diffu-sion coefficients from the slopes of the plots of MSD as a func-tion of time. The molecular diffusion coefficients (DH2O, DOTf,and DLn, Ln = Gd3+, Dy3+, or Ho3+) in water/[EMIm][OTf]were calculated from the slopes of MSD plots from 500 to15 000 ps (Table III).

To study the effect of the metal ion on molecular diffusion,the diffusion coefficients of water and lanthanide ions weredetermined for Gd3+, Dy3+, and Ho3+ in water/[EMIm][OTf]

FIG. 3. The distance trajectories of the water Oatoms with (a) Gd3+, (b) Dy3+, and (c) Ho3+ inwater/[EMIm][OTf]. At t = 0 ps, the first shell watermolecules are colored in black, the second shell onesare in red, and other solvation shells are in gray. Water-exchange events between the second shell and the bulkwere observed during the simulations.

024503-6 Tu et al. J. Chem. Phys. 148, 024503 (2018)

(Table III). All three lanthanide ions have similar diffusioncoefficients in water/[EMIm][OTf]: 1.53 × 10�10 cm2/s forGd3+, 2.88 × 10�10 cm2/s for Dy3+, and 2.35 × 10�10 cm2/sfor Ho3+. The effect of the metal ion on the diffusion coef-ficients of water molecules in water/[EMIm][OTf] is also notsignificant, with the diffusion coefficients of water (DH2O) cor-responding to 1.94 × 10�8 in Gd3+/water/[EMIm][OTf], 1.80× 10�8 cm2/s in Dy3+/water/[EMIm][OTf], and 1.33 × 10�8

cm2/s in Ho3+/water/[EMIm][OTf].The calculated diffusion coefficients of water (DH2O)

were compared to our previously reported values in wateror water/[EMIm][EtSO4] to investigate the solvent effect ondiffusion of water molecules. Table III shows that the diffu-sion coefficients of water in water/[EMIm][OTf] are in therange of 1.33 × 10�8 to 1.94 × 10�8 cm2/s, slower thanthose in water (1.59 × 10�5 to 1.63 × 10�5 cm2/s).33 Theslower molecular diffusion of water in water/[EMIm][OTf]is primarily due to the formation of intermolecular hydro-gen bonds between water and [OTf]� anions. The diffusioncoefficients of [OTf]� are in the range of 1.45 × 10�9 to2.39 × 10�9 cm2/s in water/[EMIm][OTf], suggesting that thehydrogen bonds between water and [OTf]� anions slow thediffusion of water in water/[EMIm][OTf]. The diffusion ofmolecules influenced by hydrogen-bond interactions was alsoobserved in our previous study in water/[EMIm][EtSO4].33

In addition, water molecules diffuse more rapidly inwater/[EMIm][OTf] (1.33 × 10�8 to 1.94 × 10�8 cm2/s) thanin water/[EMIm][EtSO4] (1.40 × 10�8 to 8.64 × 10�9 cm2/s),and this difference is consistent with the 17O-NMR exper-imental results demonstrating that water-exchange rates oflanthanide ions are faster in water/[EMIm][OTf] than in water/[EMIm][EtSO4].

E. Water-exchange dynamics of lanthanide ionsin [EMIm][OTf]

Two methods can be used to calculate the water-exchangerates, namely, the survival function proposed by Impey et al.62

and the direct method,63 accounting for all incoming andoutgoing water molecules throughout the whole simulationtrajectory. In this work, the direct method was chosen because

TABLE IV. Water-exchange rates (s�1) of lanthanide ions determined by17O-NMR experiments.

Ion Watera,b Water/[EMIm][EtSO4]c Water/[EMIm][OTf]

Gd3+ 8.30× 108 5.08× 106 1.30× 107

Dy3+ 4.34× 108 3.64× 107 1.40× 108

Ho3+ 2.14× 108 4.61× 107 1.50× 108

aReference 58.bReference 59.cReference 37.

TABLE V. Calculated average rates of water-exchange between the secondshell and the bulk in water/[EMIm][OTf].

Metal ions CNav Nex τex (s) kex (s�1)

Gd3+ 1.19 3 7.9× 10�9 1.3× 108

Dy3+ 1.52 6 5.1× 10�9 2.0× 108

Ho3+ 1.95 10 3.9× 10�9 2.6× 108

this method treats the associative and dissociative exchangeprocesses equally. Similar to the Impey procedure, the directmethod also needs the time parameter t∗ for defining a realexchange event. In this work, the parameter t∗ is taken to be 2ps, which means that if a water molecule enters or leaves thesecond shell (i.e., 4.0 Å < distance of Ln–Owater < 5.5 Å) fora time period longer than 2 ps, the event is counted as one realexchange process. The average residence time (τex) of watercan be defined as

τex =tsim · CNav

Nex,

where tsim is the whole simulation time, CNav is the averagenumber of water molecules in the second shell, and Nex is thenumber of water-exchange events between the second shelland the bulk. The distances of the lanthanide ion with waterO atoms at various solvation shells were analyzed through-out the whole simulation time to record all exchange eventsof water. In Fig. 3, the Ln–Owater distance trajectories showthat no water exchange events occurred from the first sol-vation shell of lanthanide ions. Nevertheless, a number of

FIG. 4. MD snapshots for a water-exchange event on Ho3+ during the simulation time. The water molecules colored in green and blue represent the incomingand outgoing water molecules, respectively. At t = 0 ps, there are six [OTf]� anions (black) and one water molecule (gray) in the first solvation shell of Ho3+,and the second shell contains two [OTf]� anions and two water molecules. Two second shell water molecules are strongly oriented toward Ho3+. At t = 7706 ps,the blue water molecule dissociates from the second coordination shell of Ho3+ and forms hydrogen bond with the first shell [OTf]�. Between t = 7707 ps andt = 7779 ps, blue and green water molecules exchange in the bulk. At t = 7780 ps, the green water from the second shell joins the second coordination shell ofHo3+ and replaces the original blue water.

024503-7 Tu et al. J. Chem. Phys. 148, 024503 (2018)

FIG. 5. The average total interactionenergies of lanthanide ions with a [OTf]anion and a water in (a) the first shelland (b) the second shell. In the firstshell, the averaged Ln–[OTf]� interac-tion energies are calculated from theaverage of six Ln–[OTf]� interactionenergies because there are six first shell[OTf]� anions coordinating to the lan-thanide ion. In the second shell, the aver-aged interaction energies for Ln–[OTf]�

and Ln–water are, respectively, calcu-lated from the average of two Ln–[OTf]�

and the average of two Ln–water inter-action energies because there are two[OTf]� anions and two water moleculessurrounding around the lanthanide ion.

second shell water-exchange processes were observed dur-ing the MD simulations. The calculated water-exchange rates(kex), the inverse of mean residence time (τex), were deter-mined from the simulation time of 20 ns and listed in Table V.As shown in Table V and Fig. 3, the calculated water-exchangerates are in the order of Gd3+ < Dy3+ < Ho3+. The increasingtrend for the rates is similar to that in water/[EMIm][EtSO4]and is consistent with the 17O-NMR experiments (Tables IVand V).

Further information regarding water-exchange events canbe obtained by examining the snapshots of lanthanide ions withthe inner-sphere solvent molecules from the MD trajectories.Figure 4 shows a representative example of the water-exchangeprocess of a lanthanide ion in water/[EMIm][OTf]. At thebeginning of the simulations (t = 0 ps in Fig. 4), all lanthanideions were coordinated by six [OTf]� anions and one watermolecule in the first solvation shell. Six [OTf]� anions forma trigonal prism structure, and a water molecule is located atone of the square faces of the trigonal prism structure. The sec-ond solvation shell consists of two water molecules and two[OTf]� anions. Two water molecules form hydrogen bondswith two H atoms of the first-shell water, and the O atomsof the second-shell water molecules are pointed toward thelanthanide ion, showing strong dipole interactions betweenthe water O atoms and the lanthanide ion. During the simu-lation, both the [OTf]� anions and water molecules undergorapid rotational motions around the lanthanide ion. In someoccasions, the rotational motions cause the second shell waterto form hydrogen bonds with the O or F atoms of the firstshell [OTf]�, disrupting the interaction of the lanthanide ionwith the second shell water molecules and leading to the dis-sociation of a water from the second shell to the bulk (bluewater at t = 7706–7707 ps in Fig. 4). Once the water leavesthe second shell, the outgoing water becomes randomly ori-ented toward the lanthanide ion. The entering water can bethe original outgoing water or other water molecules from theouter-sphere.

Intermolecular interaction energies of Ln–[OTf]� and Ln–water were calculated for selected snapshots from the simu-lation trajectories to understand the effect of the metal ionon the water exchange rates in water/[EMIm][OTf]. All inter-molecular interactions were determined using the AMOEBAforce field and TINKER program.64 The averaged interactionenergies between the lanthanide ion and [OTf]� anions andbetween the lanthanide ion and water molecules are summa-rized in Fig. 5. The interaction energies of the lanthanide ionwith [OTf]� anions and water are dependent on the size ofthe lanthanide ion. In the first solvation shell [Fig. 5(a)], both[OTf]� anion and water bind more tightly to Ho3+ than Gd3+

due to the larger charge density of Ho3+. On the other hand,interaction energies of the lanthanide ions with the second shell[OTf]� anions and water become less negative when the size ofthe lanthanide ion decreases from Gd3+ to Ho3+[Fig. 5(b)]. Apossible cause for the decreasing interactions of Ln–water andLn–[OTf]� involves a larger screening effect resulting from thestronger interaction between the smaller lanthanide ion and thefirst shell [OTf]�. The first shell [OTf]� anions bind to Ho3+

more strongly than Gd3+, making it more difficult for Ho3+

to interact with the second shell [OTf]� and water comparedto Gd3+. As a result, the second shell water molecules aroundHo3+ are more labile than those around Gd3+, and the trendof Gd3+ < Dy3+ < Ho3+ is seen for water-exchange rates inwater/[EMIm][OTf].

IV. CONCLUSIONS

Experimental results show that the water-exchange ratesof lanthanide ions in water/[EMIm][OTf] increase in the orderof Gd3+ <Dy3+ <Ho3+. The trend is similar to that observed inwater/[EMIm][EtSO4]. To gain further insight into the water-exchange events in water/[EMIm][OTf], we performed clas-sical MD simulations using the AMOEBA polarizable forcefield. Our simulations are in good agreement with experi-ment with respect to the trend of water-exchange rates. By

024503-8 Tu et al. J. Chem. Phys. 148, 024503 (2018)

analyzing the MD trajectories, we observed that the water-exchange event for a lanthanide ion occurred between thesecond shell and bulk in water/[EMIm][OTf]. The exchangerate of the second-shell water with the bulk water depends onthe relative binding strength of the lanthanide ion with the firstshell [OTf]� anions. The [OTf]� anion binds to the smallerlanthanide ions more tightly, but this causes the more screen-ing effect to the second shell water molecules. The strongerscreening effect weakens the interaction of the smaller lan-thanide ion with the second shell water, facilitating waterexchange from the second shell of the smaller lanthanideion. As a result, the trend of Gd3+ < Dy3+ < Ho3+ is seenfor water-exchange rates in water/[EMIm][OTf]. Althoughthe trend of water-exchange rates in water/[EMIm][OTf]is similar to that in water/[EMIm][EtSO4], our simula-tion indicates that the process of water exchange for lan-thanide ions in water/[EMIm][OTf] is different from that inwater/[EMIm][EtSO4]. This study suggests that the second-shell water exchange should be considered when interpreting17O-NMR data, and it provides a possible mechanism formanipulation of water-exchange dynamics through selectionof different ionic liquids as solvents.

SUPPLEMENTARY MATERIAL

See supplementary material for definitions for all localframes, multipoles, and intra- and inter-molecular interactionsfor the [EMIm][OTf] ion pair. MD simulation results for den-sity and heat of vaporization, self-diffusion coefficients, andmean residence time.

ACKNOWLEDGMENTS

Y.-J. Tu thanks Wayne State University for a ThomasRumble Fellowship. M.J.A. acknowledges the National Sci-ence Foundation for support (Grant No. CHE-0955000). Theauthors also thank Wayne State computing grid for com-putational resources and R. L. Chamika Lenora for helpfuldiscussion.

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