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Chemical Physics Letters 619 (2015) 158–162

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Chemical Physics Letters

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Lithium(I) in liquid ammonia: A quantum mechanical charge field(QMCF) molecular dynamics simulation study

Niko Prasetyoa, Lorenz R. Canaval c, Karna Wijayaa,b, Ria Armunantoa,b,∗

a Austrian-IndonesianCentre (AIC) for Computational Chemistry, Gadjah Mada University, Sekip Utara, Yogyakarta 55281, Indonesiab Department of Chemistry, Faculty of Mathematics and Natural Sciences,Gadjah MadaUniversity, SekipUtara, Yogyakarta55281, Indonesiac Theoretical ChemistryDivision, Institute of General, Inorganic and Theoretical Chemistry, Universityof Innsbruck, Innrain 80-82,

A-6020 Innsbruck, Austria

a r t i c l e i n f o

Article history:

Received 7 November 2014Infinal form 28 November 2014Available online 4 December 2014

a b s t r a c t

The solvation of Li(I) in liquid ammoniahasbeeninvestigatedbyan ab initio quantum mechanical charge-field molecular dynamics (QMCF-MD) simulation. Being the first simulation of a metal cation in liquidammoniaemploying this methodology, the work yieldsa wide range of accurate structural and dynamicaldata. Li(I) is tetrahedrally coordinated by four ammonia molecules in the first solvation shell at a distanceof2.075 Å.Two ligand exchange attemptshave beenobserved within12 psof simulation time. The secondsolvation shell shows a more labile structure with numerous successful exchanges. The results are inexcellent agreement with experiments.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Lithium is a metal of high interest in industry because of itsapplications in modern technologies such as lithium batteries,which are an essential part of mobile electronic devices [1]. Inacademia, lithium is often used as a starting point to assess newtheoretical methods in computationalchemistrybecauseof itssim-plicity.

The solvation of lithium in liquid ammonia has been subjectof standard computational chemistry methods such as ab initioHartree–Fock [2] and Møller–Plesset-2 (MP2) [3], ab initio self consistent field for molecular interactions (SCF-MI) [4] and den-sity functional theory (DFT) calculations [5] Various simulationmethods such as moleculardynamics simulations [3,6], a quantummechanical molecular mechanical molecular dynamics (QM/MM-MD) simulation [7] and a Monte Carlo simulation using a three

body potential [8] have previously been reported. Experimentally,neutron diffraction [9,10] and X-raydiffraction [11], infrared spec-troscopy [12] and inelastic X-ray scattering [13] have been used toinvestigate the solvation properties of lithium in liquid ammonia.Ab initio calculations in gas phase cannot yield any informationabout dynamical properties and solvent influence of the systemat hand. Both the pair potential approach and the Monte Carlo

∗ Corresponding author at: Austrian-Indonesian Centre (AIC) for ComputationalChemistry,Gadjah Mada University, SekipUtara,Yogyakarta 55281, Indonesia.

E-mail address: [email protected] (R. Armunanto).

simulation showed results differing from experimental data, andQM/MM simulations have not offered details of dynamical prop-

erties such as mean residence times of ligands, ion-ammoniavibrational spectra and detailed insights of the second solvationshell.

Nowadays, computer resources are sufficient to perform sim-ulations with a large quantum mechanical region to analyze thestructural andpicosecond dynamicalproperties of a metal ionplusits solvation layers accurately. The quantum mechanical charge-field molecular dynamics (QMCF-MD) methodhas proven to be anaccurate method to study highly charged ions [14,15], heavymetalions [16,17], oxo-anions [18] small molecules [19–22] and metal-organic [23,24] compounds in aqueous solution. To the best of ourknowledge, no application of the QMCF-MD method on metals inliquid ammonia has been reported so far. In this letter, we presentthe first application of the QMCF framework to investigate Li(I) in

liquid ammonia. From the simulation data, structural propertiessuch as radial distribution functions (RDFs), angular distributionfunction (ADFs) and coordination number distribution (CNDs) areevaluated along with mean residence times (MRTs) of ligands andion-ammonia vibrational frequencies.

2. Method

The QMCF-MD methodology [25] is an enhancement of con-ventional QM/MM approaches [26–29], which does not requireany potential functions for any species in the system investigated

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N. Prasetyo et al. / Chemical Physics Letters 619 (2015) 158–162 159

except of the solvent—solvent interactions. The scheme allows toneglect non-Coulomb interactions between the core zone and theMM region. The forces in thedifferent zones arecalculated accord-ing to Eqs. (1)–(3). This is the main advantage of the QMCF ansatz,because the construction of such potentials is a very difficult andtime consuminglabor, sometimesbeing impossible. TheQM regionintheQMCFmethodisenlargedandconsistsoftwo subregions: thecore zoneand the layer zone. Thecorezonecontains the soluteandthe first solvation shell, whereas the layer region contains furthersolvent molecules [30], which results in a higher computationaleffort.

F core J = F QM J

(1)

F layer J =

F QM J +

M I =1

qMM I qQM

J

r 2IJ

1+ 2

ε+ 12ε− 1

r IJ

r c

3+ F nC IJ (2)

F MM J =

N 1+N 2I = 1

I /= J

qMM I qQM

J

r 2IJ

+

N 2I =1

F nC IJ (3)

where F core J corresponds to the quantum mechanical forces actingon a particle J in the core region. F layer

J corresponds to thequantum

mechanical forces acting on a particle J in the layer region and F MM J

corresponds tothe forcesacting ona particle J in the MMregion. Toensurea smoothtransitionof theparticles between theQM andtheMM region, a small smoothing layer is defined (Eq. (4)), S (r ) beinga smoothing function as described in literature [25].

F smooth J = S (r )(F layer J

= F MM J )+ F MM J (4)

TheMRTs of the ligands belonging to thesolvationshellsof lithiumwere evaluated by the ‘direct’ method (Eq. (5)) [31].

0.5 =t simulationN av

N 0.5ex

(5)

t simulation represents the total simulation time, N av is the averagecoordination number of a particle in the respective shell and N 0.5exis thenumberof exchange events persisting 0.5ps. A sustainabilitycoefficient can be defined as

S ex =N 0.5ex

N 0.0ex(6)

where N 0.0ex is the number of all transitions through a shell bound-ary. The inverse of sustainability coefficient (Rex) indicates thenumber exchange attempts required for a successful exchange.

The ion-ammonia vibrational spectrum was evaluated usingvelocity auto-correlation functions (VACFs) C (t ) defined as

C (t ) =

N t I

N J v J (t I )v J (t I + t )

N t N N t

J v J (t I )v J (t I )

(7)

N is the number of particles, N t is the number of time origins,t I and v J denotes a certain velocity component of particle J . Thepowerspectrumwasobtainedbya subsequentFourier transforma-tion. Ion-ammonia vibrational frequencies were computed usingthe approximative normal coordinate analysis [32]. Frequenciesobtained via Hartree–Fock calculations are often scaled by 0.89in order to correct the missing electron correlation and the influ-ence of vacuum environment [33,34]. However, in this study thevalues were not scaled because our simulation included explicitsolvent thatprovideda realisticnon-vacuumenvironment, and theinfluence of electron correlation is expected to be small.

Table 1

Characteristic values of Li–N and Li–H radial distribution functions obtained fromQMCF-MD simulation.a

rM1 rm1 N(m1) rM2 rm2 N(m2)

Atompair

Li N 2.075 3.08 4.05 4.82 6.60 25Li H 2.625 3.28 12.82 4.88 6.40 75

a rMi and rmi arethe distancesin Å ofthe ith maximaand minimaobservedin thecorresponding RDF. N(mi) is theaverage coordinationnumber of the ith shell.

2.1. Simulation protocol

For the QMCF-MD simulation, a cubic box with side lengthof 20.7 Å containing one Li(I) ion and 215 ammonia moleculeswas used. Periodic boundary conditions, the minimum imageconvention and an NVT ensemble were applied. The simulationtemperature was kept constant at 235.15K using the Berendsenweak coupling algorithm [35] with a relaxation time of 0.1ps. Thedensity of the system was kept constant at 0.690g/cm3, corre-sponding to the density of pure liquid ammonia at 235.15K. Aflexible model of ammonia including intra- and inter-molecularpotentials was used in the MM region [6]. The radii of quantum

mechanical core zone and layer zone were set to 3.4 and 6.6 Å,respectively. A smoothing zone of 0.2 Å was applied at the bor-der of the QM and the MM region. All atoms in the QM region(core zone and layer zone) were treated at the Hartree–Fock levelof theoryusingthewell establishedDZP Dunning [36] basis sets. Tointegrate the equation of motion, a second-order Adams-Bashforthpredictor-corrector algorithm was used with a time step of 0.2 fs.To correct thecutoffof the long-range interaction above 10.3 Å,thereaction field approach was used [37]. The system was heated to700K for 2 ps and then re-equilibrated at 235.15K for 2ps. Samp-ling was done every fifth step during a simulation time of 12ps.All QM calculations within the simulation were executed with theTURBOMOLE 5.9 package [38,39]. The popular VMD package wasemployed to visually analyze the trajectory [40].

3. Result and discussion

The Li+–N and Li+–H RDFs are displayed in Figure 1a and struc-tural characteristics are listed in Table 1. There are two solvationshells, the first one ranging from 1.78 to 3.08 Å with an averagecoordinationnumberof 4.05. This coordinationnumberis in excel-lent agreement with data from experiments employing neutrondiffraction [9,10] and X-ray diffraction [11]. The first Li–N RDFpeak located at 2.075 Å is also in excellent agreement with exper-imental values of 2.01 and 2.06 Å from X-ray [11] and neutrondiffraction measurements [9,10], respectively (see Table 2). In thework at hand, the hydrogen bonds between first and second shellare described by quantum mechanics, whereas an earlier QM/MM

simulation only included the first solvation shell in the QM treat-ment [7], resulting in a slightly enlarged ion-ammonia distance.Earlier Monte Carlo and pair potential simulations not includingthree-body potentials report a wrong coordination number of six[6,8].

The second shell ranges from 3.08 to 6.60 Å, the maximum Li–Nprobability being located at 4.82 Å. This shell contains approx-imately 25 ammonia molecules. This value is larger than thecoordination number of the second hydration shell of lithium(I)in water [1]. Hayama et al. [11] reported a value of 30 for the coor-dination number and a second shell Li–N RDF maximum at 5.50 ÅemployingX-raymeasurements. Theweakly pronouncednon-zerovalleyof the Li+–NRDFbetween thefirst andsecondshell indicatesfew ligand exchange events between these shells. The non-zero

Li+

–N RDF value after 6.5 Å indicates that the second solvation


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Figure 1. (a) Li–N (solid line)and Li–H (dashed line)radial distribution functions including the corresponding integration information, and (b) angular distributionfunctionN–Li–N in the first solvation shell of the Li+ ion.

shell is more labile, and a number of ligand exchange processesare observed between the second solvation shell and the bulk.

The coordination numbers obtained from the RDFs are averagevalues. A detailed analysis of the coordination number distri-bution for the first and second shell is displayed in Figure 3.Occurring in 95% of the configurations found during the sim-ulation, the preferred coordination number is four for the firstsolvation shell, indicating a rather stable structure. The probabil-ity of a fivefold configuration was found to be 5%. For the secondshell, a broader coordination number distribution ranging from 21to 28 was observed with a maximum at 25. The probability of each coordination number is less than 30%, which indicates thatthe second solvation shell is less stable allowing frequent ligandexchanges events with the bulk environment (see Figure 4). Asnapshot fromthesimulationtrajectorydepictingthetetrahedrallyarrangedammonia moleculesof thefirst solvationshell is providedin Figure 3b.

To elucidate the structure of first shell solvation, an N–Li–NADF analysis was performed (see Figure 1b). A single peak rangingfrom 80◦ to 140◦ with a maximum at 107.5◦ indicates a flexibletetrahedral arrangement. The absence of other peaks excludes thepossibility of a four-fold planar coordination geometry. A slightlypronounced shoulder near 80◦ represents the small probability of a [Li(NH3)5]+ configuration. Neutron diffraction [9,10] and X-raydiffraction [11] experiments confirm that the configuration of thefirst shell solvationis tetrahedral,which wasalso found employinga QM/MM simulation [7].

To evaluate thepicosecond dynamics of thesystem, MRTvaluesfor each solvation shell were calculated using the ‘direct’ method

[31]. No MRT value for the ammonia ligands in the first shell canbe provided, as no successful exchange events were observed dur-ing the simulation. However, two ligand exchange attempts werefound at 2.65 and at 10.95ps simulation time (Figures 2b and 3a,markstA1 and tA2, respectively). Forthe secondshell, theMRT valueamounts to 2.8ps. This is slightly higher than the value for liquidammonia reported from a QM/MMsimulation(1.62 ps) [41] andforliquidammonia that containsoneNH4+ ion(1.82ps) [42]. This indi-cates that Li+ has a stronger interaction with ammonia comparedto NH4+. A number of 107 successful exchange events were foundfor the second shell. The Rex value of first solvation shell is zerobecause no successful ligand exchanges were found. For the sec-ond solvation shell, this number amounts to 5.8. This value showsthe strong influence of Li(I) on liquid ammonia up to the secondsolvation shell.

Figure 2b depicts the evolution of the root-mean-square-deviation (RMSD) of lithium and its first shell ligands from anideal tetrahedral arrangement. A peak at 2.65ps (mark tA1) isfound, which represents the first ligand exchange attempt (seealso Figure 3a). Along with an increase of thecoordination numberfrom 4 to 5, which indicates an associative exchange mechanism,a change from the tetrahedral geometry (Figure 3b) to a trigo-nal bipyramidal ligand arrangement (Figure 3c) is observed. Thisgeometry is also found forthe secondexchangeattempt at10.95ps(marktA2),however, less perfect dueto theevent’s less pronounced

Table 2

Structural properties of first solvationshell of Li+: Li+–N distance (d) in Å and coordinationnumber (CN).

Method d CN Geometry System Refs.

QMCF-MD simulation 2.075 4 Tetrahedral Liquid ammonia: 215 ammonia molecules, 1 Li+ ion; 235.15K;QM treatment: first and second solvationshell

This work

QM/MM simulation 2.15 4 Tetrahedral Liquid ammonia: 215 ammonia molecules, 1 Li+ ion; 235K;QM treatment: first solvationshell only

[7]

Monte Carlo simulation – 6 Octahedral Liquid ammonia: 201 ammonia molecules, 1 Li+ ion; 277K;pair potential plus three-body interactions

[8]

Pair potential simulation 2.29 6 Octahedral Liquid ammonia: 215 ammonia molecules, 1 Li+ ion; 235K;pairwise interactions

[6]

Ab initio SCF-MI calculation – 4 Tetrahedral Gas phase Li–ammonia clusters; HF/6-31+G* [4]Classical MD 2.105 4 Tetrahedral Liquid ammonia; 239.8 K [3]DFT calculation 2.15 4 Tetrahedral Gas phase Li(NH3)4+-cluster [2]X-ray diffraction 2.01 4 Tetrahedral Liquid ammonia; 200 K; 22 MPMa lithium [11]ND 2.06 4 Tetrahedral Li 21 MPMa in liquidammonia [9]ND – 4 Tetrahedral Liquid ammonia; 230 K; 21 MPMa lithium [10]

a

Mole percent metal.


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Figure 2. (a) Coordination number distribution of the first and second solvation shell, and (b) evolution of the root-mean-square-deviation of the first shell coordinationgeometry from an ideal tetrahedral arrangement. Marks tA1 and tA2 indicate thetwo observed ligand exchange attempts during the simulation time of 12ps.

Figure3. (a) Evolution of selected Li(I)–N distancesduringthe simulation.The bor-derline of the first and second shell is shown at 3 08 Å. Marks tA1 and tA2 indicate

the two observed ligand exchange attempts during the simulation time of 12ps. Adetailed plot is given for the first exchange attempt. Snapshots obtained from theQMCF-MD simulationdepicting, (b) an idealtetrahedralfirst shellarrangement,and(c) a trigonal bipyramidalcoordination geometryobservedat theexchangeattemptat tA1.

strength. The RMSD plot shows a second peak located at 9.8ps,whichcorrespondstoastronglysqueezedtetrahedral coordination.

Thepowerspectrumof lithium(I)in liquidammoniais displayedin Figure 4. The maximum is located at 358cm−1 and a smallerpeak is found at 550 cm−1. This corresponds to force constants of 35 Nm−1 and 82.8 Nm−1, respectively. These values are in verygood agreement with the experimentally observed frequencies of 361 and 561cm−1 (35.6 and 86.0 Nm−1) for the Li(I)–N vibra-

tional stretchingof [Li(NH3)n]+

species in liquidammonia [43], and

Figure4. PowerspectrumofLi+ inliquidammoniaobtainedvia Fouriertransformedvelocity auto-correlation functionsfrom theQMCF-MD simulation.For comparison,experimentally obtained valuesare depicted as single.

the IR absorptions of 7Li–NH3 (320cm−1), Li–NH2D (335cm−1) forlithium–ammonia complexes in solid argon [44]. Deviations of theresults obtained from the QMCF-MD simulation from the experi-mentalvaluesmay beattributed tothedifferentconcentrationsandisotopes, effects of counter ions and different experimental setups

of the systems investigated.To conclude, a rather stable structurewith a coordinationnum-ber of 4 was observed for lithium(I) in liquid ammonia. In contrast,lithium(I)in aqueous solutionpossesa more flexible first hydrationshell [1], the average coordination number being 4.5 and the MRTvalue amounting to 2.56ps [45].

4. Conclusions

The solvationstructureanddynamics of Li(I) in liquidammoniahave been studied using an ab initio QMCF-MD simulation. The12ps long simulation shows that the Li(I) ion is coordinated tofour ammonia molecules with a Li–N distance of 2.075 Å and atetrahedral configuration. Structural properties such as RDF, ADF

and CND are in good agreement with experimental data. The first


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solvation shell is rather stable, no successful ligand exchangeevents occur, compared to the second shell, which is more labileand shows an average coordination number of 25. The QMCF-MDsimulation has yielded results for structural and dynamics of thesolvated lithium(I) ion, which are in excellent agreement withavailable experimental data.

Acknowledgements

FinancialsupportforthisworkfromaMScgrantofthe IndonesiaEndowment Fund for Education Ministry of Finance RepublikIndonesia (LPDP Kementrian Keuangan RI) for Niko Prasetyo (S-557/LPDP/2013) is gratefully acknowledged. Financial supportfrom a PhD grant of the Leopold-Franzens-University of Innsbruck(Rector Univ. Prof. Dr. Dr.hc.mult. Tilmann D. Märk) for Lorenz R.Canaval is gratefully acknowledged. This work was supported bythe Austrian Ministry of Science BMWF as part of the UniInfras-trukturprogramm of the Focal Point Scientific Computing at theUniversity of Innsbruck.

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