Staff Site Universitas Negeri Yogyakarta cpl hf ammonia

ContentslistsavailableatScienceDirect

Chemical

Physics

Letters

j o ur na l h o me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / c p l e t t

Investigation

of

structural

and

dynamical

properties

of

hafnium(IV)

ion

in

liquid

ammonia:

An

ab

initio

QM/MM

molecular

dynamics

simulation

Suwardi

1

,

Harno

Dwi

Pranowo,

Ria

Armunanto

∗

DepartmentofChemistry,FacultyofMathematicsandNaturalSciences,Austrian–IndonesianCentre(AIC)forComputationalChemistry, GadjahMadaUniversity,Indonesia

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received4June2015 Infinalform17July2015 Availableonline29July2015

a

b

s

t

r

a

c

t

ThestructureanddynamicsofHf4+_{ioninliquidammoniahavebeeninvestigatedbyanabinitio}

quan-tummechanicsmolecularmechanics(QM/MM)moleculardynamicssimulation.Thestructuraldatawas obtainedintermsofradialdistribution,coordinationnumberandangulardistribution,andthenthe dynamicsinmeanligandresidencetime.TheHf4+_{ioniscoordinatedbyfiveammoniamoleculesinthe}

firstsolvationshellshowingadistortedsquarepyramidalstructurewithanaverageHf4+_{–Ndistanceof}

2.38 ˚A.Noammonialigandwasobservedforexchangeprocessesbetweenthefirstandsecondshells. ©2015ElsevierB.V.Allrightsreserved.

1. Introduction

Interestinstudyingcomplexformationofmetalionshasgrown rapidly.Itisnecessarytounderstandtheinteractionsofmetalions witha ligandinbiochemical, and chemicalprocesses. Research onmetalinteractionswithproteinshasdeveloped intherecent years[1–3].Thequestionthatarisesthenhowtounderstandthe reactivityofthesemetals.Inasolutionsystemreactivityofmetal ionsisaffectedbythecoordinationshellofthemetalions[4].In thiscontext,themoleculardynamicssimulationplaysan impor-tantroletoinvestigatethestructureofsolvationofthemetalion anditsreactivity.Characteristicsofsolvatedionsinwaterorliquid ammoniahavebeenatopicofspecialinterestsincesuchdetailed knowledgeisessentialforunderstandingtheroleoftheseionsin chemicalandbiologicalprocesses[5–7].Liquidammoniahasthe weakesthydrogenbondsinnatureanditsassociatedionsalsoplay anessentialroleinthechemistryoffertilizers,biochemical pro-cessesoftheliver,kidneysandintestines,andavarietyoforganic reactions[8–13].Hafnium(Hf)fromgroup4hasbeenknownas implantmaterialsbutitsbiocompatibilityoflittle-knownone[14]. TheHf4+_{ioncouldbesolvatedinwaterandalsoinliquidammonia.}

Indeed,thestructureinvestigationofHf4+_{inaqueoussolutionhas}

∗_{Correspondingauthor.}

E-mailaddress:ria.armunanto@ugm.ac.id(R.Armunanto).

1 _{Permanentaddress.DepartmentofChemistryEducation,Facultyof} Mathemat-icsandNaturalSciences,YogyakartaStateUniversity,Yogyakarta,Indonesia.

beencarriedoutbythespectroscopyaswellasQuantumMechanics ChargeField(QMCF)methodwhereasthestructuralanddynamical aspectfortheHf4+_{ioninliquidammoniahasnotbeenreportedso}

far[15–21].However,thereisnomanyinvestigationsofmetalions

inliquidammonia.Therefore,itisstillinterestingtoinvestigatethe solvationofHf4+_{inliquidammonia.}

The pentaammoniates of MF4, namely M(NH3)4F4·NH3 (1,

M=Zr; 2,M=Hf)are formedifAg3M2F14 and liquidNH3 were

prolongedinthestorage.Compounds1and2arealsoformedin thereactionoftheMF4withliquidNH3inweeks.TheHf4+–N

dis-tanceof2.383 ˚AhasbeenknownbytheX-raydiffractionmethod

[22].

ThehydrationstructureofsometetravalentionsasU4+_,Th4+_,

Hf4+_,andZr4+_{hasbeenextensivelyinvestigatedbythediffraction,}

spectroscopy,andcomputersimulationmethods[23–27].Hybrid quantum mechanics/molecular mechanics molecular (QM/MM MD)dynamicssimulationmethodshavesuccessfullyinvestigated structuralanddynamicalpropertiesofmetalionsinwateraswell asinliquidammonia.Thesimulationmethodhasthusbecomean alternativetoexperiments,in particularwheretheexperiments reachtheirlimitations[15–17].Determinationsofthestructureand dynamicspropertiesofsolvationionsareverysensitivetothe accu-racyofthesimulationmethods.Itisknownthattheinvestigations ofthesolvationofmetalionsbyQM/MMMDmethodsprovidea highlevelofaccuracy.Therefore,inthepresentwork,weperformed aQM/MMMDsimulationforHf4+_{inliquidammonia,inorderto}

investigatethestructureanddynamicsofthesolvatedHf4+_ionin

liquidammoniaat235.15K.

Table1

Hafnium(IV)–ammoniadistances(r),bindingenergiesperammonialigandobtained byquantummechanicalcalculationsofHf4+_{–ammoniacomplexatHF,MP2,CCSD,} andB3LYPlevels.

Method r Bindingenergy

(Å) (kcal/mol)

HF 2.24 −152.06

MP2 2.25 −160.75

CCSD 2.25 −158.95

B3LYP 2.21 −167.51

2. Methods

2.1. Constructionofpotentialfunction

TherearetwostepsthatmustbedonepriortoQM/MM sim-ulationcouldberun, thatis selecting theproperbasis sets for Hf4+_{,NandHatomsandcalculationmethodappliedinthe} quan-tummechanicszone.Accordingtotheliterature,DZPbasis sets forHandNatomscouldbeappliedsuccessfullyandhavebeen selected,therefore,alsointhisinvestigation[15,28].TheLANL2DZ ECPbasissetsofHfwithaminormodification(sandpbasis func-tionswiththe smallestexponent have beenremoved to make thebasissetsmorecompatiblewiththeHf4+_{ionratherthanthe}

hafniumatom)wasselectedforHf4+_{,includingtherelativistically}

inordertobecompatiblewithhafnium(IV)ion[29].Thelevelsof theoryforQMregionnamely,Hartree–Fock(HF),MP2,CCSD,and B3LYPwereappliedinenergycalculationusingGaussian09 pro-gram,optimizingthegeometryofHf4+_–NH

3complex.Theresult

showsthatHFcalculatedenergyclosestothemostcorrelatedCCSD

asseeninTable1.Inrecentinvestigationsofalikeionicsystems,

resultsofHFcalculationswereingoodagreementwith experimen-taldata,whereaselectroncorrelationmethodssuchasMP2and CCSDseemedtohavemoreexpensiveandconsumingtime,and eventhecurrenthybridB3LYPfunctionalsometimesprovideapoor resultoratbestresulttakealongcomputationtime[28].Therefore, Hartree–FockmethodwaschosentodescribetheQMpartinthe simulation.

Thetwo-bodyenergies,E2bd,betweenammoniaandHf4+ion wereevaluatedbysubtractingtheabinitio energiesof the iso-latedspeciesE_Hf4+andENH₃ fromthoseofthemonosolvates[30] E_Hf(NH

3)4+

E2bd=E_Hf(NH

3)4+−EHf4+−ENH3 (1)

ThenewpairpotentialofHf4+_–NH

3 systemwasconstructed.

More than 7600 ab initio energy points were generated at Hartree–FocklevelwiththemodifiedLANL2DZECPbasissetsfor Hf4+_{andDZPbasissetsforNandHatomsusingTurbomoleprogram}

[31–33].Thefollowingpairpotentialfunctionwasconstructedand

usedinthesimulation,

E2bd_fit =

q_Hf4+qN

r +

AN

r5 +

BN

r9 + CN

r11+ DN

r12

+

3

i=1

q_Hf4+qH

ri

+AH

r4 +

BH

r5 +

CH

r6 +

DH

r12

(2)

ThefittingparametersofA,B,CandDarelistedinTable2.The q_Hf4+,qNandqHarethechargeofhafnium,nitrogen,and hydro-gen,respectively,andrandriaretheHf4+–NandHf4+–Hdistances,

respectively.Thenetchargesofnitrogenandhydrogenweresetto

−0.8022and0.2674,respectively.Thegeometryofammoniawas

keptconstantthroughoutthewholecalculationatits experimen-talgasphasevalues(N–H=1.0124 ˚A,H–N–H=106.68◦_)[15,16].The

corrected3-bodyenergy(E3bd_corr)wascalculatedasthefollowing formula:

E3bdcorr=

Eab_AMA−E_Mab−2E_Aab

−E2bd_MA(r1)−E2bd_MA(r2)

−E_AA2bd(r3) (3)

whereab,2bddenoteabinitioandpairenergy;MAandAAindicated ion–ammoniaandammonia–ammoniainteractions;r1,r2,andr3

areaccordingtothedistanceofion-ammonia(1),ion–ammonia(2), andammonia(1)–ammonia(2),respectively.Thecorrected3-body energy was generated at Restricted Hartree–Fock (RHF). The obtainedthree-bodycorrectionfunctionwas

E3bd_Fit =0.684e0.447(r1+r2)_e−0.233r3_(CL−r1)2_(CL−r2)2 ₍₄₎

wherer1 andr2 arethedistancesHf4+–N1andHf4+–N2,

respec-tively,andr3isthedistancebetweenN1andN2.TheCLisacutoff

limitsetto6.0 ˚A,afterwhichthree-bodytermsbecomenegligible. TheQM/MMsimulationsystemisdividedintotwoparts,aregion thatincludestheionandthefirstsolvationshell(QM)aretreated byquantum mechanicsandremainingarea(MM)by molecular mechanics.Thesystemforceisdescribedbythefollowingformula

Ftot=F_MMsys +(F_QMQM−F_QMMM)S(r) (5)

whereF_MMsys istheMMforceofthewholesystemandF_QMQMandF_QMMM areQMandMMforcesintheQMregionwhileFtotisthetotalforce

actingonaparticle. Toensureacontinuouschangeofforces, a smoothingfunctionS(r)isappliedbetweentheradiir0andr1:

S(r)=1, forr≤r1

S(r)=

(r2₀−r2)2(r₀2+2r2−3r2₁)

(r₀2−r₁2)3 , forr1<r≤r0 S(r)=0, forr>r0

(6)

FreemigrationofligandsbetweenQMandMMregionispermitted inthisapproach[15–17].

Table2

Theoptimizedparametersoftheanalytical2-bodypotentialfunctionforHf4+_{–ammoniainteraction.}

2-Body AN BN CN DN

(kcal/molA5_{) (kcal/molA}9_{) (kcal/molA}11_{) (kcal/molA}12₎

Hf4+_{–N −13579.1072059 618783.1566433 −2950364.7296899 2609462.3322842}

2-Body AH BH CH DH

(kcal/molA4_{) (kcal/molA}5_{) (kcal/molA}6_{) (kcal/molA}12₎

Table3

ThestructureparametersofthesolvatedHf4+_{inliquidammoniadeterminedbythe}

classicalandQM/MMMDsimulations.

ClassicalMD QM/MMMD Experimentc

r1Hf4+

–Na 2.51 2.38 2.383

r2Hf4+

–Na 5.27 5.31 –

CN1stb _{5.00 5.00 5.00}

CN2ndb _{∼34.70 ∼30.00 –}

N–Hf4+_–Nangle(◦_{) 73.90/146.70 90.00/173.00 –}

a_{FirstandsecondpeakmaximumofHf}4+_–NRDFinÅ. b_{Coordinationnumbersofthefirstandsecondsolvationshell.}

c _{BasedonX-raydiffractionmeasurementofthecrystalofHf(NH3)4F4·NH3.}

2.2. DetailsofQM/MM-MDsimulation

ThesimulationwascarriedoutinthecanonicalNVT ensem-ble,consistingofoneHf4+_ionand215NH

3 moleculesinacubic

boxof20.8 ˚Asidelength,correspondingtothedensityofthe sys-tem0.690g/cm3_{.Thesimulationtemperaturewaskeptconstant}

at235.15K usingtheBerendsen algorithm.The flexible ammo-niamodelincludingintra-andinter-molecularpotentialwasused. Consequently,thetime stepof thesimulationwassetto0.2fs, whichallowsforexplicitmovementofthehydrogen.Acutoffof 10.40 ˚AwassetexceptforN–HandH–Hnon-Coulombic interac-tionswhereitwassetto6.0and5.0 ˚A.Thereactionfieldmethod wasusedtoaccountforlong-rangeelectrostaticinteractions.

Theclassical2-bodypotentialmoleculardynamicssimulation hasbeenperformedfirstfor100psandcontinuedwith2-body+ 3-bodypotentialfor100ps.Then,a90psoftheQM/MMsimulation wascarriedoutfromtheequilibriumconfigurationoftheclassical simulation.ToensurethefullinclusionofthefirstshellintotheQM zonetheradiusoftheQMspherewassetto3.9 ˚Ainaccordancewith theHf4+_{–NRDFobtainedfromtheclassicalsimulation.Theworkof}

theMDsimulationswereperformedinAustrian–Indonesian Cen-ter(AIC)forComputationalChemistry,GadjahMadaUniversity, Yogyakarta,Indonesia.

3. Resultsanddiscussion

3.1. Structure

ThestructureofsolvationofHf4+_{inliquidammoniahasbeen}

obtainedby QM/MMsimulation at theHF level.The structural propertiesareconfirmedonseveralparameterssuchasRadial Dis-tributionFunction(RDF),CoordinationNumberDistribution(CND), AngleDistributionFunction(ADF).Theirparametervaluesobtained fromtheclassicalaswellasQM/MMsimulationarepresentedin

Table3. The Hf4+_{–N and Hf}4+_{–H RDFs aredepicted in Figure1}

thatobtainedbytheQM/MMsimulationatHartree–Focklevel.The maximumpeakofHf4+_{–NRDFislocatedat2.38 ˚Ainthefirstshell}

whilethefirstmaximumpeakinclassical2-body+3-bodypotential simulationsisobservedat2.51 ˚A.TheHf4+_{–Ndistanceof2.38 ˚Ais}

consistentwithexperimentaldata2.383 ˚AobtainedbyKrausetal.

[22].Theprobabilitiesg_Hf4+–_N(r)betweenthefirstandsecondshell equaltozerothatindicatenoligandexchangetooccurbetweenthe twoshellsduringsimulation.Abroadpeaklocatedbetween4.2 and6.4 ˚Awithamaximumat5.31 ˚Aindicatedforhighflexibilityof ammoniamoleculeswithinthisshell.

Coordinationnumber distributionfor solvatedHf4+ _{in liquid}

ammoniaderivedfromtheclassicalandQM/MMsimulationswere displayedinFigure2.AccordingtotheQM/MMsimulation, coor-dinationnumberof5observedinthefirstsolvationshellwitha 100%occurrenceisinagreementwiththeexperimentaldatawhile thecoordination numberof10isobtainedfromtheclassical 2-bodypotentialsimulations.Givingcorrection3-bodyeffecttothe 2-bodypotentialshowedadecreasetothecoordinationnumber5

Figure1. TheradialdistributionfunctionsofHf4+_–NandHf4+_{–Handtheirrunning} integrationnumbersobtainedbyQM/MM-MDsimulation.

withanearly100%occurrence.Thecoordinationnumberin sec-ondshellrangedfrom28to34fortheclassical2-body+3-body potentialand27–33forQM/MM-MDsimulations(average:30.2) whileifonlyusing2-bodypotentialthebroadcoordination num-berdistributionwithahighoccurrenceofabout27wasobtained.As comparison,thesecondsolvationshellcontainsabout30ammonia moleculesinthecaseofsolvationLi+_{inliquidammonia[34].}

Thesolvationstructurecouldbecharacterizedonthebasisof angular distributionfunction. Angular distributionof N–Hf4+_–N

anglesinthefirstsolvationshellwasdepictedinFigure3a.Inthe distributionplotsoftheN–Hf4+_{–Nangles,theobtainedtwopeaks}

bytheclassicalsimulationarelocatedat73.90◦_and146.70◦_.The

changesoftheN–Hf4+_{–Nanglesarefoundafterthemany-body}

Figure3.(a)TheangulardistributionofN–Hf4+_{–Nanglesuptothefirstminimum} oftheHf4+_{–NRDFs,(b)distortedsquarepyramidalstructureofthesolvationofHf}4+ inliquidammonia(snapshottakenbyTmolex).

correctionshavebeenincluded.Asharppeakwasobservedat90◦

whilethebroadpeakappearedat173◦_{andaminimumoccurring}

at150◦_{.Theexistenceofthefirstpeakat90}◦_{withahighprobability}

andthesecondpeakat173◦_(almost180◦_{)indicatedthestructureof}

Figure4.Noammonialigandsmigrationbetweenfirstandsecondsolvationshell areobserved.Theammonialigandexchangesareobservedbetweensecond solva-tionshellandbulk.

Table4

Meanligandresidencetimes(MRT),inps,numberofaccountedexchangeevents (Nex)obtainedbydirectmethodasafunctionoft*,andsustainabilitycoefficient

(Sex).

tsim t*=0ps t*=0.5ps Sex 1/Sex

ps N0ex Nex0.5

Secondshell 90 1398 1.943 533 5.096 0.381 2.625

Hf(NH3)54+complextendstoasquarepyramidalstructurewiththe Hf4+_{ionliftedabovetheaveragenitrogenplane(Figure3b)whereas} foranidealsquarepyramidalstructurehas90◦_and180◦_.As

com-parison,structureofsolidcopper(II)complexwithammoniahas beenreported,includingcoordinationoffour(squareplanar)and five(squarepyramidal)nitrogensandsix(distortedsquare bipyra-midal)nitrogens[2,35]whileforNa(NH3)5+couldbeassignedto

twomainstructures,namelyatrigonalbipyramidalandasquare pyramidal[36].

3.2. Dynamics

Ligandexchangeofammoniabetweenthefirstandsecondshell isnotobservedfor90pssimulationasdisplayedinFigure4,while theligandexchangesareoccurredbetweenligandsinthesecond solvationshellandbulk.Ultrafastligandexchangeisimportantto indicatethereactivityof Hf4+ _{ion.It ispossibletomeasurethe}

numberofexchangeeventsleadingtoalonger-lastingchangein thesolvation structure bycomparingthe number ofaccounted exchangeeventswitht*=0.5ps

Nex0.5

andt*=0ps

N0ex

,defining

asustainabilitycoefficient:

Sex= N

0.5 ex

Nex0

(7)

Itsinverse(1/Sex)accountshowmanyborder-crossingattemptsare

neededtoproduceonelonger-lastingchangeinthesolvation struc-tureofanindividualion[21,37].Somedynamicpropertiessuchas thenumberofligandexchange,meanligandresidencetime(MRT), andthesustainabilityofthemigrationprocessarelistedinTable4. Themeanligandresidencetimeinthesecondsolvationshellof Hf4+_{was5.096ps.Incontrast,theMRTinthesecondshellis}

sig-nificantlysmallerthaninwater(0.5ps=15.5ps)[19],indicatingfor anincreasedliabilityofthesecondshellinthecaseofammonia.On theotherhand,thesustainabilitycoefficientSexofligandmigration

hasavalueof0.381,thecorresponding1/Sexis2.625,whichmeans

thatlessthanthreeattemptstoleaveorenterthesecondsolvation shellareneeded,toachieveoneexchangeprocess,whichlastsat least0.5ps.

4. Conclusion

ThesimulationHf4+_{ioninliquidammoniahasbeenperformed}

successfully by the QM/MM method. The QM/MM simulation resultsindicatedthatthestructureofthefirstsolvationshell con-sistsoffiveammoniamoleculestendstoformasquarepyramidal structure.TheHf4+_{–Ndistanceof2.38 ˚Aisinaccordancewiththe}

experimentalX-raydiffractiondata.Thereisnoligandexchange betweenthesecondshellandthefirstshellduringthesimulation of90ps.Theresidencetimeoftheligandinthesecondsolvation shellis5.096ps.Thisvalueissmallerthaninwater,indicatinga highflexibilityofthesecondshellinthecaseofammonia.

Acknowledgements

Indonesiawhereasthesoftwareandhardwareweresupportedby theAustrian–Indonesian Center(AIC)for Computational Chem-istry,GadjahMadaUniversityaregratefullyacknowledged.

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