A Molecular Dynamics study of propane phase diagram on a parallel platform

ALESSANDROCOSTANTINI

DepartmentofChemistry,UniversityofPerugia

1.Introduction

Theaimofmoleculardynamicsistoperformmolecularbasedsimulationsofcomplexsystemstoreproducetheirproperties.Theincreasingavailabilityofcomput-ingpowerondistributedplatformsismakingitthisincreasinglymorefeasible.DuringmyworkasagrantholderoftheHPC-EuropaprojectIcarriedoutamoleculardynamicssimulationofPropaneinliquidandgasphaseinordertoestimateinapriorifashionsomethermodynamicspropertiesofthesystemandtobuildtherelatedphasediagram.Todothis,twodifferentforcefieldswereused:

a)OPLS/AMBERall-atomspotential[1];b)theatom-bondpotential[2,3]

2.TheOPLS/AMBERall-atomsforcefield

IntheOPLS/AMBERforcefield[1]thenonbondedinteractionsarerepresentedbyaLennard-JonesplusCoulombterms:

4235

612mol:amol:b2󰀁󰀁ssqiqjeijij

VOPLS󰀁󰀄1󰀅󰀂4eij12À6fij

rrrijijijijwhereqiandqjarethechargesofatomiandjrespectively,eisthechargeofthe

electron,eij,sijandrijarethedepth,theequilibriumandtheactualdistancerespectivelyoftheijdiatom.Ineq.1fijisequalto1forallijinteractions.Thesameexpressionisusedforintramolecularnonbondedinteractionsbetweenallpairsofatomsseparatedbythreeormorebonds.Theintermolecularinteractionsforbending(eq.2)andtorsional(eq.3)motionsarerepresentedas

󰀁

󰀄2󰀅Ku󰀄uÀueq󰀅2Vangle󰀁

angle

󰀄3󰀅Vdihedral

whereuisthebendingangle,ueqisitsequilibriumvalue(thatcorrespondsto109:5󰀆forC-C-C,C-C-HandH-C-H),fiisthedihedralangleandV1,V2andV3arethecoefficients

iÂiÂ󰀁ViÂÀÁÃV2ÀÁÃV3ÀÁÃ11󰀂cosfi󰀂1󰀂cos2fi󰀂1󰀂cos3fi󰀁

222i

AMOLECULARDYNAMICSSTUDYOFPROPANEPHASEDIAGRAMONAPARALLELETC.

55oftheFourierseries.InthepresentsystemallthebondlengthshavebeensetconstantandthetotalpotentialenergyVofthesystemisgivenas󰀄4󰀅

V󰀁VOPLS󰀂Vangle󰀂Vdihedral

3.TheAtom-Bondformulation

Thealternativeformulationoftheatom-bondinteraction[3]makesuseofthebondpolarizabilityadditivitytoreproducetheintermolecularrepulsionandattractioncomponentsasfollows󰀄5󰀅where

V󰀁

atom󰀁󰀁bondi

j

ÀÁ

Vijrij;wij

ÀÁ󰀋nij󰀄rij;wij󰀅Q󰀊

ÀÁÀÁr0ijwijmSÀÁVrij;wij󰀁eijwijRÀrijnijrij;wijÀm

ÀÁ󰀊ÀÁ󰀋m5

nijrij;wijr0ijwijÀÁ󰀂

rijnijrij;wijÀm4

P

󰀄6󰀅

Inequations5and6theindicesiandjhaveadifferentmeaningfromthatoftheall

atomsformulationsbecausetheindexiindicatestheatomwhileindexjindicatesthebond.Therefore,ineq.5and6,rijisthedistancebetweentheatomiandthedispersioncenterofthebondj,wijistheplanaranglethatrijformswiththejbondaxis,r0ijistheequilibriumvalueofrijandeijisthevalueoftheenergyassociatedwiththeijatom-bondatr0ij.Ineq.6mistakenforanyneutral-neutralsystemequalto6andÀinteractionÁ

nijrij;wijiscalculatedusingthefollowingequation:

232

ÀÁrij

ÀÁnijrij;wij󰀁b󰀂4:0󰀄7󰀅

r0ijwijwithbbeingaconstantparameterwithinabroadclassofsystemswhichcharacterizesthenatureandthehardnessofÀtheÁinteractingÀÁparticles(inourcaseb󰀁10).Theangulardependenceofbothr0ijwijandeijwijisusuallyparametrizedintermsofparallel󰀄k󰀅andperpendicular󰀄c󰀅contributionsasfollows

ÀÁÀÁÀÁeijwij󰀁ecijsin2wij󰀂ekijcos2wij󰀄8󰀅󰀄9󰀅

ÀÁÀÁÀÁr0ijwij󰀁r0cijsin2wij󰀂r0kijcos2wij

wherer0cij,r0kij,ecijandekijrepresentthewelllocationanddepthforperpendicularandparallelapproachesrespectively.InthepresentsystemthemoleculesofPropanehavebeenconstrainedtoberigidattheirequilibriumgeometry.

56ALESSANDROCOSTANTINI

TABLE1±PropertiesofthePropanesystemcalculatedonIntelXEONmachine.

OPLS/AMBER

Phaseliquidgasliquidgas

MoleculesTemperature

/K

886464

200288200288

Pressure/bar252.37.61.03Atom-Bond

Phaseliquidgasliquidgas

MoleculesTemperature

/K

886464

200288200288

Pressure/bar2.42.71.31.05

Density/kgmÀ36.052.9133.95.29

Simulationtime/ps

50505050

Elapsedtime/s4424553103536554

Density/kgmÀ36803.666382.72

Simulationtime/ps

50505050

Elapsedtime/s58320963043772

4.Resourcesusedandresults

ThecalculationswereperformedusingtheDL_POLY[4]softwarepackageontwodifferentmachines:

󰀉aoneprocessorIntelXEONmachineattheSchoolofChemistry,EdinburghUniversity;

󰀉theIBMBlue_Gene/Lcluster(1064nodes,4.7Tflops)attheEdinburghParallelComputerCenter(EPCC),EdinburghUniversity.

Allthecalculationswerecarriedoutusingthesamestatisticalensemble(npt)attwodifferenttemperatures(200Kand288K)inordertosimulateboththeliquidandthegasphaseoutofequilibrium.TheIntelXEONmachinewasusedtoobtainapreliminaryindicationonthesuitabilityoftheadoptedpotentialstodescribetheinteractionofthesystem.TheresultsobtainedareshowninTable1.

TABLE2±PropertiesofPropanesystemandelapsedtimecalculatedonIBMBlue_Gene/Lmachine

OPLS/AMBERpotential

Phaseliquidgasliquidgas

Molecules512512512512

Nodes3232128128

TemperaturePressure

/K/bar

200288200288

1.271.011.221.02

DensitySimulationElapsed/kgmÀ3time/pstime/s5732.695743.11

5010050100

1220915957853216490

AMOLECULARDYNAMICSSTUDYOFPROPANEPHASEDIAGRAMONAPARALLELETC.

57Asshownbythetabletheatom-bondformulationoftheinteractionseemstobe,ontheaverage,lessefficientthantheOPLS/AMBERone.Moreover,italsoseemstobelessappropriatetoreproducetheexperimentaldensitydatareportedintheliterature(respectively582KgmÀ3and1:92KgmÀ3fortheliquidatT󰀁230KandthegasatT󰀁288KatP󰀁1atm)[5].Toimprovethequalityofthesimulationwehaveincreasedthenumberofmoleculesofthesystemandcarriedoutanewbatchofcalculationsfor512moleculesusingtheOPLS/AMBERpotentialandimplementingDL_POLYontheBlue_Gene/Lmachine.ResultsobtainedbyrunningDL_POLYinparallelon32and128nodesfor512moleculesareshowninTable2.

5.Conclusion

TheHPC-Europaprogrammegavemethepossibilityofincreasingmycommandofdistributedcomputingtechniquesandallowedmetoperformmoleculardynamicscalculationsforrealisticsystem.TheuseofaonenodeIntelXEONallowedmetocomparetheaccuracyandtheefficiencyofthetwoforcefieldsproposedforthestudyofpropanebulksystembyconsideringasmallnumberofmolecules.ThemassivebyparallelcalculationsperformedontheBlue_Gene/LIBMclusterallowedme,instead,tostudyalargeensambleofPropanemoleculesandinvestigateitsthermodynamicsproperties.Inourcalculationsfoundthatwhenthenumberofmoleculesincreases,thecalculatedvalueofthedensityofthesystemgetsclosertothedatagivenintheliteratureespeciallywhenusingtheOPLS/AMBERformulationoftheinteraction.However,itwasratherdisappointingtomeasurelowspeedupfortheparallelcalculationsatanincreasingnumberofprocessors.Anincrease,infact,ofthenumberofprocessorsofafactorof4(from32to128)leadstoareductionoftheelapsedtimeofthecalculationsofonlyafactor1/3.PossiblewayoutofthisproblemcouldbetheuseofadifferentparallelizationmodelforDL_POLYandthedevelopmentofagridbasedapproach.

Acknowledgements.ThisworkwascarriedoutundertheHPC-EUROPAproject(RII3-CT-2003-506079),withthesupportoftheEuropeanCommunity±ResearchInfrastructureActionundertheFP6StructuringtheEuropeanResearchAreaProgramme.

Publications

[1][2]

ÁandF.PIRANI,``ParallelcalculationofPropanebulkproperties''A.COSTANTINI,A.LAGANA

LectureNotesinComputerScience,2006,inpress.

Á,F.PIRANI,A.MARISandW.CAMINATI,``AbinitioandEmpiricalAtomA.COSTANTINI,A.LAGANA

BondFormulationoftheinteractionoftheDimethylether-ArSystem'',LectureNotesinComputerScience,(2005),3480,1046.

58[3]

ALESSANDROCOSTANTINI

``Simulationsofmoleculardynamicsofspectroscopicpropertiesofsimpleorganicsystems'',abstractofthe34thNationalCongressofChemicalPhysics,Siena,Italy,2005.

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