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1、BasicsofmoleculardynamicsEquationsofmotionforMDsimulationsTheclassicalMDsimulationsboildowntonumericallyintegratingNewton’sequationsofmotionfortheparticlesLennard-JonespotentialOneofthemostfamouspairpotentialsforvanderWaalssystemsistheLennard-Jonespoten
2、tialLennard-JonesPotentialDimensionlessUnitsAdvantagesofusingdimensionlessunits:thepossibilitytoworkwithnumericalvaluesoftheorderofunity,insteadofthetypicallyverysmallvaluesassociatedwiththeatomicscalethesimplificationoftheequationsofmotion,duetotheabso
3、rptionoftheparametersdefiningthemodelintotheunitsthepossibilityofscalingtheresultsforawholeclassofsystemsdescribedbythesamemodel.DimensionlessunitsWhenusingLennard-Jonespotentialsinsimulations,themostappropriatesystemofunitsadoptsσ,mandεasunitsoflength,
4、massandenergy,respectively,andimpliesmakingthereplacements:IntegrationoftheNewtonianEquationClassesofMDintegrators:low-ordermethods–leapfrog,Verlet,velocityVerlet–easyimplementation,stabilitypredictor-correctormethods–highaccuracyforlargetime-stepsBound
5、aryConditionInitialstateAtomsareplacedinaBCC,FCCorDiamondlatticestructureVelocitiesarerandomlyassignedtotheatoms.Toachievefasterequilibrationatomscanbeassignedvelocitieswiththeexpectedequilibriumvelocity,i.e.Maxwelldistribution.Temperatureadjustment:Bri
6、ngingthesystemtorequiredaveragetemperaturerequiresvelocityrescaling.Gradualenergydriftdependsondifferentfactors-integrationmethod,potentialfunction,valueoftimestepandambienttemperature.ConservationLawsMomentumandenergyaretobeconservedthroughoutthesimula
7、tionperiodMomentumconservationisintrinsictothealgorithmandboundaryconditionEnergyconservationissensitivetothechoiceofintegrationmethodandsizeofthetimestepAngularmomentumconservationisnottakenintoaccountEquilibrationForsmallsystemswhosepropertyfluctuatec
8、onsiderably,characterizingequilibriumbecomesdifficultAveragingoveraseriesoftimestepsreducesthefluctuation,butdifferentquantitiesrelaxtotheirequilibriumaveragesatdifferentratesAsimplemeasureofequilibrationistherateatwhichtheveloci
