Basic molecular dynamics

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1、2.8BASICMOLECULARDYNAMICSJuLiDepartmentofMaterialsScienceandEngineering,OhioStateUniversity,Columbus,OH,USAAworkingdefinitionofmoleculardynamics(MD)simulationistechniquebywhichonegeneratestheatomictrajectoriesofasystemofNparticlesbynumericalintegrationofNewton’seq

2、uationofmotion,foraspecificinteratomicpotential,withcertaininitialcondition(IC)andboundarycondition(BC).Consider,forexample(seeFig.1),asystemwithNatomsinavolume
.Wecandefineitsinternalenergy:E≡K+U,whereKisthekineticenergy,
N1K≡m

3、x˙(t)

4、2,(1)ii2i=1andUisthepotentiale

5、nergy,3NU=U(x(t)).(2)x3N(t)denotesthecollectiveof3Dcoordinatesx(t),x(t),...,x(t).12NNotethatEshouldbeaconservedquantity,i.e.,aconstantoftime,ifthesystemistrulyisolated.OnecanoftentreataMDsimulationlikeanexperiment.BelowisacommonflowchartofanordinaryMDrun:[systemse

6、tup][equilibration][simulationrun][output]sampleselection→samplepreparation→propertyaverage→dataanalysis(pot.,N,IC,BC)(achieveT,P)(runLsteps)(propertycalc.)inwhichwefine-tunethesystemuntilitreachesthedesiredcondition(here,temperatureTandpressureP),andthenperformpr

7、opertyaverages,forinstancecalculatingtheradialdistributionfunctiong(r)[1]orthermalcon-ductivity[2].Onemayalsoperformanon-equilibriumMDcalculation,duringwhichthesystemissubjectedtoperturbationalorlargeexternaldrivingforces,565S.Yip(ed.),HandbookofMaterialsModeling

8、,565–588.c2005Springer.PrintedintheNetherlands.566J.LiNparticlesxi(t)zyxFigure1.IllustrationoftheMDsimulationsystem.andweanalyzeitsnon-equilibriumresponse,suchasinmanymechanicaldeformationsimulations.TherearefivekeyingredientstoaMDsimulation,whichareboundarycondi

9、tion,initialcondition,forcecalculation,integrator/ensemble,andprop-ertycalculation.Abriefoverviewofthemisgivenbelow,followedbymorespecificdiscussions.Boundarycondition.Therearetwomajortypesofboundaryconditions:isolatedboundarycondition(IBC)andperiodicboundarycondi

10、tion(PBC).IBCisideallysuitedforstudyingclustersandmolecules,whilePBCissuitedforstudyingbulkliquidsandsolids.Therecouldalsobemixedboundarycon-ditionssuchasslabo