演示文稿周期性邊界條件

優(yōu)質文檔精選周期性邊界條件當前1頁，總共26頁。AnalysisofthePotentialEnergyExternalpotentialPairpotentialabout90%ThreebodycontributionInFCCcrystal,upto10%Effectivepairpotential當前2頁，總共26頁。1.7.1EffectivepairpotentialforsphericalmoleculesHard-spherepotentialForthepurposesofinvestigatinggeneralpropertiesofliquidsandforcomparisonwiththeory,highlyidealizedpairpotentialsmaybeofvalue.Inthissection,Iwillintroducehard-sphere,square-well,YukawaandLennard-Jonespotentials,etc.isthediameterofhardspheres當前3頁，總共26頁。Square-WellpotentialSWpotentialisthesimplestoneincludingtheattractiveforcesandcanbeappliedtoinertgasesandsomenon-polarsubstances,etc.當前4頁，總共26頁。YukawapotentialWhen,itcanbeusedtomodelArreasonablywell.Yukwapotentialcanalsobeusedtomodelplasma,colloidalparticles,andsomeelectricalinteractions.當前5頁，總共26頁。Lennard-JonespotentialForargon:當前6頁，總共26頁。CodesforcalculatingthetotalpotentialV=0.0DO100I=1,N-1RXI=RX(I)RYI=RY(I)RZI=RZ(I) DO100J=I+1,N RXIJ=RXI-RX(J) RYIJ=RYI-RY(J) RZIJ=RZI-RZ(J) RIJSQ=RXIJ**2+RYIJ**2+RZIJ**2 SR2=SIGSQ/RIJSQ SR6=SR2*SR2*SR2 SR12=SR6**2 V=V+SR12-SR6100CONTINUEV=V*4.0*EPSLONThecoordinatevectorsofLJatomsarestoredinthreearraysRX(I),RY(I),RZ(I)Calculate當前7頁，總共26頁。PotentialsforionsAsimpleapproachtoconstructpotentialsforionsistosupplementoneoftheabovepairpotentialswiththeCoulombcharge-chargeinteraction:WhereXmaybeHS,SW,LJ.Thepopularoneis:當前8頁，總共26頁。1.7.2potentialformacromoleculesTheenergy,V,isafunctionoftheatomicpositions,R,ofalltheatomsinthesystem,theseareusuallyexpressedintermofCartesiancoordinates.Thevalueoftheenergyiscalculatedasasumofinternal,orbondedterms,whichdescribethebonds,anglesandbondrotationsinamolecule,andasumofexternalornonbondedterms.Thesetermsaccountforinteractionsbetweennonbondedatomsoratomsseparatedby3ormorecovalentbonds.當前9頁，總共26頁。BondedpotentialBondangle-bendBond-strentchTorsion(rotate-along-bond)當前10頁，總共26頁。Angle-bendpotentialThedeviationofanglesfromtheirreferencevaluesisfrequentlydescribedusingaHooke’slaworharmonicpotential:當前11頁，總共26頁。Bond-stretchpotential當前12頁，總共26頁。TorsionpotentialTorsionalpotentialsarealmostalwaysexpressedasacosineseriesexpansion.‘barrier’heightDetermineswherethetorsionanglepassesthroughitsminimumvalue.Thenumberofminimumpointsinthefunctionasthebondisrotatedthrough2.當前13頁，總共26頁。1.8ReducedUnitsWhyusereducedunit?Avoidsthepossibleembarrassmentofconductingessentiallyduplicatesimulations.Andtherearealsotechnicaladvantagesintheuseofreducedunitsduetothesimulationboxisinthemagnitudeofmolecularscale.Density

Temperature

Energy

Pressure

Force

Torque

SurfacetensionTime當前14頁，總共26頁。Reducedunit----continueDiffusioncoefficient

ViscosityThermalconductivitySIUnits:W/(mK)Pasm2/sTestofunit(Forexample,viscosity):當前15頁，總共26頁。Reducedunit----continueItshouldbepointedthatallthereducedunitsintheprevioustwoslidesarebasedonLennard-Jonesinteractionpotential.Forhardspherefluid,thereducedunitsareobtainedusingkBTtoreplace.Thereducedunitsforotherpropertiessuchaschemicalpotentialandheatcapacitycanbededucedfromtheunitsgiveninthissection.Especially,forelectrolytesolution,wecanuseSurfacechargedensity:當前16頁，總共26頁。1.9SimulationBoxandItsBoundaryConditionsComputersimulationsareusuallyperformedonasmallnumberofmolecules,10<N<10,000.ThetimetakenforadoubleloopusedtoevaluatetheforcesandpotentialenergyisproportionaltoN2.Whetherornotthecubeissurroundedbyacontainingwall,moleculesonthesurfacewillexperiencequitedifferentforcesfrommoleculesinthebulk.Itisessentialtoproposepropermethodstoovercometheproblemofsurfaceeffects.當前17頁，總共26頁。1.9.1SimulationboxxyzCubeHexagonalprismxyzExample:DNAsimulation當前18頁，總共26頁。1.9.1Simulationbox---continueTruncatedoctahedronRhombicdodecahedron當前19頁，總共26頁。1.9.2PeriodicboundaryconditionBAHDGFEC當前20頁，總共26頁。BAHDGFECInacubicbox,thecutoffdistanceissetequaltoL/2.

Minimumimageconvention當前21頁，總共26頁。AEAsideviewofthebox(b)AtopviewoftheboxBDCAEHFGSimulationofmoleculesinslit-likepore當前22頁，總共26頁。1.9.3ComputercodeforperiodicboundariesHowdowehandleperiodicboundariesandtheminimumimageconventioninasimulationprogram?Letusassume,initially,theNmoleculesinthesimulationliewithacubicboxofsideBOXL,withtheoriginatitscenter,i.e.,allcoordinatelieintherange(-BOXL/2,BOXL/2).Afterthemoleculeshavebeenmoved,wemusttestthepositionimmediatelyusingaFORTRANIF

statement.IF(RX(I).GT.BOXL2)RX(I)=RX(I)-BOXLIF(RX(I).LT.-BOXL2)RX(I)=RX(I)+BOXL當前23頁，總共26頁。AnalternativecodeforperiodicboundariesAnalternativetotheIFstatementistouseFORTRANarithmetic

functions:RX(I)=RX(I)-BOXL*ANINT(RX(I)/BOXL)ThefunctionANINT(X)returnsthenearestintegertoX,convertingtheresultsbacktotypeREAL.Forexample,ANINT(-0.49)=0;ANINT(-0.55)=-1

ThefunctionANINT(X)isdifferentfromAINT(X).AINT(X)returnstheintegralpartofX.TheuseofIFstatementinsidetheinnerloop,particularlyonpipelinemachines,istobeavoided.當前24頁，總共26頁。1.9.4ComputercodeforminimumimageconventionImmediatelyaftercalculatinga