演示文稿周期性邊界條件

優(yōu)質(zhì)文檔精選周期性邊界條件目前一頁\總數(shù)二十六頁\編于十六點AnalysisofthePotentialEnergyExternalpotentialPairpotentialabout90%ThreebodycontributionInFCCcrystal,upto10%Effectivepairpotential目前二頁\總數(shù)二十六頁\編于十六點1.7.1EffectivepairpotentialforsphericalmoleculesHard-spherepotentialForthepurposesofinvestigatinggeneralpropertiesofliquidsandforcomparisonwiththeory,highlyidealizedpairpotentialsmaybeofvalue.Inthissection,Iwillintroducehard-sphere,square-well,YukawaandLennard-Jonespotentials,etc.isthediameterofhardspheres目前三頁\總數(shù)二十六頁\編于十六點Square-WellpotentialSWpotentialisthesimplestoneincludingtheattractiveforcesandcanbeappliedtoinertgasesandsomenon-polarsubstances,etc.目前四頁\總數(shù)二十六頁\編于十六點YukawapotentialWhen,itcanbeusedtomodelArreasonablywell.Yukwapotentialcanalsobeusedtomodelplasma,colloidalparticles,andsomeelectricalinteractions.目前五頁\總數(shù)二十六頁\編于十六點Lennard-JonespotentialForargon:目前六頁\總數(shù)二十六頁\編于十六點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目前七頁\總數(shù)二十六頁\編于十六點PotentialsforionsAsimpleapproachtoconstructpotentialsforionsistosupplementoneoftheabovepairpotentialswiththeCoulombcharge-chargeinteraction:WhereXmaybeHS,SW,LJ.Thepopularoneis:目前八頁\總數(shù)二十六頁\編于十六點1.7.2potentialformacromoleculesTheenergy,V,isafunctionoftheatomicpositions,R,ofalltheatomsinthesystem,theseareusuallyexpressedintermofCartesiancoordinates.Thevalueoftheenergyiscalculatedasasumofinternal,orbondedterms,whichdescribethebonds,anglesandbondrotationsinamolecule,andasumofexternalornonbondedterms.Thesetermsaccountforinteractionsbetweennonbondedatomsoratomsseparatedby3ormorecovalentbonds.目前九頁\總數(shù)二十六頁\編于十六點BondedpotentialBondangle-bendBond-strentchTorsion(rotate-along-bond)目前十頁\總數(shù)二十六頁\編于十六點Angle-bendpotentialThedeviationofanglesfromtheirreferencevaluesisfrequentlydescribedusingaHooke’slaworharmonicpotential:目前十一頁\總數(shù)二十六頁\編于十六點Bond-stretchpotential目前十二頁\總數(shù)二十六頁\編于十六點TorsionpotentialTorsionalpotentialsarealmostalwaysexpressedasacosineseriesexpansion.‘barrier’heightDetermineswherethetorsionanglepassesthroughitsminimumvalue.Thenumberofminimumpointsinthefunctionasthebondisrotatedthrough2.目前十三頁\總數(shù)二十六頁\編于十六點1.8ReducedUnitsWhyusereducedunit?Avoidsthepossibleembarrassmentofconductingessentiallyduplicatesimulations.Andtherearealsotechnicaladvantagesintheuseofreducedunitsduetothesimulationboxisinthemagnitudeofmolecularscale.Density

Temperature

Energy

Pressure

Force

Torque

SurfacetensionTime目前十四頁\總數(shù)二十六頁\編于十六點Reducedunit----continueDiffusioncoefficient

ViscosityThermalconductivitySIUnits:W/(mK)Pasm2/sTestofunit(Forexample,viscosity):目前十五頁\總數(shù)二十六頁\編于十六點Reducedunit----continueItshouldbepointedthatallthereducedunitsintheprevioustwoslidesarebasedonLennard-Jonesinteractionpotential.Forhardspherefluid,thereducedunitsareobtainedusingkBTtoreplace.Thereducedunitsforotherpropertiessuchaschemicalpotentialandheatcapacitycanbededucedfromtheunitsgiveninthissection.Especially,forelectrolytesolution,wecanuseSurfacechargedensity:目前十六頁\總數(shù)二十六頁\編于十六點1.9SimulationBoxandItsBoundaryConditionsComputersimulationsareusuallyperformedonasmallnumberofmolecules,10<N<10,000.ThetimetakenforadoubleloopusedtoevaluatetheforcesandpotentialenergyisproportionaltoN2.Whetherornotthecubeissurroundedbyacontainingwall,moleculesonthesurfacewillexperiencequitedifferentforcesfrommoleculesinthebulk.Itisessentialtoproposepropermethodstoovercometheproblemofsurfaceeffects.目前十七頁\總數(shù)二十六頁\編于十六點1.9.1SimulationboxxyzCubeHexagonalprismxyzExample:DNAsimulation目前十八頁\總數(shù)二十六頁\編于十六點1.9.1Simulationbox---continueTruncatedoctahedronRhombicdodecahedron目前十九頁\總數(shù)二十六頁\編于十六點1.9.2PeriodicboundaryconditionBAHDGFEC目前二十頁\總數(shù)二十六頁\編于十六點BAHDGFECInacubicbox,thecutoffdistanceissetequaltoL/2.

Minimumimageconvention目前二十一頁\總數(shù)二十六頁\編于十六點AEAsideviewofthebox(b)AtopviewoftheboxBDCAEHFGSimulationofmoleculesinslit-likepore目前二十二頁\總數(shù)二十六頁\編于十六點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目前二十三頁\總數(shù)二十六頁\編于十六點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.目前二十四頁\總數(shù)二十六頁\編于十六點1.9.4ComputercodeforminimumimageconventionImmediatelyaftercalculating