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1、1.7ModelSystemandInteractionPotentialInmostofthiscourse,themicroscopicofasystemmaybespecifiedintermsofthepositionandmomentaofaconstituentsetofparticles.Inthiscasetherapidmotionoftheelectronshavebeenaveragedout.HamiltonianKineticenergyPotentialenergyAnalysisofthePotentialEnergyExternalpotentialPai
2、rpotentialabout90%ThreebodycontributionInFCCcrystal,upto10%Effectivepairpotential1.7.1Effectivepairpotentialforsphericalmolecules1.7.1.1Hard-spherepotentialForthepurposesofinvestigatinggeneralpropertiesofliquidsandforcomparisonwiththeory,highlyidealizedpairpotentialsmaybeofvalue.Inthissection,Iwi
3、llintroducehard-sphere,square-well,YukawaandLennard-Jonespotentials,etc.isthediameterofhardspheres1.7.1.2Square-WellpotentialSWpotentialisthesimplestoneincludingtheattractiveforcesandcanbeappliedtoinertgasesandsomenon-polarsubstances,etc.1.7.1.3YukawapotentialWhen,itcanbeusedtomodelArreasonablywe
4、ll.Yukwapotentialcanalsobeusedtomodelplasma,colloidalparticles,andsomeelectricalinteractions.1.7.1.4Lennard-JonespotentialForargon:CodesforcalculatingthetotalpotentialV=0.0DO100I=1,N-1RXI=RX(I)RYI=RY(I)RZI=RZ(I)DO100J=I+1,NRXIJ=RXI-RX(J)RYIJ=RYI-RY(J)RZIJ=RZI-RZ(J)RIJSQ=RXIJ**2+RYIJ**2+RZIJ**2SR2
5、=SIGSQ/RIJSQSR6=SR2*SR2*SR2SR12=SR6**2V=V+SR12-SR6100CONTINUEV=V*4.0*EPSLONThecoordinatevectorsofLJatomsarestoredinthreearraysRX(I),RY(I),RZ(I)Calculate1.7.1.5PotentialsforionsAsimpleapproachtoconstructpotentialsforionsistosupplementoneoftheabovepairpotentialswiththeCoulombcharge-chargeinteractio
6、n:WhereXmaybeHS,SW,LJ.Thepopularoneis:1.7.2potentialformacromoleculesTheenergy,V,isafunctionoftheatomicpositions,R,ofalltheatomsinthesystem,theseareusuallyexpressedintermofCartesiancoordinates.Thevalueoftheenergyiscalculatedasasumofinternal,orbondedterms,whichdescribethebonds,anglesandbondrotatio
7、nsinamolecule,andasumofexternalornonbondedterms.Thesetermsaccountforinteractionsbetweennonbondedatomsoratomsseparatedby3ormorecovalentbonds.BondedpotentialBondangle-bendBond-strentchTorsion(rotate-along-bond)Angle-bend
