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1、JOURNALOFCOMPUTATIONAL.PHYSICS23,321-341(1977)NumericalintegrationoftheCartesianEquationsofMotionofaSystemwithConstraints:MolecularDynamicsofn-AlkanesJEAN-PAULRYCKAERT*,GIOVANNICICCOTTI+,ANDHERMANJ.C.BERENDSEN*CentreEuroptendeCalculAtomiqueetMolhxlaire(CECAM),Bhtiment506,U
2、mbersitdeParisXI,91405Orsay,FranceReceivedJuly19,1976Anumericalalgorithmintegratingthe3NCartesianequationsofmotionofasystemofNpointssubjecttoholonomicconstraintsisformulated.Therelationsofconstraintremainperfectlyfulfilledateachstepofthetrajectorydespitetheapproximatechara
3、cterofnumeric-alintegration.Themethodisappliedtoamoleculardynamicssimulationofaliquidof64n-butanemoleculesandcomparedtoasimulationusinggeneralizedcoordinates.Themethodshouldbeusefulformoleculardynamicscalculationsonlargemoleculeswithinternaldegreesoffreedom.1.INTR~D~JCTI~N
4、Themethodofmoleculardynamics(MD),whichhasbeenwidelyusedinthepastforstudyingsimpleliquidsandsolids,hasmorerecentlybeenappliedtomolecularsystemswithinternaldegreesoffreedomsuchasN,[l],H,O[2]andevenC,H,,[3].InapplyingtheMDmethodthreeproblemsarise:(a)thechoiceofasuitablemechan
5、i-calmodel,(b)thederivationoftheequationsofmotionofthesystemand(c)thechoiceofanefficientalgorithmforthenumericalintegrationoftheseequations.Inpolyatomicmolecules,thefastinternalvibrationsareusuallydecoupledfromrotationalandtranslationalmotionsandcanthereforebefrozenbyintro
6、ducingacertainnumberofrigidbondsandanglesintheskeletonofthemolecule.Forexample,Nzbecomesarod,H,OarigidtriangleandC4H,,anonrigidsolidwithoneinternalrotation[l,2,31.Theclassicalwaytotreatsuchsystemsisintermsofgeneralizedcoordinates(Lagrange-Hamiltonformalism),butasthenumbero
7、finternaldegreesoffreedomincreasesitrapidlybecomeshardertowritedownexplicitlytheappropriateequationsofmotion.*Fact&desSciences,UniversiteLibredeBruxelles,Brussels,Belgium.+GruppoNazionalediStrutturadellaMateria,ConsiglioNazionaledelleRicerche,andIstitutodiFisicaG.Marconi,U
8、niversitadiRoma,Roma,Italy.*LaboratoryofPhysicalChemistry,TheUniversityofGroningen,Zemike
