(1988)JPC_Kosloff_Time-Dependent Quantum-Mechanical Methods for Molecular Dynamics

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1、J.Phys.Chem.1988,92,2087-21002087FEATUREARTICLETime-DependentQuantum-MechanicalMethodsforMolecularDynamicsRonnieKosloffDepartmentofPhysicalChemistryandTheFritzHaberResearchCenterforMolecularDynamics,TheHebrewUniversity,Jerusalem91904,Israel(Received:December7,1987)Thebasicframework

2、oftime-dependentquantum-mechanicalmethodsformoleculardynamicscalculationsisdescribed.Thecentralproblemaddressedbycomputationalmethodsisadiscreterepresentationofphasespace.Inclassicalmechanics,phasespaceisrepresentedbyasetofpointswhereasinquantummechanicsitisrepresentedbyadiscreteHi

3、lbertspace.Thediscretizationdescribedinthispaperisbasedoncollocation.Specialcasesofthismethodincludethediscretevariablerepresentation(DVR)andtheFouriermethod.TheFouriermethodisabletorepresentasysteminphasespacewiththeefficiencyofonesamplingpointperunitvolumeinphasespaceh,sothat,wit

4、htheproperchoiceoftheinitialwavefunction,exponentialconvergenceisobtainedinrelationtothenumberofsamplingpoints.ThenumericalefficiencyoftheFouriermethodleadstotheconclusionthatcomputationaleffortscalessemilinearlywiththevolumeinthephasespaceoccupiedbythemolecularsystem.Methodsoftime

5、propagationaredescribedfortime-dependentandtime-independentHamiltonians.Thetime-independentapproachesarebasedonapolynomialexpansionoftheevolutionoperator.Twooftheseapproaches,theChebychevpropagationandtheLanczosrecurrence,arealsocompared.MethodstoobtaintheRamanspectradirectlybyusin

6、gtheChebychevpropagationmethodareshown.Fortime-dependentproblemsunitaryshort-timepropagatorsaredescribed:thesecond-orderdifferencingandthesplitoperator.Considerationofallthesemethodshasledtoscalinglawsofcomputation.Theconclusionfromsuchscalinglawsisthat,forsimulationsofcomplexmolec

7、ularsystems,approximationtechniqueshavetobeemployedwhichreducethedimensionalityoftheproblem.Thetime-dependentself-consistentfield(TDSCF)issuggested.Finally,abriefdescriptionispresentedofcurrentapplicationsofthetime-dependentmethod.I.Introductiontemperatureswhichenablescontrolofthei

8、nitialmolecularstate.Chemi