Introduction.to.Ab.Initio.Molecular.Dynamics

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1、LectureNotesIntroductiontoAbInitioMolecularDynamicsJ¨urgHutterPhysicalChemistryInstituteUniversityofZurichWinterthurerstrasse1908057Zurich,Switzerlandhutter@pci.unizh.chSeptember14,2002Contents1MolecularDynamics41.1Introduction...........................

2、........41.2EquationsofMotion..............................41.3MicrocanonicalEnsemble............................51.4NumericalIntegration.............................61.5ExtendedSystemApproach..........................81.5.1Barostats.....................

3、...........81.5.2Thermostats...............................102AbinitioMolecularDynamics122.1Born–OppenheimerMolecularDynamics...................142.1.1ForcesinBOMD............................152.2Car–ParrinelloMolecularDynamics......................162.2

4、.1HowtoControlAdiabaticity?.....................182.2.2ForcesinCPMD............................192.2.3VelocityVerletEquationsforCPMD.................192.3ComparingBOMDandCPMD........................203PlaneWaves243.1UnitCellandPlaneWaveBasis.............

5、...........243.2KineticEnergyandLocalPotentials.....................263.3ElectrostaticEnergy..............................273.4ExchangeandCorrelationEnergy.......................293.5Car–ParrinelloEquations............................304Pseudopotentials3

6、34.1WhyPseudopotentials?............................334.2Norm–ConservingPseudopotentials......................354.2.1Hamann–Schl¨uter–ChiangConditions.................354.2.2Bachelet-Hamann-Schl¨uter(BHS)form................374.2.3KerkerPseudopotentials.

7、.......................3714.2.4Trouiller–MartinsPseudopotentials..................384.2.5KineticEnergyOptimizedPseudopotentials.............384.3PseudopotentialsinthePlaneWaveBasis..................394.3.1Gauss–HermitIntegration.......................404

8、.3.2Kleinman–BylanderScheme......................414.4Dual–SpaceGaussianPseudopotentials....................434.5Example:PseudopotentialsforOxygen....................445Implementation475.1TotalEnergyandGradients...........