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THETRANSFERHAMILTONIAN:ATOOLFORLARGESCALE,ACCURATE, MOLECULARDYNAMICSSIMULATIONSUSINGQUANTUMMECHANICAL POTENTIALS By DECARLOSE.TAYLOR ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2004 Copyright2004 by DECARLOSE.TAYLOR ACKNOWLEDGMENTS IwouldliketothankDr.RodneyBartlettforhisguidanceandsupportofmy scientificendeavorsduringmytimeattheUniversityofFlorida. Also,specialthanksgo tothelateDr.MichaelZemerwithwhomIworkedinitiallybeforejoiningtheBartlett researchgroup. VerybigthanksgotoDr.KeithRungeforhisadvisementandencouragementon mattersofscientificandnon-academicinterestandforhispatience. Also,IthankDrs. MarshallCoryandAjithPereraforanswering(alwaysinatimelyfashion)mymany questionsconcerningfortrancodeorquantumtheoryingeneral. IamgratefultoDr.YngveOhmandMrs.JudyParkerfortheirkindwordsof encouragementanddrollsensesofhumor. Finally,IwouldliketoacknowledgeMs.ValerieBuieforherunwaveringsupport overthefinaltwoyearsofmygraduatestudies. Also,IthankDr.MondeQhobosheane withwhomIsharedanapartmentformyfirstfiveyearsinFlorida. iii 1 TABLEOFCONTENTS Page ACKNOWLEDGMENTS iii ABSTRACT vii OVERVIEWOFDISSERTATION 1 MOLECULARDYNAMICS 2 Introduction 2 PredictiveSimulation 2 MolecularDynamicsPotentials 5 ClassicalPotentials 5 Twobodypotentials 6 Threebodypotentials 8 QuantumPotentials 1 Densityfunctionalpotentials 13 Semiempiricalpotentials-TightbindingandNDDOmodels 13 Conclusion 17 TRANSFERHAMILTONIAN 20 Introduction 20 TheoreticalFormulation 20 CoupledClusterTheoryFormulation 22 DensityFunctionalTheoryFormulation 25 FunctionalForm 27 OneCenter-OneElectronIntegrals 28 TwoCenter-OneElectronIntegrals 29 OneCenter-TwoElectronRepulsionIntegrals 30 Two-CenterTwoElectronRepulsionIntegrals 30 NuclearRepulsionEnergy 32 ComputationalProcedure 32 Parameterization 33 Conclusion 34 IV EXAMPLETRANSFERHAMILTONIANS 35 Introduction 35 ParameterizationProcedure 35 GeneticAlgorithms 35 Newton-RaphsonAlgorithms 36 PerformanceOfAlgorithms 37 Procedure 39 TransferHamiltonianExamples 39 Ethane 39 Disilane 40 Conclusion 42 FRACTURESIMULATIONS 43 Introduction 43 Fracture 43 TransferHamiltonian-Silica 44 ReferenceCluster 45 ReferenceDataForPyrosilicicAcid 46 Parameterization 47 ValidationOfPotential 47 Application 56 FractureOfNanorod 56 HybridDynamicsOfNanorod 59 Conclusion 62 HYDROLYTICWEAKENING 66 Introduction 66 HydrolyticWeakening 66 TransferHamiltonian 68 Parameterization 68 Validation 69 SimulationsOfHydrolyticWeakening 70 HydrolyticWeakeningInSilicaRing 71 HydrolyticWeakeninginNanorod 73 Conclusion 73 v APPENDIXCONVERGEDPARAMETERVALUES 79 LISTOFREFERENCES 83 BIOGRAPHICALSKETCH 88 vi AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy THETRANSFERHAMILTONIAN:ATOOLFORLARGESCALE,ACCURATE, MOLECULARDYNAMICSSIMULATIONSUSINGQUANTUMMECHANICAL POTENTIALS By DeCarlosE.Taylor May2004 Chair: RodneyJ.Bartlett MajorDepartment: Chemistry Theaccuracyofamoleculardynamicssimulationiscontingentuponthequalityof thepotentialsusedtocomputetheintermolecularforcesontheconstituentatoms. The mostaccuratepotentialsarethosewhichresultfromfirstprinciplesquantummechanics computationssuchascoupledclustertheory;however,forlargescalemolecular dynamicswhichmaybeontheorderof1000’sofatoms,thisiscomputationallynot feasibleasmostabinitiopotentialsarelimitedto10’sor100’sofatoms. Inorderto avoidthiscomputationalbottleneck,theconceptofatransferHamiltonianisintroduced. ThetransferHamiltonianisalowrank,quantummechanicaloperatorwhosematrix elementsarecomputedfromparametricfunctionalforms. Theparameterswhich constitutethetransferHamiltonianarefittoabinitiocoupledclustertheoryresults (ionizationpotentials,geometry,dissociationenergies,etc.)forseveralsmallmodel systemswhichmimicthelocalstructureofthetargetsimulationsystem. Thetransfer Hamiltonianisapplicabletosystemsfarbeyondthereachofabinitiocoupledcluster theory,yetitretainstheaccuracyofthefirstprinciplescomputation. Further,sincethe transferHamiltoniancanberapidlyevaluated,itisusefulforon-the-flymolecular dynamicssimulationsandgivesresultswhicharemoreaccuratethanthoseobtainable usingaclassicalpotential. CHAPTER 1 OVERVIEWOFDISSERTATION Thefocusofthisdissertationistheaccuratedescriptionofmoleculesand materialsusingmoleculardynamicssimulations. Chapter2introducesmolecular dynamics,definestheterm“predictivesimulation,”anddetailstherelianceofthe simulationresultsonthequalityofthepotentialused. Also,acritiqueofsomeexisting potentialsfoundintheliteratureofbothclassicalandquantumformsisgivenandthe necessityforimprovedpotentialsdelineated. Chapter3introducesthetransferHamiltoniananddiscussesitsformalfoundation intermsofcoupledclusteranddensityfunctionaltheories. Followingthemoreformal arguments,thefunctionalformoftheoperatorisoutlinedandproceduresforcomputation ofthematrixelementspresented. RepresentativeexamplesoftransferHamiltoniansfor varioussystemsaregiveninChapter4,andapresentationoftheparameterization strategyisoutlined. ThefifthandsixthchapterscontainparameterizationsoftransferHamiltonians applicabletosilicaandsilicainthepresenceofwaterrespectively. Severaltestsusedto validatethepotentialsarediscussed,andinChapter5aprototypicalsiliconoxide nanorodisfracturedviamoleculardynamicsusingthenewquantumandstandard classicalpotentials. Chapter6presentssimulationsofthenanorodinthepresenceof wateranddemonstratestheexperimentallyobservablephenomenonknownashydrolytic weakeningwherebywatercausesadramaticdecreaseinthestrengthofsilica. 1 CHAPTER2 MOLECULARDYNAMICS Introduction Thischapterintroducesmoleculardynamicssimulationanddefinestheterm “predictivesimulation.” Also,anoverviewofsomeoftheclassicalandquantum potentialsavailableintheliterature,withafocusonthoseapplicabletosilicaandsilicon, ispresented. Theshortcomingsoftheavailablepotentialswillbediscussedandtheneed formorechemicallyaccuratepotentialswillbedemonstrated. PredictiveSimulation Moleculardynamicssimulationshavecontributedimmenselytotheunderstanding ofthechemo-mechanicalbehavioroflargemoleculesandmaterials[1]. Givenasetof initialconditions(positionsandmomenta),andtheforceofinteractionamongthe constituentparticles,moleculardynamicscomputesthephasespacetrajectoriesofthe particleswhichconstitutethematerialofinterest[2-4], Giventhesetrajectories,the chemo-mechanicalpropertiesofmaterialsandtheirresponsetoexternalperturbationscan bestudiedattheatomisticlevel. Theabilitytoconductstudieswithsuchcoarsegrained refinementallowsresearcherstoelucidatetheunderlyingreactionmechanismswhich determinemacroscopicproperties. Inclassicalmoleculardynamics,atomicpositionsareobtainedbyintegrating Newton’sequationofmotion Fk(t)= mk rk(0= dVdr(r) (2.1) k 2

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