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Structure and dynamics of heterogeneous molecular systems

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Title:
Structure and dynamics of heterogeneous molecular systems
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English
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Roney, Alfred B
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University of South Florida
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Tampa, Fla
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Subjects / Keywords:
Propanol
Water
Liquid
Polarizability
Dipoles
Spectra
Signal processing
Thole
Model
Dissertations, Academic -- Chemistry -- Doctoral -- USF
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Abstract:
Although current classical force fields describe homogeneous single-componentsystems fairly well, they do not represent the response of an individual molecule's electronic structure to its local environment with enough detail to reliably predict atomic motions in interfacial regions such as a solvation structure or liquid surface.Since most chemical processes of non-trivial interest involve two or more dissimilar molecules interacting at a short distance, molecular models must accurately simulate the interactions between different molecular species as well as bulk behavior in order to provide useful information. Results from two simulation studies are presented to illustrate both the utility of current point-charge electrostatics models in liquid structure determination and the critical importance of modeling induction effects in liquid water.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2006.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
Statement of Responsibility:
by Alfred B. Roney.
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Title from PDF of title page.
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Document formatted into pages; contains 148 pages.
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Includes vita.

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aleph - 001909987
oclc - 173258063
usfldc doi - E14-SFE0001678
usfldc handle - e14.1678
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Structure and dynamics of heterogeneous molecular systems
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Although current classical force fields describe homogeneous single-componentsystems fairly well, they do not represent the response of an individual molecule's electronic structure to its local environment with enough detail to reliably predict atomic motions in interfacial regions such as a solvation structure or liquid surface.Since most chemical processes of non-trivial interest involve two or more dissimilar molecules interacting at a short distance, molecular models must accurately simulate the interactions between different molecular species as well as bulk behavior in order to provide useful information. Results from two simulation studies are presented to illustrate both the utility of current point-charge electrostatics models in liquid structure determination and the critical importance of modeling induction effects in liquid water.
502
Dissertation (Ph.D.)--University of South Florida, 2006.
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Includes bibliographical references.
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Text (Electronic dissertation) in PDF format.
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System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
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Title from PDF of title page.
Document formatted into pages; contains 148 pages.
Includes vita.
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Adviser: Brian Space, Ph.D.
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Propanol.
Water.
Liquid.
Polarizability.
Dipoles.
Spectra.
Signal processing.
Thole.
Model.
690
Dissertations, Academic
z USF
x Chemistry
Doctoral.
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StructureandDynamicsofHeterogeneousMolecularSystemsbyAlfredB.RoneyAdissertationsubmittedinpartialfulllmentoftherequirementsforthedegreeofDoctorofPhilosophyDepartmentofChemistryCollegeofArtsandSciencesUniversityofSouthFloridaMajorProfessor:BrianSpace,Ph.D.VenkatBethanabotla,Ph.D.AlfredoCardenas,Ph.D.RandyLarsen,Ph.D.JenniferLewis,Ph.D.DateofApproval:July14,2006Keywords:propanol,water,liquid,polarizability,dipoles,spectra,signal,processing,Thole,modelcCopyright2006,AlfredB.Roney

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AcknowledgmentsIshouldrstthankmywife,Shellie,forherlovingsupportduringtheendlesshoursofcodingandwritingthatleduptothecompletionofthisjourney.Wordscan'texpressthedepthofmygratitudetoher.Iwouldhavenevergottenthisfarinmyacademiccareerwithouttheencourage-mentandsupportofmyparents,andforthatIthankthem.Iwouldalsoliketothankmyadvisor,Dr.BrianSpace,forhisamazingpatienceandthoughtfuladvice,aswellasmycommittee:Dr.VenkatBethanabotla,Dr.AlfredoCardenas,Dr.RandyLarsenandDr.JenniferLewis.TheirsometimesdicultquestionshelpedmeturnthedisparatetopicsoftheworkI'vedoneduringgraduateschoolintoacoherentwhole.AnadditionalthankyougoestoDr.PrestonMoore.Withouthisgeneroushelpandhospitalitythepolarizablewatercodewouldneverhavebeencompleted.Lastly,Iwouldliketothankmyfellowresearchgroupmembers,bothpastandpresent:Dr.HeatherAhlborn,Dr.RussellDevane,Dr.AngelaPerry,Dr.ChristinaRidleyKaspyrzk,TonyGreen,ChristineNiepert,AbeSternandJonBelof.Thefriendshipandcamaraderieofthisgroupisunrivaled.

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NotetoReaderNotetoReader:Theoriginalofthisdocumentcontainscolorthatisnecessaryforunderstandingthedata.TheoriginaldissertationisonlewiththeUSFlibraryinTampa,Florida.

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TableofContentsListofTablesivListofFiguresvAbstractviii1Introduction12AnalysisMethods32.1Introduction.............................32.2StructuralDetermination......................4Hydrogen-BondIdentication...................4Nearest-NeighborHistograms...................5RadialDistributionFunctions...................6Kirkwood-BuIntegrals......................72.3SpectralEstimation.........................8IRAbsorption............................8DataFilteringMethods.......................10FilterSelectionforSpectroscopicObservables..........123AggregationBehaviorofAqueousn-Propanol183.1Introduction.............................18i

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3.2Background&Methodology....................20RamanSpectroscopy........................20AggregateStructure-ExperimentalEvidence..........21AnalysisMethods..........................23ComputationalDetails.......................243.3Results&Discussion........................31ModelValidation..........................31Hydrogen-BondCoordinationResults...............32MolecularDistributions.......................40Cluster-StateDependentRadialDistributionFunctions.....443.4Conclusions&FutureDirection..................494ModelingPolarizationEectsforWater644.1Introduction.............................644.2Theory................................66Electrostatics............................67InteractionTensorExpressions...................69ElectrostaticInteractions......................72ApplequistModel..........................73TholeModel.............................75EwaldSums.............................774.3MolecularDynamicsMethods...................82ComputationalDetails.......................83PotentialSurfaceModel......................85FittingMethodology........................884.4Results&Discussion........................95ii

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FinalFitParameters........................95StructuralResults..........................100BulkSpectra............................104Hydrogen-bondRearrangement..................1254.5ConclusionandFutureDirection..................131References141AbouttheAuthorEndPageiii

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ListofTables3.1Nomenclature..............................193.2Harmonicoscillatorpotentialparameters...............253.3Torsionpotentialparameters......................263.4Lennard-JonesPotentialparameters..................273.5Kirkwood-BuIntegralresults.....................353.6Hydrogen-bondcoordinationnumbers.................374.1Oxygen-HydrogenBondingPotential.................854.2Hydrogen-HydrogenBendingPotential................864.3Cross-bondPotentialParameters...................864.4Intermolecularpairpotentials.....................874.5ElectrostaticParameters........................874.6Dimersimulationtemperaturestatistics................94iv

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ListofFigures2.1Unltereddipoleautocorrelationfunctionandpowerspectrum...152.2IRlineshapelterspecication.....................162.3Filtereddipoleautocorrelationfunction................173.1Ramanspectrumofhydrogen-bondstretchingbands........303.2Simulationsnapshotsof16%n-propanol...............363.3Clustersizehistogramsfor16%n-propanol..............383.4Snapshotsofindividualn-propanolaggregates............393.5Moleculargijrplots,16%n-propanol................513.6Moleculargijrplots,16%n-propanol................523.7Functionalgijrplots,16%n-propanol...............533.8Functionalgijrplots,100%n-propanol...............543.9Nearest-neighborhistograms,unimodaldistributions........553.10Nearest-neighborhistograms,bimodaldistributions.........563.11Nearest-neighborhistograms,wateroxygens,16%n-propanol....573.12Snapshotsofarepresentativewatercluster,16%n-propanol....583.13Cluster-statedependentgr,hydrophilic,16%n-propanol.....593.14Cluster-statedependentgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOWr,16%n-propanol.......603.15Cluster-statedependentgr,hydrophilic,16%n-propanol.....613.16Cluster-statedependentgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHr,16%n-propanol........62v

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3.17Schematicdiagramofproposedmicellestructure...........634.1Polarizationeectsonpotentialenergysurfaceofwater.......704.2Conicaldampingdistributiontensormultipliers...........804.3Exponentialdampingdistributiontensormultipliers.........814.4Quasi-blackbodynoise-shapinglter..................984.5Agreementcriterionvs.facc,addg...................994.6Experimentalwatergr........................1054.7Radialdistributionfunctions......................1064.8Radialdistributionfunctions,2ndneighbor..............1074.9Proposedlinearchainstructureforliquidwater...........1084.10Chainstructureisolatedfrombulkpolarizablesimulation......1094.11AsymmetricchargemodelEPSRresults...............1104.12Ab.initiowatergr..........................1114.13Radialdistributionfunctions,structuraltting............1124.14SPC/FIRspectrumvs.experiment..................1134.15PolarizablemodelIRspectrumvs.experiment............1144.16IRspectrum,intermolecularregion..................1154.17IRspectrumbendingregion......................1164.18PolarizablemodelIRspectrumvs.experiment............1174.19IRspectrumstretchingregion.....................1184.20Experimentalcouplingassignmentsvs.Fourieranalysis.......1194.21Modelcouplingassignmentsvs.Fourieranalysis...........1204.22Dimerhydrogenbondrearrangementpathways............1254.23Temperature-dependentdimerspectra,inter-rotationalband....1334.24Temperature-dependentdimerspectra,O{Hstretch.........134vi

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4.25Temperature-dependentdimerspectra,H{O{Hbend........1354.26Counter-rotationtransitionstate...................1364.27Bifurcationtransitionstate.......................1374.28Donor-acceptorrole-reversaltransitionstate.............1384.29Donor-acceptorrole-reversal,non-polarizabledimer.........1394.30Donor-acceptorrole-reversal,averagespectralcontribution.....140vii

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StructureandDynamicsofHeterogeneousMolecularSystemsAlfredB.RoneyABSTRACTAlthoughcurrentclassicalforceeldsdescribehomogeneoussingle-componentsystemsfairlywell,theydonotrepresenttheresponseofanindividualmolecule'selectronicstructuretoitslocalenvironmentwithenoughdetailtoreliablypredictatomicmotionsininterfacialregionssuchasasolvationstructureorliquidsurface.Sincemostchemicalprocessesofnon-trivialinterestinvolvetwoormoredissimilarmoleculesinteractingatashortdistance,molecularmodelsmustaccuratelysimulatetheinteractionsbetweendierentmolecularspeciesaswellasbulkbehaviorinordertoprovideusefulinformation.Resultsfromtwosimulationstudiesarepresentedtoillustrateboththeutilityofcurrentpoint-chargeelectrostaticsmodelsinliquidstructuredeterminationandthecriticalimportanceofmodelinginductioneectsinliquidwater.viii

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Chapter1IntroductionThesimulationofheterogeneousliquidsystemsisanimportantandchallengingareaofresearch,andmuchprogresshasbeenmade.Despitethecombinedeortsoftheworldwidescienticcommunityoverthelastcentury,however,manysupposedlysimplequestionslackadenitiveanswer.Thisdissertationwillpresentresearchintotwoopenexperimentalquestionsrelatedtoheterogeneousliquidsystems.Chapter3presentsaproposedaggregationstructureandmechanismforaqueousn-propanolunderambientconditions.Thissystemappearstoretainkeyintermolecu-larfeaturesoftheRamanspectraofthepurecomponentsevenwhensolvated,whichisstrangeconsideringthatwaterisinnitelymisciblewithmostalcoholsoflowmolecu-larweight.Thus,amolecularly-detaileddescriptionofthephenomenaresponsibleforthisobservationcanprovideavaluableindicatorofthetypeandextentofstructuralchangesinducedatthesolute-solventinterface.Usingmoleculardynamicsmethodstosimulatethemixingbehavioroftwoliquidsisaconvenientmethodfordetermin-ingtheirinteractionsinsolution,andthischapterclearlydemonstratesthis.Itdoes,however,raisequestionsaboutthedenitionofhydrogenbondinganditsimportanceinthetheoreticaldescriptionofforcesatinterfaces.Sincetheexactforcesexperiencedbyamoleculedirectlydependuponthelocalarrangementofitsnearestneighbors,wemustgetthiskeyinteractionrighttoaccuratelypredicthydrationstructures.1

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Oneofthemostimportantproblemsinmodernmolecularsimulationisdetermin-ingthelocalarrangementofliquidwaterandhowitproducestheconfusingarrayofexperimentalmeasurementsresponsibleforthecurrentdebateoverthestructureoftheliquid.Thedescriptionofwatersolvationiscriticaltotheaccuratetheoreticalmodelingofbiologicalandenvironmentalprocesses,thereforesimulationsofthesesystemsmustreproducethecorrectstructureandlocaldynamicsofwater.Chapter4presentsthecurrentstatusofongoingresearchintothemodelingofnon-pairwise-additiveelectrostaticinteractions,orpolarization,"inthecontextofthecurrentdebate.Thesemany-body"interactionsarisefromtheelectronicstructuredistor-tionsinducedinsystemsofmanymoleculesincloseproximity,suchaswaterunderallbutthemostextremeconditions.Thendingsofthisstudysupportarecentlypro-posedandhighlycontroversialhypothesisaboutthestructureofliquidwater,whilesimultaneouslyprovidinginsightintotheoriginsofanas-yetunidentiedfeatureoftheinfraredspectrumofliquidwater.Chapter2presentsashortsummaryoftheanalysismethodsusedtodeterminebothstructuralanddynamicobservablesfromsimulationoutput.Thesemethodsrepresenttheprimarytoolsusedinthesubsequentchapters,andthereforewenowproceedtotheirdescription.2

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Chapter2AnalysisMethods2.1IntroductionTheabilitytodisplaymolecularphenomenavisuallywithatomisticdetailstandsasoneofthegreateststrengthsofmolecularsimulationmethods.Researchershavetheabilitytowatchanentirechemicalsystem,agroupofmolecules,orasingleatomasitmovesthroughtimeandspaceasacomputer-generatedanimation.Onitsown,thiscapabilityprovideslittlemorethanaqualitativeideaoftheinteractionsinvolvedinasimulatedchemicalprocess.Furthermore,theoverabundanceofvisualinformationprovidedbyatypicalanimationofamolecularsystemmakestheobservationofspecicphenomenadicultfortheunaidedeye.Whencoupledwithanalysismethodsmadepossiblebytheatomistically-detailedrecordsgeneratedduringamolecularsimulation,however,researcherscansortthroughthecluttertoidentifyandisolatespecicmoleculareventsorstructures.Thischapterpresentsthepost-simulationanalysismethodsusedtodetermineliquidstructureanddynamicsinthestudiespresentedbythefollowingchapters,andtomakedirectconnectionsbetweenthesimulationoutputandexperimentalobservables.3

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2.2StructuralDeterminationTheforcesexperiencedbyonemoleculeinthepresenceofanotherdependonboththeirseparationandrelativearrangements.Theseforcescanbequitedirectional,causingcertainlow-energyarrangementstodominatethedistributionofpossiblecongurations,thusthespecicmotionsobservedbyanexperimentwillalmostex-clusivelyresultfromthesedominantcongurations.Atomistically-detailedsimulationmethodsareapowerfultoolfordeterminingthespeciccongurationsandtrajecto-riestakenbyamolecularsystemasitexploresitspotentialenergysurface,andinthissectionwewillpresentsomeoftheanalyticalandtheoreticaltoolsusedtoidentifyandcharacterizestructuralphenomena.Hydrogen-BondIdenticationAsearchalgorithmfordetectinghydrogenbondswasdevelopedusingpurelygeomet-riccriteriafromtheliterature.[1]Althoughthevalidityofthisapproachhasbeencalledintoquestioninlightofrecentexperiments,itremainstheindustrystandard"inthesimulationcommunityduetoitseaseofimplementationandlowcomputationalcostcomparedtoenergy-basedmethods.Fromtheidenticationofhydrogenbondedpairs,coordinationnumberscanbecalculated.Specicaggregatesofmoleculesmayalsobeidentiedfromthelistofhydrogen-bondedneighborsgeneratedbythispre-scription.Additionally,thespecicprocessesresponsibleforhydrogen-bondrear-rangementcanbelocatedthroughtheanalysisoftrajectorysamplesequences.Thus,thismethodprovidesacriticalinsightintotheroleofhydrogen-bondinginhydrationprocesses,andallowsscientiststoisolatekeymotionsandstructuresresponsibleforunexplainedbehaviors.4

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Locatinghydrogenbondsusingthissystemisstraightforward.First,performasearchforoxygenatompairspossessinganinter-atomicradiusof2.5{3.2A.Amongoxygenpairsidentiedaspossessingthecorrectseparation,calculatetheintermolec-ularhydrogen{oxygendistancerOHforeachhydrogenmolecularlybondedtoamemberofthecandidateO{Opair.IfrOHfallsbetween1.5{2.2A,calculatethehydrogenbondangleOHOformedbythecandidateO{HOtriad.IfOHOfallsbetween130{180,therespectivemoleculesareconsideredtobehydrogenbonded.Nearest-NeighborHistogramsHavingmorethanonespeciespresentinasystemusuallyresultsintheexistenceofmultiplestatesforasinglespecies.Forinstance,watermoleculeslocatedinaninterfacialregionmayexhibitadierentcoordinationstructurethanthoseinthebulk.Theresultingcoordinationstructuresmaysignicantlyalterthedynamicbehaviorofparticipatingmolecules,andthusthelocationofdeviationsfromanaveragestructureareofcriticalimportance.Thenearest-neighborhistogrammethoddetectsthesecoordinationdierencesquicklyandeciently,andinaquantitativemanner.Thismethodisimplementedaccordingtoasimplealgorithm.Foreachmoleculeoratomicoordinatedbyamoleculeoratomj,calculateallradialdistancesrijforeachmoleculeofspeciesiandsavetheminanarray.Acutovalueandpairlistmaybeusedasacriteriaforselectingonlyneighborswithinaspecicradius.Sortthisarrayintoascendingorder,andusetherstNelementsofeacharraytoincrementtheappropriatebinofahistogramassociatedwitheacharrayelement.Thehistogramsarenormalizedbydividingthebinsbythenumberofspeciesipresent,andaveragedbydividingeachbinbythenumberofcongurationsanalyzed.ThesehistogramsrepresentthedistributionofdistancestothenearestNneighborsofspeciesi.5

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Thisanalysisisusefulindiscerningthevariationinsolvationstructureofagivenspecies.Forexample,abulkwatersimulationwhichaccuratelyreectsthetextbookdescriptionofwaterstructurewillproducenearlyidenticalresultsfortherstfourhistograms,andthedistributionofdistanceswillbemonotonic.Eachsuccessivecoordinationspherewillproducesimilarresults,withthepeakofthedistributionshiftedtoreectthecoordinationdistanceandthenumberofidenticalarraysequaltothenumberofcoordinatedatomsatthedistanceindicatedbythecenterofthedistribution'speak.Ifmultiplecoordinationstatesexist,however,thehistogramswillexhibitmultiplepeakscorrespondingtothenumberofcoordinatingatomsandthedistancestothecoordinationshells.RadialDistributionFunctionsTomakeconnectionwithexperimentandtofurtherunderstandthesolutionstruc-ture,variousradialdistributionfunctions,gijrwerecalculated.Althoughthereistechnicallynoexperimentalmeasurementofthesequantitiesthatcanexplicitlyre-solvethecoordination-dependentfeaturesofamolecularliquidorsolution,theyareformallyrelatedtoawidevarietyofexperimentalquantitiesandthusareofprimevalueindeterminingtheaveragelocalstructureofasubstance.Theradialdistribu-tionfunctionisformallydenedforisotropicsystemsby[2]:gijr=jrij idrij=jrij hji.1wherejrijistheaveragenumberdensityofspeciesjinasphericalshellofradiusrijcenteredatspeciesi,andidrijisthethedensityofanidealgasatthethesamenumberdensityhjiasmoleculej.Theradialdistributionfunctioniseasilycalculatedfromthecoordinateoutputofamoleculardynamicssimulationbycreatingahistogramoftheradialdistancesrij,calculatingtheaveragedensityofspeciesj6

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withinthesphericalshelldenedbythebinlocationanddimensions,anddividingtheresultingdensitybytheensembleaveragedensityofjtogivegijratthelocationofthecenterofthebin.Thespeciesrepresentedbyiandjcanbeeitherthecenterofmassofamolecule,oranyatomofinterestonamolecule.Additionally,withcarefulattentiontonor-malizationtheymayalsobechosentorepresentthecenterofmassoraspecicatomfromamoleculeinaspecicaggregationstate,suchasmoleculesthataremembersofahydrogen-bondedchain.Thesefunctionsprovideagooddescriptionoftheshort-rangeorderpresentinliquids.[3].Theyalsoallowtheestimationofsingle-componentaggregatesizesbyintegratingovertherstneighborpeak:hNii=1+4hiirminZ0giirr2dr.2wherehiiistheaveragenumberdensityofspeciesi.Bychoosingrminasthelocationoftherstminimumingiir,hNiibecomesthenumberofmoleculescomprisinganaggregate.Kirkwood-BuIntegralsKirkwood-Buintegrals[4],Gij,arederivedfromintegralsofgijrandcanbeconsideredtobeameasureoftheaverageexcessordecitofspeciesjaroundspeciesi.Theyareformallydenedby:Gij=1Z0[gijr)]TJ/F15 11.9552 Tf 11.9551 0 Td[(1]4r2dr.3Whilethereisnoextantdirectexperimentalmeasurementofgijrformulti-componentsystems,Gijcanbeexperimentallymeasuredbyavarietyofmethods.[5,6]ThismakesGijanexcellentmeasureofthedegreeofaggregationandaconvenientpointforcomparisonwithexperiment.7

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2.3SpectralEstimationMuchofwhatweknowaboutthestructureanddynamicsofmolecularsystemscomesfromspectroscopicexperiments.InfraredIRabsorptionexperimentsareofparticu-larimportance,astheyprobemolecularvibrationsarisingfrombothintramolecularandintermolecularforces.Thus,themodelingofvibration-probingexperimentscanprovidecriticalinsightsintotherelationshipsbetweenvibrationalmodesandstruc-turalfeaturessincetheycanbedirectlyrelatedtosimulatedquantities.Unfortu-nately,theaccuratemodelingoftheseexperimentsrequiresextraordinarycomputa-tionalresources,thusanyalgorithmicimprovementinthecalculationofspectroscopicobservablesthatdoesnotinvokeexcessiveapproximationscanbeconsideredanim-portantadvancement.Thissectionpresentsonesuchmethod,anovelalgorithmforcalculatingIRabsorptionlineshapesfromsimulationoutputdataviadiscretetime-domainconvolution,ordigitalltering."Thisalgorithmisquitegeneralinnature,andcanbeadaptedtootherdynamicobservablesdescribedbytime-correlationfunc-tionsusingtheprescriptiondescribedinthefollowingsubsections.IRAbsorptionTheabsorptionlineshapeofasystemofuctuatingchargescanbewrittenintermsofthepowerspectrumofthedipolemomentoperatorjM!j2,where!isthefrequencyoftheincidenteld.[3]ThisistypicallywrittenasafunctionoftheFouriertrans-formofthedipolemomentautocorrelationfunction,jM!j2=FT[hMMti].AlthoughwecanonlycalculatetherealpartofhMMtifromclassicalmolec-ulardynamicsdata,wecanrelatethisquantitytoexperimentthroughthefollowing8

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mathematically-equivalentrelationships:[7,8]n!!=42 3cV~!tanh~ 2!FT[hMMti].4n=164 3cVhtanhh 2FT[hMMti].5Theimplementationofequations2.4&2.5appearstobeastraightforwardpro-cess.Thedipoleautocorrelationfunctioniscalculatedfromasequenceofsamplesofthesystemdipole,andtheresultispassedtoadiscreteFouriertransformpro-gram.Oncetransformedintothefrequencydomain,multiplicationbyawell-denedfunctionappliesthecorrectionneededtobringtheclassicaldipolepowerspectrumintoagreementwithitsquantumcounterpart.Thesimplicityofthetheoreticalde-scriptionhidesthecomplexityofitsproperimplementation.Theclassicaldipoleautocorrelationfunctioncandecayveryslowly,andthuscontainsalargeamountofextremely-lowfrequencycomponents.Thelonglagwindowrequiredtocapturetheentiredecayprocessreducestheratioofobservationlengthtoinputdatasetlength,requiringlargedatasetsandhencemoresimulationtimetogenerateawell-convergedaverage.Thisproblemisillustratedbytheslightasymmetryinat=hMMtipresentedinFigure2.1.Forcomputationallydemandingsimulationtechniques,thegenerationofsucientdatatoensurereliableconvergenceofatime-correlationfunc-tionpresentsamajorobstacle,renderingmanytheoreticaldescriptionsintractablebyconventionalmeans.WecanovercomethisissuebyusingthepropertiesoftheFouriertransformtomovethebulkoftheprocessingintothetimedomain.WerstrewriteEquation2.5usingthecorrelationtheoremandlinearitypropertytoexpandFT[hMMti],n=164 3cVhtanhh 2XMM2.69

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where2x;y;zdenotesthethreeCartesiandimensions.WethenperformanalgebraicrearrangementofEquation2.6,n=164 3cVh)]TJ/F34 11.9552 Tf 14.5637 8.0878 Td[(i 2X[i2M]tanhh 2M.7followedbytheapplicationofthederivativeandconvolutiontheoremstoarriveatthenaltime-domainexpression,usingthe~symboltodenoteconvolution.n=164 3cVh)]TJ/F34 11.9552 Tf 14.5637 8.0877 Td[(i 2XFTd dtMMt~)]TJ/F34 11.9552 Tf 9.2984 0 Td[(i2 hcsch)]TJ/F34 11.9552 Tf 9.2985 0 Td[(i22 ht.8TheactualimplementationofEquation2.8willbediscussedinSection2.3.DataFilteringMethodsThenatureofdigitalcomputationsystemsenforcesnite-precisionmathematics,andthusthepotentialfordatacorruptionduetotruncationexists.Therefore,ifwewishtomeasureaveryweaksignalinthepresenceofanotherstrongsignal,itbehoovesusequalizethesignalsasearlyaspossibleinthesignalpath.Foraquantitysuchasthesystemdipole,theactofsummingthevectorcomponentscanpotentiallycon-taminateweakhigh-frequencysignals,particularlycouplinginformation,duetotheoverwhelmingamountoflow-frequencyintermolecularinformationpresent.Figure2.1illustratestheproblemwellasitrelatestothecalculationofIRabsorptionline-shapes,butthesamedicultyexistsfornearlyalltheoreticaldescriptionsbasedupontime-correlationfunctions.Inordertoalleviatethispotentialproblem,thissectionwillpresenttheanalyticalproofofanalgorithmforlteringatomicquantitiespriortosummationandtime-correlationanalysis.10

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Wewillstartbyexpandingthetwo-timeautocorrelationfunctionofasumofvectorsintermsofthecomponentsoftheindividualvectorswhicharesummed.Webeginbydeningthedotproductoftwovectors,ij=Xi;j;.9wherethesubscriptindex2x;y;zindicatesacomponentofaCartesianvector,andtheindicesi;jidentifyaparticularvectorinasetofvectors.Forthepurposeofthisproof,iandjindicatesinglemoleculesinasetofmoleculescomprisingasimulation,andthesubscriptedtime-varyingscalarquantityi;tindicatesthevalueofthe-componentofforithmoleculeofasampledcongurationcorrespondingtotimetinaseriesofcongurationsamples.Mostquantitiesofinterestcomputedfrommoleculardynamicssimulationsdependuponthesumofasetofvectors,st=Pit.Weusestodenoteageneralizedvectorsumsuchasthesystemdipoleormomentumofasinglemoleculecomprisedofmultipleatoms.Wemustthereforeexpresstheassociatedtime-correlationfunctionsassumsofthecorrelationfunctionsoftheindividualmolecularvectorcomponents,at=hssti=Xhs;s;ti=Xat.10thenreplacethesystemvector'sCartesiancomponentswithsumsoftherespectivecomponentsoftheindividualatomicvectorsandapplythecorrelationtheoremandthelinearitypropertyoftheFourierTransformtoarriveat:XXiXjhi;j;ti=at,a=XXiXji;j;.1111

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Theprecedingderivationshowsthattheo-diagonalcross-correlationfunctionsplayalargeroleintheobservedpowerspectrumforavectoreld.Furthermore,sinceingeneralhi;j;ti6=)-166(hj;i;ti,non-randomnoisepresentinthesys-temmaynotbecanceledwhenthevectorsumisperformedpriortoautocorrelation.Thismayrequireexcessiveaveragingortheuseofhigh-precisiondatarepresentationinanalreadyexpensivecomputation.Thus,thereisadistinctadvantagetoperform-ingfrequency-domainmanipulationspriortosummationwhenworkingwithvectorsums.Weimplementadigitallterasatime-domainconvolutionofthesequencei;twithalterimpulseresponse"functionht,denotingthelteroutputwithaprime0.ApplyingtheconvolutiontheoremgivesthefollowingFouriertransformpair,i;t~ht=0i;t,0i;=i;h.12WesubstitutetheprecedingresultintoEquation2.11toarriveata0=XXiXj[i;h][j;h].13Wethenperformasimplealgebraicrearrangementtoarriveatthepowerspectrumofthesystemintermsofthesumofthelteredvectorss0t:jsj2=jhj)]TJ/F18 7.9701 Tf 6.5865 0 Td[(2js0j2.14FilterSelectionforSpectroscopicObservablesIntheory,Equation2.14indicatesthatwecanextractthepowerspectrumatallfrequencies,providedthath6=0,butinrealitytheniteprecisionofdigital12

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computationsystemsmaycorruptsomeofthelteredinformation.Additionally,iftheimpulseresponsefunctionrequiresalargenumberoftime-domainsamplestodescribethedesiredfrequency-spacemultiplication,thesamesummationerrorsthatwearetryingtoavoidwillcreepbackintothecalculation.Tomakemattersworse,truncationerrorsinducedbydigitalltersarecorrelatedtothesignalamplitude,[9]whichcancontaminatecorrelationsignalswhenperforminghigher-orderspectralanalysis.Wemustthereforechoosehtcarefullytoavoiddatacorruptioninthefrequencybandofinterest.WebeginbyconsideringadirectimplementationoftheconvolutionspeciedbyEquation2.8.Thederivativeofthedipoleisapproximatedbythenite-dierencemethod,whichcanbeexpressedastheinputdataconvolvedwiththefunctionht=f0.5,-0.5g,h=isininnormalizedfrequencyrepresentation.[10]WemustthereforemultiplyjM0j2by=sint,wheretisthesamplingperiod,inordertocorrectforthehigh-frequencyroll-oinherentintheapproximation.Thefunctioncsch22t=hcanbeimplementedtomachineprecisionwith128sampleswhent=0.004psandthesimulationtemperatureis298K,butFigure2.2demon-stratesthatthenite-dierenceapproximationtothederivativecanalsobeusedasareasonableapproximationforcscht,achieving10%agreementwiththede-siredfrequency-spaceresultfortypicalmoleculardynamicssimulations.Wethereforeimplementthefollowingexpression,n=164 3cVhtanhh 2 sin2tXjFT[hM0M0ti]j.1513

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whencomputingsimulatedIRabsorptionlineshapes.Thisreducesthecomputationalburdenofthelteringoperationbyafactorof64whilesimultaneouslyreducingtheamountoftruncationerrors,particularlysinceht=f0.5,-0.5gcanbestoredwithinniteprecisionusingIEEEoating-pointrepresentation.[11]Thedecaytimeofthetime-correlationfunctionisreducedbyseveralordersofmagnitude,asFigure2.3attests,allowingmuchsmallerdatasetstobeused.14

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Figure2.1:Classicaldipoleautocorrelationfunctionandpowerspectrumofa200ps64-waterSPC/Fsimulation,priortonormalization.Signicantcorrelationspersistforatleast20psinbothdirectionsrelativetotheorigin,andaslightasymmetryduetoincompleteconvergenceisvisible.Thelow-frequencyleakageintothebaselineofthepowerspectrumiseightordersofmagnitudegreaterthanthemaximumintensityofthedesiredsignal,evenafterwindowingtheautocorrelationfunction.15

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Figure2.2:Fouriertransformpairfortanhupperpane,presentedwiththeFouriertransformofthenite-dierenceoperatorandthecorrectionfactorneededtousethetime-domainnite-dierenceoperatorasanapproximationtocsch.Normalizedcoordinatesareused,whichplacestheNyquistfrequencyatx=0:5.16

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Figure2.3:Dipoleautocorrelationfunctionofadatasetlteredattheatomiclevelusingthenite-dierenceoperatorastheimpulseresponsefunction.TheFouriertransformofthisdatasetdiersfromtheresultusingtheltersderivedfromEquation2.8bylessthat10%.17

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Chapter3AggregationBehaviorofAqueousn-Propanol3.1IntroductionAqueoussolutionsofaliphaticalcoholsndmanyuses,fromcleaningproductsandchromatographysolventstobeveragesandfoodadditives.Whilemuchisknownaboutthemacroscopicchemicalbehaviorofthesesolutions,thesolvationstructureispoorlyunderstoodformanyaqueousalcohols.Multiplestudiesindicatethatalcoholmoleculesaggregateinaqueoussolution,butstudiesofthen-propanolaggregationindicatedbyRamanspectra[12],small-angleX-rayscatteringSAXS[13,14],small-angleneutronscatteringSANS[15],andthermodynamicdata[14,16,17]donotprovideanatomisticallydetaileddescriptionofthemicroscopicallyheterogeneoussolutions.Theexistenceofhydrogen-bondedchainsofsolutemoleculeshasbeensuggestedbyexperimentsonmanyaliphaticalcohols.[16,18]Signicanthydrophobicinteractionsforalcoholspossessinglargehydrocarbonfunctionalitieswerealsoindicated.[12,13,18

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18]Whilemanystudiesconrmthatsomesortofclusteringdoesoccurinn-propanol,priortothepublicationofthisstudyonlythehydrationstructuresofsinglemoleculesanddilutesolutionsofn-propanolhadbeenreported.[19]Table3.1presentsthenomenclatureusedthroughoutthischaptertodescribetheaggregationmechanismsofaqueousn-propanolderivedfromMDsimulation. AtomSymbolDenitions Symbol Denition CA -carbonofn-propanol CM methylcarbonofn-propanol OH hydroxyloxygenofn-propanol HO hydroxylhydrogenofn-propanol OW oxygenofwater PrexDenitions Prex n-propanol H2O c memberofchain memberofbulkNcluster10 u non-chain non-bulk Table3.1:Nomenclature.Atomdenitionsandclusterstateprexesusedinthispaper.19

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3.2Background&MethodologyRamanSpectroscopySuggestiveevidenceofaggregationispresentinalow-frequencyRamanspectroscopystudyofalcohol/watersolutions,whichispresentedhereasFigure3.1.[12]TheintensitiesoftheabsorptionbandsattributedtointermolecularO{HOstretchingbetweenhydrogen-bondedalcoholswereobservedtovaryinapiecewise-linearfashionwithalcoholmolefraction.Additionally,theintensityoftheO{HOstretchingbandforwater-waterhydrogenbondsvarieslinearlywiththewatermolefraction.ThislinearrelationshippermitstheRamanspectraforaqueoussolutionsofmethanol,ethanol,n-propanol,2-propanol,andt-butanoltoberepresentedassimplelinearcombinationsofthepurecomponents'spectrabetween0{300cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1accordingtotheformula:R;=aR;0+bR;1.1whereR;istheRamansignalatwavenumbers,isthemolefractionofalcohol,andaandbareempiricalcoecients.Sincebothbandsofinterestareintermolecularstretchingmodes,theirlinearvariancewithconcentrationindicatesthatthehydrogenbondstructureofbothcomponentsislargelyunaectedinsolution.Thisimpliesthatdespitethefactthatn-propanolandwaterareinnitelymiscible,thesolutionisfarfromhomogeneousandsuggeststhatbothn-propanolandwaterformaggregatesthatmimic,atleastspectroscopically,thestructureoftherespectivepurecomponents.20

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Forn-propanol,theintermolecularO{HOstretchingbandofinterestislocatedat69cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Thecoecientsaandb,whileregionallylinear,exhibitinectionpointsat20%and50%mole-fractionofn-propanolinagreementwiththerespectivemin-imumandmaximumoftheheatofmixingforn-propanol.Theseinectionpointscoincidewithasuspectedtransitionfromn-propanolclustersinwatersolventatp<10%,toseparateclustersofn-propanolandwaterat20%p60%,andnallytowaterclustersinthen-propanolsolventatp>60%.[12]Theseareonlyqualitativeobservations,however,withoutamolecularlydetailedexplanation.Nonetheless,for-mationofdierentsolvationstructureswithconcentrationisstronglysuggestedbytheseobservationsandMDisanidealmethodtoidentifythestructuresinvolved.AggregateStructure-ExperimentalEvidenceMuchoftheexistingworkonaqueoussolutionsoflowmolecularweightaliphaticalcoholsindicatesthatthehydroxylgroupsfromthealcoholmoleculesformhydrogen-bondedchains,withthealkyltailsextendingintothesolvent.Inthisstructure,eachhydroxyloxygendonatesandacceptsonehydrogenfromanotherhydroxylgroup,foratotaloftwohydrogenbondspermoleculeofalcohol.[16]X-raydiractionandmassspectrometrystudies[18]indicatethatformethanolthesechainstaketwoforms,cis-andtrans-,basedupontheorientationofthealkylgroups.Thenumberofmoleculescomprisingthesechainsisdirectlyproportionaltotheconcentrationofmethanol,andtheO{Ospacingalongthechainsdecreases4%asthemolefractionvaries21

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fromm=0%tom=100%.Ethanol,2-propanol,andt-butanolalsoexhibitsimilarbehavior.Severaldierencesintheaggregationbehaviorofn-propanolcomparedtootheralcoholshavebeennoted.OnesignicantdierenceisthetemperaturedependenceoftheDebyecorrelationlength,anindicationofthecorrelationdistanceofdensityuctuationsinasolution.[20]Whilethecorrelationlengthoft-butanolexhibitsatemperaturedependence,thecorrelationlengthofn-propanolisindependentoftem-perature.Thetemperaturedependencefort-butanolisattributedtothemelting"ofanice-likecagestructuresurroundingthet-butylgroupwithincreasingtempera-ture,thereforethelackoftemperaturedependenceforn-propanolsuggeststhatnosimilarhydrationstructureexistsaroundthen-propylgroups.[13,21]Additionally,noclathrate-hydratecrystalstructureofn-propanolhasbeenobserved,despitetheexistenceofthesestructuresfor2-propanolandt-butanol.Thisindicatesasignicantdierenceinthehydrationstructureofn-propanolwhencomparedtothesesimilarmolecules,andsuggeststhatthealkyltailsofn-propanoldisruptthewaterstructureenoughtopreventtheformationofahydrogen-bondedwaternetworksurroundingthehydrophobicfunctionalities.Italsosuggeststhatthesefunctionalgroupsmaybeexcludedfromthewaterstructurebysoluteaggregation.22

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AnalysisMethodsAnimationsofthesystemwereproducedfromtheMDsimulationsandrenderedinordertoobtainaqualitativevisualideaoftheaggregationphenomena.Snapshotsofindividualcongurationsweretakenhighlightingdierentmolecularsolvationphe-nomenaincluding,forexample,sortingspeciesbytheirhydrogenbondingenviron-ment.Asanexample,Figures3.2a-cpresentasnapshotofatypicaln-propanol-waterMDsimulationwithallspecies3.2bandthewater3.2aandn-propanol3.2cremoved.Sincehydrogenbondingistheprimarymethodofaggregationindicatedbyspec-troscopicdata,asearchforhydrogenbondswasperformedoneachatomiccongura-tionusingcriteriafromtheliterature.[1]Fromtheidenticationofhydrogenbondedpairs,coordinationnumberswerecalculatedandindividualaggregatesofmoleculeswereidentied.Detailedhistogramsofchainandclustersizeswerecalculatedforthevariousspeciesandsubspeciestobedescribedbelow.Inordertodeterminethetypeandextentofstructuredisruptionspresentinthesystem,nearest-neighborhis-togramswerealsocalculatedforOW{OW,CA{CA,CM{CM,CA{OW,CM{OW,OH{OH,andOH{OW.Kirkwood-Buintegralswerecomputedfromtheradialdis-tributionfunctionsusingatrapezoid-rulebasedintegrationroutine.Gpp,Gpw,Gww,GCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(CA,GCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OW,GOW)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OW,GOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OH,andGOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWwerecalculatedandcomparedtoexperiment.Molecularradialdistributionfunctionsweregeneratedforsolute-solutegppr,23

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solute-solventgpwr,andsolvent-solventgwwrusingthecenterofmassofthemoleculesastheirlocation.Theseresultswerecomparedtogijrdatacalculatedusingthe-carboncoordinatesofn-propanolCAandtheoxygencoordinatesofwaterOWasthemolecularcoordinatesduetotheproximityoftheseatomstothecenterofmass.Additionally,Functionalradialdistributionfunctionswerecalculated,includinggOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHr,gOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(HOr,andgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWr.AsdescribedinSection2.2,bothsoluteandsolventcanbesortedintogroupsaccordingtotheirhydrogenbondingstate,resultinginthecreationoffourspecies:chainn-propanol,freen-propanol,bulkwater,andnon-bulkwater.Chainn-propanolmoleculesaredenedasn-propanolmoleculesthatarehydrogenbondedtoothern-propanolmolecules.Freen-propanolmoleculesarenothydrogenbondedtoanyothern-propanolmolecules.Bulkwaterisdenedaswaterclustersconsistingof10ormoremembers,asdeterminedfromthecoordinationdata.Allremainingwatermoleculesareconsideredtobeaseparatespeciesfromthebulk.Functionalradialdistributionfunctionswerecalculatedforthesefourspeciesinordertodecomposeboththemolecularandfunctionalradialdistributionfunctionsandilluminatethevariousintermolecularinteractionsresponsiblefortheobservedaggregation.ComputationalDetailsTheMDproductionrunsproducedtrajectoriesbysolvingdynamicalequationsofmotionusingamodiedformofthevelocity-Verletalgorithmthattakesadvantage24

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ofmultipletimestepintegration.[22]ModiedOPLSparameterswereused.[23,24]Allmoleculeswerefullyexibleandharmonicstretchingandbendinginteractionswereused.TheharmonicpotentialparametersarepresentedinTable3.2.Forn-propanol,torsionswererepresentedbyapowerseriesusingthecoecientspresentedinTable3.3.Additionally,one{fourintramolecularinteractionswererepresentedbyLennard-JonespotentialspresentedinTable3.4. n-propanol AtomPair kfK A2 reqA2 C{C 311903 1.526 C{H 342088 1.09 C{O 321965 1.41 O{H 556395 0.96 water AtomPair kfK A2 reqA2 O{H 556395 0.9572 H{H 556395 1.5136 Table3.2:Harmonicoscillatorpotentialparametersusedforthemoleculardynamicssimulations.)]TJ/F20 11.9552 Tf 5.4795 -9.6838 Td[(VHOr=1 2kfr)]TJ/F20 11.9552 Tf 11.9551 0 Td[(req2IntermolecularinteractionsweremodeledbyLennard-Jones6{12potentialsandpoint-chargeelectrostaticinteractions.TheLennard-Jonesparametersusedtomodeltheintermolecularpotentialswereidenticaltotheparametersusedtomodelin-tramolecularone{fourinteractions.Theelectrostaticpotentialsurfaceswererep-resentedbypartial-chargeslocatedonspeciedatomsofeachmolecule.Long-range25

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Atomsequence p0 p1 p2 p3 X1|C|O|X2 41.9225 )]TJ/F15 11.9552 Tf 9.2985 0 Td[(125.767 0.00 167.69 X1|C|C|X2 39.1277 )]TJ/F15 11.9552 Tf 9.2985 0 Td[(117.383 0.00 156.511 Table3.3:Torsionpotentialparametersforn-propanolusedforthemoleculardy-namicssimulations,inKelvinK.Vtorsion=1 2PkpkcoskelectrostaticinteractionswerecalculatedusingEwaldsums.[25]Forn-propanol,thehydroxyloxygenwasassignedachargeof)]TJ/F15 11.9552 Tf 9.2985 0 Td[(0.728e,thehydroxylhydrogenwasas-signedachargeof+0.431e,andthe-carbonwasassignedachargeof+0.297e.Theremainingatomsborenocharges.Thischargedistributionproducedadipolemomentof2.36D.Whilesubstantiallylargerthanthegasphasedipolemoment.68D,thisvaluemimicstheincreaseinthedipolemomentobservedforpolarmoleculesinthecondensedphase,andisproportionallysimilartotheincreaseindipolemomentforliquidphasewater.[26]Forwater,theoxygenatomwasassignedachargeof)]TJ/F15 11.9552 Tf 9.2985 0 Td[(0.82eandthehydrogenswereassignedchargesof+0.41e.Simulationsof16%molefractionn-propanolinwaterwereperformedusinga2,523atomsystem.Thissystemconsistedof91n-propanolmoleculesand477SPCEwatermolecules,withcubicperiodicboundaryconditions.ALinuxBeowulfclustercomposedof1.8GHzAMDAthlonnodesperformedthecomputations,usingtheMPIversionofacodedevelopedattheCenterforMolecularModelingattheUniversityof26

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Atom A K C 3.39967 55.0359 Haliphatic 2.47135 7.8982 Opropanol 3.06647 105.846 Owater 3.15075 76.4666 Table3.4:Lennard-Jonespotentialparametersusedtomodelintermolecularandone{fourintramolecularinteractions.VLJr=4h)]TJ/F21 7.9701 Tf 6.675 -4.9766 Td[( r12)]TJ/F25 11.9552 Tf 11.9552 9.6838 Td[()]TJ/F21 7.9701 Tf 6.675 -4.9766 Td[( r6iPennsylvania,whichusestime-reversibleintegrationandextendedsystemtechniques.[22,27]Theprocessingloadwasdistributedovertwonodes,whichresultedinaprocessingrateof0.90spertimestepwitha1.0fstimestep.Thesimulationwascarriedoutinthreephases.Intherstphase,aninitialsetofatomiccoordinateswhichevenlydistributedthen-propanolandwatermoleculesonasimplecubiclatticewasassignedrandomvelocitiessampledfromaGaussiandistributionandthevelocitieswerescaledsothattheinitialtemperaturewas293K.Thesystemwasallowedtoequilibrateintheisothermal-isobaricNPTensembleusingextendedLagrangiantechniques.[22]Multipletimescaleintegrationwasused,withthelong-rangeintermolecularforcescalculatedevery1.0fs,forcesduetotorsionscalculatedevery0.5fsandotherintramolecularforcescalculatedevery0.125fs.Quantitiesofinterest,suchasthevolume,temperature,pressure,andtotalextended27

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systemandcomponentenergies,weremonitoredevery0.01ps.Theexternalpressurewassetto1.0atmandthebarostatfrequencywaschosenas1.0ps)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.[22,28]Thesecondphasebeganonceastablevolumehadbeenachievedthrougha100pssimulation.Volumedatawascollectedfor2.0ns.Fromthistheaveragevolumewascalculated,andtheperiodicboundarieswereadjustedfromtheirinstantaneousvaluestothecalculatedvalues.ThisconvertedthesystemtoanNVTensemblewithanoveralldensityof0.91g=cm3,whichisinreasonableagreementwiththeacceptedvalueof0.9311g=cm3.[26]EachatominthesystemwasthenassignedanewrandomvelocitysampledfromaGaussiandistribution.Thevelocitieswereinitiallyscaledtogiveatemperatureof4.0K,andthesystemwasallowedtoequilibratefor1.0psatthistemperatureinordertoresolveanybadcontactsresultingfromthesuddenchangeoftheperiodicbound-arylengthwithoutdisruptingtheaggregatestructure.Thissecondequilibrationwasnecessarysincetheatomiccoordinateswerenotscaledtotthenewperiodicbound-aries.AfurtherNVTsimulationof9.0psat293Kthenensuredthatthesystemdynamicswerestable.Inthenalproductionphaseatomiccoordinateswerecollectedforsubsequentanalysis.First,100setsof10.0pseachwerecollectedandusedtocalculategijr.Usingtimedependentplotsofgijrfromtheequilibratingsystemitwasdeterminedthattheradialdistributionfunctionshadconvergedtostablevaluesafter200ps,suggestingthatequilibriumhadbeenachieved.A2nssimulationwasthenperformed28

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togenerateatomiccongurationsforanalysis.Forcomparison,controlsystemsofpuren-propanolandwaterweresimulatedusingidenticalpotentialparameters.Forn-propanol,a256-moleculesimulationwasequilibratedinamanneridenticaltothemixedsystem.Thisgaveandensityof0.86g=cm3,avaluewithin6.4%oftheacceptedvalueof0.8034g=cm3.[26]Forwater,a512-moleculesystemwaspreparedusingthesamemethod,resultinginadensityof0.95g=cm3.Thisvalueiswithin5.2%oftheexperimentaldensityofpurewateratthesimulationtemperature0.9982g=cm3.[26]Bothsystemswereusedtogenerate2nsofcongurationsintheNVTensemble.Thesesetsofatomiccoordinateswerethenanalyzedusingthesamemethodsasthesimulatedsolutiontogeneratecomparisondata.29

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Figure3.1:RamanspectrumoftheintermolecularO{HOstretchingbandforvariousconcentrationsofn-propanolinwater.Thespectraappearstobealinearcombinationofthespectraofthepurecomponents.FigureexcerptedfromReference[12].30

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3.3Results&DiscussionModelValidationKirkwood-BuIntegralvaluescomparedwithexperimentaldataarepresentedasTable3.5.Table3.5demonstratesthegoodagreementthatisobtainedwhentheintegralsareperformedwiththehydroxyloxygenoralphacarbonofthepropanol.Usingthehydroxyloxygen,theresultingvaluesdierbyonly6%and4%,respec-tively,providingstrongevidencethatthemodelisreasonable.TheoverallagreementofGijvaluesfromtheMDsimulationwithexperimentalresultsconrmsthatthemodelsystemisagoodrepresentationoftheaggregationphenomenaobservedbyexperiment.Fromvisualinspectionofthesystemanimationitcanbeobservedthatn-propanolformedexclusiveaggregatesinagreementwithconclusionsfromtheRamanandscat-teringstudies.[12{15]AsshowninFigure3.2a,notdisplayingthewatermoleculesrevealedlargeopenspacesoccupiedbybulkwater,andnotdisplayingthen-propanolmoleculesinFigure3.2crevealedthattheaggregateswerelargelyanhydrous.Fig-ures3.2d-fshowasnapshotofsubsetsofn-propanolmoleculesgroupedaccordingtochainmembershipasdenedabove.Itisapparentthatthechainsthemselvesself-aggregateinadditiontohydrophobicassociationwiththefreen-propanol.31

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Hydrogen-BondCoordinationResultsDespitetheevidenceofcomponentstructurepreservationintheRamanspectra,thecoordinationdatapresentedinTable3.6indicatesthatthehydrogen-bondingstruc-turesofbothn-propanolandwateraresignicantlyaecteduponmixing.Whileonlyslightlymorethan1%ofthealcoholmoleculesdonotformhydrogenbondswithotheralcoholmoleculesintheneatsimulations,morethanhalfofthealcoholmoleculesarefree"inthemixture.Furthermore,theoccurrenceoftriple-coordinatedmoleculesintheneatsimulationisnearlyseventimestheoccurrenceoftriple-coordinationinthepresenceofwater.Thestructureofpurewaterissimilarlydisruptedinthepres-enceofn-propanol.Almostvetimesthenumberoffree"watermoleculeswerefoundinthesolutionsimulationwhencomparedtothecontrolsystem,andanoverallreductioninhydrogenbondingwasobservedcomparedtothepurewatersimulation.Thehydrogen-bondingdatarevealsmuchaboutthetypesofaggregationphenom-enapresent.Onaverage,approximately46n-propanolmoleculesoutof911%donotformhydrogenbondswithothern-propanol,approximately32moleculesaresingly-coordinatedwithothern-propanol,andapproximately12n-propanolaredoubly-coordinated.Onaverage,onetriple-coordinatedn-propanolmoleculewasobservedinhalfofthecongurations,resultinginabranchedchain.Sincethesingly-coordinatedn-propanolmoleculesterminatethechains,ignoringthebranchedchainsindicatesthatanaveragecongurationcontains16chains.Ifitisassumedthatnochainslargerthanthreemembersinsizeexist,thecoordinationdataimpliesthatat32

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leastfourchains5%aredimers.Ifweassumethatonlyonechainwithmorethantwomembersexists,thenamaximumof94%ofthechainscanbedimers.Thecoor-dinationhistogramofn-propanolinFigure3.3,conrmsthatinfactmorethanhalfofthechainaggregatesaredimers,andthatchainsofuptofourn-propanolappearineveryatomiccongurationsampled.Chainsofuptosixteenmemberswereobserved,albeitinfrequently.SnapshotsofseveralchainstakenfromvarioussetsofatomiccoordinatesareincludedasFigure3.4.Inthesechains,thealkyltailsofn-propanolturnawayfromthechainbackboneofO{HOhydrogenbonds,presumablyduetostericeects.Inthismanner,thelargerchainscreateastructuresimilartoahighly-branchedhydrocarbonmolecule,whichresultsinalargehydrophobicsurfaceareaforthechain.Thisstructurealsoshieldsthehydrogenbondsfrominteractionwiththebulksolvent,whichmayberesponsibleforthelinearindependenceoftheO{HOstretchingbandsforn-propanolandwater.[12]ThecoordinationdatapresentedinTable3.6alsosuggeststhattheaggregatestructureismicellarinnature.Despitetheexistenceoflargesingle-componentre-gionsintheliquid,substantialhydrogenbondingbetweenn-propanolandwaterwasobserved.Sinceonly17%ofthen-propanolmoleculeswerenothydrogenbondedtowaterwhileslightlylessthanhalfofalln-propanolmoleculesweremembersofchains,itcanbededucedthatwaterformshydrogenbondstotheO{HObackboneofthechains.Ifweassertthatalcoholsparticipateinamaximumoftwohydrogenbonds,thenonecanimplythatthesehydrogenbondsoccuronlyattheterminalhydroxyl33

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groupsofthechains.[16]Thislong-heldtheoryiscontradicted,however,bytheob-servanceofasubstantialpercentageofn-propanolmoleculespossessing3hydrogenbondstowater.Duetothewater-exclusionobservedinthesystemvisualizations,itcanbeassumedforthissystemthatthechain-waterinteractionsoccurprimarilyattheendsofthechains.FurtherevidenceofthishypothesiswillbepresentedinSection3.3.Theaggregatestructuredisruptsthestructureofbulkwaterattheinterfacetosomedegree,asdeterminedfromdatapresentedinTable3.6.Herewendthat,onaverage,1.03%ofwatermoleculesarecoordinatedwithveotherwaters,1.90%ofwatermoleculesarefreeofanyhydrogenbondstootherwatermoleculesandmostwatermoleculesareformingtwo{fourhydrogenbonds,consistentwiththedisruptedtetrahedralnetworkdescriptionofneatliquidwater.Aninterestingoccurrenceistheexistenceofasignicantnumberofwatermolecules.58%hydrogenbondedtotwon-propanolmolecules,suggestingtheexistenceofcompositechains.Giventhenumberofn-propanolmoleculesdoubly-coordinatedwithwater,atleastonen-propanol{waterchainexists.Therearepossiblyupto15n-propanol2H2Otrimersinanaverageconguration,withtheremainingdoublycoordinatedwatersformingbridgesbetweenann-propanolchainandafreen-propanolorchain.Thisisapossiblemechanismtoexplaintheproposedshifttowaterclustersinbulkn-propanolforconcentrationsabovep=0:6.Theoccasionalobservanceofcoordinationwiththreeormoren-propanolmoleculescorroboratesthisidea.34

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MoleculePair Gij i j MD SANS SAXS n-propanol n-propanol 1109 1270 OH OH 1044 CA CA 1395 n-propanol H2O -1129 -1210 OH OW -1176 CA OW -1342 H2O H2O 818 960 OW OW 1032 Table3.5:GijvaluescalculatedfromthegijrdatapresentedinFigures3.5and3.7comparedtoresultsfromsmall-angleneutronscatteringSANS[15]andsmall-angleX-rayscatteringSAXS[13]experiments.Notethatexperimentalagreementdeteriorateswhenthesiteofofhydrogenbonding,i.e.theoxygenatom,isnotusedasthelocationofthemolecule.35

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Figure3.2:Snapshotsoftworepresentativecongurationsfromthemoleculardynam-icssimulation.Waterandn-propanoldonotintermingleappreciably,inaccordancewithexperimentalevidence.Additionally,hydrogenbondedchainsofn-propanolmoleculesaggregatewithotherchainsandwithfreen-propanolthroughahydropho-bicassociationoftheiralkylgroups.36

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MoleculePair CoordinationNumber central coordinated 0 1 2 3 4 5 n-propanol n-propanol 51.26% 35.06% 13.14% 0.55% 0.00% 0.00% n-propanol water 16.67% 34.60% 35.75% 12.79% 0.19% 0.00% water n-propanol 76.83% 19.12% 3.58% 0.45% 0.02% 0.00% water water 1.90% 11.75% 30.06% 36.17% 19.09% 1.03% puren-propanol 1.07% 13.50% 81.76% 3.66% 0.001% 0.00% purewater 0.41% 5.65% 23.58% 40.39% 28.17% 1.78% Table3.6:Percentageofthecentralmoleculehavingthespeciednumberofhydro-genbondswiththecoordinatingmolecule.Forexample,12.79%ofthen-propanolmoleculesarehydrogenbondedtothreewatermolecules,while0.45%ofthewatermoleculesarehydrogenbondedtothreen-propanolmolecules.Includedforcompar-isoninthebottomtworowsaretheself-coordinationdataforsimulatedsystemsofn-propanolandwater,respectively.Insignicantoccurrencesofcoordinationnumbersgreaterthan5arenotincludedinthistable.37

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Figure3.3:Histogramoftheaveragenumberofn-propanolchainsorwaterclustersofagivensizenumberofmoleculesobservedinanaverageconguration.38

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Figure3.4:Snapshotsofhydrogen-bondedchainsofn-propanolrepresentingthevar-iouschainsizespresent.Abranchhead"isann-propanolmoleculethatacceptstwohydrogenbondsfromn-propanolanddonatesonetoathirdn-propanol,resultinginafork"inthechain.Notethatthealkyltailsformalargehydrophobicvolumethatshieldsthechainbackbonefromexposuretothesolvent.39

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Figure3.3presentsahistogramofthesizesofsmallwateraggregatesobserved.Inadditiontotheonelargeclusterofbulkwaterobservedineverycongurationnotshown,smallclustersofupto23watermoleculeswereobserved.Themajorityofthesesmallclustersaredimers,andFigure3.12demonstratesthattheyoccurprimarilyattheinterfacebetweenn-propanolaggregatesandbulkwater.Thisgurealsoindicatesthat,surprisingly,thefreewatersexistprimarilyintheregionsoccupiedbythebulksolvent.Smallclustersoftenormorewaterappearsoinfrequentlythattheywereconsideredbulkwaterforthecluster-statedependentgrdatadiscussedinSection3.3.MolecularDistributionsThemolecularandfunctionalgrplotsinFigures3.5and3.7providefurtherchar-acterizationofthetypesandextentofaggregationphenomena.Inthen-propanol{n-propanolcase,gpprfromFigure3.5isnearlyidenticaltogpprforneatn-propanol.Thisisstrongevidencethatthestructureofneatn-propanolispreservedinaque-oussolution.Therstpeakofgpprfortheaqueoussolution,whenintegratedusingEquation2.2,indicatesthattheaveragen-propanolclusteriscomprisedof10members,muchlargerthananycommonly-observedchaininthesimulation.Thisdiscrepancycanbeattributedtohydrophobicassociation.DespitetheproximityofCAtothecenterofmass,gCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(CArdierssignicantlyfromgpprrevealingthattherstpeakingppractuallyistheaverageofatleast40

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twotypesofrst-neighborinteractionsfortheaqueoussolution.Thesharprstpeakat4.5Acanbethoughtofasachainsignature,andthebroadshoulderfrom5{6.5Acanbeattributedtothehydrophobicassociationofalkyltailsfromneighboringn-propanolmolecules.ThisstructuralfeatureofgCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(CAralsoexistsinthedataforthepuren-propanolsystem,althoughthemagnitudesoftheindividualfeaturesaremodulated.Thesimilarintensitiesoftherstpeakresultsfromthehigherextentofhydrogenbondingintheneatsystem.Theelevatedhydrophobicshoulderontheplotforthesolutionindicatesthatthealkyltailarelocalized,resultingintheincreasedratiooftheirdensityatthisradiuscomparedtotheoveralldensityofn-propanolinthesolution.Thesimilaritiesinthelineshapesofthetwosystemssuggeststhattheaggregatesresembleregionsofpuren-propanolsurroundedbypurewater.Figure3.7providesevidenceofbothchainformationandhydrophobicaggregationofmultiplechains.ThelocationoftherstneighborpeakofgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrslightlyo-centerbetweentherstandsecondpeaksofgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(HOrisanunmistakablesignatureoftheO{HOatomsequenceofthechains,asisthesimilarityinthepeakspacingbetweengOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrandgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWr.Theexistenceofslightthirdandfourthneigh-borpeaksconrmthepersistenceofchainshavingatleastvemembers.Identicalshort-rangefeaturesexistinthecontrolsystemdata,buttheabsolutemagnitudesofthedataforthesolutionareslightlyelevatedabovethecontrolsduetoaggrega-tion.Oneimportantdierenceinthetwosystemsisthebroadrisefrom6{14AingOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrforthesolution.Thisfeatureresultsfromthehydrophobicassociationof41

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neighboringchainsthroughtheiralkyltails.ThisattributionwillbediscussedfurtherinSection3.3.Thesizeandspacingoftheaggregatescanbediscernedbycomparinggpwrwithgppr.Thelargetroughfrom4.5{7.65Aresultsfromwaterexclusioninsidethen-propanolaggregates,andalsoindicatesthattheaggregatesexhibitanaverageradiusof7.65A.Itscoincidencewiththerstpeakofgpprshowsthattherstpeakingpprisindeedrepresentativeofaggregation,andthattheclustersarespacedanaverageof9.6Aapart.Furtherevidenceoftwotypesofinteractionsbetweenn-propanolcanbeobservedbycomparinggpwrwithgCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWr.Therst-neighborpeakofgpwrexhibitsbimodality,withaslightpeakat3.5Agrowingfromthesideofalargerpeakat4.2A.Therstpeakcoincideswiththerst-neighborpeakofgCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWr,indicatingthattwomechanismsofinteractionwithwaterexistforn-propanol.Furthermore,themechanismthatresultsinacloserassociationtothecenterofmassdoesnotoccurveryoften,suggestingthatoneofthespeciesdenedbythisinteractionisshieldedfrombulkwater.Furthermore,whilegCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWrshowsevidenceofexposuretobulkwaterinitsregularly-spacedhumpsandtroughs,thecenter-of-massbasedgpwrlacksthispattern.Thisiscompellingevidencefortheexistenceofamicellestructure.ThedatapresentedinFigures3.9and3.10justifythedivisionofn-propanolintotwospeciesbaseduponhydrogen-bondingstate.Figure3.9showstherst-neighbordistancedistributionsforthehydrophobicsectionofthen-propanolmolecule,and42

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theirunimodalityrevealsthattheirmechanismofassociationisindependentofchainstate.Furthermore,thebroadnessoftheCA{CAandCM{CMpeakscorrespondstotheamorphousnatureofthesenonpolarinteractions.ThecoincidenceofthemaximumofCA{OWandCM{OWat3.5Aindicatesthattheirinteractionwiththebulkisparalleltotheinterface,suggestingacylindricalmicellestructurecenteredaroundthechainbackbone.ThisiscorroboratedbythelongtailoftheCM{OWcurve,whichindicatesthatasignicantportionofthemethylgroupsareburiedinsidetheaggregates.Alsoworthyofmentionisthelackofashoulderfrom5{6.5AontheCA{CAcurve,whichsuggestthatthe-carbonsaggregateindependentlyofhydrogenbonding,despitetheirproximitytothehydroxylgroup.Sincethechainstructureforn-propanolplacesthe-carbonsinsuchcloseprox-imity,itissurprisingthattwopeaksrepresentingthechainandfreespecieswerenotobservedintheCA{CArst-neighborhistogram.Thissupportstheideathathy-drophobicaggregationisindependentofhydrogenbonding,andalsoprovidesfurtherevidenceofcompositechains.ThehistogramofOH{OHdistancesfromFigure3.10indicatesthatthehydroxylgroupsofn-propanolmoleculesareseparatedby2.75Ainthechains,andby4.6Aforfreen-propanol.Thespacingofthefreen-propanolfromthisgraphcoincideswithwithsecondneighborpeakfromgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrfromFig-ure3.7.WhenconsideredinlightofthecoordinationdataandthelackofasecondpeakintherstneighbordistributionforCA{CA,thisindicatesthatthecontribu-tionofcompositen-propanol{waterchainsissignicant.Thesecompositechainsare43

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interpretedascomprisingtheouterlayerofatwo-speciesmicelle,withthehydroxylgroupsfromthecompositechainsforminghydrogenbondswiththebulkwater,andsuspendingthehydrophobicchainstructuresinthesolventthroughtheinteractionoftheirpropylgroupswiththoseofthechainmembers.Signicantwaterstructuredisruptioncanbedeterminedbytheexistenceofuptosevenwaterneighborsathydrogen-bonddistanceforwater,asdemonstratedbycoincidentpeaksat2.75AinallthedistributionspresentedinFigure3.11.Therstneighbordistributionalsoindicatesthatwatercanbedividedintotwospeciesbaseduponclustersize.Whilemostfreewaterexistseitherinthebulksolventoratthesolvent-aggregateinterface,asobservedinFigure3.12,thehumpintherstneighbordistributionforOW{OWindicatesthatoccasionallyawatermoleculeispulledawayfromtheinterfacebyann-propanolmolecule.Cluster-statedependentgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWrdataconrmsthatinterfacialextractiondoesoccurforbothsinglewatermoleculesaswellassmallclusters,whichwillbediscussedfurtherinSection3.3.Cluster-StateDependentRadialDistributionFunctionsFromtheanalysisofdatapresentedanddiscussedabove,itwasdeterminedthatn-propanolformedachain-centeredmicellestructurewithalayerofdisruptedwaterattheinterface.Radialdistributionfunctionsweregeneratedwhichtreatedchainandfreen-propanolasseparatespecies,andusedthesmallwaterclustersasanapproxi-matewaytodividewaterintobulksolventanddisruptedwaterinordertoprobethe44

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waterstructuredisruptionatthen-propanolaggregate-bulkwaterinterface.InFigure3.13,therst-neighborpeakintensityratiosforbothguOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWr:gcOH)]TJ/F21 7.9701 Tf 6.5866 0 Td[(cOWrandguCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWr:gcCA)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrare3:1.Thisrevealsthatthefreen-propanolmoleculesarethreetimesmorelikelythanchainn-propanoltobehydrogenbondedtobulkwater.Thisstrengthenstheideathatfreen-propanolmoleculesformasurroundinglayerthatshieldsthechainsfromexposuretobulkwater.ThebroadeningofthesecondpeakinguOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrmayindicatethatwaterstruc-turedisruptiondoesoccurattheaggregateinterface,butthatthisdisruptiondoesnotusuallyresultinthecompleteextractionofasmallsolventcluster.Despitethetendencyofthen-propanolchainstobesurroundedbyfreen-propanol,thesignatureofthewaterstructureingcOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrindicatesthattheyareexposedtothebulksolventtoasignicantdegree,andthattheirexposuredoesnotresultinthesametypeofstructuredisruptionthatisobservedforthefreen-propanol.Thisalsoagreeswiththeideaofanoblongsphericalmicellestructure,sinceitindicatesthatthechainendsarenotalwaysshieldedfromthebulk.Figure3.14providesevidencethattheextractionofsmallwaterclustersoccursprimarilyattheendsofthechains.TheexistenceofasecondneighborpeakingcOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOWrthatishardlydiscernibleinguOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOWrindicatesthatthefreen-propanolarelesslikelytopullasmallclusterintotheaggregateregion.Freen-propanolaremorelikelytodisruptthewaterstructure,however,asindicatedbythelackofbroadeningofthesecondneighborpeakingcOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWr.45

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Thetendencyofthefreen-propanoltoturntheiralkylgroupsawayfromthebulksolventandtowardsotheralkylgroupsisdescribedbyFigure3.15.The3:2ratioofintensitiesfortheslightrst-neighborpeaksofguCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWr:gcCM)]TJ/F21 7.9701 Tf 6.5866 0 Td[(cOWrsupportstheideaofamicellestructuresinceitindicatesthatfreen-propanolmoleculesareex-posedtoahighernumberofwatermolecules.BothgcCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrandguCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrshowamarkeddecitinthedensityofwaterinclosecoordinationwiththehy-drophobicportionofn-propanol.Theyalsolackthe2.75Apeakspacingsignatureassociatedwithexposuretothesolvent.Thelackofasharprst-neighborpeakforbothgcCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrandguCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrindicatesthatthesmallamountofcloseassociationofthemethylgroupandwateroccurswithoutawell-denedstructure.Bothfunctionsalsoexhibitaregionofdepressedintensityextendingto7.5Awhichcoincideswiththewater-exclusiontroughobservedingpwr.TheindependenceofthehydrophobicassociationinclusterformationcanalsobeseeninFigure3.15.AnoverallsimilarityinthestructureofCM{CMinteractions,asindicatedbycoincidentpeaksat4A,5.25A,and8{9A,aswellasasimilarminimumat7A,indicatesthatthealkyltailinteractionresultsinthesametypeofhydrophobicassociationregardlessofchainstate.TheoverallelevationofintensityofgcCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cCMrcanbeattributedtothelargehydrophobicsurfaceareapresentedbythechains,whichresultsinagreatertendencytoaggregate,butitssimilarityinstructuretogcCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uCMrandguCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uCMrassertsthatthehydrophobicinteractionmechanismisunaectedbyhydrogenbondingatthehydroxylgroup.46

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Thechain-chainhydrophobicaggregationinterpretedfromgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHriscon-rmedbygcOH)]TJ/F21 7.9701 Tf 6.5866 0 Td[(cOHrfromFigure3.16.Distinctneighborpeakscanbeobservedouttothefourthneighbor,indicatingve-memberchains.Thethirdandfourthneighborpeakslieontopofabroadregionofincreasedintensityfrom6{13.5Awhichcoin-cideswiththesecondpeakingppr.Thischain{chainaggregationresultsfromthehydrophobicassociationofthealkyltails,whichareturnedoutandawayfromthehydrogen-bondbackbone.Inthismanner,thechainsaggregatewiththemselvesasifeachchainwereahighlybranchedhydrocarbon,sincethehydrophilicgroupsareonlyexposedtothebulksolventattheendsofthechains,andarepossiblyfurthershieldedfrombulkwaterbymicellarn-propanolmoleculesandwater{n-propanolcompositechainsattachedtothechainterminus.FurtherevidenceoftheexistenceofthecompositechainscanbefoundinFigure3.16.TheregularpeakstructureofgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrappearsinallthreegrplots.Sincethechainstructureisdenedbyhydrogenbonding,gcOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOHrexhibitsaverystrongpeakat2.75A,andthelackofintensityforgcOH)]TJ/F21 7.9701 Tf 6.5866 0 Td[(uOHrandguOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOHrintheregionbetween2.5{3.25Aindicatesthatunlessn-propanolmoleculesarehy-drogenbondedtogether,theirhydroxylgroupsdonotassociateclosely.Freen-propanolinsteadtendstoassociatewithbothfreeandchainn-propanolataspacingof5A,whichcoincideswiththesecondneighborpeaksofgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHr,gOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWr,gOW)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWr,andgcOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOHr.Thisindicatesthatbothspeciesparticipateincom-positechains,wheren-propanolmoleculesaredisplacedfromthechainbackbone47

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andsubstitutedbyawatermolecule.Theexistenceofrstandsecondneighborpeaksat5Aand7A,respectively,inguOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOHrindicatethatbothn-propanol{H2O{n-propanolandn-propanol{H2O2{n-propanolstructuresform,withthesingle-waterstructurepreferred.Similarstructuresalsojoinchainsandcompositechains,asdeterminedbythesimilarpeakstructuresofgcOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOHr.Furthermore,thesechain{compositechainstructuresparticipateinchain-chainhydrophobicaggre-gation,asthegeneralriseingcOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOHrfrom6.5{14.75Ademonstrates.Uptothispoint,littlehasbeensaidaboutthemicellestructureotherthantheobservationthatthemethylgroupstendtoburythemselvesinanoblongsphericalaggregatestructure.Themicellesappeartobelargelyamorphous,withnowell-denedstructuresobservedotherthanthepureandcompositechains.Specically,guCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cCMrfromFigure3.15exhibitsthesamerstneighborpeaklocationasbothgcCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cCMrandguCM)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uCMr,whichrulesouttheexistenceofmicellestructureswherethefreen-propanolmoleculesinsertintothespacesbetweenthealternatingpendantalkylgroupsofthechains.Thechainsandcompositechainstendtobeexcludedfromthewaterstructuremuchlikeahydrocarbon,andaresuspendedinthesolutionbythemicellarn-propanolmolecules.Thesemicellarn-propanolmoleculesformaninterfacebetweentheaggregatesandthesolventbydonatinghydrogenbondstothewaterstructure,andturningtheiralkylgroupstowardsthealiphaticshellsurroundingthechainbackbones.48

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3.4Conclusions&FutureDirectionTheanalysisofthemoleculardynamicsindicatesthatat16%molefraction,n-propanolformsanamorphousmicellecenteredaroundahydrogen-bondedchainstruc-tureresemblingthepuren-propanolstructure.Thesestructuresconsistofbothpuren-propanolchains,aswellaschainsthatincludewatermoleculesinthehydrogen-bondbackbone.Thesechainsturntheirpendantalkylgroupsoutandawayfromthebackbone,andtheresultingstructureresemblesahighly-branchedaliphatichydrocar-bonwithhydrophilicsitesattheendsofthechains.Thenon-polaraliphaticregionsoftheclustersthenaggregatetogetherinamannersimilartobranched-chainhydro-carbonsinwater,andaresuspendedinthepolarsolventbyn-propanolmoleculeswhichturntheiralkyltailsinwardtowardsthechainsandformhydrogenbondswiththesolvent,disruptingthewaterstructureouttothesecondhydrationsphere,asdeterminedbypeakbroadeningingOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWr.Thisstructureisbestdescribedassmalldroplets"ofneatn-propanolemulsiedbythefree"n-propanolmolecules.AsimpliedschematicrepresentationoftheaggregatestructureisgivenbyFigure3.17.Thecurrentmethodofsortingwaterintobulksolventandinterfacialwaterneedsrenement.Sincethepresentmethodusesonlythehydrogenbondingdatatosortthewatermolecules,ahighlydisruptedclusterofwaterneedsonlyonehydrogenbondtothebulksolventtobeconsideredapartofthebulk.Amorecomprehensivemethodofwaterstructureanalysisshouldbeimplemented.Onepossibilityistheuse49

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oforderparameterssuchasthoseusedbyFidlerandRodger[19],whichtakeintoaccounttheneartetrahedralbondinganglesofwater.Theabilityofthechainterminalhydroxylgroupstoextractsmallclustersofwaterfromthebulksolventissignicantinthatitprovidesamechanismforthetransitionfromseparateclustersofn-propanolandwateratp60%towaterclustersinn-propanolsolventatp>60%.Itissuspectedthatastheconcentrationofn-propanolisincreased,boththenumberandsizeofthesmallwaterclusterswillincrease,andtheseclusterswillbecutofromtheeachotherbysurroundingn-propanolatthehighestconcentrations.Additionally,asthemolefractionisreducedtop<10%,thetransitionton-propanolclustersinbulksolventshouldalsobeobservedbyareductioninthesizeandnumberofsmallwaterclustersformed.Additionally,thestructuredisruptionobservedinthisstudyshouldresultinanincreaseintheamountoffreeO{HstretchingsignalpresentintheIRspectrumforwater,andshouldproducepeakcomponentsthataresimilartotheIRspectrumofeithergasphaseorinterfacialwater.50

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Figure3.5:Plotsofgijrvs.distance,r,forn-propanol{n-propanolgppr,n-propanol{watergpwr,andwater{watergwwr.Lineslabeledwiththesub-scriptsP"andW"usedthecenterofmassoftherespectivemoleculesasthelocationofthemolecule.Allotherlinesusedthesubscriptedatomasthelocationofthemolecule.Concentrationsaregivenasmolefractionofn-propanol.Notethatfor16%n-propanol,gpprisnearlyidenticaltogpprfor100%n-propanol,whichispresentedasFigure3.6.51

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Figure3.6:Controlsystemgijr,forcomparisontoFigure3.5.52

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Figure3.7:ComparisonofgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrwithgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWrandgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(HOr.Theal-ternatingpeaksofgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrandgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(HOrforthe16%n-propanolsolutionareindicativeofhydrogenbondedchains.Thisalternatingstructureisclearlyobserv-ableintheneatn-propanoldata.AlsonotethesimilarityofthepeakstructuresofgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHrandgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWrforthe16%n-propanolsolution.Acomparisonplotoftheseradialdistributionsforpuren-propanolispresentedasFigure3.8.53

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Figure3.8:Controlsystemgijr,forcomparisontoFigure3.7.54

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Figure3.9:DistributionsoftheradialdistancetotherstneighborforCA{CA,CM{CM,CA{OW,andCM{OW.Notethenearunimodalityofthedistributions.55

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Figure3.10:DistributionsoftheradialdistancetotherstneighborforOH{OHandOH{OW.Notethebimodalityofthedistributions.56

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Figure3.11:Distributionsoftheradialdistancebetweenwateroxygensfortherstsevenneighbors.Notethatuptosevenwatermoleculesarefoundintherstcoordi-nationsphere,despitethefactthatnomorethan5hydrogenbondswereobservedforasinglewatermoleculeinthe16%n-propanolsolution.Alsonotethattheplateauontherst-neighbordistributionissimilartotherst-neighbordistributionforOH{OW.57

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Figure3.12:Snapshotsofarepresentativecongurationfromthemoleculardynamicssimulationareshownthatdisplaysthenatureofsolvationforasingleaqueousn-propanolclusterwiththesurroundingn-propanolmoleculeshiddenforvisualization.Thesolvatingwaterischaracterizedasfreenothydrogenbondedtootherwatermolecules,clustered,andbulk-like.Notethattheclusteredandfreewatermoleculesformacurvedinterfacebetweenthebulkwaterregionandtheregionoccupiedbythen-propanolaggregates.58

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Figure3.13:Cluster-statedependentgrplotsshowingtheinteractionsofthehy-drophilicendofn-propanolwithbulkwater.NotethatguOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(cOWrisquitesimilarinstructuretogOW)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OWrforneatwaterfromFigure3.5.59

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Figure3.14:Cluster-statedependentgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(uOWr.NotethatonlygcOH)]TJ/F21 7.9701 Tf 6.5866 0 Td[(uOWrhasasignicantsecondneighborpeakfornon-bulkwaters,indicatingthatthechainendsaremorelikelytoextractsmallclustersfromthesolvent-micelleinterface.60

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Figure3.15:Cluster-statedependentgrplotsshowingtheinteractionsofthehy-drophobicendofn-propanol.Thesimilaritiesinthelineshapesindicatethatthealkyltailinteractionsareindependentofhydrogenbondingstatusofn-propanol.61

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Figure3.16:Cluster-statedependentgOH)]TJ/F21 7.9701 Tf 6.5865 0 Td[(OHr.Notethattherst-neighborpeaksforinteractionsinvolvingfreen-propanolcoincidewiththesecondneighborpeakforthen-propanolchains,neglectingtheremnantsofchainformationobservedbetween0{3.5A.Thisisstrongevidencefortheexistenceofcompositechainsoftheformn-propanol{H2Ox{n-propanol.62

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Figure3.17:Simpliedtwo-dimensionaldiagramofthetypesofstructuresobservedinthesolution.Oxygenatomsarehighlightedinred.Molecularbondsareindicatedbysolidblacklines,andhydrogen-bondsarerepresentedbydottedlines.Thealkylhydrogensarenotshown.63

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Chapter4ModelingPolarizationEectsforWater4.1IntroductionForpracticalpurposesthereexistsonlyonekindofwater,yetthissinglemoleculeexhibitsawiderangeofbehaviors.Fromactingasthesolventinnearlyallknownbiologicalprocessestollingstructuralrolesinmanybiologically-activeproteins,thecomplexbehaviorofwaterrepresentsoneofthegreatestsimulationchallengesknown.Inorderforawatermodeltobevalidinheterogeneoussystemssuchassolutionsorinterfaces,itmustaccuratelymodelthestructureanddynamicsofbothbulkliquidwaterandvaporphasewater,whilecapturingthetransitionbehaviorsatinterfaces.Itmustalsoreactappropriatelytothepresenceofbothpolarandnon-polarsolutes.DevelopmentofpotentialenergysurfacesforwaterbeganwiththeworkofBernalandFowlerin1933[30],andcontinuestobeanactiveareaofresearch.[31,32]Despiteyearsofresearchanddevelopment,thegoalofauniversalpotentialsurfacedescribingthefullrangeofexperimentalobservablesremainsanelusivegoal.64

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OneofthemorepopularmodelsinusetodayistheSimplePointCharge/Flexible"SPC/Fmodel.Thismodelrepresentstheelectrostaticpotentialsurfacearoundthemoleculeusingpartialpointchargesttoreproducethepressureandpotentialen-ergyofliquidwater.[33,34]Theresultingpartialchargesareassumedtoreproducetheaverageliquidphasemoleculardipoleforwater,aquantitythathasnotyetbeenaccuratelymeasuredbyexperiment.Unfortunately,thismeansthatataliquid-vaporinterfacethevapormoleculesdonotexhibittheknownvapor-phasemoleculardipole,andhencethismodelcannotaccuratelyrepresentthedynamicsofwaterundertheseconditionsifpolarizationplaysasignicantroleinthedynamicsofwater.Sincetheelectrostaticpotentialsurfaceisalsogenerallybelievedtobesensitivetoitsspecicenvironment,watermoleculescoordinatinganotherspecieswillnotbeadequatelydescribedbyamodelwhichalwaysexhibitstheaveragepolarizationofabulksampleofneatwater.Modelingpolarizationisnotatrivialendeavor.Inadditiontothebonddipolechangesbroughtaboutbyintramolecularmotions,thepresenceofexternaleldsdis-torttheelectronicstructure.AnexampleofthetypesofpolarizationeectsexhibitedbywaterispresentedinFigure4.1.Iftheexternaleldsresultfromthepresenceofnearbymolecules,theseelectronicstructuredistortionscanpotentiallyinducesimilardistortionsonallofitsneighbors,whichinturninducenewdistortions.Theresultingmany-bodyeectscanproducemotionsandforcesthatareimpossibletopredictusingstaticpointcharges.Sincethesecooperative/anti-cooperative"eectsarethought65

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tobeasignicantcontributortomoleculardynamics,andespeciallyimportantfortheaccuratedescriptionofwater,[35]itisimperativethattheybeincludedinanyforceeldthatwillbeusedtomodelsystemsthatarecapableofproducingsignicantstructuralvariation.Manypolarizablemodelsforwaterexistintheliterature,andsomegivereasonableapproximationstotheenergy,dynamicsandstructure.Anexcellentrecentdiscussionofthestateoftheart"inclassicalwaterpotentialdevelopmentwasgivenbyFinney.[31]OfparticularinterestaremodelsbasedupontheTholemodelduetoitssuccessinthecalculationofspectroscopicobservables.[8,36{40]ThischapterpresentsresearchintotheadditionoftheTholepolarizationmodeltotheexistingSPC/Fmodelinanattempttocreateamoreaccuratemodelforstudyingthedynamicsofsolutionsandinterfaces.4.2TheoryItisoftenthecasethatmultiplesimpleapproximationsareusedtorepresenttheelec-trostaticinteractionsofamolecularsystem.Whenconstructingapotentialsurfaceforperformingmoleculardynamicssimulations,onemustalwaysweightheneedforaccuracyagainstthecomputationaldemandsofthespecictheoreticaldescriptionchosen.Ifitcanbedemonstratedthattheelectronicstructurechangesaectingtheintermolecularpotentialsurfacearesmallandsmooth,thepolarizationeectscanbemodeledinanaveragemannerusingtuned"partialpointchargesstrategically66

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placedwithinthestructureofamolecule.Thismethodofmodelingtheelectrostaticpotentialsurfaceassumesthatapairwise-additivedescriptionofintermolecularinter-actionsissucient,anassumptionthatmaynotholdtrueasexperimentandtheoryslowlyconvergetowardsagreaterunderstandingofmolecularinteractions.Still,thecomputationaleciencyofthesemodelsmakethemanattractivealternativetoamorerigorousdescriptionoftheelectrostaticinteractions.Itwillbedemonstratedlaterinthischapterthatthepoint-chargeapproximationtechniqueexhibitssignicantlydierentstructuresandvibrationaldynamicsforwa-terthanwhenpolarizationistreatedexplicitly.Exacerbatingmattersisthelackofsuciently-detailedexperimentaldataneededtoperformapreciset"oftheem-piricalpotentialsurfacetophysicalrealityatintermolecularlengthscales.Thus,aversatileandcomputationally-ecienttheoreticaldescriptionofpolarizableelectro-staticsisnecessarytoinvestigatemany-bodyeectsinsimulationdynamics.Suchatheoreticaldescriptionmustbeeasilymodiedand/orcombinedwithothercalcu-lationsinordertodevelopageneral-purposesimulationprogram.Itistothistaskwhichwenowturn.ElectrostaticsTheSPC/Fmodelrepresentstheelectrostaticpotentialsurfacesurroundingawatermoleculebyplacingpartialpointchargesateachoftheatomiccenters.Thesechargesarethenassumedtointeractwiththepointchargesonothermoleculesviaclassical67

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electrostatics.Thepotentialatsiteiduetoapointchargelocatedatsitejisthereforei=qj 40rij.Forconvenience,wedeneourunitsofchargetobenormalizedby1 p 40,removingthe1 40termfromthepotentialexpression.Thus,wehavedenedthepotentialexperiencedbyparticleiinasystemofNpointchargesasi=NXj=1;j6=iqj rij.1whererij=jri)]TJ/F41 11.9552 Tf 11.9894 0 Td[(rjj.Thisexpressionisthestartingpointforalloftheenergy,eldandforcederivations.Sincethepotentialsurfaceofamoleculecanchangeinthepresenceofanexternaleld,wewillneedtoincludeaninductionmechanismthatcorrectsthepotentialsurfaceautomaticallyinamannerthatapproximatesphysicalreality.Wewillusevariabledipolemomentslocatedateachatomtodescribetheelectrostaticpotentialdierencesinducedinasinglemoleculebytheeldofitsneighbors.Thedipolemomentofasystemofchargesisdenedaccordingtotherelationship,=N>1Xiqiri.2andthisexpressiongivesthetotaldipolemomentforamoleculeconsistingofonlypointchargesifiisrestrictedtoparticlesonaspecicmolecule.Thequantityricanalsobeinterpretedasthelocationofthecenter-of-chargeoftheelectronicstructuresurroundinganatom,andisalsoindependentoftheorigin.Itisimportanttonotethatthismodelusesanabstractionoftheformaldenitionofadipole,removingtherequirementthatitconsistofmultiplechargesitesandallowingittoexistatasingle68

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pointfortheoreticalpurposes.Thelengthoftheseparationvectoristhusassumedtobesmallcomparedtotheinteratomiclengthscale,andforconveniencewetreattheresultingdipoleasthoughitresidesatthenucleus.InteractionTensorExpressionsEquation4.1denesazero-rankelectrostaticmonopoleinteractiontensor.Fromthisexpression,inaccordancewithPrincipleC"fromThole,[36]asetofsuccessively-rankedtensorsusedtocalculatetheenergy,eldandforcebetweenanytwopointchargesordipolesarederivedbytakingsuccessivegradientsof1 rij.Thisresultsinthefollowinginteractiontensors,usingthenotationandsignconventionsofNymandandLinse:[41]Tij=1 rij.3Tij=rTij=rij; r3ij.4Tij=rrTij=3rij;rij; r5ij)]TJ/F20 11.9552 Tf 13.1506 8.0877 Td[( r3ij.5Tij=rrrTij=15rij;rij;rij; r7ij)]TJ/F15 11.9552 Tf 13.1507 8.0877 Td[(3rij;+rij;+rij; r5ij.6where;;2fx,y,zg,rij;isthe-componentofrijandr=@ @rij;.T,TandTarethe-,-and-componentsoftheinteractiontensors.Thesetensorsaresymmetric,afeaturethatcanbeconvenientlyexploitedforoptimizationandmemory-conservationpurposes.69

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Figure4.1:Polarizationeectsonthewatermonomerpotentialsurfacecausedbythepresenceofahydrogen-bondedneighbor.Thepositivepotentialregionoftheacceptormoleculehasbeenextendedoutwardinthedirectionofitshydrogens,andthenegativepotentialduetothelone-pairelectronsonthenon-interactingsideoftheacceptoroxygenhasbeengreatlyreduced.Additionally,thepositivepotentialofthedonor'sfreehydrogendropssignicantly,andthenegativepotentialduetothelonepairsofthedonoroxygenincreasesnoticeably.Recentexperimentsindicatethatthesespecicpolarizationeectspersistinbulkliquidwaterunderambientconditions.[29]ElectrostaticpotentialcalculatedusingtheGAMESSelectronicstructurepackage,andrenderedusingtheMacMolPlotapplication.70

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ItcanbeshownthatforanyinteractiontensoroftheformTij=f0 rijwheref0isanarbitraryfunctionofrij,thefollowingusefulexpressionsarevalid:Tij=rij; r3ijf1.7Tij=3rij;rij; r5ijf2)]TJ/F20 11.9552 Tf 13.1507 8.0878 Td[( r3ijf1.8Tij=15rij;rij;rij; r7ijf3)]TJ/F15 11.9552 Tf 13.1506 8.0877 Td[(3rij;+rij;+rij; r5ijf2.9wherethetensorcoecientfunctionsfnaregivenbyf1=f0)]TJ/F20 11.9552 Tf 11.9552 0 Td[(r@ @rf0.10f2=f1)]TJ/F15 11.9552 Tf 13.1507 8.0877 Td[(1 3r@ @rf1.11f3=f2)]TJ/F15 11.9552 Tf 13.1507 8.0878 Td[(1 5r@ @rf2.12Foranite-sizedsystemofpointchargesanddipoles,f0=1,andtheseexpressionsreducetotheexpressionsgivenbyEquations4.3-4.6.Anotherusefulpropertyisthatforanyadditively-combinedtensorcoecientfunctionf0=g0+h0,usingassociativityandthesumruleforderivatives,f1=g0+h0)]TJ/F20 11.9552 Tf 11.9551 0 Td[(rg00+h00=g1+h1.13f2=g1+h1)]TJ/F15 11.9552 Tf 13.1507 8.0878 Td[(1 3rg01+h01=g2+h2.14f3=g2+h2)]TJ/F15 11.9552 Tf 13.1507 8.0878 Td[(1 5rg02+h02=g3+h3.15Theutilityoftheserelationshipswillbemadeapparentbelow.71

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ElectrostaticInteractionsInordertoperformasimulationofthedynamicsofchargedparticles,wemustknowtheforcesactinguponthem.Werstdenetheelectrostaticinteractionpotentialenergyofparticleiasthechargeonparticleimultipliedbythepotentialatsiteriduetoallotherchargesatsitesrjwherej6=iinthesystemofinterest,thensumoverallitoarriveatthetotalelectrostaticpotentialenergyU.Theresultingexpressionforthepotentialenergyofasystemofchargesisthus:U=1 2NXi;j6=iqiTijqj.16Wenextdenetheeldatsiteiasthegradientofthepotential:Ei;=Xj6=iTijqj.17andtheforceasthegradientofthepotentialenergy.Fi;=qiXj6=iTijqj.18Forasystemofpointdipoles,wedenethepotentialatsiteriduetothepointdipolesjas:i=Xj6=iTijj;.19Forimplementationpurposestherewillbeachargeandpointdipoleassociatedwitheachatomonthemolecule.Therefore,charge-charge,charge-dipole,dipole-chargeanddipole-dipoleinteractionsmustbeincludedinthetotalexpression.Atermexpressingthecontributionoftheelectronicstructuredistortiontotheenergy72

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mustalsobeincluded,andistypicallyreferredtoasthepolarizationenergy."Theresultingexpressionsfortheenergy,eldandforceare:U=1 2Xi;j6=iqiTijqj+qiTijj;)]TJ/F20 11.9552 Tf 11.9552 0 Td[(i;Tijqj)]TJ/F20 11.9552 Tf 11.9552 0 Td[(i;Tijj;+1 2Xi)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1i2i.20Ei;=Xj6=iTijqj+Tijj;4.21Fi;=Xj6=iqiTijqj+qiTijj;)]TJ/F20 11.9552 Tf 11.9552 0 Td[(i;Tijqj)]TJ/F20 11.9552 Tf 11.9552 0 Td[(i;Tijj;.22Notethatthepolarizationterms)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1i2iareindependentoftheparticlecoordinates,andthereforedonotappearintheexpressionsfortheeldorforce.ApplequistModelTheproposedmodelusesanatomdipoleinteractionmodelinitiallydevelopedbySilberstein,adaptedtoincludemany-bodydipole-dipoleinteractionsbyApplequistet.al,thenmodiedtopreventnumericalinstabilitybyThole.[36,42,43]Thedipolesarenotstatic,nordotheyexistintheabsenceofanexternaleld.Theyinsteadsimulatethereactionofanatom'selectronicstructuretoanappliedeld.Sincedipole-induceddipoleforcescannotbeadequatelyrepresentedinasimplepairwise-additivemanner,wemustaccountfortheinteractionofinduceddipoles.AlthoughitwillbeclearlydemonstratedthattheApplequistmodelisunsuitableformodelingdensemolecularsystems,itprovidesasolidfoundationfortheimplementationofbetterpolarizationmodels.Thus,wewillpresentthismodelhereasajumping-o"pointforthedevelopmentandimplementationofdistribution-basedpolarizableelectrostaticsmodels.73

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TheApplequistmodelrepresentsdipoleinductionlinearlybyassociatinganisotropicpolarizabilityvaluewitheachatom.Thisquantitypossessesunitsofvolume.Thedipoleinducedonatomiisthusi=iEi.23Eachoftheseinduceddipolesproducesaeldofitsown,andthiseldchangesthevalueofforallotherparticles.Thisresultsinthefollowingexpressionforthedipoleonparticleiinanite-sizedsystemofparticles:i;=iXj6=iTijqj)]TJ/F20 11.9552 Tf 11.9552 0 Td[(Tijj;.24Theself-consistentformofEquation4.24presentsaseriouschallengetothistheory'snumericalimplementation.Inordertocomputetheinduceddipoles,onemustknowthevalueoftheeldateachpoint,andtheelddependsonthedipolesaswellasthecharges.RearrangingEquation4.24intothefollowingform)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1ii;+Xj6=iTijj;=Xj6=iTijqj.25allowssolutionbymatrixinversion,buttheprohibitivecomputationalexpenseofthismethodrestrictsitsusetosmallsystemsconsistingofafewhundredatoms.Iterativesolutionmethodsprovideamoreecientalternative.Inthesemethods,theinitialdipolevaluescalculatedfromtheeldofthepointchargesareusedtore-calculatetheeldandproduceanewsetofinduceddipoles.Thisrecalculation/inductioncyclerepeatsuntiltwosubsequentsetsofdipolevaluesdierbylessthananarbitrarytolerancecriterion.Thesemethodsarebynomeanscomputationallycheap,"buttheydoprovideatractablealternativetolargematrixmethods.74

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TholeModelAseriousproblemwiththeApplequistmodelcanbedemonstratedbyconsideringasimplediatomicmolecule.WeletArepresentthepolarizabilityofatomA,BrepresentthepolarizabilityofatomB,andrrepresenttheirbondingdistance.SolvingEquation4.25forthissystemproducesthewidely-knownresultk=A+B+4AB r3 1)]TJ/F18 7.9701 Tf 13.1507 5.0455 Td[(4AB r6.26?=A+B)]TJ/F18 7.9701 Tf 13.1507 5.0455 Td[(2AB r3 1)]TJ/F21 7.9701 Tf 13.1506 5.0455 Td[(AB r6.27wherekisthepolarizabilityalongtheinteratomicaxis,and?isthepolarizabilityperpendiculartotheinteratomicaxis.[43]Theseequationsexhibittheunfortunatepropertyofasymptoticallyapproachinginnityasrapproaches6p 4ABand6p AB,respectively.Innitepolarizabilitiesarenotobservedinnature,sothispresentsamajorimpedimenttotheimplementationofthispolarizationmodelintoamoleculardynamicsprogramgiventhecloseproximityofatomsduringcollisions.Inordertopreventtheonsetofinnitepolarization,TholemodiedApplequist'smodelbyreplacingsomeofthepointchargesanddipoleswithsphericallysymmetricdistributionsthatsmearout"thechargesanddipoles.[36]Byreplacingonepointchargeandpointdipoleonaninteractingpairofparticleswithsuitabledistributions,thecombinedpolarizabilityofthepairshrinkstoamorereasonablevaluewhenrij!6p AB.Tholetestedseveralformsofthedistributionfunction,recommendingaconicaldampingfunctionasthebestchoiceforcalculatingmolecularpolarizabilities.75

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Thediscontinuityofthisfunctionrendersitunsuitableformoleculardynamics,asFigures4.2&4.3illustrate.[44{46]Toremedythis,2=3a 4e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3isimplementedinstead.Theparameteraisthewidthoftheexponentialdistribution,andS=rij 6p ij.WiththismodicationtheexpressionfortheeldatparticleiduetoadistributedchargeonparticlejatascalardistancerbecomesEij=1 A3r2rZ03a 4e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3r2dr=1)]TJ/F20 11.9552 Tf 11.9551 0 Td[(e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3 r2.28Sincetheeldisdenedbyd dr,weintegrateequation4.28todeterminethemonopolepotentialfunctionij=1)]TJ/F20 11.9552 Tf 11.9551 0 Td[(e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3+3p aS\0502 3;aS3 r.29where)1(a;b=1Rbta)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(tdtistheincompletegammafunction."[45,47]Notingthatthepointchargetensorcoecientfunctionf0=1hasbeenreplacedbyafunctionofrij,thenumeratorofijcanbeusedtodeneanewsetoftensorcoecientfunctionshn,h0=1)]TJ/F20 11.9552 Tf 11.9552 0 Td[(e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3+3p aS\0502 3;aS3.30h1=1)]TJ/F20 11.9552 Tf 11.9552 0 Td[(e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3.31h2=1)]TJ/F20 11.9552 Tf 11.9552 0 Td[(e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3+aS3.32h3=1)]TJ/F15 11.9552 Tf 13.1507 8.0878 Td[(1 5e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(aS3+aS3+3aS34.33Thesefunctions,whensubstitutedforfninthetensorequationspresentedinSection4.2,implementtheTholemodelforasystemofchargesandinduceddipoles.76

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EwaldSumsSincethepotentialtensorforapointchargefallstozeroslowlyduetother)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1factor,simulationsofbulkpropertiesusingnitesystemsmustusealargenumberofparticlestoensurethatatthelargestvaluesofrijinthesystemijbecomeseectivelyzero.ThispresentsanenormouscomputationalchallengeforsimulationsofliquidsandsolidssincethenumberofpairsisproportionaltoN2particles.[2,48]Thesameproblemexistsforinnitelyperiodicsystems,asthesystemmustbelargeenoughfortheelectrostaticpotentialcontributionofapairatthecutodistancetobeessentiallyzero.Compoundingmattersisthenon-additivenatureoftheTholemodel,astheostensiblyshort-rangedipolepairinteractionshavebeenfoundtobequitesensitivetoerrorsinthetreatmentofinteractionsatthecutodistance.Althoughthemostcomputationallyecientmethodforhandlinglong-rangedipoleinteractionsisthereactioneldmethod,thismethodassumesahomogeneousdielec-triccontinuumsurroundingthecutoradius,renderingitunsuitableforheteroge-neoussystems.[49]Theapplicationofarbitrarysplinesandsmoothingtothedipoleinteractiontensorsisphysicallyquestionable,thereforeEwaldsummationwascho-sen.Ewaldsummationcalculatesthelong-rangecontributionstothepotential,eldandforceinadditiontoaccountingforpotentialtruncationinaninnitelyperiodicsystemifproperlytuned.[25,50]Inthismethodanoppositely-chargeddistributionsurroundseachchargeanddipole.Gaussiandistributionsarecommonlyused,andthisdistributionservestoscreentheinteractionbetweentwopairssuchthatthepo-77

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tentialforapairofchargesseparatedbytheperiodiclengthofthesystemeectivelyvanishesbelowthelimitofnumericalsignicance.AslongasasmoothlyvaryingdistributionwithanexactFouriertransformisused,wemaythencalculatetheen-ergycontributionofeachparticleinteractingwithneighboringperiodicimagesofthesystemusingFouriertransformmethods.Sinceweareperformingthecalculationforasystemofpointchargesinsteadofscreenedcharges,wemustthensubtracttheelectrostaticcontributionsofasetofdistributionshavingthesamepolarityasthepointchargesandawidthequaltothescreeningdistributions.OfparticularinterestforthisprojectisthecombinationoftheTholemodelwithEwaldsummation,sincethismethodcanbetunedtominimizepotentialcutonoise.Fortunately,thecombinationofEwaldsummationwiththeTholemodelonlyeectsthescreened,orreal-space,"calculations,sincethesmearing"distributionsarenarrowenoughtobeeectivelytreatedaspointchargeswellbeforethepotentialcutodistanceisreached.ThepotentialatsiteiduetoaGaussianchargedistributionlocatedatsitejpossessingatotalchargeof1isij=erfrij rij.34whereisthewidthofthedistribution,alsoknownastheconvergenceparameter,"anderfistheerrorfunction."[41]Thescreenedreal-space"potentialforasystemofpointchargesisthereforei=Xj;j6=iqj1 rij)]TJ/F25 11.9552 Tf 13.1158 11.3575 Td[(Xj;j6=iqjerfrij rij=Xj:j6=iqjerfcrij rij.3578

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whereerfc=1:0)]TJ/F15 11.9552 Tf 11.9552 0 Td[(erf.Ifwedenethefollowingredundantexpressions,Ga=rij.36Gb=)]TJ/F15 11.9552 Tf 9.2984 0 Td[(erfGa4.37Gc=e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(G2a p .38thenaccordingtoEquations4.10-4.12theEwaldmethodtensorcoecientsareg0=Gb.39g1=g0+2GaGc.40g2=g1+4 3G3aGc.41g3=g2+8 15G5aGc.42Thesefunctionsgnareaddedtohn=1forasystemconsistingonlyofpointchargesandpointdipoles.79

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Figure4.2:Leadingscalarmultiplierforthehighest-ordertermfromeachofthefourtensorsneededtoimplementtheconicaldampingdistributionasaforceeld.Thesedistributionsgivethebesttforthemolecularpolarizabilityofasinglemolecule,butdonotresultinstabledynamicsduetotheabruptdiscontinuityintheforcetensor.80

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Figure4.3:Leadingscalarmultiplierforthehighest-ordertermfromeachofthefourtensorsneededtoimplementthe2dampingdistributionasaforceeld.Thesedistributionsallowstrongerpolarization,butdonotdestabilizetheintegrator.81

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4.3MolecularDynamicsMethodsDuringtheinitialplanningofthisprojectitwasfoundthatnoexistingandreadily-availablegeneral-purposemolecularsimulationcodewassuitableformodicationtoincludetheelectrostaticsmodelderivedinthepreceedingsection.Manypublic-domaincodeswereinvestigated,andallwereeithertoofragile"towarrantextensivemodication,orwerebuiltusinglegacydata-structuresthatareinherentlyinecientonmodernmicroprocessorarchitectures.Additionally,themajorityofexistingpro-gramsarewrittenalmostentirelyinFORTRAN.Thislanguagelackskeyconstructsandoperatorsneededtoimplementavarietyofcommonplatform-independentnon-mathematicaloptimizations.Italsofailstoprovidedynamicmemoryallocationfa-cilitiesinallbutthemostrecentdialectsofthelanguage.Itscolumn-major"matrixstorageschemedoesnotworkwellwithcache-basedarchitectures,either,andpro-cessorsofthistypenduseinnearlyallhigh-performancecomputingsystems.TheC"programminglanguagewasdesignedfortheexplicitpurposeofwritingoperatingsystemsandrelatedutilities.Despitethis,itsmemory-managementfacili-tiesandwealthofoperatorsmorethanosetitslackofanativecomplexnumbertypeandmissingexponentoperator.Additionally,therelaxedvariablenamingrestrictionsallowprogramstobewritteninaself-documentingfashionwhichfacilitatesquickde-buggingandeasymaintenance.Furthermore,theabilitytodenedatastructuresastypesallowsalevelofdataencapsulationthatisallbutimpossiblewiththeFOR-TRANcommonblock"facility.Althoughthelearningcurveforthislanguagecan82

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bequitedaunting,itsexibilityandpowerhavemadeitthestandardprogramminglanguageinmanyelds.Therefore,theC"languagewaschosentowritetheinitialsimulationprogram,withtheintentofusingtheprogram'sarchitectureasthemodelforanewhigh-performancegeneral-purposesimulationpackagedesignedspecicallyformodernprocessors.ComputationalDetailsSimulationsof2-,3-,64-and512-moleculesystemswereperformedusingawater-specicsimulationcode.CodedentirelyinISOC89"usingtheportablethreadslibrary"forparallelization,thiscodeimplementstheThole2polarizationmodelinconjunctionwithamodiedimplementationoftheSimplePointCharge/Flexible"SPC/Fmodel.[34]VelocityverletinthemicrocanonicalNVEensemblewaschosenastheintegrationmethod.Allmodelparameterswereimplementedasmacrosandusedtobuildoptimizeddatastructuresthatminimizedataredundancyandmaximizelocalityofreferencewhileremaininggeneralenoughtoalloweasymodication.[11]Cubicperiodicboundarieswereused,andthesimulationcellvolumewasxedtoreproducetheaccepteddensityofliquidwaterat298Kand1atm.Verletlistsbasedonthecenters-of-massofthemoleculeswereusedtoimplementpotentialcutosandpreventtherepetitivecalculationofpairseparationdistancesduringthedipoleiterationprocess.83

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Usingatimestepof0.5fswithVerletlistsupdatedeveryothertimestep,thecalculationsgenerallytook10longertocompletewhencomparedtotheCPU-hoursneededtocalculateanequivalentsimulatedtimeusingthebaseSPC/FmodelwiththeCM3Dmoleculardynamicspackage.[22,27]Acutodistanceofhalftheperiodicdistance2.574Awasemployedforallpairwiseinteractions,resultinginthestorageofapproximately68,400molecularpairsandtheircorrespondingtensorsets.Thisresultedinatotalmemoryfootprintofapproximately512megabytes.Asistypicalofmoleculardynamicsprograms,themajorityofcomputationtimewasspentintheelectrostaticsroutines.Solutionoftheself-consistentpolarizationequationswasaccomplishedusingthesimultaneousover-relaxationmethod,"withalltensorsstoredinmemorybetweeniterations.AnimplementationofAhlstrom'smethodwasusedtoaccelerateconver-gencebygeneratinganextrapolatedguess"ofthedipolevaluesfromthevaluescalculatedduringthepreviousthreetimesteps.[51]Aconvergenceparameterof10)]TJ/F18 7.9701 Tf 6.5865 0 Td[(7DwasspeciedforthemagnitudeoftheindividualCartesiancomponentsofeachdipole.Thisresultedinaninitialiterationrateof31cycles/timestep,whichdroppedincrementallyto16cycles/timesteponcefourtimestepshadbeenperformed.Theiterationcountswerequitesensitivethethechoiceofmodelparametersandsystemsizes,andthevaluesgivenabovedescribetheparametersetwhichgavethebestagreementtothelineardiusionconstant.84

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EwaldsummationwithGaussiandistributionswereusedtocalculatethelong-rangeelectrostatics.Acompile-timeoption,implementedasamacro,determinedwhetherlong-rangecontributionstothedipoleeldwerecalculatedduringthedipoleiterationprocess.Itwasfoundthatenergyconservationwastoopoorusingthisoption,andthereforeallsimulationswereperformedwithacompletecalculationofthelong-rangeeldateachiteration.PotentialSurfaceModelAcommonmethodologyinpublishedstudieswhichdevelopedapolarizablemodelofwateristoscalethechargesofanexistingmodelforbulkwaterdowntoreproducethegas-phasedipole,thenplaceisotropicpointpolarizabilitiesoneachatomiccenter.[45,46,50]Wehaveadoptedthismethodology,adaptingtheSPC/Fmodelforuseasapolarizablemodel.AsummaryofallparametersusedtodenethepotentialsurfacesofbothSPC/FandthenewmodelaregiveninTables4.1{4.5. O{HBond VrOH=kf1)]TJ/F20 11.9552 Tf 11.9551 0 Td[(e)]TJ/F21 7.9701 Tf 6.5865 0 Td[(kbrOH)]TJ/F21 7.9701 Tf 6.5866 0 Td[(req2 kfK kbA)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1 reqA 51261.772 2.566 1.0000 Table4.1:Oxygen-HydrogenBondingPotential.IdenticaltotheSPC/Fmodel.85

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H{HBondBend VrHH=1 2kf[r)]TJ/F20 11.9552 Tf 11.9552 0 Td[(req]2 kfK A2 reqA 165370.0 1.633 Table4.2:Hydrogen-HydrogenBendingPotential.Representedasasingleharmonicbondbetweenthetwoatoms.IdenticaltotheSPC/Fmodel. CrossBonds Vrij;rjk=kfrij)]TJ/F20 11.9552 Tf 11.9552 0 Td[(reqijrjk)]TJ/F20 11.9552 Tf 11.9552 0 Td[(reqjk AtomTriple kfK A2 reqOHA reqHHA O{H{H -106408.0 1.000 1.633 H{O{H 56210.0 1.000 1.633 Table4.3:Cross-bondPotentialParameters.IdenticaltotheSPC/Fmodel.86

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Lennard-JonesParameters Vrij=4 rij12)]TJ/F25 11.9552 Tf 11.9551 13.2704 Td[( rij6 Atom K A O 78.22 3.166 H 0.00 0.000 Table4.4:IntermolecularpairpotentialsIdenticaltotheSPC/Fmodel. ElectrostaticParameters Atom qe A3 O -0.6690-0.82 0.837 H +0.3345+0.41 0.496 Table4.5:ElectrostaticParametersChargesinparenthesisareforthenon-polarizableSPC/Fmodel.PolarizabilitiesarefromThole's2distribution.[36]87

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InordertomaintainconsistencywiththeApplequistmodel,dipoleeldcalcu-lationswereperformedforallpairswithinthespeciedcutoradiusregardlessoftopologicalrelationships.Asaresult,calculationandaccumulationoftheforcesandpotentialenergyforintramoleculardipolepairswasrequiredduetothegradientrela-tionshipsbetweenthepotential,eldandforce.SimilarlytoBurnhamandBernardo,itwasfoundthattheTholemodelmustalsobeappliedtoallinteractionsinvolvingthechargesinordertoachievereasonabledynamics.[45,46]Forsimplicity,the2distributionwasusedforboththedipolesandcharges.FittingMethodologySincetheTholemodelisanempiricalmodel,theparametersmustbettoreproduceexperimentalobservables.Tholespeciesthatasingledampingwidth,aDD=0:572,issucienttoreproducethemolecularpolarizabilityofasinglemoleculeconstructedfromC,H,NandO.Previousstudieshavefoundthatthisvaluedoesnotpreventover-polarizationinabulksimulation,aconclusionalsoreachedduringthisproject.[44{46]Twopreviousstudiesalsoconcludedthatmultipledampingwidthswererequired.[45,46]Unfortunately,wefoundthatusingBurham'swidthparametersresultedinexcessivetranslationaldiusion,whileBernardo'swidthparametersresultedintoolittlediusion.Asaresult,aniterativesearchwasperformedinordertolocatetheoptimumvaluesforaccandaddusingthelineardiusioncoecientcalculatedfromthemeansquaredisplacementasthettingtarget.88

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Implementingseparatedampingwidthsforthechargesanddipolesintroducesseveralcomplications.Althoughintuitionimpliesthatthevalueofacdshouldfallsomewherebetweenaccandadd,perhapsasacd=p accaddoracd=1 2accadd,thishasnotyetbeeninvestigated.Forexpediency,wehaveadoptedthemethodologyofBurnham,asimpliedbyBernardo,ofusingacd=acc.Thisresultsinthestorageofvetensorsofvariousrankperatomicpairwithlong-rangeeldcontributionsincludedinthecalculation,orsixperpairiflong-rangeeldcontributionsareignored.Fittingwasperformedusingamulti-stepprocess.Inallsimulations,itwasfoundthatatimestepvalueoft=0.5fsprovidedthebestratioofdipolesolveriterationstototalsimulationtime,maximizingtheratioofsimulatedtimetorunningtime.Inordertominimizenumericalerror,theelectrostaticsroutinesweretunedtogiveseven-gureconvergenceintheHamiltonian,andthedipoleconvergencecriterionwassetto110)]TJ/F18 7.9701 Tf 6.5865 0 Td[(7D.First,astable512-moleculecongurationwasobtainedbymini-mizingacongurationgeneratedbyanon-polarizableSPC/Fsimulationtoeliminateover-polarizationduetobadcontactdistances.Inordertoconserveprocessingtime,asingleminimizedcongurationwasusedasthestartingpointforallsubsequentsteps.Next,theresultingcongurationwasassignedrandomvelocitiestakenfromaGaussiandistributionofrandomdeviates,nettranslationofthesystemwassub-tracted,andthevelocitieswerescaledtoproduceaninstantaneoustemperatureof50K.Thesystemwasallowedtoequilibratefor5ps,withthetemperaturemaintainedviaasimplevelocity-scalingthermostattriggeredwheneverthetemperaturedeviated89

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by10K.Followingthisstep,anewsetofrandomvelocitieswerethenassignedtotheatoms,nettranslationwasremoved,andthevelocitieswerescaledtoproduceaninstantaneoustemperatureof298K.Thesystemwasthenallowedtore-equilibratewithscalingtriggeredat5Kfor10ps,thenfor5psat10K,andnallyfor5psat20K.Congurationsamplecollectionbeganduringthenalscalingrun,withsamplescollectedevery50fs.Thetemperaturefromthe20Ksimulationwasthenchecked,andifscalingdidnotoccur,thetemperaturescalingrangewasrelaxedto50K,andsamplecollectioncontinuedto100ps.Ifscalingdidoccur,however,the20Kscalingstepwasrepeateduntilthetemperaturestabilized,atwhichpointsamplecollectionwascontinueduntil100pswasreached.Onaverage,theaforementionedprocesstooksixweekstocompleteforasinglecandidatepotentialusingthreethreadsonemaster+twoslavesona2.8GHzdual-Xeoncomputer.Twenty-ninecandidatepotentialsweretested,resultinginatotalcombinedruntimeofapproximately44,000CPU-hours,orslightlymorethan5CPU-years.Asareferencepoint,severalcombinationsofdampingwidthsreportedasstableintheliteratureweretested,butmostwerefoundtoover-polarizeseverely,resultinginextraordinarilylowdiusionratesandotherundesiredeects.Thisprob-ablyresultsfromthecombinationofintramoleculardipole-dipoleinteractionswithmolecularexibility,asmostpublishedThole-TypeModelsusearigidatomiccong-uration.Themajorityofthesesimulationswereterminatedbeforetheycompletedtomakemoreprocessortimeavailable,resultinginatime-savingsofapproximately290

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CPU-years.Theinitialcandidatepotentialwasselectedbyusingdimersimulationstoidentifyseveralstablecombinationsofdampingwidths,andthesecombinationswereusedtodeneagridofparameterspaceandlocateacoarseapproximationtothebestt.Theprospectivecombinationwasthenbracketedbyusingalleightper-mutationsoffacc10%,add10%gplusthecandidateparametersettoperformbulksimulations.Fromeachbracketingrun,anewcandidateparametersetwaspredictedbyextrapolatingorinterpolatingthesquareddeviationsofthecalculatedlineardif-fusionconstantstozero.Astheiterationprocesswascontinued,thevariationoftheparameterswasreduced.Aswiththeliteraturevaluetests,simulationswhichclearlydidnotmatchexperimentwereterminatedtoconservecomputationalresources.Fromthenalcongurationgeneratedbythedynamicsttingprocess,threespectroscopiccalculationrunswereperformed.Foreachofthesesimulations,thesystemwasrandomizedbyassignmentofanewsetofrandomvelocities,removingnettranslation,thenscalingthevelocitiestoproduceaninstantaneoustemperatureof298K.Thetemperaturewasthenstabilizedbytwo10psscalingrunsat5Kand10K,respectively.Samplecollectionwasthenperformedevery4fsoverthecourseofa75pssimulation,andthespectrawascomputedusingthemethodpresentedinSection2.3.Thespectralresultsfromthethreesimulationswerethenaveraged,andtheirradialdistributionfunctionswerecheckedtoverifythattheaverageliquidstructurehadnotchanged.91

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Smallersystemsizesweretested,buttheirdynamicsdieredconsiderablyfromthe512-watersystem.Unfortunately,theseverecomputationalburdenofthesimula-tionspreventthetestingoflargersystemsizestoruleoutperiodicityeectswithoutextensivemodicationstothesimulationcodeorlong-termexclusiveaccesstoamassivesymmetricmulti-processormachine.Additionally,relaxingtheelectrostaticconvergenceparameterstogive3-gureconvergenceintheHamiltonianandadipolermsconvergencelevelof110)]TJ/F18 7.9701 Tf 6.5865 0 Td[(6Dproducedsignicantlydierentdynamicalre-sults,althoughthenaltwasstillwithin22%oftheexperimentaltargetandthestructuralresultsdidnotexhibitanoticeablechange.Inordertoinvestigatetheeectsofhydrogenbondreorganizationonthespectra,asetofdimersimulationswereperformed.Thetraditionalmethodofassigningrandomvelocitiestotheatomswasfoundtobeinadequateforthisinvestigation,asittendedtoimpartalargenetangularmomentumtothecluster,andtheCorioliseectsrandomlysplitthesimulatedspectrainanunpredictableway.Thus,anewrandom-energyinputmethodwasdeveloped.Aminimum-energydimerwaspreparedbysettingthevelocitiesofallatomsinatestcongurationtozeroandallowingthetwomoleculestofallintoeachotherinthepresenceofaquasi-blackbodyexternalnoiseeldgeneratedbyconvolvingasequenceofGaussianrandomdeviateswiththelterpresentedinFigure4.4.AlthoughthislterdoesnotexhibitthebandasymmetryassociatedwithaPlanckdistribution,itsantisymmetriccharacterensuresthatenergyisequallylikelytobeaddedorremovedfromthesystemduetoitstime-92

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domainrepresentationofht=f+0.5,0.0,-0.5g.Aseparaterandomsequencewasgeneratedforeachcomponentoftheeldvectorforeachoftheatoms,andaddedtothestaticchargeeldpriortothebeginningofthedipolecalculation.TheeldwasscaledsothatitspresencewasclearlyvisibleintheHamiltonianwithoutcausingasignicantenergydriftordisruptionofshort-timescaledynamics.Thevelocitieswereresettozeroateachexcursionoutsideofthemaximumallowedtemperature.Onceastabletemperaturehadbeenreachedinthepresenceofthesimulatedthermalnoise,thenoiseintensitywasreducedandthescalingprocesswasrepeated.Oncethetemperaturehadbeenstabilizedinthepresenceofnoiseatatemperatureof110)]TJ/F18 7.9701 Tf 6.5865 0 Td[(21K,thenoisewasremoved,azero-velocityrestartwasperformedwithascalingtriggertemperatureof110)]TJ/F18 7.9701 Tf 6.5865 0 Td[(23K,andanalminimizationrunwasperformed.Thisprocesswasrepeatedforsixtrials,eachstartingfromadierentrandomizedinitialconguration,andeachresultinginthesameminimum-energystructure,threeofwhichwerebit-identicalintheirbinaryrepresentation.Oncetheminimum-energydimercongurationwasidentied,themoleculesweretranslatedapartalongtheO{Ointeratomicvectorbyvaryingamounts,andallowedtointeractfor10psinthepresenceofarandomeldtoensurethatthesystemdynamicswerestableandsucientlyrandomized.Thisresultedinfoursystemsatapproximatetemperaturesof4K,21K,46Kand84K.Thesesystemswerethenrunfor100psinthepresenceofnoise,andarestartlewasgeneratedevery1000steps.5ps.The200restartlesgeneratedwerethenrunfor400pswithout93

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DimerSimulationTemperatures hTi;K hTi dT dt;K=ps 3.5 9:910)]TJ/F18 7.9701 Tf 6.5865 0 Td[(2 +8:910)]TJ/F18 7.9701 Tf 6.5865 0 Td[(6 20.8 7:310)]TJ/F18 7.9701 Tf 6.5865 0 Td[(2 )]TJ/F15 11.9552 Tf 9.2985 0 Td[(3:910)]TJ/F18 7.9701 Tf 6.5865 0 Td[(7 46.0 1:1 +2:010)]TJ/F18 7.9701 Tf 6.5865 0 Td[(2 84.4 6:610)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1 +2:210)]TJ/F18 7.9701 Tf 6.5865 0 Td[(3 Table4.6:Averagetemperature,standarddeviationoftheaveragetemperature,andaveragetemperaturedriftrateforthedimersimulationsusedtostudyhydrogen-bondrearrangement.Asetof200simulationsof400psinlengthwereusedforeachtemperaturetocalculatethedatapresentedhere.thesimulatedthermalnoise,andsampleswerecollectedevery4fs.Theaveragetemperature,standarddeviationofaveragetemperaturesandaveragetemperaturedriftarereportedinTable4.6.Theoutputofthesesimulationswereusedtocomputeaveragespectra.Additionally,transition-specicspectralfeatureswerecalculatedbylocatinghydrogen-bondrearrangementeventsandcomputingtheaverageDFTofasamplewindowcenteredoneachoftheobservedevents.94

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4.4Results&DiscussionFittinganewwatermoleculeisanarduousprocess,asthereismuchvariationinthereportedexperimentalmeasurementsofatomic-scaledynamics,andtheoreticaldescriptionsofthepotentialsurfaceoftenincludearbitraryempiricalapproximationssuchasthepoint{distributioninteractionsintheTholemodelasdiscussedinSections4.2&4.3.Surprisingly,anddespitealloftheadvancesincomputationalpowerandexperimentaltechnologyduringthelast50years,boththestructureandthedynamicsofambientliquidwaterarestillopenquestions.Untilaclearconsensusbackedbyunambiguousexperimentalevidenceisreachedregardingthemicroscopicdetailsofliquidwater,itwillremainimpossibletodeterminewhetheranywatermodelprovidesaphysicallyvaliddescriptionofthelocalstructureanditsrelationshiptotheobservedvibrationaldynamics.Thus,theimpliedpurposeofwatermodeldevelopmentistoprovideinsightintowhichstructures,vibrationsanddiusionprocessesareneededtoaccuratelydescribetheinteractionsofwatermoleculesinallenvironments.Withcontinueddevelopmentandfurtherexperimentalprogress,thegoalofapredictiveuniversalwatermodel"mayonedaybereached.FinalFitParametersInordertoprovideanewpoint-of-viewfromwhichtoaddresstherelationshipbetweenstructureanddynamics,awell-characterizedbulktransportquantitywaschosenasthetargetobservable.Thettingtobulkdynamicsisnovel,aspolarizablewater95

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modelsaregenerallyparameterizedandtusingsmallH2Onclusters,n2f2,...,20g,duetothecomputationalburdenoftheself-consistenteldcalculation.[45,52]Thebulk-ttingapproachhasbeensuggestedintheliteraturebyseveralstudies.[53{56]Althoughtheseparticularstudiesrefertostructuralquantitiesasattingtarget,theover-archingthemeofthissuggestionisthatsystem-sizeeectsmayspanmuchlargerdistancesthanpreviouslythought,andsmallclustersmaynotadequatelycapturethesubtletiesofthepotentialsurfacenecessarytoensureanaccuratebulksimulation.GiventhatthereisconsiderableroomforimprovementinthequalityofexperimentalmeasurementsofmicrostructuralquantitiessuchastheKirkwood-Buintegral,[31,53]andthatthestructureofliquidwaterasinterpretedfromscatteringexperimentsiscurrentlyatopicofintensedebate,[29,57{61]thelineardiusionconstantwasinsteadchosentotthepolarizabilitymodel.Thebestagreementwiththelineardiusionconstantwasobtainedusingtheval-uesacc=0:31andadd=0:21,resultinginatranslationaldiusionconstantof0.244A/ps.SeeFigure4.5Thisdiusionrateiswithin12%oftheacceptedvalue.[62]Furthermore,therotationalanisotropyagreeswellwithcurrentexperimentalevi-dence.RecentnuclearmagneticresonancestudiesonneatD2OhavedeterminedthatOH:OOP=1:33.[63]ThequantitiesOHandOOPrefertothedecorrelationtimesoftheO{Hbondvectorandcross-productofthetwoO{Hbondvectors,respectively.Thebest-tparametersgiveavalueof1:46forthisratio,within13%oftheexper-imentalmeasurementforD2O.Althoughthedirectcomparisonofthisquantityto96

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thatofsimulatedH2Oisquestionableatbest,noexperimentalmeasurementofthisratioforH2Ohasbeenreported.Overall,thevalidityofthemodelpresentedinthischaptermustbeviewedwithsomesuspicion,ascomputationalnecessitymandatedveryshortsimulationsandthusthepossibilityofcorrelationwiththeinitialcongurationexists.Additionally,thedynamicsofmolecularsystemshavebeenfoundtovarysignigantlywiththetuningparametersandsystemsizebythisauthorandothers.[49]Adetailedstudyoftheseeectsbeyondtheaforementionedconvergencecriteriadependencecheckhasyettobeperformed,againduetoprohibitivecomputationalrequirements.Thus,furtherresearchandtestingisneededtoconrmthattheseresultsarelegitimate,andthat512moleculesunderambientconditionssucientlyeliminatesartifactscausedbylong-rangemany-bodyinteractionsspanningtheperiodicboundaries.Despitetheselegitimateconcerns,thecurrentmodelclearlyexhibitssomeinterestingbehaviorsdirectlyrelatedtothecurrentdebatesoverthestructureofliquidwaterandthecalculationofspectroscopicobservablesfromclassicalsimulations.97

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Figure4.4:TransferfunctionofthelterusedtoconvertGaussianrandomdeviatesintoasequenceofsmoothlyband-limitedrandomdeviatesusedtomodelthermalnoiseinthelocalelectriceldofeachmolecule.98

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Figure4.5:Bulkdynamicswerettothelineardiusionconstant.Inthisploterr=Dtrial)]TJ/F20 11.9552 Tf 10.7115 0 Td[(Dexperiment,whereDisthelineardiusionconstant.ExperimentaldatatakenfromReference[62].99

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StructuralResultsTheprimarypointofcomparisonforintermolecularstructureistheradialdistributionfunction,orRDF.Sincetherelativearrangementsofnearestneighborsaectsboththetransferofenergyandthespecicdiusionprocessesthatoccurinaliquid,theaccuratereproductionofthiskeystructuralquantityiscriticaltotheproperdescriptionofmoleculardynamicsinbothliquidsandsolids.Unfortunately,theexperimentalandtheoreticalcommunitieshavenotyetreachedaconsensusregardingthiscrucialquantityandtheunderlyinglocalstructureforwater.Theradialdistributionfunctionofliquidwaterisobtainedexperimentallyfromphotonorparticlescatteringexperimentsprimarilybytwomethods.TheEmpiricalPotentialStructureRenement"EPSRmethodpioneeredbyA.K.Sopermodiesanexistingpotentialmodeluntilthesimulatedstructurefactorsagreewithexperi-mentalmeasurements,atwhichpointthesimulatedgrisassumedtorepresenttheradialdistributionofatomsintheexperimentally-probedliquid.[68]AnalternativemethoddevelopedbySorensenet.alusesabasisset"ofradialdistributionfunctionsfromsimulationsinconjunctionwithexperimentalcurvesandtheoreticalpredictionstotaradialdistributionfunctionRDFtothemeasuredstructurefactors.[67]Thecommonfactoremployedbybothofthesemethodsistheuseofmolecularsimula-tiontechniquestogenerateRDFsusedtorepresentthenalresult.Giventhatmostmolecularmodelsforwaterweredevelopedwhilethetetrahedralstructureofliquidwaterwasnotanopenquestion,thepossibilityexiststhatthesemethodscanslant100

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theinterpretationofscatteringresultstowardsatetrahedraldescriptionduetotheuseofmolecularmodelsdesignedtoreproducethisstructure.Asanexample,considerthemostrecentO{ORDFforwaterpublishedbyHuraet.alandpresentedhereasFigure4.6.Theevenly-spacedunimodalpeakstructureclearlyindicatesthatthestructureofliquidwateristetrahedral,inagreementwiththelong-standingtextbookdescriptionofliquidwater'sstructure.UsingthesameexperimentaldataasHuraet.al,however,SoperappliedEPSRusinganasymmet-richydrogenpoint-chargemodelforwaterandarrivedatasimilarRDF,withtheexceptionofanaddedpeakontheoutsideofthesecond-neighborpeakattributedtotheexistenceoflinear3-memberhydrogen-bondedchains.[65]SeeFigures4.11&4.9ThisresultagreeswiththendingsofarecentandcontroversialX-rayAbsorb-tionSpectroscopyXASandX-RayRamanSpectroscopyXRSstudybyWernetet.al.[29]Inthisstudy,itwasfoundthatthepresenceofhydrogenbondscauseelectronicstructureshiftsthatintroduceanasymmetricchargedistributionbetweenthetwohydrogens.Theresultingelectronicstructuredistortiondecreasesthepartialpositivechargeofthenon-donorhydrogen,whichpreventstheformationofmorethantwostrong"hydrogenbondsbyasinglewatermonomer.Thisresultsinadominanthydrationstructurecomposedofsingle-donor{single-acceptormolecules.Theauthorsassertthatthisindicatesthatthestructureofliquidwatercannotbetetrahedral,butisinsteadcomposedofstronglyhydrogen-bondedringsandchainsconnectedbyaweaklyhydrogen-bondednetwork.Lessthansixmonthsafterthepublicationofthe101

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Wernetstudy,anindependentXASstudybySmithet.aldirectlychallengedtheirresults,assertingthatthewaterstructureproposedbyWernetet.alresultsfromtheirdenitionofthehydrogenbond,andthattheirresultisinfactconsistentwithatetrahedralliquidstructure.[58{60]Thenewpolarizablemodelpresentedinthischapterappearstosupportthecon-troversialconclusionsofWernetet.albyexhibitingthestructuralfeatureduetoasymmetricchargedistributiondemonstratedbySoper.Asamplethree-memberhydrogen-bondedchainisolatedfromthebulksimulationispresentedinFigure4.10,andtheradialdistributionfunctionsgeneratedwithandwithoutexplicitpolariza-tionarecomparedtotheHuraet.alresultinFigures4.7&4.8.Therst-neighborstructureappearstobeunaectedwhencomparedtothenon-polarizablemodel'sRDF,andtheshapeandpositionoftherstsecond-neighbor"peakfromthepolar-izablesimulationmatchestheshapeoftheexperimentalRDF,althoughitsintensityisclearlyattenuatedbythepresenceofacompetingstructure.WhileHead-GordonandJohnsondrawthereasonableconclusioninasubsequentarticlethattheassump-tionofstatichydrogenchargeassymetryisincorrect,[57]themodelpresentedinthischapterclearlydemonstratesthatastaticchargeasymmetryinthemodelisnotnecessarytoreproducethedisputedstructuralfeature.ThestructuralfeatureinquestionwasalsopresentinanabintiosimulationstudydonebySpriket.althatwasdiscussedinanarticleonwaterstructuredeterminationbySorensonet.al.[66,67]Thisfeaturewasreasonablydismissedasasystemsize102

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eectbythelatterauthors,andtheaformentionedRDFispresentedhereasFigure4.12.Intuitionandcommonsimulationexperiencedoimplythattheprobabilityofnitesystemeectsarehighfora32-moleculesimulationsuchastheonepublishedbySpriket.al.Whatisintrigingaboutthisparticularfeature'sattributiontonite-sizeeects,however,isthatthemodelpresentedinthischapterwasttodynamicsdatausingabaseelectrostaticsmodelthatreproducesatetrahedralliquidstructureinexcellentagreementwiththeHuraet.alresultbytreatingpolarizationinanaveragemanner.Thus,itwasanticipatedthatthestructurewouldremaintetrahedralaftertheinclusionofexplicitpolarizationeectsintothegas-phasemodel.Furthermore,ttingwasperformedusingasystemsizethatshouldpreventtheobservationofnite-systemeects.[49]Despitetheseprecautionsthenewmodelclearlyexhibitsthisextrapeak,whichpresentssomeseriousandcomputationallychallengingimplicationsforthesimulationcommunityiftheattributionofthisfeaturetonite-systemsizeeectsiscorrect.Attemptingtore-tthemodeltoreproducetheRDFpresentedinFigure4.6de-stroyedboththediusiondynamicsandtherst-neighborpeakagreementwithoutcompletelyeliminatingthequestionablefeature,asFigure4.13demonstrates.Thus,onecanconcludethatthereappearstobeadirectlinkbetweenthestructureanddynamicsofliquidwater,andthislinkisclearlyrelatedtotheinclusionofelectronicstructuredistortioneectsintheclassicalpotentialmodel.Thisissimilartotheargu-mentputforthbyWernetet.al.Thus,anindependentthirdexperimentalobservable103

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isneededtodeterminewhichinterpretationoftheX-rayabsorptionandscatteringexperimentsiscorrect.Thefollowingsectionspresentspectroscopicobservablescal-culatedusingthenewpolarizablemodel,andwilldemonstrateonepotentiallinkbetweenthehydrogenbondrearrangementdynamicsandthebulkstructureofliquidwaterthatmaybedirectlyrelatedtothecurrentstructuralcontroversy.BulkSpectraAsstatedpreviously,thisprojectdidnotintendtochallengelong-heldassumptionsaboutthestructureofliquidwater,butwasinsteadsimplyanattempttocreateamoreaccuratemodelofwaterdynamicsatinterfaces.Despitethisaim,comparingtheIRspectrumcomputedbythesetwomodelsprovidessomeevidencethattheWernetet.alhypothesismaybecorrect,althoughtheseresultsareunderminedbytheratherpoorcondencelevelofthet.Thissectionwillattempttodemonstratethatusinganexplicitlypolarizablemodelwithpropertreatmentoflong-rangeelectrostaticscanproducequalitativelyaccurateIRlineshapes,particularlyinthebendingregion.Thisandthefollowingsectionwillalsodemonstratethattheassociationband"maybedirectevidenceofanasymmetricmany-bodypolarizationeect,andthatthepresenceofthisbandinthepolarizablesimulationresultsmayindicatethatthestructurepredictedbythismodelisclosertophysicalrealitythanthatpredictedbySPC/F.104

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Figure4.6:ExperimentalradialdistributionfunctionforwaterasdeterminedbyX-rayscatteringexperiments.DatafromReference[64]downloadedfromhttp://thglab.lbl.gov/.105

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Figure4.7:Comparisonofmolecularradialdistributionfunctionsforthetwomodelsandexperiment.Bothsimulationsystemswerecomposedof512atoms.Thenon-polarizablesystemwassimulatedintheNVTensemble,whilethepolarizablemodelwassimulatedintheNVEensemble.ExperimentaldatafromReference[64].106

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Figure4.8:Comparisonofmolecularradialdistributionfunctionsforthetwomodelsandexperimentintheregionofthesecondhydrationsphere.Bothmodelsexhibitastructuralshiftoutwardstartingatthesecondneighbor.ExperimentaldatafromReference[64].107

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Figure4.9:Proposedlinearchainstructureforliquidwater.DarkblueshadingoffreehydrogensH2representstheirincreasedelectronegativityasindicatedbyrecentXRSandXASexperiments,andthustheirreducedcapacityfortheformationofhydrogenbonds.FigureexcerptedfromFigure1inReference[57].108

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Figure4.10:Smallwaterchainfromthepolarizablesimulation.Theasymmetricelectronicstructuredistortionthoughttoberesponsiblefortheformationofchainstructuresispresentintheinduceddipoles,whichareshownhereasvectorsextendingfromeachatom.TheO{O{Oangleis92,indicatingthatthismaybeabrokentrimerstructure.109

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Figure4.11:AsymmetricchargemodelEPSR-determinedRDFforwatercomparedtoarecentexperimentalRDF.[64,65]Usingadierentmethodwiththesameex-perimentalinputproducesastrikinglydierentresult.FigureexcerptedfromFigure4inReference[57].110

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Figure4.12:AbinitioRDFfora5pssimulationof32watermoleculesbySpriket.al[66]dashedlinecomparedtorecentlydeterminedRDFforwatersolidline.Thissimulationexhibitsasecond-neighborfeaturesimilartothatproducedbythemodelpresentedinthiswork.FigureexcerptedfromFigure9ainReference[67]andeditedtoremoveanotherdatasetforclarity.111

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Figure4.13:Comparisonofmolecularradialdistributionfunctionsforthestructuralttingattempt.ExperimentaldatafromReference[64].112

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Figure4.14:SimulatedIRspectrumofa64-waternon-polarizableSPC/Fsystemat300K,inarbitraryunits.ExperimentaldatatakenfromReference[69].Post-processeddipolesobtainedfrom[70].113

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Figure4.15:SimulatedIRspectrumofa512-waterpolarizableSPC/Fsystemat300K,inarbitraryunits.ExperimentaldatatakenfromReference[69].114

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Figure4.16:Comparisonofintermolecularregionsforthetwomodelsandexperiment.Althoughthenon-polarizablemodeldoesabetterjobofcapturingbandpositionsandintensities,thepolarizablesimulationdoesabetterjobofreproducingthebandlineshapes.ExperimentaldatatakenfromReference[69].115

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Figure4.17:Comparisonofthebendingregionslogarithmicy-scaleforthetwomodelsandexperiment,highlightingtheabsenceofanassociationband"inthenon-polarizablesimulation.ExperimentaldatatakenfromReference[69].116

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Figure4.18:Comparisonoftheregionsbetweenthelibrationalbandandbendingbandlogarithmicy-scale.Thesimulatedbandcenteredat1158cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1istheresultofexcessivecouplingsbetweentheO{Ostretchingandbendingmotions.ExperimentaldatatakenfromReference[69].117

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Figure4.19:ComparisonoftheO{Hstretchingregionslogarithmicy-scaleforthetwomodelsandexperiment.Althoughthenon-polarizablesimulationexhibitsbetteragreementwiththeoverallbandcenter,itdoesnotcapturethesmallfeatureat4000cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Thispeakmaybered-shiftedforthenon-polarizablesimulation,disappearingintheexcessivewidthofthebandcomparedtoexperiment.ExperimentaldatatakenfromReference[69].118

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Figure4.20:Experimentalspectrumwithproposedassignmentsfortheassociationband"superimposedasimpulses.Peakassignmentsfromtheliteratureindicatedbyblackimpulses.ExperimentaldatatakenfromReference[69].Noneoftheproposedassignmentsareproperlyalignedwiththecenteroftheband,andthered-sidesplittingpeakisclearlyabsent.119

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Figure4.21:Modelspectrumwithproposedassignmentsfortheassociationband"superimposedasimpulses.Noneofthesuspectedcouplingsthoughttoberesponsibleforthisbandareproperlyalignedwiththebandcenter.Peakassignmentssuperim-posedasimpulses.120

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Theexperimentally-observedassociationband"at2125cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1hasbeenattributedintheliteraturetoacombinationbandorcouplingbetweenthelibrationalandbend-ingmodes,butthereexistsnoclearconsensusregardingitsexactorigin.[71{73]Ifitisacouplingsuchasacollision-inducedmodulationofthebendingsignalamplitudeviacooperativepolarizationeects,suchasthoseresponsibleforthespurioussimulatedpeakat1123cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1inFigure4.18,thenelementaryprinciplesfromFourieranalysisindicatethatthecenterofthemodulatingbandshouldbefoundat2125)]TJ/F15 11.9552 Tf 10.8074 0 Td[(1644=481cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Additionally,adierence-frequencybandanalagoustotheaforementionederrorsignalshouldbeobservedat1163cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Figure4.20demonstratesthatifadierence-frequencyassociationbandispresent,itismaskedtothepointofindis-tinguishabilitybytheelevatedbaselineinthisregion.Closeinspectionoftheexper-imentaldatainthisregionindicatesthepresenceofasetoffaintpeaks,buttheirintensitiesaretooweaktodrawanydeniteconclusionsotherthanthattheylineupwiththeover-couplingsignalpresentinthesimulationFigure4.18.Figure4.20alsodemonstratesthatthemaximumpeakintensityofneithertheO{Ostretchat183cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1northelibrationalbandat686cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1coincidewith481cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Whileitispossiblethatthismaybethecouplingofthebendtoanon-infraredactivemotion,thelackofadierence-frequencybandwouldunderminethisassignmentaswell.Ithasalsobeensuggestedthatthisbandmaybethethirdharmonicofthestrongestlibrationalband86cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(13=2059cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.[71,74]Thisassignmentdiersfromtheacceptedvalueforthecenteroftheassociationbandby66cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Dividing121

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thecenteroftheassociationbandby3indicatesthatthispeakcouldpossiblybethethirdharmonicoftheshoulderfeature,buttheapparentcenteroftheshoulderismisalignedbyatleast35cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1,anditsintensityappearstooweaktoaccountfortheobservedintensityoftheassociationband.Additionally,nootherharmonicsofthelibrationalbandaredenitivelypresent,furtherunderminingthishypothesis.IfweconsiderthedierencefrequencygeneratedbytheO{Ostretchandlibra-tionalmodes,weshouldexpectabeatfrequencyof503cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Thisdiersfromtheexpectedmodulationfrequencyby22cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1,butwestilldonotseethered-sideofthesplitthatamodulationbythisbeatwouldgenerate.ThelevelofcoherencebetweentheO{Ostretchingandlibrationalmotionsthatwouldberequiredtoproducethisbeatisalsohighlyunlikelyinaliquid,andisespeciallysoinadisorderedliquiddominatedbyringsandchains.Althoughacombinationbandhasnotbeendeni-tivelyruledout,theanalysispresentedheresuggeststhatthispeakistheresultofauniquephenomenon.Sincethisspectralfeatureappearsinthepolarizablesimulationbutisabsentfromthenon-polarizablesimulation,amany-bodypolarizationeectisindicated.Thesimulatedspectrumofa64-moleculebulkwatersystemat300KusingthebaseSPC/FmodelispresentedasFigure4.14.Herewendexcellentagreementwithexperimentfortherelativeintensitiesandpositionsoftheinter-rotationalandstretchingband,althoughtheshapesofthesebandsdierconsiderablyfromexper-iment.Thebendingbandisfartoostrong,however,andisblue-shiftedfromthe122

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experimentally-determinedpositionby196cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Furthermore,theassociationband"isclearlyabsent,asFigure4.17demonstrates.Thesimulatedspectrumofa512-moleculepolarizablesimulationispresentedasFigure4.15.Thebandpositionsareallblue-shifted,most-noticablythebendingandstretchingbands.Theseblueshiftsarenotsurprising,astheintermolecularpotentialhasnotyetbeenmodiedtoremovetheimplicithandlingofpotentialtermsthatareexplicitlyincludedinthepolarizationmodel.Thiseectismoststrikingforthestretchingband,whichispresentedasFigure4.19.Theoveralllineshapeforthisbandhasimproved,buttheentirebandhasbeenshifted,presumablyduetotheadditionofintramoleculardipole-dipoleinteractions.Thelineshapesoftheinter-rotationalbandandbendingbandarealsoimproved,asFigures4.16&4.17illustrate,andtheassociationband"missingfromthenon-polarizablesimulationisclearlyvisible.Despitethequalitativeimprovementintheshapeoftheinter-rotationalband,bothlobesarestilltoosharpwhencomparedtoexperiment.Compoundingmattersisthe196cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1blue-shiftofthecentralbendingpeakrelativetotheexperimentally-measuredpositionofthispeak.ThespectralresultssuggestthattheattractiveportionoftheLennard-Jones6{12potential,whichamongothereectsmodelstheaverageattractionoftwoatomsduetouctationsintheirelectronicstructure,orvanderWaalsforce,istoostrong.Theresultingover-bindingofnearestneighborsexplainswhytheobservedintensitiesofthered-sidecouplingbandaresostrong,asthisspurioussub-structureobserved123

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between1057{1571cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1issimplythemodulationoftheamplitudeofthebendingmodesduetoover-polarization.TheproblemofvanderWaalsforcemodelingincon-junctionwithpolarizableforceshasbeenaddressedinpreviousmodeldevelopmentstudies,usuallybythereplacementoftheubiquitousLennard-Jones6{12potentialbyanotherfunctionalform.[44,45]Itisquitepossiblethatreplacingtheintermolec-ularLennard-Jonespotentialtermwithapurelyrepulsivepotentialandtuningthebendingpotentialtoreproducetheexperimentalpositionwillbroadenthelineshapesandreducetheintensityofthisbandsothatitmatchestheweakripplesobservedintheexperimentaldata.Replacingthepoint-charge{distributiondampingschemewithamorephysicallyreasonabledistribution-basedelectrostaticsmodelmayalsoalleviatethisclearlynon-physicalsignal.Sinceintramoleculardipoleinteractionsareallowed,boththe3-bodycross-bond"termandtheanharmonicitytermintheO{Hbondingpotentialwillneedtobemodiedaswell,asthemany-bodyeectsthesetermsaremeanttohandlearenowexplicitlyincluded.124

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Hydrogen-bondRearrangement Figure4.22:Thewaterdimerexhibitsthreetunnelingpathwaysthatrearrangetheground-statehydrogen-bondconguration.AcceptorswitchingASexchangesthelone-pairelectronsontheacceptormolecule,interchangetunnelingIexchangestherolesofdonorandacceptormolecules,andbifurcationtunnelingBexchangesthedonorhydrogens.Similarnon-tunnelingmotionswereobservedindimersimulationsusingboththepolarizableandnon-polarizablemodels.GraphicexcerptedfromFig-ure1inReference[75].Smallwaterclustersareconsideredbymanyscientiststobethebasicbuildingblocksofliquidwaterstructure.[45,46,52,76{88]Withthisinmind,asetofdimersimulationswereperformedtostudythehydrogenbondrearrangementmechanismspresentinthesimulation.Fromthesesimulations,threedistinctrearrangementmo-tionswereisolatedandtheirspectralsignatureswerecharacterized.Althoughthese125

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rearrangementmechanismsbynomeansdirectlycorrespondtothetunnelingpath-waysresponsibleforhydrogen-bondrearrangementintheground-stateofthewaterdimer,theydoprovideapossibleexplanationforthesourceoftheassociationband."Theacceptedtunnelingmechanismsforhydrogenbondrearrangementintheground-statedimerarepresentedinFigure4.22.[52]Therst,acceptorswitch-ing"AS,exchangesthelone-pairelectronswhichparticipateinthehydrogen-bondviaarotationofthedonormolecule'sfreehydrogenalongtheO{Oaxisthroughtheplaneoftheacceptor.Thisrearrangementisinitiatedbyaipoftheacceptormolecule,andisfollowedbya180rotationoftheentireclusteralongtheO{Oaxis.Thesecond,interchangetunneling"I,resultsinthereversalofthedonor-acceptorrolesandoccursviaseveralpathways.EachofthesepathwayspossessesatransitionstatewithparallelO{HbondsarrangedinacyclicO{HO{Hpattern,andiscompletedbya180end-over-endrotationofthecluster.Thethird,bifurcationtunneling"B,exchangesthedonorhydrogensviaaconcertedipoftheacceptorandrotationofthedonor.Unliketheothertwotunnelingpathways,bifurcationtun-neling"andclassicalbifurcation"exhibitidenticalmotions.Whileoneshouldnotexpecttoseetruetunnelinginaclassicalsimulation,hydrogen-bondrearrangementmechanismsthatexhibitsimilarmotionsandachieveequivalentrearrangementswereidentied.Therstoftheserearrangementmechanismsisasemi-freecounter-rotationofthedonorandacceptorthatisobservedat20KandpresentedinFigure4.26.Al-126

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thoughthemotionappearstoconsistofarotationofthefreehydrogenofthedonorthroughtheplaneoftheacceptorinconcertwithaipoftheacceptoracrosstheO{Oaxis,theconsistencyoftheippingmotionhasyettobedenitivelyconrmed.Thismotioninducedasignicantsplittingofthebendingandasymmetricstretchsignals,asevidencedbyFigures4.24&4.25.Adistinctnarrowingandblue-shiftoftheinter-rotationalbandswasalsoobserved,asshowninFigure4.23.Thesplitting,narrowingandblue-shiftdisappearedinthehighertemperaturesimulations,presum-ablyduetothedisruptionsinrotationalmotioncausedbytheotherhydrogen-bondrearrangementmechanisms.Furthermore,nodistinctoscillatorysignalisobservedinthepotentialenergywhilethefreehydrogenofthedonorcrossestheplaneoftheacceptor.Asaresult,thismotionisprobablynotimportantindescribingthespectraofneatwater,especiallysincefreerotationishinderedinbothliquidwaterandice.Itdoesexhibitahighlyasymmetricalpolarizationstate,however,whichisinterestingconsideringthedebatediscussedinSection4.4,althoughnotentirelysurprisingduetoitsasymmetricalgeometry.At80K,amotionstrikinglysimilartobifurcation"isobserved.Thehydrogen-bondisbroken,andduringthistimethedonorexhibitsasymmetricalpolarization.AnimageofthistransitionstateispresentedalongwiththepotentialenergycurveofatypicaltrajectoryasFigure4.27.Aswiththecounter-rotationalmotion,nooscillationisevident.Furthermore,nodistinctspectralsignaturewasisolated.Thus,itappearsthatthismotionisnotthesourceoftheassociationband."127

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Atboth40Kand80K,adonor-acceptorrole-reversingmotionconsistingoftwoconcertedrotationsisobserved.Thismotionexhibitsatransitionstatesimilartothatofinterchangetunneling,"duringwhichthehydrogen-bondisbrokenandreformedaccordingtothegeometriccriteriadescribedinSection2.2.ThistransitionstateconsistsofacyclicO{Harrangement,withthefreehydrogensdisplacedslightlyfromplanargeometryintoatrans-conguration.Althoughthepolarizationstateoftheen-tireclusterappearsanti-symmetric,thepolarizationstateofeachindividualmoleculeishighlyasymmetrical.Interestingly,adistinctoscillationaroundthepotentialmin-imumofthiscongurationisclearlyvisibleinFigure4.28.Furthermore,Figure4.29demonstratesthatthisoscillationdoesnotoccurforanon-polarizablesimulation,providingclearevidencethatthisphenomenonisamany-bodypolarizationeect,andthuswillnotappearinanon-polarizablebulksimulation.Additionally,thefactthattheobservedoscillationoccursforthisrearrangementbutdoesnotoccurduringbifurcationstronglysuggeststhattheasymmetricpolarizationstatemayplayarole.Inordertoconrmthattheoscillationobservedinthepotentialenergyfortherole-reversalisinfrared-active,thecentraltimeofeachtransitionwasassumedtobethemidpointbetweenhydrogen-bondbreakageandformation,andlistofthesetimeswerecompiledforeachsimulation.Atotalof192transitionswereobservedat40K,whichcorrespondstoanaveragefrequencyofoccurrenceof0.96persimulation,or2.4ns)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.At80K,thisnumberincreasedto5014transitions,correspondingtoanaveragefrequencyofoccurrenceof25.1persimulation,or62.7ns)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1.Thestandarddeviations128

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ofthenumberoftransitionsobservedinasinglesimulationrunwere1:129and24:32,respectively.A512-pointsamplet01.024psofthelteredsystemdipolecenteredateachtransitiontimewasthenextractedandusedtocalculatetheDFTinordertoapprox-imatetheIRsignalduetothetransition.A4th-orderHannwindowwasemployedbothtominimizespectralleakageandreducethecontributionofdipoleuctuationsasafunctionofdistancefromthetimeorigin.[89]ThecomplexDFTswereaveragedsothatsignalspresentinthewindowbutnotcorrelatedwiththetransitionwouldcanceloutwithaveragingduetotheirincoherentphase,andapowerspectrumwascomputedfromtheaverage.Thisensuredthatonlythosesignalsdirectlyassociatedwiththetransitionwouldappearinthenalaverage.Nofurtherprocessingwasapplied.TheresultsofthisanalysisarepresentedinFigure4.30.Herewendthatalthoughthesignalofinterestismaskedintheaveragedimerspectrum,thesignalextractionalgorithmdescribedaboveisolatesasignalthatappearstocoincidequitewellwiththepositionsofthetwounidentiedweakbandspresentinboththeexperimentaldataandthepolarizablesimulation,yetismissingfromthenon-polarizablesimulation.Thecandidateassociationband"signalappearstobeblue-shiftedfromboththeexperimentalpositionandthebulksimulationposition,butthebendingbandintheaveragedimerspectrumisred-shiftedfromitsbulksimulationposition.Thissuggeststhatthemotionsresponsibleforthisbandmaynotinvolvethebendingvibrations,129

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whichdoesnotsupportthecombination-bandhypothesis.Additionally,thepositionofthestretchingbandduringthetransitionappearstobeblue-shiftedsothatitlinesupwiththetinyfeatureobservedat4000cm)]TJ/F18 7.9701 Tf 6.5865 0 Td[(1inboththeexperimentaldataandthepolarizablesimulation.Thisfeatureisalsomissingfromthenon-polarizablesimulation,andthustheidenticationandtuningofthevibrationsresponsibleforthesetwobandsinthepolarizablemodelmayprovideaconvenientreferencepointfortuningthemodelforspectroscopicpurposesifitcanbedemonstratedthatthistransitionstateisinfactresponsiblefortheassociationband."Theaboveanalysiswasrepeatedfordimersinthepresenceofsimulatedthermalnoise,andthenoisehadnosignicanteectoneithertheaveragespectraorthetransientsignal,indicatingthepossibilitythatthisvibrationalmodecouldstillbeobservedintheeldofothermolecules.ThedimerstudypresentedinthissectionmayalsoprovidefurtherevidenceinsupportoftheWernethypothesis.Inorderforasignalthisweaktobevisibleinthebulkliquid,asubstantialamountofconcertedrotationalmotionsmustbepresentintheliquidstructure.Furthermore,large-scaleconcertedmotionsmayamplifythesignaltothepointofdetectability.Althoughthetetrahedralstructurehypothesissuggeststhattheserotationswouldbetoohinderedtooccuratagreaterfrequencythaninthedimer,theidenticationofthistransientsignalsuggestsamechanismforhydrogen-bondrearrangementsthatagreeswiththemoredisorderedwaterstructuresuggestedbyWernetet.al,andmayprovideanexperimentaltestthatcouldendthe130

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debate.Ifthistransientsignalcanbeisolatedinthebulksimulationandcharacter-ized,itcouldpossiblysolvetwomysteriessurroundingwaterandmovethescienticcommunityonestepclosertotheelusiveuniversalwatermodel."4.5ConclusionandFutureDirectionThequestionthatremainstobeanswered,then,isexactlywhatphysicalphenomenonisresponsiblefortheseweakspectralfeaturesthatarepresentinboththepolarizablesimulationspectraandexperimentalmeasurement,butareabsentfromthenon-polarizablesimulation.Additionally,theexactmotionsresponsiblefortheobserveredspectrainthedimersimulationswillhavetobedetermined,andtheirpresenceinthebulksimulationmustbeconrmed.Inordertoperformadenitiveidenticationofthemodespresent,ab.initiosimulationmethodsmustbeusedtoconrmthattheobservedmodesareinfactphysicallyvalidandresultinthesamespectralsignatureastheclassicalapproximations.Ifthistransientmotionanditscorrespondingspectralfeatureareindeedfoundtobephysicallyvalid,itmustthenbedeterminedwhetherthismotionisrelatedtoasymmetricchargedistributionsandthedisputedsecond-neighborfeatureobservedintheRDF.Iftheaforementionedquestionscanbeansweredinthearmative,thenitwillbeacompellingdemonstrationofthepredictivepowerofclassicalmoleculardynamicsmethods.Itwillalsoprovideadenitivetesttoendthedebate,ifonlytemporarily.Whilethisisnosmalltask,clearprogresshasbeenmade.Onlyimprovedtting,131

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largersystemsizes,longersimulationsandcontinuedresearchanddevelopmentofthewaterpotentialsurfacewilldeterminewhetherthisispossible.Clearly,thejuryisstillout.132

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Figure4.23:Temperature-dependentdimerspectraintheinter-rotationalregion.Eachdatasetistheaverageof200simulationsof400psinlengths80nstotalinitiatedfromevenly-spacedcongurationsamplestakenfroma100pssimulationstimulatedbyband-limitednoise.Eachdatasetrepresentstheeectofaddinganewhydrogen-bondrearrangementmotion.133

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Figure4.24:Temperature-dependentdimerspectraintheO{Hstretchingregion.Eachdatasetrepresentstheeectofaddinganewhydrogen-bondrearrangementmotion.134

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Figure4.25:Temperature-dependentdimerspectraintheH{O{Hbendingregion.Eachdatasetrepresentstheeectofactivatinganewhydrogen-bondrearrangementmotion.135

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Figure4.26:Simulationsnapshotandpotentialenergyplotforadimercounter-rotation.Thepolarizationforthistransitionstateishighlyasymmetrical.Hydrogen-bondbreakagedoesnotoccuraccordingtothegeometricalcriteriadenedinSection2.2136

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Figure4.27:Simulationsnapshotandpotentialenergyplotforadimerbifurca-tion.Thepolarizationforthedonorisroughlysymmetricalinthistransitionstate.Hydrogen-bondbreakageandformationareindicatedbyverticaldashedlines.137

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Figure4.28:Simulationsnapshotandpotentialenergyplotforadimerdonor-acceptorrole-reversal.Thepolarizationofthemoleculesparticipatinginthistransitionstateishighlyasymmetrical,andanoscillationaroundthetransition-stateminimumenergyisclearlyvisible.Hydrogen-bondbreakageandformationareindicatedbyverticaldashedlines.138

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Figure4.29:Potentialenergyforadimerduringadonor-acceptorrole-reversalob-servedduringanon-polarizablesimulation.Nooscillationispresent.Hydrogen-bondbreakageandformationareindicatedbyverticaldashedlines.139

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Figure4.30:Averagespectrumforthedimertransitionstateduringadonor-acceptorrole-reversal,withtheaveragedimerspectrumgreenlineandestimatedbulkbandpositionsfromthepolarizablesimulationblackimpulsesincludedforcomparison.140

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AbouttheAuthorAlfredB.RoneyreceivedaBachelorofScienceDegreefromtheUniversityofSouthernMississippiinAugustof1997.HeenteredtheDoctoralProgramattheUniversityofSouthFloridaintheSummerof2001,andjoinedtheresearchgroupofProfessorBrianSpaceatthesametime.Inadditiontograduatestudyandrelatedresearch,Mr.Roneyprovidedtechnicalconsultingservicesintheeldsofacousticsandsignalprocessingtoseverallocalclients.SomeoftheresearchpresentedinthisdissertationhasbeenpublishedintheJournalofPhysicalChemistry.