Molecular theories and simulation of ions and pola

arXiv:physics/9806023v2[physics.chem-ph]24Jul1998MoleculartheoriesandsimulationofionsandpolarmoleculesinwaterGerhardHummer,LawrenceR.Pratt,AngelE.Garc´ıaTheoreticalDivision,LosAlamosNationalLaboratory,LosAlamos,NewMexico87545USALA-UR-98-1947(February2,2008)1AbstractRecentdevelopmentsinmoleculartheoriesandsimulationofionsandpo-larmoleculesinwaterarereviewed.Thehydrationofimidazoleandimida-zoliumsolutesisusedtoexemplifythetheoreticalissues.Thetreatmentoflong-rangedelectrostaticinteractionsinsimulationsisdiscussedextensively.ItisarguedthattheEwaldapproachisaneasywaytogetcorrecthydra-tionfreeenergiesinthethermodynamiclimitfrommolecularcalculations;andthatmolecularsimulationswithEwaldinteractionsandperiodicbound-aryconditionscanalsobemoreefficientthanmanycommonalternatives.TheEwaldtreatmentpermitsaconclusiveextrapolationtoinfinitesystemsize.Accurateresultsforwell-definedmodelshavepermittedcarefultestingofsimpletheoriesofelectrostatichydrationfreeenergies,suchasdielectriccontinuummodels.Thepicturethatemergesfromsuchtestingisthatthemostprominentfailingsofthesimplesttheoriesareassociatedwithsolventprotonconformationsthatleadtonon-gaussianfluctuationsofelectrostaticpotentials.Thus,themostfavorablecasesforsecond-orderperturbationthe-oriesaremonoatomicpositiveions.Forpolarandanionicsolutes,continuumorgaussiantheoriesarelessaccurate.Theappreciationofthespecificdefi-cienciesofthosesimplemodelshaveledtonewconcepts,multistategaussianandquasi-chemicaltheories,thataddressthecasesforwhichthesimplerthe-oriesfail.Itisarguedthat,relativetodirectdielectriccontinuumtreatments,thequasi-chemicaltheoriesprovideabettertheoreticalorganizationforthecomputationalstudyoftheelectronicstructureofsolutionspecies.21.IntroductionWater,themostcommonlyencounteredliquid,exertsbothchemicalandphysicalinflu-encesonaqueousmolecularprocesses.Hydrationeffectsareoftendividedintohydrophobicandhydrophiliccategories.Hydrophilicsolutesaretypicallyionicorpolarspeciesandmayparticipateinchemicalinteractionswiththewatersolvent.BecauseofthelongrangeoftheelectrostaticinteractionsandtheirstrengthrelativetokBT,hydrophilichydrationpresentsdistinctiveconceptualandpracticalissuesforunderstandingandpredictingtheinfluenceofhydrationonchemicalandbiochemicaleventsinwater.Aprincipalandlong-standingtechnicalissueisthetreatmentofinfinitelylong-rangedinteractionsinthecontextofasampleoffinitesize.1Recentworkhashelpedtoresolvethisproblem.Onealgorithmicapproachtotreatmentoflong-rangedinteractionsistheuseofEwaldinteractionswithintheconventionalperiodicboundaryconditions.2WeargueherethattheEwaldapproachisaneasywaytogetcorrecthydrationfreeenergiesfrommolecularcalculations,thatis,toachievewellcharacterizedresultsappropriatetothethermodynamiclimitinwhichthesystemsizetendstoinfinityforgivendensitiesandtemperature.Whatismore:molecularsimulationswithEwaldinteractionsandperiodicboundaryconditionscanalsobemoreefficientthanrougherapproximationsthatareoftenemployedtocomputehydrationfreeenergiesformolecularlywell-definedproblems.Weanticipateresultsbelowbynotingthatweobtainaccurate,thermodynamiclimitingresultsforthehydrationfreeenergyofimidazolewithasfewas16watermoleculesincludedinthesimulation.ThepricetobepaidforthisaccuracyandefficiencyisadditionaleffortinunderstandingEwaldcalculationsfromaphysicalviewpointandinimplementingEwaldinteractions,2itsequivalents,3–7andalternatives.8–10Thephysicalissuesmotivatingsimulationcalculationsofthistyperevolvearounddielec-triccontinuummodelsofhydrationofionicandpolarsolutes.11Itisnaturalandcommonforasimplifiedapproximationtoprovideaconceptualbaselineforconsideringmoreaccuratetheoreticalresults.Buttheconversecomparisonisforemostforthiswork.Thetheoreticaleffortsoverrecentyearshaveprovidedsharpertestsofthevalidityofthecontinuumap-proachthanmerely:isanempiricallycorrecthydrationfreeenergyobtained?Recentworkhasclarifiedthatthedielectricmodelsaresimpleimplementationsofthermodynamicper-turbationtheorythroughsecond-orderinelectrostaticcouplingparameterssuchassolutecharges;12–14dielectricmodelscanalsobeconsideredasimpleimplementationofanansatzthatelectrostaticpotentialfluctuationsaredistributedaccordingtoagaussianprobabilitydensity,15ortheycanbeconsideredasimplifiedlinearresponsetheory.16–18Second-orderperturbationtheorywasfoundtobesatisfactoryforsomesolutessuchasalkaliions,14butunsatisfactoryforwater13,19andanions.14Inthelattercases,ofcourse,anaposterioriadjustmentofcavityradiicouldstillproducethecorrecthydrationfreeenergies.20However,themoreambitiousmoleculartheorytiesthevaluesofradiiparameterstomolecu-larpropertiesthatdependonthethermodynamicstateofthesystem(temperature,pressure,andcompositionofthesolvent)andtonon-electrostaticcharacteristicsofthesolute-solventinteractions.Theradiiarenotseparatelyadjustablewhenviewedfromthatdeeperlevelofmoleculartheory.However,theradiicanbewell-definedandarenotpropertiesofthesolutesalonebutincorporateinformationaboutthesolventandthermodynamicstate.Forwaterasasolvent,thecaseofexclusiveconcernhere,themostprominentfailingsofsecond-orderperturbationtheorya