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RESEARCHARTICLE Copyright©2013AmericanScienticPublishersAllrightsreservedPrintedintheUnitedStatesofAmericaJournalofComputationalandTheoreticalNanoscienceVol.10,1 9,2013OptimalApproachTrajectoriesforaHydrogenDonationToolinPositionallyControlledDiamondMechanosynthesisDenisTarasov,EkaterinaIzotova,DianaAlishevaNataliaAkberova Authortowhomcorrespondenceshouldbeaddressed.forSi,Ge,Sn,PbandIn,andCmechanosynthesisisbeingefforted. RESEARCHARTICLETarasovetal.OptimalApproachTrajectoriesforaHydrogenDonationToolinPositionallyControlledDiamondMechanosynthesisandprovideguidanceonearlydevelopmenttargetsaspartofacomprehensivenear-termDMSimplementation2.COMPUTATIONALMETHODSAllstudieswereconductedusingDensityFunctionalThe-ory(DFT)inthePC-GAMESSversionoftheGAMESS(US)QCpackagerunningonacomputationalcluster106,800CPU-hoursofruntimeat1GHz,andincluded2,620separatevalid-structurecalculations.TheworkwasperformedprimarilyattheKazanBranchoftheJointSupercomputerCenterattheRussianAcademyofSciencesofRASusingtheMVS100KFsystemcon-sistingof80nodeswith2QuadCoreIntelXeonE5450(3GHz)processorspernode.Afewadditionalcompu-tationswereperformedusingfourIntelCorei7baseddesktopcomputersatKazanFederalUniversity.Asinpreviouswork,allenergieswerecalculatedwiththe6-311G(d,p)//3-21G(2d,p)basissetusingB3LYPwhichisahybridHartree-Fock/DFTmethodusingBeckesthree-parametergradient-correctedexchangefunctional(B3)withtheLee Yang Parrcorrelationfunctional(LYP).Zero-pointcorrectionsarenotmadetotheenergydata(1)thedifferencesbetweenenergieswithandwithoutacorrectionaresmall,(2)thenumberofpointstobeevaluatedislarge(manythousandsinthisstudy),and(3)thecomputationalexpenseishuge(e.g.,analyticalsecondderivativesforspin-unrestrictedcalculationsarenotimplementedinPC-GAMESSandthecalculationofnumericalfrequenciesrequiresabouttwiceasmuchCPUtimeasgeometryoptimizations).Thepresentworkexaminesthepositionallycontrolledmechanosyntheticreactioninwhichahydrogendonationtool(HDon)donatesasinglehydrogenatomtoacarbonatomataradicalsiteonanadamantanecageworkpieceat(1)abridgeheadposition(Fig.2(B))and(2)aside-wallposition.TheHDontoolandtheadamantanecageworkpieceareconstrainedbyxingthepositionsofthethreesidewallcarbonatoms(CHgroups)inthetooltipadamantanebasethatarelocatedonthesideofthecagefarthestfromtheactiveradicalsiteofthetool,andthesimilaratomsinthebaseoftheadamantanecagework-piece.Eachtoolandworkpiecewerethusxedpreciselyinspacebyconstrainingjust3baseatomsineachstructurefromthestartofeachrun,thenthesystemwasallowedtorelaxtoitsequilibriumgeometryduringtherun.Thismethodprovidesthebestmodelforanticipatedactuallab-oratoryconditionsinwhichanexperimentalistwillcon-troltooltippositionbyapplyingforcesthroughalargerdiamondlatticehandlestructureafxedbehindthebasestructureofthetooltip.Foreachrun,eachtooltipbasewaspositionallyconstrainedtoaspecicsphericalcoordinate Fig.3.Above:Coordinatesystemdenitionforthepositionallycon-trolleddonationofhydrogenatomH22toadamantanebridgeheadradicalsiteatcarbonatomC37,deningphi(andtheta(,includingatomlabels;drawingshowssystempositionedatapproximately(.Below:Denitionofthetooltipaxialrotationanglerho(,below,withthe-axis(greendot)pointingoutofthepage.yellow,Hblue,Geplane)anddirection)inxedincrements,andtoseveralxedradialdistances,andtheincomingtooltipwasalsoconstrainedtoaspecicaxialrotationalThetooltipgeometryandcoordinatesystemforthebridgeheaddonationreactionisshowninFigure3.TherstcoordinateoriginOisdenedasthepointequidistantfromthexedcarbonatomsC30,C31,andC36intheworkpieceadamantanebase,andlyingintheplanecon-tainingthoseatoms.TheaxisliesperpendiculartotheC30/C31/C36planeandpointsfromoriginOtoasecondoriginOwhichisinitiallycoincidentwithatomC37intheadamantanebase,2.592ÅawayfromO.TheoriginatesatO,liesperpendiculartotheaxis,andrunsparalleltoavectorpointingfromoriginOtoatomC30.axisalsooriginatesatOandliesperpendiculartoaxesfollowingtheright-handrule,runningpar-alleltoavectorpointingfromatomC31toatomC36.TheapproachingHDontoolisinitiallyorientedrelativetotheadamantaneworkpiecesuchthatalineextendingback-wardsthroughatomsC37(originO)andgermaniumatomGe16perpendicularlypenetratestheplanedenedbythe3xedHDontoolbasecarbonatoms(C2,C4,andC9),intersectingathirdoriginOwhichliesintheC2/C4/C9J.Comput.Theor.Nanosci.10,1 9, RESEARCHARTICLETarasovetal.OptimalApproachTrajectoriesforaHydrogenDonationToolinPositionallyControlledDiamondMechanosynthesis3.2.HydrogenDonationtoSidewallSiteForapositionallycontrolledHatomdonationfromanHDontooltoasidewallradicalpositiononanadamantaneworkpiece,Figure9showsthe2DPESatthepre-transfer Fig.10.2DPES(endoergicblue,exoergicred,excludedgray)atthetool-workpieceH-transferseparationdistanceR1Åusingapproachtrajectoriesintherange(forhydrogendonationfromHDontoasidewallradicalsiteonanadamantaneworkpiece(top);atbottom,sphericalrepresentationsofthesmoothedPESasafunctionoftooltippositionalanglesexpressedonaCartesianXYZcoordinatesystemoverlaytheadamantaneworkpiecewithtargetedradicalcarbonatomC35anditsremaininghydrogenatomvisibleatcenter. Fig.11.2DPES(endoergicblue,exoergicred,excludedgray)atatool-workpiecepost-transferseparationdistance5.9Åusingapproachtrajectoriesintherange(forhydrogendonationfromHDontoasidewallradicalsiteonanadamantaneworkpiece(top);atbottom,sphericalrepresentationsofthesmoothedPESasafunctionoftooltippositionalanglesexpressedonaCartesianXYZcoordinatesystemoverlaytheadamantaneworkpiecewithtargetedradicalcarbonatomC35anditsremaininghydrogenatomvisibleatcenter.tool-workpieceseparationdistance2Åforapproachtrajectoriesintherange(Figure10showsthesamePESat1ÅandFigure11showsthePESat9Å,againforapproachJ.Comput.Theor.Nanosci.10,1 9, RESEARCHARTICLETarasovetal.OptimalApproachTrajectoriesforaHydrogenDonationToolinPositionallyControlledDiamondMechanosynthesis4.CONCLUSIONSTheuseofpreciselyappliedmechanicalforcestoinducesite-specicchemicaltransformationsiscalledpositionalmechanosynthesis,anddiamondisanimportantearlytar-getforachievingmechanosynthesisexperimentally.Akeystepindiamondmechanosynthesis(DMS)mayemployaGe-substitutedadamantane-basedhydrogendonationtool(HDon)forthesite-specicmechanicalhydrogenationofdepassivateddiamondsurfaces,thuseliminatingaradicalsitethatwouldotherwiseremainchemicallyactiveandtherebystabilizingtheworkpiece.Inthispaperweunder-takethersttheoreticalstudyoftool-workpieceoperatingenvelopesandoptimaltooltiptrajectoriesforapositionallycontrolledhydrogendonationtoolduringscanning-probebasedUHVdiamondmechanosynthesis.Theresultsofourstudymayhelptodeneequipmentandtooltipmotionrequirementsthatareneededtoexecutetheproposedreac-tionsequenceexperimentally.Theoptimalapproachtrajectorywithminimumreac-tionbarrierforapositionallycontrolledHatomdonationfromanHDontooltoabridgeheadradicalpositiononanadamantaneworkpieceisasimple(trajectory,wherehydrogenatomtransferoccursexoergi-callyby0.50eVat1ÅaftertheincomingHDontoolsurmountsaminimumbarrierheightof16eV.ThelargestpossibleexoergicrangefortrajectoriesinwhichtheHDontoolisappliedtothisworkpieceappearstobe,although(isprobablyrequiredforreliableroomtemperatureoper-ation;toolrotationanglehaslittleeffectonreactionenergetics.Thebarrierisaminimumof162eVusingtrajectorywheretransferoccursat1Å,risingto18eVat(reachingamaximumof56eVforthemosthighlyangledviabletrajectoriesat(transferoccursat5.9Å.TheHdonationreactionfailsfora(trajectoryatalateralmis-placementerrorof0.6Åfor1Åandat1.1Åfor9Å,butfailsat0.5Åforamorehighlyangled(trajectoryat9Å.Theoptimalapproachtrajectorywithminimumreac-tionbarrierforapositionallycontrolledHatomdona-tionfromanHDontooltoasidewallradicalpositiononanadamantaneworkpieceistwofold:asmallerregionnear(andalargerregionnear.Respectively,thesetwoexoergicregionsexpandthesizeoftheviableangulartra-jectorywindowsfromapproximately2Å,toapproximately1Å.9Å,thereisonelargeexoergicregionprovidingatleastsomeselectionofexoergictrajectoriesforanyandforanywithviabletrajectoriescontinuouslyavailablethroughoutthe(range.Thereactionbarrierhasminimumsfor(trajectories,andreactionbarriersremainrel-ativelylow(3eV)foraroughlyregionaround,+10and(.TheHdonationreactionfailsfora(,60trajectoryatalateralmisplacementerrorof0.6Åfor1Å.ReferencesD.M.EiglerandE.K.Schweizer,Nature344,524(R.A.Freitas,Jr,andR.C.Merkle,J.Comput.Theor.Nanosci.5,760(D.Tarasov,N.Akberova,E.Izotova,D.Alisheva,M.Astaev,andR.A.FreitasJr,J.Comput.Theor.Nanosci.7,325(N.Oyabu,O.Custance,I.Yi,Y.Sugawara,andS.Morita,Rev.Lett.90,176102(N.Oyabu,O.Custance,M.Abe,andS.Moritabe,AbstractsofSeventhInternationalConferenceonNon-ContactAtomicForceMicroscopy,Seattle,Washington,USA,September(),vol.34,pp.12 15.Y.Sugimoto,P.Pou,O.Custance,P.Jelinek,M.Abe,R.Perez,andS.Morita,322,413(P.Moriarty,DigitalMatter:TowardsMechanisedMechanosynthesis,EPSRCFellowshipProposal(D.Tarasov,E.Izotova,D.Alisheva,N.Akberova,andR.A.FreitasJr,J.Comput.Theor.Nanosci.8,147(D.Tarasov,E.Izotova,D.Alisheva,N.Akberova,andR.A.Freitas,Jr,J.Comput.Theor.Nanosci.9,144(E.Srinivasan,H.Yang,andG.N.Parsons,J.Chem.Phys.105,5467S.Sugahara,K.Hosaka,andM.Matsumura,App.Surf.Sci.327(C.Chatgilialoglu,M.Ballestri,J.Escudie,andI.Pailhous,Organometallics18,2395(L.Song,W.Wu,K.Dong,P.C.Hiberty,andS.Shaik,J.Phys.Chem.A106,11361(T.I.DrozdovaandE.T.Denisov,Kinet.Catal.43,10(J.OlanderandK.M.E.Larsson,ThinSolidFilms458,191(B.Temelso,C.D.Sherrill,R.C.Merkle,andR.A.FreitasJr,J.Phys.Chem.A111,8677(B.J.McIntyre,M.Salmeron,andG.A.Somorjai,265,1415W.T.Muller,D.L.Klein,T.Lee,J.Clarke,P.L.McEuen,andP.G.268,272(D.H.HuangandY.Yamamoto,Appl.Phys.A64,R419(C.Thirstrup,M.Sakurai,T.Nakayama,andM.Aono,Surf.Sci.411,203(AlexA.Granovsky,PC-GAMESSversion7.1wwwhttp://classic.chem.msu.su/gran/gamess/index.html(Somecomputationsusedversion7.0),(M.W.Schmidt,K.K.Baldridge,J.A.Boatz,S.T.Elbert,M.S.Gordon,J.H.Jensen,S.Koseki,N.Matsunaga,K.A.Nguyen,S.Su,T.L.Windus,M.Dupuis,andJ.A.Montgomery,J.Comput.Chem.14,1347(A.D.Becke,J.Chem.Phys.98,5648(C.Lee,W.Yang,andR.G.Parr,Phys.Rev.B.37,785(Received:11February2013.Accepted:24February2013.J.Comput.Theor.Nanosci.10,1 9,