ARTICLES Li and Truhlar nanoparticles are often a mixture of many isomers with similar Their melting has recently been the subject of extensive energies equilibrating with each other.7s -48 their experimental 5.42-44 and theoretical study. 14.19,27.33.34,40.82 86 melting transitions have the same ambiguity Jarrold et al.used multicollision-induced dissociation to measure The distinction between clusters and nanoparticles is not strict, the heat capacities of Al cationic clusters with n=16-48.44 and we use the generic name particles to refer to both of them. 31-38,43 49-63,36 and 63-83.42 They found that for some Aluminum particles have been of great experimenta clusters the heat capacity curve has a well-defined sharp peak, and theoretical4.19.27.29.33.34.39.40.43.57-86 interest for decades. while for others the heat capacity curve is relatively flat and featureless.Taking the temperature To at which C has a (45)Doye,J.P.K.:Calvo.F.Phys.Rev.Lett.2001.86,3570.Doye, maximum as the melting temperature,they found that the J.P.K.:Calvo,F.J.Chem.Phys.2003.119.12680. melting temperature depends greatly on particle size,and even (46)Wang.G.M.:Blaisten-Barojas,E;Roitberg.A.E.J.Chem.Plrys. a change in size by a single atom can make huge differences 2001.115.3640. Monte Carlo439(MC)and molecular dynamics' 4192733.408384 (47)Baletto,F.:Rapallo,A.;Rossi,G.;Ferrando,R.Phys.Rev.B 2004. 69,235421.RossiG.;Rapallo,A.:Mottet.C.:Fortunelli,A.;Baletto. (MD)simulations confirmed the experimental findings.How- F.:Ferrando.R.Phys.Rev.Lett.2004.93.105503. ever,Tp is not enough to characterize a melting transition since (48)Li,Z.H.;Jasper,A.W.:Truhlar,D.G.J.Am.Chem.Soc.2007, the solid and liquid states in finite systems have not been well 129.14899. (49)de Heer,W.A.:Milani,P.:Chatelain,A.Plrys.Rev.Lett.1989,63. defined.Moreover,for those particles with featureless and flat 2834. heat capacity curves,Tp has large uncertainties and should be (50)Lerme.J.:Pellarin.M.:Vialle.J.L.:Baguenard.B.:Broyer.M.Phrys. treated with caution. Rev.Lett.1992,68,2818.Baguenard,B.;Pellarin,M.:Lerme,J.; Vialle,J.L;Broyer,M.J.Chem.Phys.1994,100.754. For the particle sizes studied here,most atoms need to be (51)Martin.T.P.:Naher,U.:Schaber.H.Chem.Phrys.Lett.1992,199. classified as surface atoms rather than as interior atoms with 470. bulk properties characteristic of a macroscopic particle.Except (52)Jarrold.M.F.:Bower.J.E.J.Phys.Chem.1993.97.1746.Jarrold. for a few small clusters,Al13,14 Al3-,83 and Al14.83 available M.F.;Bower,J.E.J.Chem.Phrys.1993,98.2399.Jarrold,M.F.J. Phs.Chem.1995,99,11. simulations of Al cluster melting all use empirical analytical (53)Cha.C.Y.:Gantefor,G.:Eberhardt,W.J.Chem.Phys.1994,100. potential functions,but it is not possible to accurately param- 995.Gantefor,G.;Eberhardt,W.Chem.Phys.Lett.1994,217,600. etrize empirical potentials in the cluster and nanoparticle regime (54)Li,X.:Wu.H.:Wang,X.B.:Wang,L.S.Phys.Rev.Lett.1998,8/. 1909. due to a lack of experimental data for systems with a significant (55)Akola,J.;Manninen,M.;Hakkinen,H.;Landman,U.:Li,X.:Wang. fraction of atoms in nonbulk (e.g.,surface)positions.24.87 L.S.Phys.Rev.B 1999.60.11297.Akola.J.:Manninen.M.: Recently,economical and accurate analytic potentials for Hakkinen,H.;Landman,U.;Li,X.:Wang,L.S.Phys.Rev.B 2000, 62.13216.Kuznetsov,A.E.:Boldyrev,A.I.:Zhai,H.J.;Li,X.: aluminum systems have been developed by fitting to results of Wang,L.S.J.Am.Chem.Soc.2002,124,111791. well-validated electronic-structure calculations'for Al clusters (56)Schnepf.A.:Schnockel,H.Angew.Chem..Int.Ed.2002.41.3532. (57)Jones.R.O.Phrys.Rev.Lett.1991,67.224.Jones.R.O.J.Chem. and nanoparticles as well as to experimental bulk properties. Because pairwise additive potentials are inaccurate for real Phys.1993.99,1194 (58)Cheng,H.-P.;Berry,R.S.;Whetten,R.L.Phrys.Rev.B 1991,43, metals,including metal clusters and metal nanoparticles,these 10647. analytic potentials include many-body effects(i.e.,the potentials (59)Yi,J.Y.:Oh,D.J.U.;Bernholc,J.Phrys.Rev.Lett.1991,67,1248 are not pairwise additive).The many-body (nonpairwise,NP) (60)Rothlisberger.U.:Andreoni,W.:Giannozzi,P./Chem.Phys.1992. 96,1594. potentials named NP-A and NP-B are the most accurate (61)Elbayyariz,Z.;Erkoc,S.Phys.Status Solidi B:Basic Res.1992. potentials available for aluminum systems8 or any metal 170.103. nanoparticles.The potentials have been successfully applied to (62)Peslherbe,G.H.:Hase,W.L.J.Chemn.Phrys.1994,101.8535. aluminum systems to study the vapor-liquid coexistence of (63)Streitz.F.H.:Mintmire.J.W.P/rys.Rev.B 1994.50.11996. 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(84)Boyiikata,M.:Guivenc,Z.B.Brazilian J.Phys.2006,36,720 (75)Zope,R.R.:Baruah,T.Phrys.Rev.B 2001,64,053202. (85)Puri,P.:Yang,V.J.Phys.Chem.C 2007,111,11776. (76)Deshpande.M.D.:Kanhere.D.G.:Vasiliev,I.:Martin,R.M.Phys (86)Poland,D.J.Chem.Plrys.2007,126,054507. Reu.B2003.035428」 (87)Yang,M.;Jackson,K.A.:Koehler,C.;Frauenheim,T.;Jellinek,J. (77)Joswig,J.-0.:Springborg,M.Phys.Rev.B 2003,68,085408. J.Chem.Pys.2006.124,24308. (78)Schultz,N.E.;Staszewska,G.:Staszewski,P.:Truhlar,D.G.J.Phys. (88)Jasper.A.W.;Staszewski,P.:Staszewski,G.;Schultz,N.E.;Truhlar. Chem.B2004.108.4850. D.G.J.Phys.Chem.B 2004.108.8996.Jasper.A.W.:Schultz. (79)Sebetci,A.;Guivenc,Z.B.Modeling Simul.Mater.Sci.Eng.2005. N.E.;Truhlar,D.G.J.Phys.Chem.B 2005,109,3915. 13,683. (89)Bhatt,D;Jasper,A.W.;Schultz,N.E.;Siepmann,J.I.;Truhlar (80)Peng.P.:Li.G.:Zheng,C.:Han,S.:Liu.R.Sci.China Ser.E 2006. D.G.J.Am.Chem.Soc.2006.128,4224.Bhatt,D.:Schultz.N.E.: 49,385. Jasper,A.W.;Siepmann,J.L;Truhlar,D.G.J.Phys.Chem.B 2006 (81)Li,Z.H.:Bhatt,D.:Schultz,N.E.;Siepmann,J.L:Truhlar,D.G. 110.26135. J.Phys.Chem.C2007.111.16227. (90)Li.Z.H.;Truhlar.D.G.J.Phys.Chem.C 2008,112.11109 12700J.AM.CHEM.S0C.■VOL.130,NO.38.2008nanoparticles are often a mixture of many isomers with similar energies equilibrating with each other,6,18,22,23,29,37,45-48 their melting transitions have the same ambiguity. The distinction between clusters and nanoparticles is not strict, and we use the generic name particles to refer to both of them. Aluminum particles have been of great experimental36,42-44,49-56 and theoretical14,19,27,29,33,34,39,40,43,57-86 interest for decades. Their melting has recently been the subject of extensive experimental36,42-44 and theoretical study.14,19,27,33,34,40,82-86 Jarrold et al. used multicollision-induced dissociation to measure the heat capacities of Aln cationic clusters with n ) 16-48,44 31-38,43 49-63,36 and 63-83.42 They found that for some clusters the heat capacity curve has a well-defined sharp peak, while for others the heat capacity curve is relatively flat and featureless. Taking the temperature Tp at which C has a maximum as the melting temperature, they found that the melting temperature depends greatly on particle size, and even a change in size by a single atom can make huge differences. Monte Carlo34,39 (MC) and molecular dynamics14,19,27,33,40,83,84 (MD) simulations confirmed the experimental findings. How￾ever, Tp is not enough to characterize a melting transition since the solid and liquid states in finite systems have not been well defined. Moreover, for those particles with featureless and flat heat capacity curves, Tp has large uncertainties and should be treated with caution.44 For the particle sizes studied here, most atoms need to be classified as surface atoms rather than as interior atoms with bulk properties characteristic of a macroscopic particle. Except for a few small clusters, Al13, 14 Al13-, 83 and Al14, 83 available simulations of Al cluster melting all use empirical analytical potential functions, but it is not possible to accurately param￾etrize empirical potentials in the cluster and nanoparticle regime due to a lack of experimental data for systems with a significant fraction of atoms in nonbulk (e.g., surface) positions.24,87 Recently, economical and accurate analytic potentials for aluminum systems have been developed by fitting to results of well-validated electronic-structure calculations78 for Aln clusters and nanoparticles as well as to experimental bulk properties.88 Because pairwise additive potentials are inaccurate for real metals, including metal clusters and metal nanoparticles, these analytic potentials include many-body effects (i.e., the potentials are not pairwise additive). 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