TY - JOUR

T1 - Free energies of formation of metal clusters and nanoparticles from molecular simulations

T2 - Al n with n = 2 - 60

AU - Li, Zhen Hua

AU - Bhatt, Divesh

AU - Schultz, Nathan E.

AU - Siepmann, J. Ilja

AU - Truhlar, Donald G.

PY - 2007/11/8

Y1 - 2007/11/8

N2 - Efficient simulation methods are presented for determining the standard Gibbs free energy changes for the reactions, M + M n-1 ↔ M n (R1), involved in the formation of atomic clusters and nanoparticles (also called particles) in the vapor phase. The standard Gibbs free energy of formation (Δ fG°) of a particle is obtained from these Gibbs free energy changes (ΔG°) by a recursion relationship using the experimental Δ fG° of the monomer. In the present study, this method has been applied to reactions involving Al n particles with n = 2-60. This method has been validated for n = 2, where the experimental thermodynamic properties of Al 2 have been recompiled using the latest available experimental or highly accurate theoretical data. For n = 2-4, two completely different approaches, a Monte Carlo configuration integral (MCCI) integration of partition functions and a Monte Carlo direct simulation of the equilibrium constants (MCEC), employing four wellvalidated potential energy functions have been used to calculate ΔG° of R1. Excellent agreement is observed for these two methods. Although different potential energy functions give different stage-1 results for n ≤ 10, three high-level correction (HLC) terms, namely, a correction for the potential energy difference of the global minima, another for the electronic excitation contribution, and a third based on calculating isomericrovibrational contribution, have been applied to mitigate deficiencies in the potential energy functions. For n - 2, good agreement has been found between the corrected simulation results and experimental data. For larger n, the more efficient MCEC method has been used. Finally, accurate ΔG° of R1 and thus Δ fG° of A1 n particles with n = 2-60 have been determined. This is the first example of the determination of nanoparticle free energies of formation.

AB - Efficient simulation methods are presented for determining the standard Gibbs free energy changes for the reactions, M + M n-1 ↔ M n (R1), involved in the formation of atomic clusters and nanoparticles (also called particles) in the vapor phase. The standard Gibbs free energy of formation (Δ fG°) of a particle is obtained from these Gibbs free energy changes (ΔG°) by a recursion relationship using the experimental Δ fG° of the monomer. In the present study, this method has been applied to reactions involving Al n particles with n = 2-60. This method has been validated for n = 2, where the experimental thermodynamic properties of Al 2 have been recompiled using the latest available experimental or highly accurate theoretical data. For n = 2-4, two completely different approaches, a Monte Carlo configuration integral (MCCI) integration of partition functions and a Monte Carlo direct simulation of the equilibrium constants (MCEC), employing four wellvalidated potential energy functions have been used to calculate ΔG° of R1. Excellent agreement is observed for these two methods. Although different potential energy functions give different stage-1 results for n ≤ 10, three high-level correction (HLC) terms, namely, a correction for the potential energy difference of the global minima, another for the electronic excitation contribution, and a third based on calculating isomericrovibrational contribution, have been applied to mitigate deficiencies in the potential energy functions. For n - 2, good agreement has been found between the corrected simulation results and experimental data. For larger n, the more efficient MCEC method has been used. Finally, accurate ΔG° of R1 and thus Δ fG° of A1 n particles with n = 2-60 have been determined. This is the first example of the determination of nanoparticle free energies of formation.

UR - http://www.scopus.com/inward/record.url?scp=36349004045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36349004045&partnerID=8YFLogxK

U2 - 10.1021/jp073559v

DO - 10.1021/jp073559v

M3 - Article

AN - SCOPUS:36349004045

VL - 111

SP - 16227

EP - 16242

JO - Journal of Physical Chemistry C

JF - Journal of Physical Chemistry C

SN - 1932-7447

IS - 44

ER -