Free Energies of Formation of Metal Clusters and Nanoparticles from Molecular Simulations:  Al n with n = 2−60

• Published in: Journal of physical chemistry. C 2007-11, Vol.111 (44), p.16227-16242
• Main Authors: Li, Zhen Hua, Bhatt, Divesh, Schultz, Nathan E, Siepmann, J. Ilja, Truhlar, Donald G
• Format: Article
• Language: English
• ISSN: 1932-7447; 1932-7455
• DOI: 10.1021/jp073559v

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 (Δf G°) of a particle is obtained from these Gibbs free energy changes (ΔG°) by a recursion relationship using the experimental Δf G° 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 Al2 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 well-validated 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 isomeric−rovibrational 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 Δf G° of Al n particles with n = 2−60 have been determined. This is the first example of the determination of nanoparticle free energies of formation.