Calculation of thermodynamic properties of small Lennard‐Jones clusters incorporating anharmonicity

A method for calculating thermodynamic properties of clusters from knowledge of a sample of minima on the potential energy surface using a harmonic superposition approximation is extended to incorporate anharmonicity using Morse correction terms to the density of states. Anharmonicity parameters are found for different regions of the potential energy surface by fitting to simulation results using the short‐time averaged temperature as an order parameter. The resulting analytical expression for the density of states can be used to calculate many thermodynamic properties in a variety of ensembles, which accurately reproduce simulation results. This method is illustrated for 13‐atom and 55‐atom Lennard‐Jones clusters.

[1]  David J. Wales,et al.  Coexistence in small inert gas clusters , 1993 .

[2]  David J. Wales,et al.  Melting and freezing of small argon clusters , 1990 .

[3]  R. Stephen Berry,et al.  The onset of nonrigid dynamics and the melting transition in Ar7 , 1986 .

[4]  F. Stillinger,et al.  Point defects in bcc crystals: Structures, transition kinetics, and melting implications , 1984 .

[5]  D. Wales.  Structure, dynamics and thermodynamics of small particles and inorganic clusters , 1993 .

[6]  D. Wales.  Locating stationary points for clusters in cartesian coordinates , 1993 .

[7]  D. C. Tardy,et al.  Theory of Unimolecular Reactions , 1973 .

[8]  D. Wales,et al.  Rearrangements of model (H2O)8 and (H2O)20 clusters , 1993 .

[9]  K. Lehmann,et al.  Numerical Laplace transform density of states calculation for medium and large molecules , 1993 .

[10]  David J. Wales,et al.  Rearrangements of 55‐atom Lennard‐Jones and (C60)55 clusters , 1994 .

[11]  Eberhard R. Hilf,et al.  The structure of small clusters: Multiple normal-modes model , 1993 .

[12]  A. Hindmarsh,et al.  Number Dependence of Small‐Crystal Thermodynamic Properties. I , 1972 .

[13]  P. Haarhoff.  The density of vibrational energy levels of polyatomic molecules , 1964 .

[14]  D. Wales.  CLUSTERS OF C60 MOLECULES , 1994 .

[15]  S. Weerasinghe,et al.  Absolute classical densities of states for very anharmonic systems and applications to the evaporation of rare gas clusters , 1993 .

[16]  D. Wales.  Finding saddle points for clusters , 1989 .

[17]  Michael Page,et al.  Following steepest descent reaction paths. The use of higher energy derivatives with ab initio electronic structure methods , 1990 .

[18]  Jonathan P. K. Doye,et al.  An order parameter approach to coexistence in atomic clusters , 1995 .

[19]  David Jackson McGinty,et al.  Vapor phase homogeneous nucleation and the thermodynamic properties of small clusters of argon atoms , 1971 .

[20]  Thomas L. Beck,et al.  Solid–liquid phase changes in simulated isoenergetic Ar13 , 1986 .

[21]  D. Wales,et al.  Structure and dynamics of model metal clusters , 1993 .

[22]  J. Rose,et al.  Freezing, melting, nonwetting, and coexistence in (KCl)32 , 1993 .

[23]  D. Truhlar,et al.  Vibrational partition functions calculated from limited information , 1984 .

[24]  M. Hoare,et al.  Statistical mechanics and morphology of very small atomic clusters , 1976 .

[25]  H. C. Andersen,et al.  Molecular dynamics study of melting and freezing of small Lennard-Jones clusters , 1987 .

[26]  William H. Press,et al.  Numerical recipes , 1990 .

[27]  I. R. Mcdonald,et al.  Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method , 1967 .

[28]  J. Rose,et al.  Towards elucidating the interplay of structure and dynamics in clusters: Small KCl clusters as models , 1992 .

[29]  J. Jortner,et al.  Energetic and thermodynamic size effects in molecular clusters , 1989 .

[30]  Frank H. Stillinger,et al.  Computational study of transition dynamics in 55-atom clusters , 1990 .

[31]  J. J. Burton.  Free energy of small face centred cubic clusters of atoms , 1973 .

[32]  D. Wales,et al.  Structure, dynamics, and thermodynamics of model (H2O)8 and (H2O)20 clusters , 1993 .

[33]  C. J. Tsai,et al.  Use of the histogram and jump‐walking methods for overcoming slow barrier crossing behavior in Monte Carlo simulations: Applications to the phase transitions in the (Ar)13 and (H2O)8 clusters , 1993 .

[34]  J. J. Burton.  Configuration, Energy, and Heat Capacity of Small Spherical Clusters of Atoms , 1970 .

[35]  David J. Wales,et al.  Free energy barriers to melting in atomic clusters , 1994 .

[36]  Michael A. Collins,et al.  Rigorous derivation of reaction path degeneracy in transition state theory , 1992 .

[37]  J. J. Burton.  Vibrational Frequencies and Entropies of Small Clusters of Atoms , 1972 .

[38]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[39]  R. Whetten,et al.  Statistical thermodynamics of the cluster solid-liquid transition. , 1990, Physical review letters.

[40]  S. F. Chekmarev,et al.  An analytic model for atomic clusters , 1993 .

[41]  R. Berry.  POTENTIAL SURFACES AND DYNAMICS : WHAT CLUSTERS TELL US , 1993 .