Development of reference states for use in absolute free energy calculations of atomic clusters with application to 55-atom Lennard-Jones clusters in the solid and liquid states

In this paper four reference states allowing computation of the absolute internal free energies of solid and liquid clusters are introduced and implemented. Three of these are introduced for the first time. Two of these references are useful for highly fluctional liquidlike clusters while the other two are appropriate for more rigid solidlike clusters. These reference states are combined with a finite time variational method to obtain upper and lower bounds to the absolute free energies of clusters of Lennard-Jones (LJ) atoms, LJ(4) and LJ(55), allowing the efficiency of each of the four reference states to be elucidated. The optimal references are then applied to obtain upper and lower bounds to the internal free energies (the absolute free energy in the cluster center of mass frame) of LJ(55) over a series of fixed temperatures including the solid-liquid coexistence regime. The reversible scaling method, recently introduced by de Koning, Antonelli, and Yip, is then used to extend the results over a continuous range of temperatures. Estimation of the rotational free energy allows comparisons to free energies of LJ(55) in the nonrotating center of mass frame as estimated by Doye and Wales. (C) 2000 American Institute of Physics. [S0021-9606(00)51631-6].