Novel methods for solid-state free-energy calculations

In our first work, we introduce the Harmonic Perturbation method. We examine the ability of two-stage free-energy perturbation methods to yield solid-phase free energies using a system of harmonically coupled particles as a reference. We consider two ways to construct a reference system, one based on derivatives of the intermolecular potential of the target system of interest (the conventional choice in lattice dynamics), and the other based on analysis of pairwise configurational correlations observed in simulations of the target system. For each case we consider two perturbation techniques that compute the free energy difference between the target and reference systems while avoiding lengthy thermodynamic integration procedures. The methods are overlap sampling as optimized by Bennett, and umbrella sampling optimized in a similar fashion. Such methods require at most two simulations to yield a result, but they can fail if the target and reference do not share a sufficiently large set of relevant configurations. In particular, failure can be expected for large systems, and we examine the question of how large a system can be before this point is reached. Our test case is a system of r -12 soft spheres, and we find that for systems of up to 108 particles the methods are accurate for all temperatures up to melting; for systems of 256 particles the methods begin to break down at about half the melting temperature.;Our second work is on the development of Harmonically Targeted Temperature Perturbation method, where we examine a method for computing the change in free energy with temperature of a crystalline solid. In the method the free energy difference between nearby temperatures is calculated via overlap-sampling free-energy perturbation with Bennett's optimization. Coupled to this is a harmonically targeted perturbation that displaces the atoms in a manner consistent with the temperature change, such that for a harmonic system the free-energy difference would be recovered with no error. A series of such perturbations can be assembled to bridge larger gaps in temperature. We test this harmonically-targeted temperature-perturbation (HTTP) method through application to the inverse-power soft-potential, o ( r) = epsilon (sigma/r)", over a range of temperatures up to the melting condition. Three exponent values (n = 12, 9 and 6) for the potential are studied with different crystal structures, specifically face-centered cubic (fcc), body-centered cubic (bcc) and hexagonal close packing (hcp). Absolute free energies (classical only) for each system are obtained by implementing the series to near-zero temperature, where the harmonic model becomes very accurate. .;We continue on to study the fluid equation of state and the solid-fluid transition properties of soft-sphere system in our next work. Virial coefficients up to B8 are calculated for the soft-sphere model with exponents n = 12, 9 and 6. We demonstrate that for n = 12, the virial series truncated at B8 describes well the equation of state (EOS) of the fluid phase up to the freezing density, while for n = 9 and 6 the series departs from the correct behavior for densities of 75% and 18% of the freezing density, respectively. For these cases, Pade approximants provide a much improved description of the equation of state at high density. The EOS for these different exponent- n values are further improved by the empirical fit of B 9,fit (an empirical description of higher-order coefficients) to simulation data, using a form consistent with the known virial coefficients. Fluid-solid coexistence properties are evaluated and the results are in reasonably good agreement with the more-recent literature values.;In our final work, we further demonstrate the effectiveness of the HTTP method and extend it to systems with orientational degrees of freedom. Specifically, we calculate the absolute free energy of the linear-molecular nitrogen model of Etter et al., examining both the lowtemperature low-pressure alpha-N 2 structure and the orientationally-disordered beta-N2 phase. In each perturbation (for the alpha-N2 phase) to determine the free-energy difference between systems at adjacent temperatures, harmonic coordinate scaling is applied to both the translational and rotational degrees of freedom in the nitrogen molecule to improve the phase-space overlap of the two perturbing systems and consequently, the free-energy difference results. (Abstract shortened by UMI.)...