Constrained fluid lambda-integration: constructing a reversible thermodynamic path between the solid and liquid state.

Abstract

A novel lambda-integration path is proposed for calculating the Gibbs free energy difference between any arbitrary solid and liquid state needed for the location of melting lines. This technique involves reversibly forcing a liquid state to a solid state across the phase transition along a nonphysical path, thermodynamically coupling the two states directly. The process eliminates the need for coupling to idealized reference states as is presently performed and hence simplifies the location of phase transitions for computer simulation systems. More specifically the path involves a three stage process, whereby, initially a liquid state is transformed to a weakly attractive fluid using linear lambda-integration scaling of the intermolecular potential. In the second stage, the resulting fluid is then constrained to the required solid configurational phase space via the insertion of a periodic lattice of 3D Gaussian wells. The final stage involves reversing to full strength the main intermolecular potential while gradually turning off the constraining 3D Gaussian lattice finally resulting in a stable (or metastable) solid state. Each stage was found to be completely reversible and the resulting change in free energy was thermodynamically integrable. The methodology is demonstrated and validated by calculating solid-liquid coexistence points using the new technique and comparing to those in present literature for the truncated and shifted Lennard-Jones system. The results are found to be in good agreement. The new method is not limited to melting phase transitions and is readily applicable to any simulation methodology, simulation cell size and/or intermolecular potential including ab initio methods.