Efficient free energy calculations by variationally optimized metric scaling: Concepts and applications to the volume dependence of cluster free energies and to solid-solid phase transitions

Finite-time variational switching is an efficient method for obtaining conv erging upper and lower bounds to free energy changes by computer simulation . Over the course of the simulation, the Hamiltonian is changed continuousl y between the system of interest and a reference system for which the parti tion function has an analytic form. The bounds converge most rapidly when t he system is kept close to equilibrium throughout the switching. In this pa per we introduce the technique of metric scaling to improve adherence to eq uilibrium and thereby obtain more rapid convergence of the free energy boun ds. The method involves scaling the coordinates of the particles, perhaps i n a nonuniform way, so as to assist their natural characteristic evolution over the course of the switching. The scaling schedule can be variationally optimized to produce the best convergence of the bounds for a given Hamilt onian switching path. A correction due to the intrinsic work of scaling is made at the end of the calculation. The method is illustrated in a pedagogi cal one-dimensional example, and is then applied to the volume dependence o f cluster free energies, a property of direct relevance to vapor-liquid nuc leation theory. Order-of-magnitude improvements in efficiency are obtained in these simple examples. As a contrasting application, we use metric scali ng to calculate directly the free energy difference between face-centered-c ubic and body-centered-cubic Yukawa crystals. A continuous distortion is ap plied to the lattice, avoiding the need for separate comparison of the two phases with an independent reference system. (C) 2000 American Institute of Physics. [S0021-9606(00)52441-6].