Free energy calculation and ghost force correction for hot-QC

A new efficient variant of hot-QC, the finite temperature version of the quasicontinuum (QC) method, is presented. In the original formulation of hot-QC, a dynamically evolving atomistic region is coupled with either a dynamic (hot-QC-dynamic) or a static (hot-QC-static) continuum region. In the current work, a free energy minimization method is employed in which atom positions in both the atomistic and continuum regions always occupy equilibrium positions. The effect of ghost forces at the interface of the atomistic and continuum regions is discussed for all three variants of hot-QC using two examples: a perfect cubic crystal and a Lomer dislocation dipole. Errors due to ghost forces and due to mesh entropy are considered and the efficacy of their correction terms are evaluated. It is shown that the proposed free energy minimization method has comparable accuracy to the other methods with significantly higher efficiency.