Direct free energy estimates along a real path by means of constrained molecular dynamics

A method is presented, which can be used in the frame of the quasi harmonic analytical theory as well as Monte Carlo and Molecular Dynamics simulations to compute directly the difference between the Helmholtz free energies associated with two different configuration states. This free energy difference is obtained by thermodynamic integration along a path in configuration space. It is used with constrained molecular dynamics for different atomic arrangements in the Σ = 11 (332) tilt grain boundary in silicon observed by high resolution electron microscopy. The results are found in good agreement with an indirect iso-stress thermodynamic integration method.