The Gibbs free energy is the fundamental thermodynamic potential underlying
the relative stability of different states of matter under constant-pressure
conditions. However, computing this quantity from atomic-scale simulations is
far from trivial. As a consequence, all too often the potential energy of the
system is used as a proxy, overlooking entropic and anharmonic effects. Here we
discuss a combination of different thermodynamic integration routes to obtain
the absolute Gibbs free energy of a solid system starting from a harmonic
reference state. This approach enables the direct comparison between the free
energy of different structures, circumventing the need to sample the transition
paths between them. We showcase this thermodynamic integration scheme by
computing the Gibbs free energy associated with a vacancy in BCC iron, and the
intrinsic stacking fault free energy of nickel. These examples highlight the
pitfalls of estimating the free energy of crystallographic defects only using
the minimum potential energy, which overestimates the vacancy free energy by
60% and the stacking-fault energy by almost 300% at temperatures close to the
melting point
