On Boltzmann Averaging in Ab Initio Thermodynamics

Ab initio thermodynamics is a widespread, computationally efficient approach to predict the stable configuration of a surface in contact with a surrounding (gas or liquid) environment. In a prevalent realization of this approach, this stable configuration is simply equated with the structure in a considered candidate pool that exhibits the lowest surface free energy. Here we discuss the possibility to consider the thermal accessibility of competing, higher-energy configurations through Boltzmann averaging when the extended surface configurations and their energetics are computed within periodic boundary condition supercells. We show analytically that fully converged averages can be obtained with a candidate pool derived from exhaustive sampling in a surface unit-cell exceeding the system's correlation length. In contrast, averaging over a small pool of ad hoc assembled structures is generally ill-defined. Enumerations of a lattice-gas Hamiltonian model for on-surface oxygen adsorption at Pd(100) are employed to illustrate these considerations in a practical context.