On Boltzmann Averaging in Ab Initio Thermodynamics

TL;DR

This paper explores the use of Boltzmann averaging in ab initio thermodynamics to more accurately predict stable surface configurations by considering thermal accessibility of higher-energy states, beyond just the lowest free energy structure.

Contribution

It demonstrates that fully converged Boltzmann averages can be achieved with exhaustive sampling of surface configurations within a sufficiently large supercell, providing a more rigorous approach than small, ad hoc structure pools.

Findings

Fully converged averages require exhaustive sampling in large supercells.

Small, arbitrary structure pools lead to ill-defined averages.

Lattice-gas Hamiltonian models illustrate the practical implications.

Abstract

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.