Formulation of Multicomponent Lattice Gas Model Cluster Expansions Parameterized on Ab Initio Data: An Introduction to the Ab Initio Mean-Field Augmented Lattice Gas Modeling (AMALGM) Code

A formalism is presented for the construction of multi-component lattice gas models parameterized with ab initio (typically density functional theory) data. The Leave-Multiple-Out (LMO) and the Leave-One-Out (LOO) Cross Validation (CV) Score are showcased and practical algorithms are developed and implemented in a new code called the Ab initio Mean-field Augmented Lattice Gas Modelling (AMALGM) code. The functionality of these algorithms are demonstrated with a fully worked out example using the O/Fe(100) system. AMALGM and the formalism on which it is based is envisioned as a surface-oriented lattice gas alternative to other cluster expansion codes that are typically geared toward bulk systems whose lateral interactions between components are parameterized using an Ising model. While the formalism is created within the context of surfaces, it is equally applicable to bulk materials.