Variable Lattice Monte Carlo: A Voronoi Tessellation-Guided Structural Exploration Framework and Applications in Iron Carbides

Navigating complex potential energy surfaces to identify ground-state structures and metastable phases remains a formidable challenge in theoretical study of heterogeneous catalysts with evolving active phases, such as iron carbides in Fischer-Tropsch synthesis (FTS). Here, we propose the variable lattice Monte Carlo (VLMC) method, a geometry-guided framework for global optimization and statistical thermodynamic sampling. By integrating Voronoi tessellation, VLMC dynamically targets accessible interstitial and adsorption sites as metal lattice varies, enabling the efficient exploration of chemical space. We validate this approach through three representative cases: (1) the phase transformation from bulk χ-Fe5C2 and θ-Fe3C to η-Fe2C, (2) the carbon-induced clock reconstruction on fcc Fe(100) surface, and (3) the morphology evolution of iron carbide nanoparticles under varying carbon chemical potentials. These results establish VLMC as a robust framework for structural exploration in iron carbides and analogous systems characterized by variable metal lattice and fractional occupation of interstitial sites.