First-principles elucidation of atomic size effects using DFT-chemical pressure analysis: Origins of Ca₃₆Sn₂₃'s long-period superstructure

The space requirements of atoms are empirically known to play key roles in determining structure and reactivity across compounds ranging from simple molecules to extended solid state phases. Despite the importance of this concept, the effects of atomic size on stability remain difficult to extract from quantum mechanical calculations. Recently, we outlined a quantitative yet visual and intuitive approach to the theoretical analysis of atomic size in periodic structures: the DFT-Chemical Pressure (DFT-CP) analysis. In this Article, we describe the methodological details of this DFT-CP procedure, with a particular emphasis on refinements of the method to make it useful for a wider variety of systems. A central improvement is a new integration scheme with broader applicability than our earlier Voronoi cell method: contact volume space-partitioning. In this approach, we make explicit our assumption that the pressure at each voxel is most strongly influenced by its two closest atoms. The unit cell is divided into regions corresponding to individual interatomic contacts, with each region containing all points that share the same two closest atoms. The voxel pressures within each contact region are then averaged, resulting in effective interatomic pressures. The method is illustrated through the verification of the role of Ca-Ca repulsion (deduced earlier from empirical considerations by Corbett and co-workers) in the long-period superstructure of the W₅Si₃ type exhibited by Ca₃₆Sn ₂₃.