DFT-Chemical Pressure Analysis: Visualizing the Role of Atomic Size in Shaping the Structures of Inorganic Materials

Atomic size effects have long played a role in our empirical understanding of inorganic crystal structures. At the level of electronic structure calculations, however, the contribution of atomic size remains difficult to analyze, both alone and relative to other influences. In this paper, we extend the concepts outlined in a recent communication to develop a theoretical method for revealing the impact of the space requirements of atoms: the density functional theory-chemical pressure (DFT-CP) analysis. The influence of atomic size is most pronounced when the optimization of bonding contacts is impeded by steric repulsion at other contacts, resulting in nonideal interatomic distances. Such contacts are associated with chemical pressures (CPs) acting upon the atoms involved. The DFT-CP analysis allows for the calculation and interpretation of the CP distributions within crystal structures using DFT results. The method is demonstrated using the stability of the Ca₂Ag₇ structure over the simpler CaCu₅-type alternative adopted by its Sr-analogue, SrAg₅. A hypothetical CaCu₅-type CaAg₅ phase is found to exhibit large negative pressures on each Ca atom, which are concentrated in two symmetry-related interstitial spaces on opposite sides of the Ca nucleus. In moving to the Ca₂Ag₇ structure, relief comes to each Ca atom as a defect plane is introduced into one of these two negative-pressure regions, breaking the symmetry equivalence of the two sides and yielding a more compact Ca coordination environment. These results illustrate how the DFT-CP analysis can visually and intuitively portray how atomic size interacts with electronics in determining structure, and bridge theoretical and experimental approaches toward understanding the structural chemistry of inorganic materials.