Electron‐density critical points analysis and catastrophe theory to forecast structure instability in periodic solids

Marcello Merli; Alessandro Pavese

Index: 10.1107/S2053273317018381

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Abstract

The critical points analysis of electron density, i.e. ρ(x), from ab initio calculations is used in combination with the catastrophe theory to show a correlation between ρ(x) topology and the appearance of instability that may lead to transformations of crystal structures, as a function of pressure/temperature. In particular, this study focuses on the evolution of coalescing non‐degenerate critical points, i.e. such that ∇ρ(xc) = 0 and λ1, λ2, λ3 ≠ 0 [λ being the eigenvalues of the Hessian of ρ(x) at xc], towards degenerate critical points, i.e. ∇ρ(xc) = 0 and at least one λ equal to zero. The catastrophe theory formalism provides a mathematical tool to model ρ(x) in the neighbourhood of xc and allows one to rationalize the occurrence of instability in terms of electron‐density topology and Gibbs energy. The phase/state transitions that TiO2 (rutile structure), MgO (periclase structure) and Al2O3 (corundum structure) undergo because of pressure and/or temperature are here discussed. An agreement of 3–5% is observed between the theoretical model and experimental pressure/temperature of transformation.