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

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( x c ) = 0 and λ 1 , λ 2 , λ 3 ≠ 0 [λ being the eigenvalues of the Hessian of ρ( x ) at x c ], towards degenerate critical points, i.e . ∇ρ( x c ) = 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 x c and allows one to rationalize the occurrence of instability in terms of electron‐density topology and Gibbs energy. The phase/state transitions that TiO 2 (rutile structure), MgO (periclase structure) and Al 2 O 3 (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.