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

The critical points analysis of electron density, i.e. rho(x), from ab initio calculations is used in combination with the catastrophe theory to show a correlation between rho(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 del rho(x(c)) = 0 and lambda(1), lambda(2), lambda(3) not equal 0 [lambda being the eigenvalues of the Hessian of rho(x) at x(c)], towards degenerate critical points, i.e. del rho (x(c)) = 0 and at least one lambda equal to zero. The catastrophe theory formalism provides a mathematical tool to model rho (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 TiO2 (rutile structure), MgO (periclase structure) and Al2O3 (corundum structure) undergo because of pressure and/or temperature are here discussed. An agreement of 35% is observed between the theoretical model and experimental pressure/temperature of transformation.