Bader’s topological analysis of the electron density in the pressure-induced phase transitions/amorphization in a-quartz from the catastrophe theory viewpoint

In this work, the Bader's topological analysis of the electron density, coupled with Thom's catastrophe theory, was used to characterize the pressure-induced transformations in α-quartz. In particular, ab initio calculations of the α-quartz structures in the range 0-105 Gpa have been performed at the HF/DFT exchange-correlation terms level, using Hamiltonians based on a WC1LYP hybrid scheme. The electron densities calculated throughout the ab initio wave functions have been analysed by means of the Bader's theory, seeking for some catastrophic mechanism in the sense of Thom's theory. The analysis mainly showed that there is a typical fold catastrophe feature involving an O-O interaction at the quartz-coesite transition pressure, while the amorphization of α-quartz is coincident with an average distribution of the gradient field of the electron density around the oxygen atom which is typically observed in the free atoms. This approach is addressed to depict a phase transition from a novel viewpoint, particularly useful in predicting the stability of a compound at extreme conditions, especially in the absence of experimental data.