Use of a variable-charge interatomic potential for atomistic simulations of bulk, oxygen vacancies, and surfaces of rutileTiO2

Abstract

In this paper, interatomic potential models used for atomistic simulations of insulating oxides are revisited through the example of ${\mathrm{TiO}}_2$ rutile. The cohesive energy of oxides comprises an electrostatic part and a short-range part whose relative importance differs with the models. The electrostatic part can be evaluated by considering either point fixed atomic charges or, alternatively, charges that are allowed to vary in response to the local atomic environment, with a shielding correction to coulombic interactions at short range. We deeply analyzed this latter approach in the framework of the Rappé and Goddard QEq charge equilibration scheme. We conclude that it is an efficient model to describe heterogeneous situations due to point defects or surfaces. Moreover, whatever the description of the electrostatic part of the energy is, several short-range interatomic potentials are found to describe in an acceptable way the crystal bulk properties (cohesive energy, elastic constants, etc). To compare the efficiency of various short-range potentials, we selected the ${\mathrm{TiO}}_2$ rutile whose experimental formation energy of the oxygen vacancy is available. By combining it with the cohesive energy, we have been able to accurately analyze the energetics of ${\mathrm{TiO}}_2$ as a function of those potentials. In this paper we show first that Morse potential is not adapted to oxygen-oxygen interactions and that pair-wise potentials between $\mathrm{Ti}\text{−}\mathrm{O}$ pairs are not suitable to describe defects. As a result, we propose a model that combines the QEq description for electrostatic energy, a Buckingham potential for $\mathrm{O}\text{−}\mathrm{O}$ interactions and a $N$-body potential for the covalent part of the $\mathrm{Ti}\text{−}\mathrm{O}$ interactions. This model efficiency has been tested on bulk, oxygen vacancy, and surfaces of rutile and turned out to provide results which fit very satisfactorily the experimental data.