Polarizable interatomic force field for ${\text{TiO}}_2$ parametrized using density functional theory

We report a classical interatomic force field for ${\text{TiO}}_2$, which has been parametrized using density functional theory forces, energies, and stresses in the rutile crystal structure. The reliability of this classical potential is tested by evaluating the structural properties, equation of state, phonon properties, thermal expansion, and some thermodynamic quantities such as entropy, free energy, and specific heat under constant volume. The good agreement of our results with ab initio calculations and with experimental data, indicates that our force field describes the atomic interactions of ${\text{TiO}}_2$ in the rutile structure very well. The force field can also describe the structures of the brookite and anatase crystals with good accuracy.

Figure 1

(Color online) Volume dependence of the energy of ${\text{TiO}}_2$ in the rutile, brookite, and anatase crystal structures for our potential (red solid lines) and from LDA ab initio calculations (blue dotted lines). Energies are expressed relative to the equilibrium energy of the most stable phase.

Figure 2

(Color online) Phonon dispersion curves of ${\text{TiO}}_2$ in the rutile crystal structure from different methods. (a) Results from our new force field (black dots) compared to experiment (Ref. 19) (red circles) and ab initio (DFT-LDA) calculations (green triangles). (b) Results from the MA force field (black dots) compared to experiment (Ref. 19) (red circles) and ab initio (DFT-LDA) calculations (green triangles).

Figure 3

(Color online) Temperature dependence of the lengths of the rutile lattice vectors, expressed as percentage differences with respect to their room temperature values, i.e., $\Delta a\left(T\right)=a\left(T\right)-a\left(300\text{K}\right)$. Boxes and filled triangles refer to the experimental data of Refs. 36, 49, respectively. Blue dots are the results of MD simulations with our new force field.

Figure 4

(Color online) Thermodynamic properties of rutile ${\text{TiO}}_2$ derived from phonon properties: (a) free energy $F$; (b) entropy $S$; and (c) specific heat $C_v$ under constant volume