Density-Functional Tight-Binding Parameters for Bulk Zirconium: A Case Study for Repulsive Potentials

Abstract

Density-functional tight-binding (DFTB) parameters are presented for the simulation of the bulk phases of zirconium. Electronic parameters were obtained using a band structure fitting strategy, while two-center repulsive potentials were created by particle swarm optimization. As objective functions for the repulsive potential fitting, we employed the Birch–Murnaghan equations of state for hexagonal close-packed (HCP), body-centered cubic (BCC) and ω phases of Zr from density-functional theory (DFT). When fractional atomic coordinates are not allowed to change in the generation of the equation-of-state curves, long-range repulsive DFTB potentials are able to almost perfectly reproduce equilibrium structures, relative DFT energies of the bulk phases, and bulk moduli. However, the same potentials lead to artifacts in the DFTB potential energy surfaces when atom positions in the unit cell are allowed to fully relax during the change of unit cell parameters. Conventional short-range repulsive DFTB potentials, while inferior in their ability to reproduce DFT bulk energetics, are able to correctly reproduce the qualitative shape of the DFT potential energy surfaces, including the location of global minima, and can therefore be considered more transferable.

Development of Density-Functional Tight-Binding Parameters for the Molecular Dynamics Simulation of Zirconia, Yttria, and Yttria-Stabilized Zirconia

“…The Woods–Saxon confining potentials, orbital energies, and Hubbard parameters for Zr and Y were taken from previous studies and without modification. , These electronic parameters are found to closely mimic those of the PBE valence and conduction band structures up to 5 eV above the Fermi level for the HCP crystal structure, as shown in Figure S3. The band structures determined at the DFTB2 level show good qualitative agreement with reference PBE-PAW calculations for the metal oxides for both the valence bands and several low-lying conduction bands.…”

“…The electronic parameterizations for Zr and Y have been conducted in the previous studies employing the Woods–Saxon confining potential by taking the bulk Zr and Y band structures calculated at the PBE-PAW level of theory as refs and (see Table S1 displaying the Woods–Saxon orbital confining potential). The electronic parameterization considered valence electrons from 4d and 5s orbitals and the empty 5p orbital for the metal atoms.…”

“…In the present work, we focused on the accuracy of the metal–oxygen repulsive potentials. The cutoff radius of the Zr–Zr pair was set so that the value did not interfere with the Zr–O repulsive parameterization while maintaining a reasonable geometry of the experimental Zr bulk phase . However, such an approach did not seem to work for the case of the Y–O parameterization, as the Y–Y repulsive potential cutoff value will eventually affect the Y–O repulsive pair due to the complexity of the Y 2 O 3 structure.…”

“…The cutoff radius of the Zr−Zr pair was set so that the value did not interfere with the Zr−O repulsive parameterization while maintaining a reasonable geometry of the experimental Zr bulk phase. 46 The DFT reference data were obtained by scanning reference phases from approximately 70−130% volume of the DFT equilibrium geometry with intervals of approximately 5% of the volume. The repulsive potential was obtained by fitting the difference between the DFT and DFTB energies as a function of the pair distance presented in Figure S2.…”

Hybrid Density Functional Tight Binding (DFTB)─Molecular Mechanics Approach for a Low-Cost Expansion of DFTB Applicability

“…The modeling of many functional oxides, doped oxides, interfaces, and heterostructures could benefit from DFTB but is shut out from using its advantages due to the absence of accurate enough parameterizations. While the workflow of DFTB parameterization is understood and programs are available to compute Slater–Koster tables, − in practice, achieving an accurate (with an accuracy competitive to DFT) parameterization for each material still requires significant time and manpower investment. − Not all atom pairs, however, are equally important for the electronic structure or for their contribution to the mechanism of a material’s functionality. Consider the example, presented below, of an interface between amorphous silica and titania, which is important, in particular, for silicon-perovskite tandem solar cells .…”