Systematic development of ab initio tight-binding models for hexagonal metals

Abstract

A systematic method for building an extensible tight-binding model from ab initio calculations has been developed and tested on two hexagonal metals: Zr and Mg. The errors introduced at each level of approximation are discussed and quantified. For bulk materials, using a limited basis set of spd orbitals is shown to be sufficient to reproduce with high accuracy bulk energy versus volume curves for fcc, bcc, and hcp lattice structures, as well as the electronic density of states. However, the two-center approximation introduces errors of several tenths of eV in the pair potential, crystal-field terms, and hopping integrals. Environmentally dependent corrections to the former two have been implemented, significantly improving the accuracy. Two-center hopping integrals were corrected by taking many-center hopping integrals for a set of structures of interest, rotating them into the bond reference frame, and then fitting a smooth function through these values. Finally, a pair potential was fitted to correct remaining errors. However, this procedure is not sufficient to ensure transferability of the model, especially when point defects are introduced. In particular, it is shown to be problematic when interstitial elements are added to the model, as demonstrated in the case of octahedral self-interstitial atoms.

A deep neural network for molecular wave functions in quasi-atomic minimal basis representation

“…Semi-empirical methods and tight-binding approximations in chemistry have always tried to circumvent this issue by representing the electronic structure in a minimal or very small basis set of local atomic orbitals, which are optimized to best reproduce the results of full basis calculations. Examples of such efforts include projecting onto a minimal basis of local atomic orbitals (AOs), 34 maximally localized Wannier functions, 35 atomic orbitals in confinement potentials, 36,37 and various orbital localization schemes such as quasi-atomic minimal-basis-set orbitals (QUAMBOs). 29,30,38 In the context of creating a machine learning representation of electronic structure, transforming DFT data into a minimal representation of AOs offers important advantages: The projection onto a minimal basis reduces the number of matrix elements that need to be represented by a model of the Hamiltonian.…”

A deep neural network for molecular wave functions in quasi-atomic minimal basis representation

“…Semi-empirical methods and tight-binding approximations in chemistry have always tried to circumvent this issue by representing the electronic structure in a minimal or very small basis set of local atomic orbitals, which are optimized to best reproduce the results of full basis calculations. Examples of such efforts include projecting onto a minimal basis of local atomic orbitals (AOs), 34 maximally localized Wannier functions, 35 atomic orbitals in confinement potentials, 36,37 and various orbital localization schemes such as quasi-atomic minimal-basis-set orbitals (QUAM-BOs). 29,30,38 In the context of creating a machine learning representation of electronic structure, transforming DFT data into a minimal representation of AOs offers important advantages: The projection onto a minimal basis reduces the number of matrix elements that need to be represented by a model of the Hamiltonian.…”