Exploring the Convergence and Properties of Intrinsic Bond Orbitals in Solids

TL;DR

This paper investigates the properties and construction of localized Wannier orbitals in solids using intrinsic bond orbitals, compares solver performance, and discusses computational challenges in large supercells.

Contribution

It introduces a new approach combining the Pipek-Mezey functional with intrinsic atomic orbitals for localized Wannier orbitals and analyzes solver performance and scalability.

Findings

Orbital spreads correlate with geometric properties across materials.

Comparable sparsity patterns in the Hartree-Fock exchange matrix are observed.

Construction of Wannier orbitals in metal oxides is computationally more demanding.

Abstract

We present a study of the construction and spatial properties of localized Wannier orbitals in large supercells of insulating solids using plane waves as the underlying basis. The Pipek-Mezey (PM) functional in combination with intrinsic atomic orbitals (IAOs) as projectors is employed, resulting in so-called intrinsic bond orbitals (IBOs). Independent of the bonding type and band gap, a correlation between orbital spreads and geometric properties is observed. As a result, comparable sparsity patterns of the Hartree-Fock exchange matrix are found across all considered bulk 3D materials, exhibiting covalent bonds, polar covalent bonds, and ionic bonds. Recognizing the considerable computational effort required to construct localized Wannier orbitals for large periodic simulation cells, we address the performance and scaling of different solvers for the localization problem. This includes the Broyden-Fletcher-Goldfarb-Shanno (BFGS), Conjugate-Gradient (CG), Steepest Ascent (SA) as well as the Direct Inversion in the Iterative Subspace (DIIS) method. Each algorithm performs a Riemannian optimization under unitary matrix constraint, efficiently reaching the optimum in the "curved parameter space" on geodesics. We hereby complement the quantum chemistry and materials science literature with an introduction to this topic along with key references. The solvers have been implemented both within the Vienna Ab initio Simulation Package (VASP) and as a standalone open-source software package. Furthermore, we observe that the construction of Wannier orbitals for supercells of metal oxides presents a significant challenge, requiring approximately one order of magnitude more iteration steps than other systems studied.