A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO₃ with Hybrid DFT Functionals

Abstract

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Keywords

• basis set
• optimization
• DFT
• LCAO
• hybrid functional
• HSE