Machine learning-assisted optimization of MTO basis sets

First-principles calculations based on density functional theory (DFT) have had a significant impact on chemistry, physics, and materials science, enabling in-depth exploration of the structural and electronic properties of a wide variety of materials. Among different implementations of DFT, the plane-wave method is widely used for periodic systems because of its high accuracy. However, this method typically requires a large number of basis functions for large systems, leading to high computational costs. Localized basis sets, such as the muffin-tin orbital (MTO) method, have been introduced to provide a more efficient description of electronic structure with a reduced basis set, albeit at the cost of reduced computational accuracy. In this work, we propose an optimization strategy using machine-learning techniques to automate MTO basis-set parameters, thereby improving the accuracy and efficiency of MTO-based calculations. Default MTO parameter settings primarily focus on lattice structure and give less consideration to element-specific differences. In contrast, our optimized parameters incorporate both structural and elemental information. Based on these converged parameters, we successfully recovered missing bands for CrTe₂. For the other three materials — Si, GaAs, and CrI₃ — we achieved band improvements of up to 2 eV. Furthermore, the generalization of the machine-learned method is validated by perturbation, strain, and elemental substitution, resulting in improved band structures. Additionally, lattice-constant optimization for GaAs using the converged parameters yields closer agreement with experiment.