Convergence Analysis and Predictions for Optimizing Reciprocal Grids: A First-Principles and Machine Learning Study

When crystalline materials are investigated by performing first-principles density functional theory (DFT) calculations, the reciprocal grid should be fine enough to obtain the converged total energy and electronic structure. Herein, we performed a convergence test of the total energy for the density of reciprocal points to determine fine enough reciprocal grids for high-throughput calculations. Our results show that the nonlinearity of the band structures affects the convergence of the total energy, especially for materials with a finite band gap. We further investigate which physical properties make a finer reciprocal grid necessary based on machine learning (ML) analysis. Our developed models using DFT-based features and elemental properties-based features exhibit R² of 0.803 and 0.880, respectively. Our ML model quantitatively shows the importance of nonlinearity and band gaps in predicting errors in total energy calculations. Furthermore, our ML model using elemental features can be applied to estimate the appropriate reciprocal grid, facilitating high-throughput calculations.