Machine Learning for Diamond Materials Research

Abstract

As quantum information science advances, there is a growing demand for materials capable of exhibiting quantum effects. However, atomic-scale modeling is constrained by the computational cost of electronic-structure methods such as density-functional theory (DFT)[1]. We present machine-learning (ML) approaches that enhance standard computational methods and apply them to diamond color centers, computing electronic band structures and vibrational modes of Group IV defects, and the dynamics of hydrogen-related defects. For electronic structure calculations, Density Functional Theory does not suffice and falls short in calculating the excited states. The GW approximation provides solace. This approximation includes the self-energy of the system, resulting in better accuracy. The high computational resources required for this approach do not provide easy access to diamond defect calculations. Delta-Machine Learning (∆-ML) enables a way to reach GW accuracy with DFT level calculations as input. The vibrational modes of a crystal are obtained from the eigenvalues of the dynamical matrix, i.e., the second derivative of the potential energy with respect to nuclear positions. Ab initio calculations of this matrix are computationally expensive and become prohibitive for large systems such as color centers. A combined Density Functional Theory (DFT)-enhanced Machine Learning (ML) approach enables vibrational calculations at ab initio accuracy with significantly reduced computational cost. For molecular dynamics (MD) using DFT, a lot of computational power is required. This is why for MD runs, ML shows potential to decrease both these computational costs, and the time needed for the calculations. Initially, through exploration of ML Interatomic Potentials (MLIP)s [2], an initial ML model is made for predicting forces and energy of HV defects in diamond, being trained on ab initio DFT calculations. This ML model is then used to predict the behaviour and MD of hydrogen-vacancy (HV) defects in diamond. Hereby establishing a proof of principle for working ML models for MD runs on diamond-like systems. Figure 1-Dependence of the GW band gap (left axis) and computational cost (right axis) on the number of included bands, demonstrating the high computational cost associated with converging GW calculations.