Machine learning Hamiltonian enables scalable and accurate defect calculations: The case of oxygen vacancies in amorphous SiO$_2$

TL;DR

This paper introduces a machine learning Hamiltonian approach that enables scalable, accurate defect calculations in amorphous SiO$_2$, overcoming limitations of traditional MLIPs and DFT for large supercells.

Contribution

The authors develop a MLH model for defect energy calculations that scales linearly and improves transferability over existing MLIPs, demonstrated on oxygen vacancies in amorphous SiO$_2$.

Findings

MLH model achieves DFT-level accuracy with deviations below 50 meV.

Enables efficient structural relaxations in large supercells.

Avoids systematic energy errors typical of traditional MLIPs.

Abstract

Point defects critically influence the properties of materials and devices, yet density functional theory (DFT) remains computationally demanding for defect supercell calculations. Machine learning interatomic potentials (MLIPs) offer high efficiency but require extensive datasets. MLIPs trained only on defect configurations in small supercells exhibit systematic energy errors in larger supercells, demonstrating limited transferability. Here, we present a machine learning Hamiltonian (MLH) model-based method for calculating total energies and atomic forces in defect supercells with linear-scaling computational cost, enabling efficient structural relaxation and accurate formation energy predictions. We take oxygen vacancies in amorphous SiO$_2$ as an example and train the MLH model on defect configurations in 95-atom supercells, with the training data derived from 120 self-consistent field calculations and 12 structural relaxations. The MLH model enables efficient structural relaxations for host (defect-free) and defect systems in larger supercells, avoiding the systematic energy errors observed in MLIPs. The cancellation of energy errors between host and defect systems yields accurate formation energy predictions, with deviations from DFT below 50 meV. The proposed method holds significant potential for defect simulations in complex materials.