Machine learning method for tight-binding Hamiltonian parameterization from ab-initio band structure

Abstract

The tight-binding (TB) method is an ideal candidate for determining electronic and transport properties for a large-scale system. It describes the system as real-space Hamiltonian matrices expressed on a manageable number of parameters, leading to substantially lower computational costs than the ab-initio methods. Since the whole system is defined by the parameterization scheme, the choice of the TB parameters decides the reliability of the TB calculations. The typical empirical TB method uses the TB parameters directly from the existing parameter sets, which hardly reproduces the desired electronic structures quantitatively without specific optimizations. It is thus not suitable for quantitative studies like the transport property calculations. The ab-initio TB method derives the TB parameters from the ab-initio results through the transformation of basis functions, which achieves much higher numerical accuracy. However, it assumes prior knowledge of the basis and may encompass truncation error. Here, a machine learning method for TB Hamiltonian parameterization is proposed, within which a neural network (NN) is introduced with its neurons acting as the TB matrix elements. This method can construct the empirical TB model that reproduces the given ab-initio energy bands with predefined accuracy, which provides a fast and convenient way for TB model construction and gives insights into machine learning applications in physical problems.

Perspective on integrating machine learning into computational chemistry and materials science

“…16,83,107,124 A recent example of a deep learning framework to predict the electronic density or properties related to the density of a reference DFT method is DeepDFT. 125 A symmetryadapted method that considers geometrical covariance was proposed by Fabrizio et al 126 and Grisafi et al 127 to learn the charge density of different organic molecules via Gaussian Process Regression (GPR) models. 126,127 This model is physically inspired and learns the charge density via a sum of atom-centered basis functions with the coefficients of these functions being predicted by the ML model.…”

“…125 A symmetryadapted method that considers geometrical covariance was proposed by Fabrizio et al 126 and Grisafi et al 127 to learn the charge density of different organic molecules via Gaussian Process Regression (GPR) models. 126,127 This model is physically inspired and learns the charge density via a sum of atom-centered basis functions with the coefficients of these functions being predicted by the ML model. The authors achieve linear scaling with respect to the number of atoms and allow for size-extensive This is the author's peer reviewed, accepted manuscript.…”

“…The latter was showcased by training the density of butadiene and butane and predicting the density of octa-tetraene and octane. 127 Fabrizio et al 128 have further shown on the example of organic molecules that ML can be used to predict the on-top pair density in combination with a newly developed basis set. The ontop pair density can be used to assess electron correlation effects of a target compound, which most often cannot be described accurately using DFT.…”

“…The concept of ML-based Hamiltonian and densityfunctional surrogate models directly leads to the construction of approximate electronic structure models based on ML. Recently reported approaches include an ML-based Hückel model, 141 parametrized Frenkel 102,[142][143][144][145] and Tight-binding (TB) Hamiltonians 146 as well as semi-empirical methods with ML-tuned parameters. 147,148 .…”

A Perspective on Li/S Battery Design: Modeling and Development Approaches

“…Moreover, as model complexity increases, additional parameters will be introduced inherently, and more sophisticated exchange-correlation functionals must be developed. Therefore, parameterizing solutions must be considered in tandem, such as developing and implementing machine learning (ML) techniques to quickly parameterize models [81,82] and evaluate their efficacy [83]. ML techniques may also prove useful in developing novel exchange-correlation functionals [84].…”