Predicting HSE band gaps from PBE charge densities via neural network functionals

Abstract

Density functional theory (DFT) has become the standard for studying periodic systems for a wide range of materials properties. Originally proposed in the 1960s [1,2], this formalism states that material properties can be described as a pure functional of the charge density, eliminating the need to directly treat all the electrons in the system. This finding drastically reduced the computational costs associated with simulating realistic systems to study their unique properties.While DFT is promising for a variety of reasons, there are several shortcomings of the theory. One of the most significant shortcomings of DFT is that large systems are difficult to study. This is because some of the terms within DFT formalism are not known as a pure functional of the charge density. One example of this is the kinetic energy term, requiring explicit treatment of the Kohn-sham orbitals, drastically increasing the computational cost of DFT methods. Work in orbital-free DFT [3] has been proposed to decrease this reliance and is a promising way to achieve simulations of tens of thousands of atoms within DFT.Arising from the lack of an exact functional, a second area of concern is in predicting certain materials properties accurately. While DFT is useful for predicting formation energies, potential energy surfaces, total energies, and ground state atomic structures, it performs poorly for predicting properties that are inherently dependent on excited states. Commonly used DFT exchange-correlation approximations, such as the local density approximation (LDA) [2] and generalized gradient approximation (GGA) [4], are notoriously inaccurate at predicting key properties such as the band gap. This is generally thought to be caused by the inaccurate treatment of the self-interaction term of the electrons [5]. Higher-order methods such as the GW approximation (GWA) [6] are capable

Bandgap Engineering in the Configurational Space of Solid Solutions via Machine Learning: (Mg,Zn)O Case Study

“…For such systems, the non-linear relationship between PBE and HSE bandgaps can be established using a machine-learned transformation. 29 However, in our case the simple linear relationship will allow us to use PBE band gaps for training the bandgap predicting models, instead of the more expensive but more accurate HSE values. It can also be seen from Table 1 that, while giving better predictions than PBE, HSE still underestimates the experimental bandgaps for pure MgO and ZnO, in both cases by ∼20%.…”

“…This strong linear correlation between PBE and HSE bandgaps is not general, and in systems including transition-metal or rare-earth elements, for example, we would expect much weaker correlations. For such systems, the non-linear relationship between PBE and HSE bandgaps can be established using a machine-learned transformation . However, in our case the simple linear relationship will allow us to use PBE band gaps for training the bandgap predicting models, instead of the more expensive but more accurate HSE values.…”

Machine learning for the solution of the Schrödinger equation

“…Lentz and Kolpak [132] used NNs to predict band gaps obtained with a hybrid functional (HSE) based on electron density obtained with the PBE functional. An RSME of the gap of about 0.2 eV was achieved for a range of solid semiconductors, which was also shown to be much better than linear regression between the PBE and HSE band gaps.…”

A Deep Dive into Machine Learning Density Functional Theory for Materials Science and Chemistry

“…The most common mapping deals with the electronic exchange-correlation energy [433], [434], [435], [436], [437], [438], [439], [440], [441], [442], [443], [444], [445], [446], [447], [448], [449], [450], [451], [452], [453], [454]. As discussed in Sec.…”