Query: Predicting band gaps with hybrid density functionals

Candidate papers:

abstract: We compare the ability of four popular hybrid density functionals (B3LYP, B3PW91, HSE, and PBE0) for predicting band gaps of semiconductors and insulators over a large benchmark set using a consistent methodology. We observe no significant statistical difference in their overall performance, although the screened hybrid HSE is more accurate for typical semiconductors. HSE can improve its accuracy for large band gap materials without affecting that of semiconductors by including a larger portion of Hartree Fock exchange in its short range. Given that screened hybrids are computationally much less expensive than their global counterparts, we conclude that they are a better option for the black box prediction of band gaps.
author_names: Alejandro J Garza

Gustavo E Scuseria
title: Predicting Band Gaps with Hybrid Density Functionals.
venue: The journal of physical chemistry letters
year: 2016

abstract: Density functional theory within the local or semilocal density approximations (DFT LDA/GGA) has become a workhorse in electronic structure theory of solids, being extremely fast and reliable for energetics and structural properties, yet remaining highly inaccurate for predicting band gaps of semiconductors and insulators. Accurate prediction of band gaps using firstprinciples methods is time consuming, requiring hybrid functionals, quasi particle GW, or quantum Monte Carlo methods. Efficiently correcting DFT LDA/GGA band gaps and unveiling the main chemical and structural factors involved in this correction is desirable for discovering novel materials in high throughput calculations. In this direction, we use DFT and machine learning techniques to correct band gaps and band edge positions of a representative subset of ABO3 perovskite oxides. Relying on results of HSE06 hybrid functional calculations as target values of band gaps, we find a systematic band gap correction of ~1.5 eV for this class of materials, where ~1 eV comes from downward shifting the valence band and ~0.5 eV from uplifting the conduction band. The main chemical and structural factors determining the band gap correction are determined through a feature selection procedure.
author_names: Wei Li

Xianglin Xiao

Zhiqiang Zhang

Anderson Janotti1

Rajasekaran Sanguthevar

Bharat Medasani
title: Predicting band gaps and band edge positions of oxide perovskites using DFT and machine learning.
year: 2020

abstract: Density functional theory (DFT) has become a standard method for ab initio calculations of material properties. However, it has a number of shortcomings, particularly in predicting key properties, such as band gap and optical spectra, which are dependent on excited states. To treat such properties, more accurate approaches such as GW or DFT with hybrid functionals (including HSE, PBE0, and B3LYP, to name a few) can be employed; however, these approaches are unfeasible for many large and/or complex systems due to their high computational cost and large memory requirements. In this work, we investigate the ability to train neural networks of the traditional DFT charge density computed with a standard PBE functional to accurately predict HSE band gaps. We show that a single network PBE charge density functional can predict the HSE band gap of seven different materials silicon, gallium arsenide, molybdenum disulfide, germanium, tin phosphate, titanium phosphate, and zirconium phosphate under a wide variety of conditions with an RSME of 172.6 meV, which is 34\ better accuracy than standard regression between the PBE and HSE band gaps. This approach, which, in principle, can be used to map PBE charge densities to band gaps or other properties computed with any higher accuracy method, has the potential to decrease computational costs, increase prediction accuracy, and enable accurate high throughput screening for a wide variety of complex materials systems.
author_names: Levi C Lentz

Alexie Kolpak
title: Predicting HSE band gaps from PBE charge densities via neural network functionals.
venue: Journal of physics. Condensed matter an Institute of Physics journal
year: 2019

abstract: Accurately modeling the electronic structure of materials is a persistent challenge to high throughput screening. A promising means of balancing accuracy against computational cost are non self consistent calculations with hybrid density functional theory, where the electronic band energies are evaluated using a hybrid functional from orbitals obtained with a less demanding (semi )local functional. We have quantified the performance of this technique for predicting the physical properties of sixteen tetrahedral semiconductors with bandgaps from 0.2 5.5 eV. Provided the base functional predicts a non metallic electronic structure, bandgaps within 5 of the PBE0 and HSE06 gaps can be obtained with an order of magnitude reduction in computing time. The positions of the valence and conduction band extrema and the Fermi level are well reproduced, further enabling calculation of the band dispersion, density of states, and dielectric properties using Fermi's Golden Rule. While the error in the non self consistent total energies is ~50 meV atom 1, the energy volume curves are reproduced accurately enough to obtain the equilibrium volume and bulk modulus with minimal error. We also test the dielectric dependent scPBE0 functional and obtain bandgaps and dielectric constants to within 2.5 of the self consistent results, which amount to a significant improvement over self consistent PBE0 for a similar computational cost. We identify cases where the non self consistent approach is expected to perform poorly, and demonstrate that partial self consistency provides a practical and efficient workaround. Finally, we perform proof of concept calculations on CoO and NiO to demonstrate the applicability of the technique to strongly correlated open shell transition metal oxides.
author_names: Jonathan M Skelton

David S D Gunn

Sebastian Metz

Stephen C Parker
title: Accuracy of hybrid functionals with non self consistent Kohn Sham orbitals for predicting the properties of semiconductors.
venue: Journal of chemical theory and computation
year: 2020

abstract: The performance of two modern density functionals, HSE06 and TB mBJ, on predicting electronic structures of metal oxides, chalcogenides and nitrides, is studied in terms of band gaps, band structure and projected density of states. Contrary to GGA, hybrid functionals and GGA+U, both new functionals are able to predict band gaps with an appreciable accuracy of 25% and thus allow the screening of various classes of (mixed) metal oxides at modest computational cost. The calculated electronic structures are largely unaffected by the choice of basis functions and software implementation.
author_names: Wen-Qing Li

Christian F J Walther

Agnieszka Beata Kuc

Thomas Heine
title: Efficient Estimation of Band Gaps in Transition Metal Oxides and Chalcogenides using Density Functional Theory
year: 2013

abstract: The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree Fock (HF) exchange used in the Heyd Scuseria Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals) In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2 4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.
author_names: Jochen Heyd

Gustavo E Scuseria
title: Efficient hybrid density functional calculations in solids: assessment of the Heyd Scuseria Ernzerhof screened Coulomb hybrid functional.
venue: The Journal of chemical physics
year: 2004

abstract: Band structure calculations based on density functional theory (DFT) with local or gradient corrected exchange correlation potentials are known to severely underestimate the band gap of semiconducting and insulating materials. Alternative approaches have been proposed: from semiempirical setups, such as the so called DFT+U, to hybrid density functionals using a fraction of nonlocal Fock exchange, to modifications of semilocal density functionals. However, the resulting methods appear to be material dependent and lack theoretical rigor. The rigorous many body perturbation theory based on GW methods provides accurate results but at a very high computational cost. Hereby, we show that a linear correlation between the electronic band gaps obtained from standard DFT and GW approaches exists for most materials and argue that (1) this is a strong indication that the problem of predicting band gaps from standard DFT calculation arises from the assignment of a physical meaning to the Kohn Sham energy levels rather.
author_names: Angel Morales-Garcia

Rosendo Valero

Francesc Illas
title: An Empirical, yet Practical Way To Predict the Band Gap in Solids by Using Density Functional Band Structure Calculations
year: 2017

abstract: Significance Density functionals with Hartree Fock exchange have been widely used for a wide range of chemical applications, but the nonlocal character of exchange makes long range exchange computationally expensive for solid state calculations with periodic boundary conditions, and full exchange is nonphysical for condensed phase systems. Here, we present a screened exchange (SX) density functional, M06 SX, that is especially designed to have good accuracy for both solid state physics and chemical applications with less computational cost than full Hartree Fock exchange. The M06 SX functional gives accuracy comparable to functionals with full Hartree Fock exchange for predicting chemical properties of molecules, while also being practical with good accuracy for plane wave calculations on band gaps and lattice constants of solids. Screened exchange hybrid density functionals are especially recommended for solid state systems because they combine the advantages of hybrid functionals with the correct physics and lower computational cost associated with the attenuation of Hartree Fock exchange at long range. We present a screened exchange hybrid functional, M06 SX, that combines the functional form of the local revM06 L functional with a percentage of short range nonlocal Hartree Fock exchange. The M06 SX functional gives good results not only for a large set of training data but also for several databases quite different from the training data. The mean unsigned error (MUE) of the M06 SX functional is 2.85 kcal/mol for 418 atomic and molecular energies (AME418) in Minnesota Database 2019, which is better than all five other screened exchange hybrid functionals tested in this work. The M06 SX functional also gives especially good results for semiconductor band gaps, molecular dissociation energies, noncovalent interactions, barrier heights, and electronic excitation energies excluding long range charge transfer excitations. For the LC18 lattice constants database, the M06 SX functional gives an MUE of only 0.034 A. Therefore, the M06 SX functional is well suited for studying molecular chemistry as well as solid state physics.
author_names: Pragya Verma

Lujia Zhang

Yaqi Li

Zhonghua Liu

Donald G Truhlar

Xiao He
title: M06 SX screened exchange density functional for chemistry and solid state physics
venue: Proceedings of the National Academy of Sciences
year: 2020

abstract: The open access material databases allowed us to approach scientific questions from a completely new perspective with machine learning methods. Here, on the basis of open access databases, we focus on the classical band gap problem for predicting accurately the band gap of a crystalline compound using a machine learning approach with newly developed tuplewise graph neural networks (TGNN) which is devised to automatically generate input representation of crystal structures in tuple types and to exploit crystal level properties as one of the input features. Our method brings about a highly accurate prediction of the band gaps at hybrid functionals and GW approximation levels for multiple material data sets without heavy computational cost. Furthermore, to demonstrate the applicability of our prediction model, we provide a data set of GW band gaps for 45835 materials predicted by TGNN posing higher accuracy than standard density functional theory calculations.
author_names: Gyoung S Na

Seunghun Jang

Yea-Lee Lee

Hyunju Chang
title: Tuplewise Material Representation Based Machine Learning for Accurate Band Gap Prediction.
venue: The journal of physical chemistry. A
year: 2020

abstract: The performance of a wide variety of commonly used density functionals, as well as two screened hybrid functionals (HSE06 and TB mBJ) on predicting electronic structures of a large class of en vogue materials, such as metal oxides, chalcogenides, and nitrides, is discussed in terms of band gaps, band structures, and projected electronic densities of states. Contrary to GGA, hybrid functionals and GGA+U, both HSE06 and TB mBJ are able to predict band gaps with an appreciable accuracy of 25% and thus allow the screening of various classes of transition metal based compounds, i.e. mixed or doped materials, at modest computational cost. The calculated electronic structures are largely unaffected by the choice of basis functions and software implementation, however, might be subject to the treatment of the core electrons.
author_names: Wen-Qing Li

Christian F J Walther

Agnieszka Beata Kuc

Thomas Heine
title: Density Functional Theory and Beyond for Band Gap Screening: Performance for Transition Metal Oxides and Dichalcogenides.
venue: Journal of chemical theory and computation
year: 2013