Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band Gaps
Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard &...
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MDPI AG
2021-03-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/5/2395 |
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| author | Nicole E. Kirchner-Hall Wayne Zhao Yihuang Xiong Iurii Timrov Ismaila Dabo |
| author_facet | Nicole E. Kirchner-Hall Wayne Zhao Yihuang Xiong Iurii Timrov Ismaila Dabo |
| author_sort | Nicole E. Kirchner-Hall |
| collection | DOAJ |
| description | Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard <i>U</i> correction (DFT+<i>U</i>) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+<i>U</i> can be interpreted as an approximate spectral-potential method when <i>U</i> is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+<i>U</i> to predict band gaps. However, it is still frequent in the literature to determine the Hubbard <i>U</i> parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+<i>U</i> band gaps computed using self-consistent <i>ab initio U</i> parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or <i>p</i>-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+<i>U</i> results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+<i>U</i> may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost. |
| first_indexed | 2024-03-09T04:59:51Z |
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| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T04:59:51Z |
| publishDate | 2021-03-01 |
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| spelling | doaj.art-40e90d3db253458fa1edb25e458decc72023-12-03T13:01:03ZengMDPI AGApplied Sciences2076-34172021-03-01115239510.3390/app11052395Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band GapsNicole E. Kirchner-Hall0Wayne Zhao1Yihuang Xiong2Iurii Timrov3Ismaila Dabo4Department of Materials Science and Engineering and the Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USADepartment of Materials Science and Engineering and the Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USADepartment of Materials Science and Engineering and the Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USATheory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, SwitzerlandDepartment of Materials Science and Engineering and the Materials Research Institute, The Pennsylvania State University, University Park, PA 16802, USAAccurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard <i>U</i> correction (DFT+<i>U</i>) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+<i>U</i> can be interpreted as an approximate spectral-potential method when <i>U</i> is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+<i>U</i> to predict band gaps. However, it is still frequent in the literature to determine the Hubbard <i>U</i> parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+<i>U</i> band gaps computed using self-consistent <i>ab initio U</i> parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or <i>p</i>-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+<i>U</i> results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+<i>U</i> may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost.https://www.mdpi.com/2076-3417/11/5/2395DFT+<i>U</i>Hubbard correctionLöwdin orthogonalizationband gapself-interaction |
| spellingShingle | Nicole E. Kirchner-Hall Wayne Zhao Yihuang Xiong Iurii Timrov Ismaila Dabo Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band Gaps Applied Sciences DFT+<i>U</i> Hubbard correction Löwdin orthogonalization band gap self-interaction |
| title | Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band Gaps |
| title_full | Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band Gaps |
| title_fullStr | Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band Gaps |
| title_full_unstemmed | Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band Gaps |
| title_short | Extensive Benchmarking of DFT+<i>U</i> Calculations for Predicting Band Gaps |
| title_sort | extensive benchmarking of dft i u i calculations for predicting band gaps |
| topic | DFT+<i>U</i> Hubbard correction Löwdin orthogonalization band gap self-interaction |
| url | https://www.mdpi.com/2076-3417/11/5/2395 |
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