Machine learning prediction of HSE06-level band gaps in two-dimensional semiconductors with reference-guided graph neural networks

doi:10.1088/1674-1056/adfef8

Abstract Two-dimensional (2D) semiconductors have emerged as promising candidates in next-generation nanoelectronics and sustainable energy technologies, particularly in photoelectrochemical water splitting, due to their exceptional quantum confinement effects and tunable optoelectronic properties. Accurate determination of electronic band gaps remains a critical prerequisite for rational material design in advanced optoelectronic applications. However, the commonly used density functional theory approach with conventional functionals suffers from intrinsic deficiencies in predicting semiconductor band gaps, while calculations with higher hierarchy of functionals like the HSE06 hybrid functional or based on higher level methodologies such as GW approximation incur prohibitive computational costs. To address this challenge, here we propose a reference-guided graph neural network (RG-GNN) framework that achieves HSE06-level accuracy through efficient machine learning. Our approach uniquely embeds an input reference value for the target property with minimal elementary descriptors encoding the structural information of the materials in the model, enabling high-accuracy band gap prediction at the HSE06 level. The model achieves a mean absolute error of 0.15 eV on unseen 2D semiconductor systems compared to HSE06 band gaps. Systematic ablation studies reveal that the reference-guided mechanism reduces prediction error by 83.3% and significantly decreases training dataset requirements for model convergence compared to conventional GNN architectures. Our results demonstrates that topological atomic descriptors from primitive cells, when combined with appropriate reference values, contain sufficient information for highly accurate band gap prediction in 2D materials.

Keywords: machine learning graph neural network two-dimensional semiconductors band gaps HSE06 accuracy

Received: 09 June 2025
Revised: 19 August 2025
Accepted manuscript online: 26 August 2025

PACS:	71.15.-m	(Methods of electronic structure calculations)
	07.05.Mh	(Neural networks, fuzzy logic, artificial intelligence)
	02.70.Rr	(General statistical methods)

Fund: Guang-Ping Zhang

Corresponding Authors: Guang-Ping Zhang
E-mail: zhangguangping@sdnu.edu.cn

Cite this article:

Zhen Wan(万振), Shun-Bo Jiang(姜顺波), Yuan Li(李圆), Hui Wang(王辉), Zong-Liang Li(李宗良), and Guang-Ping Zhang(张广平) Machine learning prediction of HSE06-level band gaps in two-dimensional semiconductors with reference-guided graph neural networks 2026 Chin. Phys. B 35 037102

[1] Novoselov K S, Geim A K, Morozov S V, Jiang D E, Zhang Y S, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
[2] Geim A K and Novoselov K S 2007 Nat. Mater. 6 183
[3] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 Rev. Mod. Phys. 81 109
[4] Splendiani A, Sun L, Zhang Y B, Li T S, Kim J, Chim C Y, Galli G and Wang F 2010 Nano Lett. 10 1271
[5] Mak K F, Lee C G, Hone J, Shan J and Heinz T F 2010 Phys. Rev. Lett. 105 136805
[6] Geim A K 2009 Science 324 1530
[7] Wang Q H, Kalantar-Zadeh K, Kis A, Coleman J N and Strano M S 2012 Nat. Nanotechnol. 7 699
[8] Dean C R, Young A F, Meric I, Lee C,Wang L, Sorgenfrei S,Watanabe K, Taniguchi T, Kim P, Shepard K L and Hone J 2010 Nat. Nanotechnol. 5 722
[9] Bertolazzi S, Brivio J and Kis A 2011 ACS Nano 5 9703
[10] Radisavljevic B, Radenovic A, Brivio J, Giacometti V and Kis A 2011 Nat. Nanotechnol. 6 147
[11] Butler S Z, Hollen S M, Cao L Y, Cui Y, Gupta J A, Gutiérrez H R, Heinz T F, Hong S S, Huang J X, Ismach A F, Johnston Halperin E, Kuno M, Plashnitsa V V, Robinson R D, Ruoff R S, Salahuddin S, Shan J, Shi L, Spencer M G, Terrones M, Windl W and Goldberger J E 2013 ACS Nano 7 2898
[12] Chhowalla M, Shin H S, Eda G, Li L J, Loh K P and Zhang H 2013 Nat. Chem. 5 263
[13] Kou L Z, Chen C F and Smith S C 2015 J. Phys. Chem. Lett. 6 2794
[14] Li X and Zhu H W 2015 J. Mater. 1 33
[15] Ling X,Wang H, Huang S X, Xia F N and DresselhausMS 2015 Proc. Natl. Acad. Sci. USA 112 4523
[16] Chaves A, Azadani J G, Alsalman H, Da Costa D, Frisenda R, Chaves A, Song S H, Kim Y D, He D W, Zhou J D, Castellanos Gomez A, Peeters F M, Liu Z, Hinkle C L, Oh S H, Ye P D, Koester S J, Lee Y H, Avouris P, Wang X R and Low T 2020 npj 2D Mater. Appl. 4 29
[17] Weng M Y, Pan F and Wang L W 2020 npj Comput. Mater. 6 33
[18] Oh Y, Song S and Bae J 2024 Int. J. Mol. Sci. 25 13104
[19] Bao X T, Shi JW, Han X,Wu K M, Zeng X, Xia Y X, Zhao J H, Zhang Z Y, Du W N, Yue S, Wu X X, Wu B, Huang Y, Zhang W K and Liu X F 2025 Nano Lett. 25 2639
[20] Madani M, Lacivita V, Shin Y and Tarakanova A 2025 npj Comput. Mater. 11 15
[21] Sadeghi S N, Zebarjadi M and Esfarjani K 2019 J. Mater. Chem. C 7 7308
[22] Hu X M, Yang J L, Wang W, Zhang X J, Meng Y F, Ye Y F, Ding K N, Zhang F J and Zhang S L 2024 J. Mater. Chem. C 12 15662
[23] Alaal N and Roqan I S 2018 ACS Appl. Nano Mater. 2 202
[24] Liu T Y, Zhao X, Liu X F, Xiao W J, Luo Z J, Wang W T, Zhang Y F and Liu J C 2023 J. Energy Chem. 81 93
[25] Heyd J, Scuseria G E and Ernzerhof M 2003 J. Chem. Phys. 118 8207
[26] Heyd J, Scuseria G E and Ernzerhof M 2006 J. Chem. Phys. 124 219906
[27] Krukau A V, Vydrov O A, Izmaylov A F and Scuseria G E 2006 J. Chem. Phys. 125 224106
[28] Shishkin M and Kresse G 2007 Phys. Rev. B 75 235102
[29] Jumper J, Evans R, Pritzel A, Green T, Figurnov M, Ronneberger O, Tunyasuvunakool K, Bates R, Žídek A, Potapenko A, Bridgland A, Meyer C, Kohl S A A, Ballard A J, Cowie A, Romera-Paredes B, Nikolov S, Jain R, Adler J, Back T, Petersen S, Reiman D, Clancy E, Zielinski M, Steinegger M, Pacholska M, Berghammer T, Bodenstein S, Silver D, Vinyals O, Senior A W, Kavukcuoglu K, Kohli P and Hassabis D 2021 Nature 596 583
[30] Samatov M R, Liu D, Zhao L, Kazakova E A, Abrameshin D A, Das A, Vasenko A S and Prezhdo O V 2024 J. Phys. Chem. Lett. 15 12362
[31] Kiyohara S and Kumagai Y 2025 J. Phys. Chem. Lett. 16 5244
[32] Cui G, Guo Z, Ren X, Jiang Y, Jin X, Wu Y and Ju S 2025 J. Phys. Chem. Lett. 16 3579
[33] Tallapally D,Wang J, Potika K and EirinakiM2023 Algorithms 16 515
[34] Ma J, Liu B, Li K, Li C, Zhang F, Luo X and Qiao Y 2024 Neurocomputing 609 128490
[35] Raissi M, Perdikaris P and Karniadakis G E 2019 J. Comput. Phys. 378 686
[36] Ward L, Agrawal A, Choudhary A and Wolverton C 2016 npj Comput. Mater. 2 16028
[37] Xie T and Grossman J C 2018 Phys. Rev. Lett. 120 145301
[38] Wu Z Q, Ramsundar B, Feinberg E N, Gomes J, Geniesse C, Pappu A S, Leswing K and Pande V 2018 Chem. Sci. 9 513
[39] Hanakata P Z, Cubuk E D, Campbell D K and Park H S 2018 Phys. Rev. Lett. 121 255304
[40] Zheng X L, Zheng P and Zhang R Z 2018 Chem. Sci. 9 8426
[41] Schütt K T, Sauceda H E, Kindermans P J, Tkatchenko A and Müller K R 2018 J. Chem. Phys. 148 241722
[42] Zhu Z, Dong B, Guo H, Yang T and Zhang Z 2020 Chin. Phys. B 29 046101
[43] Chen L H, Tran H, Batra R, Kim C and Ramprasad R 2019 Comput. Mater. Sci. 170 109155
[44] Chibani S and Coudert F X 2020 APL Mater. 8 080701
[45] Zhao Y, Cui Y X, Xiong Z, Jin J, Liu Z H, Dong R Z and Hu J J 2020 ACS Omega 5 3596
[46] Wan Z, Wang Q D, Liu D and Liang J 2021 Comp. Mater. Sci. 198 110699
[47] Liu H, Xu L, Ma Z, Li Z, Li H, Zhang Y, Zhang B and Wang L L 2023 Mater. Today Commun. 36 106578
[48] Hu J, Zuo Y, Hao Y, Shu G, Wang Y, Feng M, Li X, Wang X, Sun J, Ding X, Gao Z, Zhu G and Li B 2023 Chin. Phys. B 32 046301
[49] Zhang W B, Guo J, Lv X K and Zhang F C 2024 J. Phys. Chem. Lett. 15 5413
[50] Liu B and Wang Y 2024 Chin. Phys. B 33 084401
[51] Chen Z, Wang J, Li C, Liu B, Luo D, Min Y, Fu N and Xue Q 2024 J. Mater. Chem. C 12 15444
[52] Zhang Y, Wang X, Wang Y and Zheng W 2024 Chin. Phys. B 33 070702
[53] Liu H, Weng M, Huang Y, Luo Y and Zheng Y 2025 Comput. Mater. Sci. 255 113853
[54] Zhang Z, Liu S, Xiong Q and Liu Y 2025 J. Phys. Chem. Lett. 16 738
[55] Cao B, Dong J,Wang Z andWang L 2025 J. Phys. Chem. Lett. 16 4907
[56] Haastrup S, Strange M, Pandey M, Deilmann T, Schmidt P S, Hinsche N F, Gjerding M N, Torelli D, Larsen P M, Riis-Jensen A C, Gath J, Jacobsen K W, Mortensen J J, Olsen T and Thygesen K S 2018 2D Mater. 5 042002
[57] Gjerding M N, Taghizadeh A, Rasmussen A, Ali S, Bertoldo F, Deilmann T, Knøsgaard N R, Kruse M, Larsen A H, Manti S, Pedersen T G, Petralanda U, Skovhus T, Svendsen M K, Mortensen J J, Olsen T and Thygesen K S 2021 2D Mater. 8 044002
[58] Kipf T N and Welling M 2017 arXiv e-prints arXiv:1609.02907
[59] Veličković P, Cucurull G, Casanova A, Romero A, Liò P and Bengio Y 2018 arXiv e-prints arXiv:1710.10903
[60] Chen Y T, Huang D, Zhang D X, Zeng J S, Wang N Z, Zhang H R and Yan J Y 2021 J. Comput. Phys. 445 110624
[61] Rong M, Zhang D X and Wang N Z 2022 Complex Intell. Syst. 8 4849
[62] Lebeda T, Aschebrock T, Sun J, Leppert L and Kümmel S 2023 Phys. Rev. Mater. 7 093803
[63] Kokott S, Merz F, Yao Y, Carbogno C, Rossi M, Havu V, Rampp M, Scheffler M and Blum V 2024 J. Chem. Phys. 161 024112

[1]	Machine learning of chaotic characteristics in classical nonlinear dynamics using variational quantum circuit Sheng-Chen Bai(白生辰) and Shi-Ju Ran(冉仕举). Chin. Phys. B, 2026, 35(2): 020303.
[2]	EDIS: A simulation software for dynamic ion intercalation/deintercalation processes in electrode materials Liqi Wang(王力奇), Ruijuan Xiao(肖睿娟), and Hong Li(李泓). Chin. Phys. B, 2026, 35(1): 018201.
[3]	Revealing the dynamic responses of Pb under shock loading based on DFT-accuracy machine learning potential Enze Hou(侯恩则), Xiaoyang Wang(王啸洋), and Han Wang(王涵). Chin. Phys. B, 2026, 35(1): 018701.
[4]	Machine learning-assisted optimization of MTO basis sets Zhiqiang Li(李志强) and Lei Wang(王蕾). Chin. Phys. B, 2026, 35(1): 016301.
[5]	Review of machine learning tight-binding models: Route to accurate and scalable electronic simulations Jijie Zou(邹暨捷), Zhanghao Zhouyin(周寅张皓), Shishir Kumar Pandey, and Qiangqiang Gu(顾强强). Chin. Phys. B, 2026, 35(1): 017101.
[6]	Machine learning approach to reconstruct dephasing time from solid HHG spectra Jiahao Liu(刘佳豪), Xi Zhao(赵曦), Jun Wang(王俊), and Songbin Zhang(张松斌). Chin. Phys. B, 2025, 34(9): 097804.
[7]	Hyperparameter optimization and force error correction of neuroevolution potential for predicting thermal conductivity of wurtzite GaN Zhuo Chen(陈卓), Yuejin Yuan(袁越锦), Wenyang Ding(丁文扬), Shouhang Li(李寿航), Meng An(安盟), and Gang Zhang(张刚). Chin. Phys. B, 2025, 34(8): 086110.
[8]	Graph neural networks unveil universal dynamics in directed percolation Ji-Hui Han(韩继辉), Cheng-Yi Zhang(张程义), Gao-Gao Dong(董高高), Yue-Feng Shi(石月凤), Long-Feng Zhao(赵龙峰), and Yi-Jiang Zou(邹以江). Chin. Phys. B, 2025, 34(8): 080702.
[9]	A graph neural network and multi-task learning-based decoding algorithm for enhancing XZZX code stability in biased noise Bo Xiao(肖博), Zai-Xu Fan(范在旭), Hui-Qian Sun(孙汇倩), Hong-Yang Ma(马鸿洋), and Xing-Kui Fan(范兴奎). Chin. Phys. B, 2025, 34(5): 050306.
[10]	Graph distillation with network symmetry Feng Lin(林峰) and Jia-Lin He(何嘉林). Chin. Phys. B, 2025, 34(4): 040204.
[11]	Significant increase in thermal conductivity of cathode material LiFePO₄ by Na substitution: A machine learning interatomic potential-assisted investigation Shi-Yi Li(李诗怡), Qian Liu(刘骞), Yu-Jia Zeng(曾育佳), Guofeng Xie(谢国锋), and Wu-Xing Zhou(周五星). Chin. Phys. B, 2025, 34(2): 028201.
[12]	Quantum algorithm for marginal Fisher analysis Jing Li(李静), Yanqi Song(宋燕琪), Sujuan Qin(秦素娟), Wenmin Li(李文敏), and Fei Gao(高飞). Chin. Phys. B, 2025, 34(12): 120302.
[13]	Classifying extended, localized and critical states in quasiperiodic lattices via unsupervised learning Bohan Zheng(郑博涵), Siyu Zhu(朱思宇), Xingping Zhou(周兴平), and Tong Liu(刘通). Chin. Phys. B, 2025, 34(1): 017103.
[14]	Database of ternary amorphous alloys based on machine learning Xuhe Gong(巩旭菏), Ran Li(李然), Ruijuan Xiao(肖睿娟), Tao Zhang(张涛), and Hong Li(李泓). Chin. Phys. B, 2025, 34(1): 016101.
[15]	Improving performance of screening MM/PBSA in protein-ligand interactions via machine learning Yuan-Qiang Chen(陈远强), Yao Xu(徐耀), Yu-Qiang Ma(马余强), and Hong-Ming Ding(丁泓铭). Chin. Phys. B, 2025, 34(1): 018701.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Machine learning prediction of HSE06-level band gaps in two-dimensional semiconductors with reference-guided graph neural networks

Cite this article:

Online attention