Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

CuXASNet: Rapid and accurate prediction of copper L-edge x-ray absorption spectra using machine learning

Samuel P. Gleason1,2, Matthew R. Carbone3, Deyu Lu4, and Jim Ciston1

Phys. Rev. Materials 9, 073803 – Published 10 July, 2025

DOI: https://doi.org/10.1103/xz7f-srky

Abstract

In this work, we have developed CuXASNet, a dense neural network that predicts simulated Cu L-edge x-ray absorption spectra (XAS) from atomic structures. Featurization of the Cu local environment is performed using a component of M3GNet, a graph neural network developed for predicting the potential energy surface. CuXASNet is trained on simulated spectra from FEFF9 at the multiple scattering level of theory, and can predict the L3 and L2 edges for Cu sites to quantitative accuracy. To validate our approach, we compare 14 experimental spectra extracted from the literature with the predictions of CuXASNet. The agreement of CuXASNet with experiments is shown by an average mean absolute error of 0.125 and an average Spearman's correlation coefficient of 0.891, which is comparable to FEFF9's values of 0.131 and 0.898 for the same metrics. As such, CuXASNet can rapidly predict a large number of L-edge XAS spectra at the same accuracy as FEFF9 simulations. This can be used as a drop-in replacement for multiple scattering codes for fast screening of candidate atomic structure models of a measured system. This model establishes a general framework for Cu XAS prediction, and can be extended to more computationally expensive levels of theory and to other transition metal L edges.

View figure in article

Physics Subject Headings (PhySH)

Corrections

20 August, 2025

Correction: The formatting in row 4 of Table I has been fixed. Typographical errors in the citations of Figs. 4(a), 4(b), 4(c), and 4(d) in Sec. III C have been fixed.

Article Text

Supplemental Material

References (71)

  1. F. De Groot and A. Kotani, Core Level Spectroscopy of Solids (CRC, Boca Raton, 2008)
  2. F. M. F. de Groot, J. C. Fuggle, B. T. Thole, and G. A. Sawatzky, 2p x-ray absorption of 3d transition-metal compounds: An atomic multiplet description including the crystal field, Phys. Rev. B 42, 5459 (1990).
  3. Y. Bai, Y. Wu, X. Zhou, Y. Ye, K. Nie, J. Wang, M. Xie, Z. Zhang, Z. Liu, T. Cheng, and C. Gao, Promoting nickel oxidation state transitions in single-layer NiFeB hydroxide nanosheets for efficient oxygen evolution, Nat. Commun. 13, 6094 (2022).
  4. M. Kubin, M. Guo, T. Kroll, H. Lochel, E. Kallman, M. L. Baker, R. Mitzner, S. Gul, J. Kern, A. Fohlisch, A. Erko, U. Bergmann, V. Yachandra, J. Yano, M. Lundberg, and P. Wernet, Probing the oxidation state of transition metal complexes: a case study on how charge and spin densities determine Mn L-edge X-ray absorption energies, Chem. Sci. 9, 6813 (2018).
  5. E. Marelli, J. Lyu, M. Morin, M. Leménager, T. Shang, N. S. Yüzbasi, D. Aegerter, J. Huang, N. D. Daffé, A. H. Clark, D. Sheptyakov, T. Graule, M. Nachtegaal, E. Pomjakushina, T. J. Schmidt, M. Krack, E. Fabbri, and M. Medarde, Cobalt-free layered perovskites RBaCuFeO 5+δ (R = 4f lanthanide) as electrocatalysts for the oxygen evolution reaction, EES Catal. 2, 335 (2024).
  6. K. Płacheta, A. Kot, J. Banas-Gac, M. Zając, M. Sikora, M. Radecka, and K. Zakrzewska, Evolution of surface properties of titanium oxide thin films, Appl. Surf. Sci. 608, 155046 (2023).
  7. T. Jenkins, J. A. Alarco, B. Cowie, and I. D. Mackinnon, Direct spectroscopic observation of the reversible redox mechanism in A3V2(PO4)3(A=Li,Na) cathode materials for Li-ion batteries, J. Power Sources 571, 233078 (2023).
  8. J. Yano and V. K. Yachandra, X-ray absorption spectroscopy, Photosynth. Res. 102, 241 (2009).
  9. S. P. Ong, S. Cholia, A. Jain, M. Brafman, D. Gunter, G. Ceder, and K. A. Persson, The Materials Application Programming Interface (API): A simple, flexible and efficient API for materials data based on REpresentational State Transfer (REST) principles, Comput. Mater. Sci. 97, 209 (2015).
  10. S. R. Kharel, F. Meng, X. Qu, M. R. Carbone, and D. Lu, A universal deep learning framework for materials x-ray absorption spectra, Phys. Rev. Mater. 9, 043803 (2025).
  11. K. M. P. Wheelhouse, R. L. Webster, and G. L. Beutner, Advances and applications in catalysis with earth-abundant metals, Org. Process Res. Dev. 27, 1157 (2023).
  12. K. E. Dalle, J. Warnan, J. J. Leung, B. Reuillard, I. S. Karmel, and E. Reisner, Electro- and solar-driven fuel synthesis with first row transition metal complexes, Chem. Rev. 119, 2752 (2019).
  13. W. Gao, Y. Xu, L. Fu, X. Chang, and B. Xu, Experimental evidence of distinct sites for CO2-to-CO and CO conversion on Cu in the electrochemical CO2 reduction reaction, Nat. Catal. 6, 885 (2023).
  14. M. B. Gawande, A. Goswami, F. X. Felpin, T. Asefa, X. Huang, R. Silva, X. Zou, R. Zboril, and R. S. Varma, Cu and Cu-based nanoparticles: Synthesis and applications in catalysis, Chem. Rev. 116, 3722 (2016).
  15. B. Dervaux and F. E. Du Prez, Heterogeneous azide-alkyne click chemistry: Towards metal-free end products, Chem. Sci. 3, 959 (2012).
  16. D. Astruc, L. Liang, A. Rapakousiou, and J. Ruiz, Click dendrimers and triazole-related aspects: Catalysts, mechanism, synthesis, and functions. A bridge between dendritic architectures and nanomaterials, Acc. Chem. Res. 45, 630 (2012).
  17. J. K. Mccusker, Electronic structure in the transition metal block and its implications for light harvesting, Science 363, 484 (2019).
  18. Y. Liu, S. C. Yiu, C. L. Ho, and W. Y. Wong, Recent advances in copper complexes for electrical/light energy conversion, Coord. Chem. Rev. 375, 514 (2018).
  19. M. B. Frye and L. M. Garten, Reaching the potential of ferroelectric photovoltaics, Acc. Mater. Res. 4, 906 (2023).
  20. B. O'Regan and M. Grätzel, A low-cost, high-efficiency solar cell based on dye-sensitized colloidal TiO2 films, Nature (London) 353, 737 (1991).
  21. A. K. Renfrew, E. S. O'Neill, T. W. Hambley, and E. J. New, Harnessing the properties of cobalt coordination complexes for biological application, Coord. Chem. Rev. 375, 221 (2018).
  22. C. Graham, A. Mezzadrelli, W. Senaratne, S. Pal, D. Thelen, L. Hepburn, P. Mazumder, and V. Pruneri, Towards transparent and durable copper-containing antimicrobial surfaces, Commun. Mater. 5, 39 (2024).
  23. S. Wang, H. Wu, K. Sun, J. Hu, F. Chen, W. Liu, J. Chen, B. Sun, and A. M. S. Hossain, A novel pH-responsive Fe-MOF system for enhanced cancer treatment mediated by the Fenton reaction, New J. Chem. 45, 3271 (2021).
  24. R. Cui, P. Zhao, Y. Yan, G. Bao, A. Damirin, and Z. Liu, Outstanding drug-loading/release capacity of hollow fe-metal-organic framework-based microcapsules: A potential multifunctional drug-delivery platform, Inorg. Chem. 60, 1664 (2021).
  25. G. Cibin, D. Gianolio, S. A. Parry, T. Schoonjans, O. Moore, R. Draper, L. A. Miller, A. Thoma, C. L. Doswell, and A. Graham, An open access, integrated XAS data repository at Diamond Light Source, Radiat. Phys. Chem. 175, 108479 (2020).
  26. C. Segre, IXAS XAFS Database (Center for Synchrotron Radiation Research and Instrumentation at Illinois Institute of Technology, Chicago, 2008).
  27. Y. Chen, C. Chen, C. Zheng, S. Dwaraknath, M. K. Horton, J. Cabana, J. Rehr, J. Vinson, A. Dozier, J. J. Kas, K. A. Persson, and S. P. Ong, Database of ab initio L-edge x-ray absorption near edge structure, Sci. Data 8, 153 (2021).
  28. J. Vinson, J. J. Rehr, J. J. Kas, and E. L. Shirley, Bethe-Salpeter equation calculations of core excitation spectra, Phys. Rev. B 83, 115106 (2011).
  29. J. Vinson, Advances in the ocean-3 spectroscopy package, Phys. Chem. Chem. Phys. 24, 12787 (2022).
  30. C. Zheng, C. Chen, Y. Chen, and S. P. Ong, Random forest models for accurate identification of coordination environments from x-ray absorption near-edge structure, Patterns 1, 100013 (2020).
  31. M. R. Carbone, F. Meng, C. Vorwerk, B. Maurer, F. Peschel, X. Qu, E. Stavitski, C. Draxl, J. Vinson, and D. Lu, Lightshow: a Python package for generating computational x-ray absorption spectroscopy input files, J. Open Source Softw. 8, 5182 (2023).
  32. J. J. Rehr, J. J. Kas, F. D. Vila, M. P. Prange, and K. Jorissen, Parameter-free calculations of x-ray spectra with FEFF9, Phys. Chem. Chem. Phys. 12, 5503 (2010).
  33. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder et al., Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
  34. C. Zheng, K. Mathew, C. Chen, Y. Chen, H. Tang, A. Dozier, J. J. Kas, F. D. Vila, J. J. Rehr, L. F. Piper, K. A. Persson, and S. P. Ong, Automated generation and ensemble-learned matching of X-ray absorption spectra, npj Comput. Mater. 4, 12 (2018).
  35. K. Mathew, C. Zheng, D. Winston, C. Chen, A. Dozier, J. J. Rehr, S. P. Ong, and K. A. Persson, Data descriptor: High-throughput computational x-ray absorption spectroscopy, Sci. Data 5, 180151 (2018).
  36. K. Gilmore, J. Vinson, E. L. Shirley, D. Prendergast, C. D. Pemmaraju, J. J. Kas, F. D. Vila, and J. J. Rehr, Efficient implementation of core-excitation Bethe-Salpeter equation calculations, Comput. Phys. Commun. 197, 109 (2015).
  37. S. B. Torrisi, M. R. Carbone, B. A. Rohr, J. H. Montoya, Y. Ha, J. Yano, S. K. Suram, and L. Hung, Random forest machine learning models for interpretable x-ray absorption near-edge structure spectrum-property relationships, npj Comput. Mater. 6, 109 (2020).
  38. J. Timoshenko, D. Lu, Y. Lin, and A. I. Frenkel, Supervised machine-learning-based determination of three-dimensional structure of metallic nanoparticles, J. Phys. Chem. Lett. 8, 5091 (2017).
  39. S. Tetef, N. Govind, and G. T. Seidler, Unsupervised machine learning for unbiased chemical classification in x-ray absorption spectroscopy and x-ray emission spectroscopy, Phys. Chem. Chem. Phys. 23, 23586 (2021).
  40. S. Tetef, V. Kashyap, W. M. Holden, A. Velian, N. Govind, and G. T. Seidler, Informed chemical classification of organophosphorus compounds via unsupervised machine learning of x-ray absorption spectroscopy and x-ray emission spectroscopy, J. Phys. Chem. A 126, 4862 (2022).
  41. M. Higashi and H. Ikeno, Extraction of local structure information from x-ray absorption near-edge structure: A machine learning approach, Mater. Trans. 64, 2179 (2023).
  42. M. R. Carbone, P. M. Maffettone, X. Qu, S. Yoo, and D. Lu, Accurate, uncertainty-aware classification of molecular chemical motifs from multimodal x-ray absorption spectroscopy, J. Phys. Chem. A 128, 1948 (2024).
  43. S. P. Gleason, D. Lu, and J. Ciston, Prediction of the Cu oxidation state from EELS and XAS spectra using supervised machine learning, npj Comput. Mater. 10, 221 (2024).
  44. M. Chatzidakis and G. A. Botton, Towards calibration-invariant spectroscopy using deep learning, Sci. Rep. 9, 2126 (2019).
  45. D. del-Pozo-Bueno, D. Kepaptsoglou, F. Peiró, and S. Estradé, Comparative of machine learning classification strategies for electron energy loss spectroscopy: Support vector machines and artificial neural networks, Ultramicroscopy 253, 113828 (2023).
  46. T. David, N. K. Nik Aznan, K. Garside, and T. Penfold, Towards the automated extraction of structural information from x-ray absorption spectra, Digital Discovery 2, 1461 (2023).
  47. S. A. Guda, A. S. Algasov, A. A. Guda, A. Martini, A. N. Kravtsova, A. L. Bugaev, L. V. Guda, and A. V. Soldatov, Search for analytical relations between x-ray absorption spectra descriptors and the local atomic structure using machine learning, J. Surf. Investig. 15, 934 (2021).
  48. A. A. Guda, S. A. Guda, A. Martini, A. N. Kravtsova, A. Algasov, A. Bugaev, S. P. Kubrin, L. V. Guda, P. Šot, J. A. van Bokhoven, C. Copéret, and A. V. Soldatov, Understanding x-ray absorption spectra by means of descriptors and machine learning algorithms, npj Comput. Mater. 7, 203 (2021).
  49. Z. Ji, M. Hu, and H. L. Xin, MnEdgeNet for accurate decomposition of mixed oxidation states for Mn XAS and EELS L2,3 edges without reference and calibration, Sci. Rep. 13, 14132 (2023).
  50. Y. Chen, C. Chen, I. Hwang, M. J. Davis, W. Yang, C. Sun, G. H. Lee, D. McReynolds, D. Allan, J. Marulanda Arias, S. P. Ong, and M. K. Chan, Robust machine learning inference from x-ray absorption near edge spectra through featurization, Chem. Mater. 36, 2304 (2024).
  51. C. D. Rankine, M. M. Madkhali, M. M. Madkhali, and T. J. Penfold, A deep neural network for the rapid prediction of x-ray absorption spectra, J. Phys. Chem. A 124, 4263 (2020).
  52. C. D. Rankine and T. J. Penfold, Accurate, affordable, and generalizable machine learning simulations of transition metal x-ray absorption spectra using the XANESNET deep neural network, J. Chem. Phys. 156, 164102 (2022).
  53. L. Watson, C. D. Rankine, and T. J. Penfold, Beyond structural insight: a deep neural network for the prediction of Pt L2/3-edge x-ray absorption spectra, Phys. Chem. Chem. Phys. 24, 9156 (2022).
  54. J. Hafner, Ab-initio simulations of materials using VASP: Density-functional theory and beyond, J. Comput. Chem. 29, 2044 (2008).
  55. M. W. Haverkort, M. Zwierzycki, and O. K. Andersen, Multiplet ligand-field theory using Wannier orbitals, Phys. Rev. B 85, 165113 (2012).
  56. F. Meng, B. Maurer, F. Peschel, S. Selcuk, M. Hybertsen, X. Qu, C. Vorwerk, C. Draxl, J. Vinson, and D. Lu, Multicode benchmark on simulated Ti K-edge x-ray absorption spectra of Ti-O compounds, Phys. Rev. Mater. 8, 013801 (2024).
  57. D. P. Kingma and J. Ba, Adam: A Method for Stochastic Optimization (3rd International Conference for Learning Representations, San Diego, 2014).
  58. F. Marin, A. Rohatgi, and S. Charlot, WebPlotDigitizer, a polyvalent and free software to extract spectra from old astronomical publications: application to ultraviolet spectropolarimetry (2017), https://automeris.io.
  59. S. W. Goh, A. N. Buckley, R. N. Lamb, R. A. Rosenberg, and D. Moran, The oxidation states of copper and iron in mineral sulfides, and the oxides formed on initial exposure of chalcopyrite and bornite to air, Geochim. Cosmochim. Acta 70, 2210 (2006).
  60. R. Liu, J. Chen, P. Nachimuthu, R. Gundakaram, C. Jung, J. Kim, and S. Lee, Evidence for electron-doped (n-type) superconductivity in the infinite-layer (Sr0.9La0.1)CuO2 compound by x-ray absorption near-edge spectroscopy, Solid State Commun. 118, 367 (2001).
  61. A. N. Buckley, W. M. Skinner, S. L. Harmer, A. Pring, and L. J. Fan, Electronic environments in carrollite, CuCo2S4, determined by soft x-ray photoelectron and absorption spectroscopy, Geochim. Cosmochim. Acta 73, 4452 (2009).
  62. M. Glaser, F. Ciccullo, E. Giangrisostomi, R. Ovsyannikov, A. Calzolari, and M. B. Casu, Doping and oxidation effects under ambient conditions in copper surfaces: A “real-life” CuBe surface, J. Mater. Chem. C 6, 2769 (2018).
  63. B. W. Rudyk, P. E. Blanchard, R. G. Cavell, and A. Mar, Electronic structure of lanthanum copper oxychalcogenides LaCuOCh (Ch=S, Se, Te) by x-ray photoelectron and absorption spectroscopy, J. Solid State Chem. 184, 1649 (2011).
  64. P. E. Blanchard, R. G. Cavell, and A. Mar, Electronic structure of ZrCuSiAs and ZrCuSiP by x-ray photoelectron and absorption spectroscopy, J. Solid State Chem. 183, 1536 (2010).
  65. M. Grioni, J. F. an Acker, M. T. Czyzyk, and J. C. Fuggle, Unoccupied electronic structure and core-hole effects in the x-ray-absorption spectra of Cu2O, Phys. Rev. B 45, 3309 (1992).
  66. M. R. Carbone, S. Yoo, M. Topsakal, and D. Lu, Classification of local chemical environments from x-ray absorption spectra using supervised machine learning, Phys. Rev. Mater. 3, 033604 (2019).
  67. See Supplemental Material at http://link.aps.org/supplemental/10.1103/xz7f-srky for six additional figures providing additional analysis on cuxasnet's performance and training data.
  68. N. Kitajima, K. Fujisawa, C. Fujimoto, Y. Moro-oka, S. Hashimoto, T. Kitagawa, K. Toriumi, K. Tatsumi, and A. Nakamura, Oxygen complexes and oxygen activation by transition metals, J. Am. Chem. Soc. 114, 1277 (1992).
  69. M. F. Qayyum, R. Sarangi, K. Fujisawa, T. D. P. Stack, K. D. Karlin, K. O. Hodgson, B. Hedman, and E. I. Solomon, L-edge x-ray absorption spectroscopy and DFT calculations on Cu 2O2 species: Direct electrophilic aromatic attack by side-on peroxo bridged dicopper(II) complexes, J. Am. Chem. Soc. 135, 17417 (2013).
  70. H. Kwon, T. Hsu, W. Sun, W. Jeong, F. Aydin, J. Chapman, X. Chen, M. R. Carbone, D. Lu, F. Zhou, and T. A. Pham, Spectroscopy-guided discovery of three-dimensional structures of disordered materials with diffusion models, arXiv:2312.05472.
  71. https://github.com/smglsn12/CuXASNet.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation