[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-116958-en":3,"doc-seo-116958-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},116958,34359740700684,"Finn","https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487",8,"Research & Report","Machine Learning-Aided First-Principles Calculations of Redox Potentials","A combined first-principles and machine-learning workflow predicts redox potentials for half-cell reactions on the absolute scale. Machine-learned force fields enable efficient thermodynamic integration from oxidized to reduced states to obtain accurate free-energy differences with broad-phase-space sampling. A stepwise strategy refines free energies from ML force fields to semi-local functional potentials and then to hybrid-functional results via Δ-machine learning. Using PBE0 (25% exact exchange), calculated redox potentials for Fe3+/Fe2+, Cu2+/Cu+ and Ag2+/Ag+ agree well with high-quality experimental estimates.","arXiv :2309 . 13217v2 [physics .chem-ph] 22 Mar 2024  \nMachine Learning-Aided First-Principles Calculations of Redox Potentials  \nRyosuke Jinnouchi  \nToyota Central Research and Developments Laboratories Inc. ∗  \nFerenc Karsai  \nVASP Software GmbH/Sensengasse 8, 1090 Vienna, Austria  \nGeorg Kresse†  \nComputational Materials Physics, Faculty of Physics, University of Vienna, 1090 Vienna, Austria  \n(Dated: March 26, 2024)  \nWe present a method combining first-principles calculations and machine learning to predict the redox potentials of half-cell reactions on the absolute scale. By applying machine learning force fields for thermodynamic integration from the oxidized to the reduced state, we achieve efficient statistical sampling over a broad phase space. Furthermore, through thermodynamic integration from machine learning force fields to potentials of semi-local functionals, and from semi-local functionals to hybrid functionals using ∆-machine learning, werefine the free energy with high precision step-by-step. Utilizing a hybrid functional that includes 25% exact exchange (PBE0), this method predicts the redox potentials of the three redox couples, Fe3+ /Fe2+ , Cu2+ /Cu+ , and Ag2+ /Ag+ , to be 0 .92, 0 .26, and 1 .99 V, respectively. These predictions are in good agreement with the best experimental estimates (0.77, 0.15, 1.98 V) . This work demonstrates that machine-learned surrogate models provide a flexible framework for refining the accuracy of free energy from coarse approximation methods to precise electronic structure calculations, while also facilitating sufficient statistical sampling.  \n1. INTRODUCTION  \nGreen energy and a circular economy are one of the key paradigms that our human society needs to realize in the next few decades. This implies that we need to give up on the combustion of fossil fuels. A key element to achieve this paradigm shift is the use of electrochemistry, be it for batteries and fuel cells, to convert electrical energy to hydrogen or other valuable chemicals, or to convert hydrogen back to energy without direct combustion in air.  \nThe redox potential of electron transfer (ET), Ox +ne − → Red in liquids, is an essential property for a variety of electrochemical energy conversion devices, such as batteries, fuel cells, and electrochemical fuel synthesis. It determines the alignment of redox levels relative to the Fermi level of a metal, or valence band maximum (VBM) and conduction band minimum (CBM) of semiconductor and insulator electrodes. It also determines the stability windows of ions and molecules in solutions, that is the range of voltages within which a specific ion or molecule can undergo electrochemical reactions. This information is vital to design redox species and solvent molecules, such as redox couples for redox-flow batteries [1], solvents and additives for Li-ion batteries [2–4], radical scavengers for fuel cells [5] and electrocatalysts for fuel synthesis [6, 7] .  \nUnfortunately, to date, accurate first-principles (FP) predictions of this crucial property remain challenging, with typical prediction errors around 0.5 V. Sprik and co-workers developed a thermodynamic integration (TI) method utilizing the computational standard hydrogen electrode (CSHE) [13, 14]  \n∗ [e1262@mosk.tytlabs.co.jp](e1262@mosk.tytlabs.co.jp)[ ](e1262@mosk.tytlabs.co.jp)† Also at VASP Software GmbH.  \nTABLE 1 . Redox potentials Uredox of three transition metal cations calculated by RPBE+D3, PBE0 (0.25), PBE0 (0.50), PBE0+D3 (0.25) and PBE0+D3 (0.50) using MLFF and ∆-ML. Here, values in the parenthesis are the fraction of the exact exchange. The results for 64 water molecular systems are tabulated. The absolute potential of SHE is set to 4.44 V [8] . The root means square errors (RMSE) compared to the experimental redox potentials are also shown. The results by the HSE06 functional reported by Sprik and co-workers [9] are also listed.  \n\n| XC functional | Fe | Cu | Ag | RMSE |\n| --- | --- | --- | --- | ","cbCaicvTIqtGB17o","https://ap.wps.com/l/cbCaicvTIqtGB17o","pdf",1185772,1,12,"English","en",105,"# Introduction\n## Thermodynamic integration and machine-learned force fields\n## Refinement from semi-local to hybrid functionals (Δ-machine learning)\n## Benchmark redox couples and comparison with experiment","[{\"question\":\"How does the method combine first-principles calculations with machine learning for redox potentials?\",\"answer\":\"It uses machine learning force fields for thermodynamic integration to obtain efficient free-energy sampling, then refines those results toward hybrid-functional accuracy using stepwise thermodynamic integration and Δ-machine learning.\"},{\"question\":\"What is the role of thermodynamic integration in the workflow?\",\"answer\":\"Thermodynamic integration connects the oxidized and reduced states and provides free-energy differences, enabling accurate statistical sampling over a broad phase space of configurations.\"},{\"question\":\"Which redox couples are predicted and how do the results compare with experiments?\",\"answer\":\"The approach predicts redox potentials for Fe3+/Fe2+, Cu2+/Cu+ and Ag2+/Ag+, with values that show good agreement with best experimental estimates.\"}]","Machine Learning-Aided First-Principles Calculations of Redox Potentials | 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does the method combine first-principles calculations with machine learning for redox potentials?","Question",{"text":75,"@type":76},"It uses machine learning force fields for thermodynamic integration to obtain efficient free-energy sampling, then refines those results toward hybrid-functional accuracy using stepwise thermodynamic integration and Δ-machine learning.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the role of thermodynamic integration in the workflow?",{"text":80,"@type":76},"Thermodynamic integration connects the oxidized and reduced states and provides free-energy differences, enabling accurate statistical sampling over a broad phase space of configurations.",{"name":82,"@type":73,"acceptedAnswer":83},"Which redox couples are predicted and how do the results compare with experiments?",{"text":84,"@type":76},"The approach predicts redox potentials for Fe3+/Fe2+, Cu2+/Cu+ and Ag2+/Ag+, with values that show good agreement with best experimental 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