{"id":"https://openalex.org/W7213865816","doi":"https://doi.org/10.26434/chemrxiv.15009169/v1","title":"A theory of inner-sphere reorganization energy for electrocatalysis","display_name":"A theory of inner-sphere reorganization energy for electrocatalysis","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7213865816","doi":"https://doi.org/10.26434/chemrxiv.15009169/v1"},"language":"en","primary_location":{"id":"doi:10.26434/chemrxiv.15009169/v1","doi":"https://doi.org/10.26434/chemrxiv.15009169/v1","is_oa":true,"landing_page_url":"https://doi.org/10.26434/chemrxiv.15009169/v1","pdf_url":"https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15009169/v1","source":{"id":"https://openalex.org/S4393918830","display_name":"ChemRxiv","issn_l":"2573-2293","issn":["2573-2293"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15009169/v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152355841","display_name":"Kaicong Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kaicong Yang","raw_affiliation_strings":["College of Chemistry and Molecular Sciences , Wuhan University , Wuhan 430072 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Chemistry and Molecular Sciences , Wuhan University , Wuhan 430072 , China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152380896","display_name":"Bing Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bing Huang","raw_affiliation_strings":["College of Chemistry and Molecular Sciences , Wuhan University , Wuhan 430072 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Chemistry and Molecular Sciences , Wuhan University , Wuhan 430072 , China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025466061","display_name":"Lin Zhuang","orcid":"https://orcid.org/0000-0002-5642-6735","observed_orcids":["https://orcid.org/0000-0002-5642-6735"]},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin Zhuang","raw_affiliation_strings":["College of Chemistry and Molecular Sciences , Wuhan University , Wuhan 430072 , China"],"raw_orcid":"https://orcid.org/0000-0002-5642-6735","affiliations":[{"raw_affiliation_string":"College of Chemistry and Molecular Sciences , Wuhan University , Wuhan 430072 , China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37461747"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10030","display_name":"Electrocatalysts for Energy Conversion","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2105","display_name":"Renewable Energy, Sustainability and the Environment"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10030","display_name":"Electrocatalysts for Energy Conversion","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2105","display_name":"Renewable Energy, Sustainability and the Environment"},"field":{"id":"https://openalex.org/fields/21","display_name":"Energy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11434","display_name":"Electrochemical Analysis and Applications","score":0.000699999975040555,"subfield":{"id":"https://openalex.org/subfields/1603","display_name":"Electrochemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inner-sphere-reorganization-energy","display_name":"inner-sphere reorganization energy","score":0.9259999990463257},{"id":"https://openalex.org/keywords/electrocatalysis","display_name":"electrocatalysis","score":0.9700000286102295},{"id":"https://openalex.org/keywords/marcus-theory","display_name":"Marcus theory","score":0.7799999713897705},{"id":"https://openalex.org/keywords/interfacial-polarization","display_name":"interfacial polarization","score":0.6150000095367432},{"id":"https://openalex.org/keywords/legendre-transform","display_name":"Legendre transform","score":0.7940000295639038},{"id":"https://openalex.org/keywords/free-energy-landscape","display_name":"free energy landscape","score":0.7480000257492065},{"id":"https://openalex.org/keywords/interfacial-stiffness","display_name":"interfacial stiffness","score":0.9670000076293945},{"id":"https://openalex.org/keywords/electron-transfer-kinetics","display_name":"electron transfer kinetics","score":0.6320000290870667},{"id":"https://openalex.org/keywords/electrode-potential","display_name":"electrode potential","score":0.4309999942779541}],"concepts":[{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.7307999730110168},{"id":"https://openalex.org/C33989665","wikidata":"https://www.wikidata.org/wiki/Q5357962","display_name":"Electrocatalyst","level":4,"score":0.5652999877929688},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.5430999994277954},{"id":"https://openalex.org/C89169741","wikidata":"https://www.wikidata.org/wiki/Q905122","display_name":"Marcus theory","level":4,"score":0.5123000144958496},{"id":"https://openalex.org/C205049153","wikidata":"https://www.wikidata.org/wiki/Q2698605","display_name":"Polarization (electrochemistry)","level":2,"score":0.5073000192642212},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.45669999718666077},{"id":"https://openalex.org/C57476982","wikidata":"https://www.wikidata.org/wiki/Q582857","display_name":"Transition state theory","level":4,"score":0.4447000026702881},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.42750000953674316},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C116594300","wikidata":"https://www.wikidata.org/wiki/Q908652","display_name":"Legendre transformation","level":2,"score":0.39340001344680786},{"id":"https://openalex.org/C159467904","wikidata":"https://www.wikidata.org/wiki/Q2001702","display_name":"Chemical physics","level":1,"score":0.37470000982284546},{"id":"https://openalex.org/C148898269","wikidata":"https://www.wikidata.org/wiki/Q1108792","display_name":"Kinetics","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C52859227","wikidata":"https://www.wikidata.org/wiki/Q7877","display_name":"Electrochemistry","level":3,"score":0.3646000027656555},{"id":"https://openalex.org/C125277925","wikidata":"https://www.wikidata.org/wiki/Q2572687","display_name":"Potential energy surface","level":3,"score":0.36149999499320984},{"id":"https://openalex.org/C17525397","wikidata":"https://www.wikidata.org/wiki/Q176140","display_name":"Electrode","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C55904794","wikidata":"https://www.wikidata.org/wiki/Q82682","display_name":"Redox","level":2,"score":0.3467999994754791},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C521977710","wikidata":"https://www.wikidata.org/wiki/Q81163","display_name":"Polymer","level":2,"score":0.3441999852657318},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.3424000144004822},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3352999985218048},{"id":"https://openalex.org/C41607394","wikidata":"https://www.wikidata.org/wiki/Q2420179","display_name":"Thermodynamic potential","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3249000012874603},{"id":"https://openalex.org/C131157278","wikidata":"https://www.wikidata.org/wiki/Q51363","display_name":"Thermodynamic equilibrium","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.305400013923645},{"id":"https://openalex.org/C512968161","wikidata":"https://www.wikidata.org/wiki/Q556","display_name":"Hydrogen","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.29510000348091125},{"id":"https://openalex.org/C178213299","wikidata":"https://www.wikidata.org/wiki/Q44424","display_name":"Chemical bond","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C29705727","wikidata":"https://www.wikidata.org/wiki/Q294562","display_name":"Polar","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C153262748","wikidata":"https://www.wikidata.org/wiki/Q17098449","display_name":"Legendre function","level":3,"score":0.27970001101493835},{"id":"https://openalex.org/C86369940","wikidata":"https://www.wikidata.org/wiki/Q2421183","display_name":"Activated complex","level":4,"score":0.27390000224113464},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C2994096175","wikidata":"https://www.wikidata.org/wiki/Q2445876","display_name":"Hot electron","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C95121573","wikidata":"https://www.wikidata.org/wiki/Q190474","display_name":"Activation energy","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.2612999975681305},{"id":"https://openalex.org/C112887158","wikidata":"https://www.wikidata.org/wiki/Q169324","display_name":"Hydrogen bond","level":3,"score":0.2590999901294708},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.25}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.26434/chemrxiv.15009169/v1","doi":"https://doi.org/10.26434/chemrxiv.15009169/v1","is_oa":true,"landing_page_url":"https://doi.org/10.26434/chemrxiv.15009169/v1","pdf_url":"https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15009169/v1","source":{"id":"https://openalex.org/S4393918830","display_name":"ChemRxiv","issn_l":"2573-2293","issn":["2573-2293"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.26434/chemrxiv.15009169/v1","doi":"https://doi.org/10.26434/chemrxiv.15009169/v1","is_oa":true,"landing_page_url":"https://doi.org/10.26434/chemrxiv.15009169/v1","pdf_url":"https://chemrxiv.org/doi/pdf/10.26434/chemrxiv.15009169/v1","source":{"id":"https://openalex.org/S4393918830","display_name":"ChemRxiv","issn_l":"2573-2293","issn":["2573-2293"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.75}],"study_designs":[],"awards":[{"id":"https://openalex.org/G3876699350","display_name":null,"funder_award_id":"JYB2025XDXM409","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"}],"funders":[{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213865816.pdf","grobid_xml":"https://content.openalex.org/works/W7213865816.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2007281822","https://openalex.org/W1965923613","https://openalex.org/W2050566437","https://openalex.org/W4411917928","https://openalex.org/W4417299771","https://openalex.org/W4248393999","https://openalex.org/W1971816383","https://openalex.org/W2061183337","https://openalex.org/W7090821619","https://openalex.org/W4405640786"],"abstract_inverted_index":{"In":[0],"Marcus":[1,169],"theory,":[2],"reorganization":[3,128],"energy":[4,129],"links":[5],"thermodynamics":[6,98],"and":[7,44,71,85,108,156],"kinetics":[8],"for":[9,90],"outer-sphere":[10],"electron":[11,20],"transfer,":[12],"in":[13,104],"which":[14,105],"the":[15,26,36,42,56,131,152,174],"redox":[16],"centre":[17],"exchanges":[18],"an":[19,100,119],"without":[21,74],"changing":[22],"its":[23,91],"bonding":[24,46],"to":[25,159,183],"electrode.":[27],"Most":[28],"electrocatalytic":[29],"elementary":[30,125],"steps":[31],"are":[32,112],"instead":[33],"inner-sphere":[34,127],"processes:":[35],"reacting":[37],"intermediate":[38],"is":[39,66,130,171],"part":[40],"of":[41,55,61,96,135,163,179],"interface,":[43],"surface":[45,103,109],"changes":[47],"with":[48],"charge":[49],"transfer.":[50],"A":[51,93],"general":[52],"thermodynamic":[53],"definition":[54],"full":[57],"nonequilibrium":[58],"preparation":[59],"cost":[60,134,144],"such":[62],"a":[63,75,87,123,137,146,160],"bonded":[64],"interface":[65,139],"lacking,":[67],"leaving":[68],"equilibrium":[69],"descriptors":[70],"measured":[72],"rates":[73],"common":[76],"theoretical":[77],"basis.":[78],"Here":[79],"we":[80],"define":[81],"this":[82,143,180],"quantity":[83],"thermodynamically":[84],"provide":[86],"first-principles":[88],"procedure":[89],"calculation.":[92],"Legendre":[94],"transform":[95],"fixed-potential":[97],"yields":[99],"internal":[101],"free-energy":[102,133],"interfacial":[106,165],"polarization":[107],"bond":[110],"state":[111],"coupled":[113],"variables,":[114],"while":[115],"electrode":[116],"potential":[117],"remains":[118],"external":[120],"control.":[121],"For":[122],"specified":[124],"event,":[126],"finite":[132],"preparing":[136],"product-like":[138],"before":[140],"relaxation.":[141],"Writing":[142],"as":[145,173],"Bregman":[147],"difference":[148],"separates":[149],"it":[150,158],"from":[151],"reaction":[153],"driving":[154],"force":[155],"relates":[157],"weighted":[161],"integral":[162],"local":[164],"stiffness.":[166],"The":[167],"classical":[168],"expression":[170],"recovered":[172],"one-dimensional":[175],"harmonic":[176],"charge-only":[177],"limit":[178],"framework.":[181],"Applied":[182],"Volmer":[184],"hydrogen":[185],"oxidation":[186],"on":[187]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-22T00:00:00"}
