{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T01:53:22Z","timestamp":1791251602056,"version":"4.1.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004901","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","doi-asserted-by":"publisher","award":["APQ- 02390-25"],"award-info":[{"award-number":["APQ- 02390-25"]}],"id":[{"id":"10.13039\/501100004901","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Mol Model"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>\n                      <jats:bold>Context<\/jats:bold>\n                    <\/jats:title>\n                    <jats:p>\n                      Underlying the adsorption mechanism is not a simple task due to the complexity of the process. In this context, statistical mechanics provides a versatile approach with relatively low computational cost for describing adsorption phenomena. An alternative strategy consists of obtaining the adsorption potential energy from experimental data through the solution of an inverse problem. In this work, the adsorption potential energy was determined directly from adsorption isotherms using experimental datasets for both aqueous- and gas-phase adsorption systems. The proposed methodology was compared with the traditional two-step procedure, in which the second adsorption virial coefficient is first determined and subsequently used for inversion of the potential energy. Due to the ill-posed nature of the problem, the conventional approach exhibits significant instability and error propagation. In contrast, the direct inversion method provides excellent results, achieving values of\n                      <jats:inline-formula>\n                        <jats:alternatives>\n                          <jats:tex-math>$$R^2 \\sim 0.99$$<\/jats:tex-math>\n                          <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                            <mml:mrow>\n                              <mml:msup>\n                                <mml:mi>R<\/mml:mi>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:msup>\n                              <mml:mo>\u223c<\/mml:mo>\n                              <mml:mn>0.99<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:math>\n                        <\/jats:alternatives>\n                      <\/jats:inline-formula>\n                      .\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>\n                      <jats:bold>Methods<\/jats:bold>\n                    <\/jats:title>\n                    <jats:p>A methodology grounded in statistical physics was developed to obtain the adsorption potential energy directly from isotherm data. The proposed approach formulates the problem as a tensor contraction, eliminating the need for the traditional two-step procedure involving the intermediate determination of the second adsorption virial coefficient.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1007\/s00894-026-06963-6","type":"journal-article","created":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T10:20:58Z","timestamp":1790590858000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A stable tensorial approach for inversion of adsorption potential energy from isotherm data"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4995-0800","authenticated-orcid":false,"given":"M\u00e1rcio","family":"Oliveira Alves","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felipe","family":"Silva Carvalho","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jo\u00e3o Pedro","family":"Braga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,28]]},"reference":[{"issue":"4","key":"6963_CR1","doi-asserted-by":"publisher","first-page":"4676","DOI":"10.1016\/j.jece.2018.06.060","volume":"6","author":"V Katheresan","year":"2018","unstructured":"Katheresan V, Kansedo J, Lau SY (2018) Efficiency of various recent wastewater dye removal methods: a review. J Environ Chem Eng 6(4):4676\u20134697. https:\/\/doi.org\/10.1016\/j.jece.2018.06.060","journal-title":"J Environ Chem Eng"},{"key":"6963_CR2","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.susmat.2016.06.002","volume":"9","author":"S De Gisi","year":"2016","unstructured":"De Gisi S, Lofrano G, Grassi M, Notarnicola M (2016) Characteristics and adsorption capacities of low-cost sorbents for wastewater treatment: a review. Sustain Mater Technol 9:10\u201340. https:\/\/doi.org\/10.1016\/j.susmat.2016.06.002","journal-title":"Sustain Mater Technol"},{"key":"6963_CR3","doi-asserted-by":"publisher","first-page":"100382","DOI":"10.1016\/j.clet.2021.100382","volume":"6","author":"M Sultana","year":"2022","unstructured":"Sultana M, Rownok MH, Sabrin M, Rahaman MH, Alam S (2022) A review on experimental chemically modified activated carbon to enhance dye and heavy metals adsorption. Clean Eng Technol 6:100382. https:\/\/doi.org\/10.1016\/j.clet.2021.100382","journal-title":"Clean Eng Technol"},{"key":"6963_CR4","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1016\/j.watres.2017.04.014","volume":"120","author":"HN Tran","year":"2017","unstructured":"Tran HN, You SJ, Hosseini-Bandegharaei A, Chao HP (2017) Mistakes and inconsistencies regarding adsorption of contaminants from aqueous solutions: a critical review. Water Res 120:88\u2013116. https:\/\/doi.org\/10.1016\/j.watres.2017.04.014","journal-title":"Water Res"},{"key":"6963_CR5","doi-asserted-by":"publisher","first-page":"122206","DOI":"10.1016\/j.molliq.2023.122206","volume":"384","author":"SH Alrefaee","year":"2023","unstructured":"Alrefaee SH, Aljohani M, Alkhamis K, Shaaban F, El-Desouky MG, El-Bindary AA, El-Bindary MA (2023) Adsorption and effective removal of organophosphorus pesticides from aqueous solution via novel metal-organic framework: adsorption isotherms, kinetics, and optimization via box-behnken design. J Mol Liq 384:122206. https:\/\/doi.org\/10.1016\/j.molliq.2023.122206","journal-title":"J Mol Liq"},{"key":"6963_CR6","doi-asserted-by":"publisher","first-page":"102124","DOI":"10.1016\/j.rechem.2025.102124","volume":"14","author":"LH Abid","year":"2025","unstructured":"Abid LH, Mussa ZH, Deyab IF, Al-Ameer LR, Al-Saedi HFS, Al-Qaim FF, Kamyab H, Rajendran S, Imran AF, Yaseen ZM (2025) Walnut shell as a bio-activated carbon for elimination of malachite green from its aqueous solution: adsorption isotherms, kinetics and thermodynamic studies. Results Chem 14:102124. https:\/\/doi.org\/10.1016\/j.rechem.2025.102124","journal-title":"Results Chem"},{"key":"6963_CR7","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/j.matchemphys.2019.01.047","volume":"226","author":"P Ranjan","year":"2019","unstructured":"Ranjan P, Patra T, Suin S, Narayanasamy S (2019) Inducing dye-selectivity in graphene oxide for cationic dye separation applications. Mater Chem Phys 226:350\u2013355. https:\/\/doi.org\/10.1016\/j.matchemphys.2019.01.047","journal-title":"Mater Chem Phys"},{"key":"6963_CR8","doi-asserted-by":"publisher","first-page":"2033","DOI":"10.1038\/s41467-017-02248-y","volume":"8","author":"V Erastova","year":"2017","unstructured":"Erastova V, Degiacomi MT, Fraser DG, Greenwell HC (2017) Mineral surface chemistry control for origin of prebiotic peptides. Nat Commun 8:2033. https:\/\/doi.org\/10.1038\/s41467-017-02248-y","journal-title":"Nat Commun"},{"issue":"1","key":"6963_CR9","doi-asserted-by":"publisher","first-page":"27134","DOI":"10.1038\/srep27134","volume":"6","author":"L Guo","year":"2016","unstructured":"Guo L, Xiao S, Zhang X (2016) Modeling adsorption with lattice Boltzmann equation. Sci Rep 6(1):27134. https:\/\/doi.org\/10.1038\/srep27134","journal-title":"Sci Rep"},{"key":"6963_CR10","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.molliq.2017.05.042","volume":"240","author":"PS Ghosal","year":"2017","unstructured":"Ghosal PS, Gupta AK (2017) Development of a generalized adsorption isotherm model at solid-liquid interface: a novel approach. J Mol Liq 240:21\u201324. https:\/\/doi.org\/10.1016\/j.molliq.2017.05.042","journal-title":"J Mol Liq"},{"key":"6963_CR11","doi-asserted-by":"publisher","first-page":"122612","DOI":"10.1016\/j.molliq.2023.122612","volume":"387","author":"DD Justino","year":"2023","unstructured":"Justino DD, Alves MO, Galv\u00e3o BR, Santamar\u00eda R, De Sousa FB, Ortega PF (2023) The effects of functionalization on graphene oxide for organic dye adsorption: an experimental-theoretical study using electronic structure calculations and statistical mechanical modeling. J Mol Liq 387:122612. https:\/\/doi.org\/10.1016\/j.molliq.2023.122612","journal-title":"J Mol Liq"},{"issue":"1","key":"6963_CR12","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1093\/chemse\/22.1.67","volume":"22","author":"AB Lamine","year":"1997","unstructured":"Lamine AB, Bouazra Y (1997) Application of statistical thermodynamics to the olfaction mechanism. Chem Senses 22(1):67\u201375. https:\/\/doi.org\/10.1093\/chemse\/22.1.67","journal-title":"Chem Senses"},{"issue":"2","key":"6963_CR13","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1016\/S0021-9797(03)00139-5","volume":"263","author":"M Khalfaoui","year":"2003","unstructured":"Khalfaoui M, Knani S, Hachicha M, Lamine AB (2003) New theoretical expressions for the five adsorption type isotherms classified by BET based on statistical physics treatment. J Colloid Interface Sci 263(2):350\u2013356. https:\/\/doi.org\/10.1016\/S0021-9797(03)00139-5","journal-title":"J Colloid Interface Sci"},{"key":"6963_CR14","doi-asserted-by":"publisher","unstructured":"Amaral TKM, dos Santos GO, de Oliveira PSC, Pires NJ, de Castro VG, Silva GG, Denadai AML, Alves MO, Trigueiro JPC, Lavall RL, Ortega PFR (2020) The effect of debris on the adsorption and electron-transfer capacity at the interface of oxidized carbon nanotubes. Chem Eng J 388. https:\/\/doi.org\/10.1016\/j.cej.2020.124379","DOI":"10.1016\/j.cej.2020.124379"},{"key":"6963_CR15","doi-asserted-by":"publisher","unstructured":"Machado NCF, Jesus LAM, Pinto PS, Paula FGF, Alves MO, Mendes KHA, Mambrini RV, Barrera D, Rocha V, Santamaria R, Trigueiro JPC, Lavall RL, Ortega PFR (2021) Waste-polystyrene foams-derived magnetic carbon material for adsorption and redox supercapacitor applications. J Clean Prod 313. https:\/\/doi.org\/10.1016\/j.jclepro.2021.127903","DOI":"10.1016\/j.jclepro.2021.127903"},{"key":"6963_CR16","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1007\/s00894-022-05307-4","volume":"28","author":"MO Alves","year":"2022","unstructured":"Alves MO, Ortega PFR, Carvalho FS, Braga JP (2022) Modelling the adsorption on oxidized carbon nanotubes using a statistical mechanics approach. J Mol Model 28:318. https:\/\/doi.org\/10.1007\/s00894-022-05307-4","journal-title":"J Mol Model"},{"key":"6963_CR17","doi-asserted-by":"publisher","first-page":"142293","DOI":"10.1016\/j.molstruc.2025.142293","volume":"1338","author":"Y Vieira","year":"2025","unstructured":"Vieira Y, Fuhr ACFP, da Silva BF, Silva LFO, R\u00edos ALM, Ahmad N, Irshad S, Jemli S, Dotto GL (2025) In-depth interpretations of the interactions of aromatic molecules to crosslinked surfaces using the grand canonical approach and quantum mechanics calculations. J Mol Struct 1338:142293. https:\/\/doi.org\/10.1016\/j.molstruc.2025.142293","journal-title":"J Mol Struct"},{"issue":"3","key":"6963_CR18","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1007\/s10953-025-01554-0","volume":"55","author":"K Oueslati","year":"2026","unstructured":"Oueslati K, Naifar A, Basha B, Lima EC, Aouaini F, Ben Lamine A (2026) Advanced statistical and stereographic analysis of hydroquinone adsorption using pine biochar: thermodynamic, energetic, and topographic perspectives. J Solution Chem 55(3):525\u2013546. https:\/\/doi.org\/10.1007\/s10953-025-01554-0","journal-title":"J Solution Chem"},{"issue":"2","key":"6963_CR19","doi-asserted-by":"publisher","first-page":"714","DOI":"10.1063\/1.1678304","volume":"57","author":"CJ Radke","year":"1972","unstructured":"Radke CJ, Prausnitz JM (1972) Statistical mechanics of adsorption from dilute liquid solution. J Chem Phys 57(2):714\u2013720. https:\/\/doi.org\/10.1063\/1.1678304","journal-title":"J Chem Phys"},{"key":"6963_CR20","volume-title":"An introduction to statistical thermodynamics","author":"TL Hill","year":"1986","unstructured":"Hill TL (1986) An introduction to statistical thermodynamics. Dover Publications, New York"},{"issue":"7","key":"6963_CR21","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.1590\/S0103-50532007000700008","volume":"18","author":"N Lemes","year":"2007","unstructured":"Lemes N, Borges E, Braga JP (2007) A general algorithm to solve linear and nonlinear inverse problems. J Braz Chem Soc 18(7):1342\u20131347. https:\/\/doi.org\/10.1590\/S0103-50532007000700008","journal-title":"J Braz Chem Soc"},{"key":"6963_CR22","unstructured":"Hadamard J (2014) Lectures on Cauchy\u2019s problem in linear partial differential equations. Courier Corporation, Mineola, NY"},{"key":"6963_CR23","unstructured":"Strang G (2000) Linear algebra and its applications"},{"key":"6963_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8480-7","author":"AN Tikhonov","year":"1995","unstructured":"Tikhonov AN, Goncharsky AV, Stepanov VV, Yagola AG (1995) Numerical methods for the approximate solution of ill-posed problems. Springer Dordrecht. https:\/\/doi.org\/10.1007\/978-94-015-8480-7","journal-title":"Springer Dordrecht"},{"issue":"8","key":"6963_CR25","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","volume":"79","author":"JJ Hopfield","year":"1982","unstructured":"Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci 79(8):2554\u20132558. https:\/\/doi.org\/10.1073\/pnas.79.8.2554","journal-title":"Proc Natl Acad Sci"},{"key":"6963_CR26","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1007\/s00894-022-05274-w","volume":"28","author":"FS Carvalho","year":"2022","unstructured":"Carvalho FS, Braga JP, Alves MO (2022) Adsorbate-adsorbent potential energy function from second virial coefficient data: a non-linear Hopfield neural network approach. J Mol Model 28:286. https:\/\/doi.org\/10.1007\/s00894-022-05274-w","journal-title":"J Mol Model"},{"issue":"4","key":"6963_CR27","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1021\/i160044a003","volume":"11","author":"CJ Radke","year":"1972","unstructured":"Radke CJ, Prausnitz JM (1972) Adsorption of organic solutes from dilute aqueous solution of activated carbon. Ind Eng Chem Fundam 11(4):445\u2013451. https:\/\/doi.org\/10.1021\/i160044a003","journal-title":"Ind Eng Chem Fundam"},{"issue":"4","key":"6963_CR28","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1080\/03081087.2015.1083933","volume":"64","author":"L Sun","year":"2016","unstructured":"Sun L, Zheng B, Bu C, Wei Y (2016) Moore-Penrose inverse of tensors via Einstein product. Linear Multilinear Algebra 64(4):686\u2013698. https:\/\/doi.org\/10.1080\/03081087.2015.1083933","journal-title":"Linear Multilinear Algebra"},{"key":"6963_CR29","doi-asserted-by":"publisher","first-page":"1259836","DOI":"10.3389\/fams.2023.1259836","volume":"9","author":"P Pandey","year":"2024","unstructured":"Pandey P, Kilicman A (2024) Linear to multi-linear algebra and systems using tensors. Front Appl Math Stat 9:1259836. https:\/\/doi.org\/10.3389\/fams.2023.1259836","journal-title":"Front Appl Math Stat"},{"issue":"4","key":"6963_CR30","doi-asserted-by":"publisher","first-page":"651","DOI":"10.2166\/wst.2020.347","volume":"82","author":"K Oueslati","year":"2020","unstructured":"Oueslati K, Lima EC, Ayachi F, Cunha MR, Lamine AB (2020) Modeling the removal of reactive red 120 dye from aqueous effluents by activated carbon. Water Sci Technol 82(4):651\u2013662. https:\/\/doi.org\/10.2166\/wst.2020.347","journal-title":"Water Sci Technol"},{"issue":"3","key":"6963_CR31","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1016\/j.cej.2009.08.019","volume":"155","author":"T Calvete","year":"2009","unstructured":"Calvete T, Lima EC, Cardoso NF, Dias SLP, Pavan FA (2009) Application of carbon adsorbents prepared from the Brazilian pine-fruit-shell for the removal of Procion Red MX 3B from aqueous solution\u2013Kinetic, equilibrium, and thermodynamic studies. Chem Eng J 155(3):627\u2013636. https:\/\/doi.org\/10.1016\/j.cej.2009.08.019","journal-title":"Chem Eng J"},{"key":"6963_CR32","doi-asserted-by":"publisher","first-page":"110644","DOI":"10.1016\/j.icheatmasstransfer.2026.110644","volume":"172","author":"W Sghaier","year":"2026","unstructured":"Sghaier W, Torkia YB, Aouaini F, Alrebdi T, Lamine AB (2026) Enhancing CO$$_2$$ adsorption and PSA refrigeration efficiency with activated carbon-graphene nanoplatelet composites: insights from statistical physics. Int Commun Heat Mass Transf 172:110644. https:\/\/doi.org\/10.1016\/j.icheatmasstransfer.2026.110644","journal-title":"Int Commun Heat Mass Transf"},{"key":"6963_CR33","unstructured":"Rohatgi A (2024) WebPlotDigitizer. https:\/\/automeris.io\/WebPlotDigitizer"},{"key":"6963_CR34","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0039-6028(73)90264-1","volume":"36","author":"WA Steele","year":"1973","unstructured":"Steele WA (1973) The physical interaction of gases with crystalline solids. I. Gas-solid energies and properties of isolated adsorbed atoms. Surf Sci 36:317\u2013352. https:\/\/doi.org\/10.1016\/0039-6028(73)90264-1","journal-title":"Surf Sci"},{"issue":"12","key":"6963_CR35","doi-asserted-by":"publisher","first-page":"125802","DOI":"10.1088\/1361-6501\/aa8f83","volume":"28","author":"HGT Nguyen","year":"2017","unstructured":"Nguyen HGT, Horn JC, Thommes M, van Zee RD, Espinal L (2017) Experimental aspects of buoyancy correction in measuring reliable high-pressure excess adsorption isotherms using the gravimetric method. Meas Sci Technol 28(12):125802. https:\/\/doi.org\/10.1088\/1361-6501\/aa8f83","journal-title":"Meas Sci Technol"},{"key":"6963_CR36","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.molliq.2018.05.008","volume":"263","author":"B Mohamed","year":"2018","unstructured":"Mohamed B, Qingyu Z, Moggridge GD, Abdelmottaleb BL (2018) New insight in adsorption of pyridine on the two modified adsorbents types mn200 and mn500 by means of grand canonical ensemble. J Mol Liq 263:413\u2013421. https:\/\/doi.org\/10.1016\/j.molliq.2018.05.008","journal-title":"J Mol Liq"},{"issue":"1","key":"6963_CR37","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1260\/026361702760120917","volume":"20","author":"M Khalfaoui","year":"2002","unstructured":"Khalfaoui M, Baouab M, Gauthier R, Lamine AB (2002) Dye adsorption by modified cotton: steric and energetic interpretations of model parameter behaviours. Adsorpt Sci Technol 20(1):33\u201347. https:\/\/doi.org\/10.1260\/026361702760120917","journal-title":"Adsorpt Sci Technol"},{"key":"6963_CR38","doi-asserted-by":"publisher","unstructured":"Mobarak M, Mohamed EA, Selim AQ, Mohamed FM, Sellaoui L, Bonilla-Petriciolet A, Seliem MK (2019) Statistical physics modeling and interpretation of methyl orange adsorption on high-order mesoporous composite of MCM-48 silica with treated rice husk. J Mol Liq 285:678\u2013687. https:\/\/doi.org\/10.1016\/j.molliq.2019.04.116","DOI":"10.1016\/j.molliq.2019.04.116"},{"key":"6963_CR39","doi-asserted-by":"publisher","unstructured":"Bouaziz N, Ben Manaa M, Bouzid M, Ben Lamine A (2019) Adsorption of hydrogen in defective carbon nanotube: modelling and consequent investigations using statistical physics formalism. Mol Phys 118(3):1606460. https:\/\/doi.org\/10.1080\/00268976.2019.1606460","DOI":"10.1080\/00268976.2019.1606460"},{"key":"6963_CR40","doi-asserted-by":"publisher","unstructured":"Zhang LP, Li ZC, Wei YM, Huang HT (2023) New regularization techniques for ill-conditioning problems and their applications: choices of regularization parameters. Eng Anal Bound Elem 152:347\u2013361. https:\/\/doi.org\/10.1016\/j.enganabound.2023.04.013","DOI":"10.1016\/j.enganabound.2023.04.013"}],"container-title":["Journal of Molecular Modeling"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00894-026-06963-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00894-026-06963-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00894-026-06963-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T01:28:17Z","timestamp":1791250097000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00894-026-06963-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,28]]},"references-count":40,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2026,10]]}},"alternative-id":["6963"],"URL":"https:\/\/doi.org\/10.1007\/s00894-026-06963-6","relation":{},"ISSN":["1610-2940","0948-5023"],"issn-type":[{"value":"1610-2940","type":"print"},{"value":"0948-5023","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,28]]},"assertion":[{"value":"15 May 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 September 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"390"}}