{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T14:00:04Z","timestamp":1790863204097,"version":"4.1.0"},"reference-count":55,"publisher":"American Chemical Society (ACS)","issue":"39","license":[{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T00:00:00Z","timestamp":1790035200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-045"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["22373110"],"award-info":[{"award-number":["22373110"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2020YFC1910301"],"award-info":[{"award-number":["2020YFC1910301"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Intermolecular interactions govern the condensed-phase properties of substances as well as the thermodynamic behavior and phase equilibria of solutions. A central challenge in the molecular thermodynamics of mixing is the estimation of cross-interaction energies (\u03b5AB) between unlike molecules from the pure-substance properties via combining rules\u2500a task complicated by the vast number of possible mixtures and the experimental difficulty of directly measuring cross-interaction energies. Classical Berthelot geometric-mean combining rules, originally derived for exchangeable van der Waals interactions, are inadequate for specific donor\u2013acceptor interactions such as hydrogen bonding. Hydrogen bonding is governed by two independent molecular characteristics: donor and acceptor abilities (\u03b1 and \u03b2). Consequently, the self-association energy of a pure substance is expressed as the product \u03b1\u03b2, following a Coulombic-type attraction principle. Crucially, hydrogen-bonding interactions between two unlike molecules A and B are intrinsically asymmetric and non-exchangeable (A \u2192 B \u2260 B \u2192 A) since each molecule possesses its own distinct \u03b1 and \u03b2 parameters. To address this, we propose a new combining rule in which the cross-association energy is evaluated as the sum of two cross-products: \u03b1A\u03b2B + \u03b1B\u03b2A. This model treats hydrogen bonding as mediated by two opposing monopoles (single charges) rather than dipoles, which fundamentally distinguishes it from conventional single-energy-parameter approaches, where cross-association energies are derived directly from pure-component self-association energies. To implement the model, H-bonding strengths based on the dimensionless Kamlet\u2013Taft H-bonding donor and acceptor parameters are converted into physically meaningful interaction energies. The resulting framework enables the prediction of mixture thermodynamic properties and enthalpies of mixing from pure-component parameters alone.<\/jats:p>","DOI":"10.1021\/acs.jpcb.6c03060","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T15:03:37Z","timestamp":1790089417000},"page":"10279-10290","source":"Crossref","is-referenced-by-count":1,"title":["Beyond the Geometric\nMean: A Monopole-Based Combining\nRule for Hydrogen-Bonding Cross-Interactions"],"prefix":"10.1021","volume":"130","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6461-3784","authenticated-orcid":true,"given":"Chen-Yang","family":"Liu","sequence":"first","affiliation":[{"name":"The Chinese Academy of Sciences , , ,","place":["Beijing, China, 100190"]},{"name":"University of Chinese Academy of Sciences , ,","place":["Beijing, China, 10049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2252-4258","authenticated-orcid":true,"given":"Lin-Xue","family":"Han","sequence":"additional","affiliation":[{"name":"The Chinese Academy of Sciences , , ,","place":["Beijing, China, 100190"]},{"name":"University of Chinese Academy of Sciences , ,","place":["Beijing, China, 10049"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ya-Fei","family":"Yuan","sequence":"additional","affiliation":[{"name":"The Chinese Academy of Sciences , , ,","place":["Beijing, China, 100190"]},{"name":"University of Chinese Academy of Sciences , ,","place":["Beijing, China, 10049"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"2026100109062462900_cit1","doi-asserted-by":"crossref","DOI":"10.1002\/9780470747537","volume-title":"Thermodynamic\nModels for Industrial Applications: From Classical and Advanced Mixing\nRules to Association Theories","author":"Kontogeorgis","year":"2010"},{"issue":"10","key":"2026100109062462900_cit2","doi-asserted-by":"publisher","first-page":"1626","DOI":"10.1007\/s10953-018-0821-1","article-title":"Mitigating\nComplexity: Cohesion Parameters and Related Topics. I: The Hildebrand\nSolubility Parameter","volume":"47","author":"Wilhelm","year":"2018","journal-title":"J. Solution Chem."},{"key":"2026100109062462900_cit3","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1039\/9781849730983-00084","article-title":"Mixing and\nCombining Rules","volume-title":"Applied Thermodynamics\nof Fluids","author":"Goodwin","year":"2010"},{"key":"2026100109062462900_cit4","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198520597.001.0001","volume-title":"Polymer Physics","author":"Rubinstein","year":"2003"},{"key":"2026100109062462900_cit5","first-page":"1703","article-title":"Sur le Me\u0301lange\ndes Gaz","volume":"126","author":"Berthelot","year":"1898","journal-title":"C. R. Acad. Sci. Paris"},{"issue":"2","key":"2026100109062462900_cit6","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1021\/ja00418a009","article-title":"The Solvatochromic\nComparison Method. I. The Beta-Scale\nof Solvent Hydrogen-Bond Acceptor (HBA) Basicities","volume":"98","author":"Kamlet","year":"1976","journal-title":"J. Am. Chem. Soc."},{"issue":"10","key":"2026100109062462900_cit7","doi-asserted-by":"publisher","first-page":"2886","DOI":"10.1021\/ja00426a036","article-title":"The Solvatochromic Comparison Method. 2. The Alpha-Scale\nof Solvent Hydrogen-Bond Donor (HBD) Acidities","volume":"98","author":"Taft","year":"1976","journal-title":"J. Am. Chem. Soc."},{"issue":"24","key":"2026100109062462900_cit8","doi-asserted-by":"publisher","first-page":"3666","DOI":"10.1080\/00268976.2013.831140","article-title":"The Theory\nof Non-Electrolyte Solutions: An Historical Review","volume":"111","author":"Gubbins","year":"2013","journal-title":"Mol. Phys."},{"issue":"11","key":"2026100109062462900_cit9","doi-asserted-by":"publisher","first-page":"4619","DOI":"10.1021\/acs.jced.9b00264","article-title":"Taking Another Look\nat the van der\nWaals Equation of State-Almost 150 Years Later","volume":"64","author":"Kontogeorgis","year":"2019","journal-title":"J. Chem. Eng. Data"},{"key":"2026100109062462900_cit10","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1039\/tf9605600761","article-title":"Intermolecular Forces between Unlike\nMolecules. A More\nComplete form of the Combining Rules","volume":"56","author":"Hudson","year":"1960","journal-title":"Trans.\nFaraday Soc."},{"issue":"1\u20133","key":"2026100109062462900_cit11","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.molliq.2006.12.024","article-title":"Unlike Lennard\u2013Jones\nParameters\nfor Vapor\u2013Liquid Equilibria","volume":"135","author":"Schnabel","year":"2007","journal-title":"J. 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Rev."},{"key":"2026100109062462900_cit17","doi-asserted-by":"crossref","DOI":"10.1201\/9781420006834","volume-title":"Hansen Solubility\nParameters: A User\u2019s Handbook","author":"Hansen","year":"2007","edition":"2"},{"issue":"10","key":"2026100109062462900_cit18","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1080\/08927020410001709299","article-title":"Application of Gibbs Ensemble and NPT Monte Carlo Simulation\nto the Development of Improved Processes for H2S-rich Gases","volume":"30","author":"Ungerer","year":"2004","journal-title":"Mol. Simul."},{"issue":"8","key":"2026100109062462900_cit19","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1080\/00268970010020041","article-title":"Inadequacy of the Lorentz-Berthelot\nCombining Rules\nfor Accurate Predictions of Equilibrium Properties by Molecular Simulation","volume":"99","author":"Delhommelle","year":"2001","journal-title":"Mol. Phys."},{"key":"2026100109062462900_cit20","doi-asserted-by":"publisher","first-page":"8b","DOI":"10.1039\/tf937330008b","article-title":"The General\nTheory of Molecular Forces","volume":"33","author":"London","year":"1937","journal-title":"Trans. Faraday Soc."},{"issue":"1","key":"2026100109062462900_cit21","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1021\/cr60137a003","article-title":"A Critique\nof the Theory of Solubility of Non-Electrolytes","volume":"44","author":"Hildebrand","year":"1949","journal-title":"Chem. 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Phys."},{"issue":"7","key":"2026100109062462900_cit31","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1351\/pac198557070905","article-title":"Applications\nof Solubility Parameters and Other Cohesion Parameters in Polymer\nScience and Technology","volume":"57","author":"Barton","year":"1985","journal-title":"Pure Appl. Chem."},{"issue":"38","key":"2026100109062462900_cit32","doi-asserted-by":"publisher","first-page":"21893","DOI":"10.1039\/D1CP03193G","article-title":"Polymer Solubility\nin Ionic Liquids: Dominated by Hydrogen\nBonding","volume":"23","author":"Yuan","year":"2021","journal-title":"Phys. Chem. Chem. Phys."},{"issue":"11","key":"2026100109062462900_cit33","doi-asserted-by":"publisher","first-page":"4578","DOI":"10.1021\/acs.macromol.2c00799","article-title":"Hydrogen-Bonding\nInteractions in Polymer-Organic Solvent Mixtures","volume":"55","author":"Du","year":"2022","journal-title":"Macromolecules"},{"issue":"4","key":"2026100109062462900_cit34","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1351\/pac199971040645","article-title":"Critical Compilation of Scales of\nSolvent Parameters.\nPart I. Pure, Non-hydrogen Bond Donor Solvents","volume":"71","author":"Abboud","year":"1999","journal-title":"Pure Appl. Chem."},{"issue":"8","key":"2026100109062462900_cit35","doi-asserted-by":"publisher","first-page":"2319","DOI":"10.1021\/cr00032a005","article-title":"Solvatochromic\nDyes as Solvent Polarity Indicators","volume":"94","author":"Reichardt","year":"1994","journal-title":"Chem. Rev."},{"issue":"17","key":"2026100109062462900_cit36","doi-asserted-by":"publisher","first-page":"2877","DOI":"10.1021\/jo00165a018","article-title":"Linear Solvation\nEnergy Relationships. 23. A Comprehensive Collection of the Solvatochromic\nParameters, pi*, \u03b1, and \u03b2 , and Some Methods for Simplifying\nthe Generalized Solvatochromic Equation","volume":"48","author":"Kamlet","year":"1983","journal-title":"J.\nOrg. Chem."},{"issue":"6","key":"2026100109062462900_cit37","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1039\/cs9932200409","article-title":"The Properties\nof Organic Liquids that are Relevant to their Use as Solvating Solvents","volume":"22","author":"Marcus","year":"1993","journal-title":"Chem. Soc. Rev."},{"issue":"1\u20132","key":"2026100109062462900_cit38","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/j.chroma.2003.12.004","article-title":"Determination of Sets of Solute Descriptors\nfrom Chromatographic Measurements","volume":"1037","author":"Abraham","year":"2004","journal-title":"J. Chromatogr.\nA"},{"issue":"1\u20132","key":"2026100109062462900_cit39","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.chroma.2006.06.074","article-title":"The Chemical Interpretation\nand Practice of Linear\nSolvation Energy Relationships in Chromatography","volume":"1126","author":"Vitha","year":"2006","journal-title":"J. Chromatogr. 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Chem."},{"issue":"2141","key":"2026100109062462900_cit42","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1126\/science.83.2141.21","article-title":"Dipole\nAttraction and Hydrogen Bond Formation in Their Relation to Solubility","volume":"83","author":"Hildebrand","year":"1936","journal-title":"Science"},{"issue":"1","key":"2026100109062462900_cit43","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1073\/pnas.76.1.194","article-title":"Is There\na \u201cHydrophobic Effect\u201d?","volume":"76","author":"Hildebrand","year":"1979","journal-title":"Proc.\nNatl. Acad. Sci. U. S. 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Eng. Chem. Res."},{"issue":"28","key":"2026100109062462900_cit54","doi-asserted-by":"publisher","first-page":"12465","DOI":"10.1021\/acs.iecr.9b01624","article-title":"110th Anniversary:\nA Case Study on Developing Accurate and Reliable Excess Gibbs Energy\nCorrelations for Industrial Application","volume":"58","author":"Mathias","year":"2019","journal-title":"Ind.\nEng. Chem. Res."},{"issue":"28","key":"2026100109062462900_cit55","doi-asserted-by":"publisher","first-page":"12773","DOI":"10.1021\/acs.iecr.9b02078","article-title":"Nonrandom Two-Liquid Segment Activity Coefficient Model\nwith Association Theory","volume":"58","author":"Hao","year":"2019","journal-title":"Ind. Eng. Chem. Res."}],"container-title":["The Journal of Physical\nChemistry B"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jpcb.6c03060","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article-pdf\/130\/39\/10279\/68600577\/acs.jpcb.6c03060.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article-pdf\/130\/39\/10279\/68600577\/acs.jpcb.6c03060.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T13:19:05Z","timestamp":1790860745000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article\/130\/39\/10279\/5435360\/Beyond-the-Geometric-Mean-A-Monopole-Based"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,22]]},"references-count":55,"journal-issue":{"issue":"39","published-online":{"date-parts":[[2026,9,22]]},"published-print":{"date-parts":[[2026,10,1]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jpcb.6c03060","relation":{},"ISSN":["1520-6106","1520-5207"],"issn-type":[{"value":"1520-6106","type":"print"},{"value":"1520-5207","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,22]]}}}