{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T13:22:09Z","timestamp":1789046529186,"version":"build-2803163510"},"reference-count":43,"publisher":"American Chemical Society (ACS)","issue":"36","license":[{"start":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T00:00:00Z","timestamp":1787875200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100008431","name":"Consejer?a de Educaci?n, Junta de Castilla y Le?n","doi-asserted-by":"publisher","award":["Project NADES4NATURE, Ref.: BU047P23"],"award-info":[{"award-number":["Project NADES4NATURE, Ref.: BU047P23"]}],"id":[{"id":"10.13039\/501100008431","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci?n","doi-asserted-by":"publisher","award":["Project NADESforPFAS, Ref.: PID2022-142405OB-I00"],"award-info":[{"award-number":["Project NADESforPFAS, Ref.: PID2022-142405OB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Deep eutectic solvents (DES) present a formidable challenge for property prediction due to the complex interplay of hydrogen bonding, Coulombic, dispersion, and coordination interactions that define their macroscopic behavior. Existing approaches\u2500group contribution methods, COSMO-RS, and brute-force molecular dynamics\u2500either lack transferability, require prohibitive computational cost, or obscure the physical origins of observed trends. Here we propose a graph-theoretic framework in which a DES mixture is represented as a directed, weighted, typed multigraph whose nodes are mixture components (or interaction sites) and whose edges encode pairwise interaction affinities categorized by physical type. We define a set of 11 physically interpretable graph invariants\u2500comprising three interaction loads (S_HB, S_C, S_vdW), hydrogen-bond directionality (\u0394_HB), weighted clustering coefficient (C_w), spectral radius (\u03c1(A)), algebraic connectivity (\u03bc2), modularity (Q*), global efficiency (E_g), size asymmetry (\u03a6_V), and interaction entropy (H_int)\u250011 scalar descriptors that reduce to approximately four\u2013five independent invariants for the two-node graphs used to represent binary DES (Section 9.5)\u2500and propose closed-form equations (property closures) mapping these invariants to six thermophysical properties (density, viscosity, surface tension, melting point depression, conductivity, and refractive index) cross-validated against experimental data for 15 choline chloride\u2013based DES, plus a heat-capacity closure that is proposed but not yet cross-validated owing to insufficient experimental data. Cross-validated performance meets the predefined target benchmark for density (R2 = 0.94, MAPE = 1.65%); performance for the other five properties falls below target at the current, heuristic level of parametrization, so the framework\u2019s primary demonstrated contribution at this stage is a physically transparent, mechanistically interpretable descriptor set rather than uniformly accurate prediction. The framework is designed to be parametrized from COSMO-RS interaction energies, quantum-mechanical cluster calculations, or molecular dynamics simulations, and its modular architecture enables systematic extension to ternary and higher-order systems, hydrated DES, and natural deep eutectic solvents (NADES). We discuss thermodynamic consistency constraints, uncertainty quantification strategies, and a cross-validation protocol for fitting the closure coefficients. This framework provides a computationally efficient, physically transparent bridge between molecular-level interaction data and engineering-scale property prediction for the rational design of task-specific DES.<\/jats:p>","DOI":"10.1021\/acs.jpcb.6c01054","type":"journal-article","created":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T05:34:47Z","timestamp":1788327287000},"page":"9123-9141","source":"Crossref","is-referenced-by-count":0,"title":["Graph Theory of\nDeep Eutectic Solvents: From Typed\nInteraction Networks to Property Prediction"],"prefix":"10.1021","volume":"130","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9996-2426","authenticated-orcid":true,"given":"Santiago","family":"Aparicio","sequence":"first","affiliation":[{"name":"University of Burgos , , ,","place":["Burgos, Spain, 09001"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,28]]},"reference":[{"key":"2026091008083025300_cit1","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1039\/b210714g","article-title":"Novel Solvent\nProperties of Choline Chloride\/Urea Mixtures","author":"Abbott","year":"2003","journal-title":"Chem. 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Rev."},{"key":"2026091008083025300_cit4","doi-asserted-by":"publisher","first-page":"4518","DOI":"10.1039\/C5GC01451D","article-title":"Hydrophobic Deep Eutectic Solvents\nas Water-Immiscible Extractants","volume":"17","author":"van Osch","year":"2015","journal-title":"Green Chem."},{"key":"2026091008083025300_cit5","doi-asserted-by":"publisher","first-page":"1701","DOI":"10.1104\/pp.111.178426","article-title":"Are Natural\nDeep Eutectic Solvents the Missing Link in Understanding Cellular\nMetabolism and Physiology?","volume":"156","author":"Choi","year":"2011","journal-title":"Plant Physiol."},{"key":"2026091008083025300_cit6","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1080\/17425247.2019.1604680","article-title":"Deep\nEutectic Solvents Comprising Active Pharmaceutical Ingredients in\nthe Development of Drug Delivery Systems","volume":"16","author":"Pedro","year":"2019","journal-title":"Expert\nOpin. 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F.; Vinyals, O.; Dahl, G. E. In  Neural Message Passing\nfor Quantum Chemistry, International Conference on Machine\nLearning; PMLR, 2017; pp 1263\u20131272."},{"key":"2026091008083025300_cit34","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1021\/ci500206u","article-title":"Viscosity of Ionic Liquids: An Extensive Database and\na New Group Contribution Model Based on a Feed-Forward Artificial\nNeural Network","volume":"54","author":"Paduszyn\u0301ski","year":"2014","journal-title":"J. Chem. Inf. Model."},{"key":"2026091008083025300_cit35","doi-asserted-by":"publisher","first-page":"6123","DOI":"10.1021\/jp9813286","article-title":"Structure\nof the Amide I Band of\nPeptides Measured by Femtosecond Nonlinear-Infrared Spectroscopy","volume":"102","author":"Hamm","year":"1998","journal-title":"J. Phys. Chem. 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