{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T14:06:42Z","timestamp":1789654002089,"version":"4.0.0"},"reference-count":49,"publisher":"American Chemical Society (ACS)","issue":"37","license":[{"start":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T00:00:00Z","timestamp":1788307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,9,17]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Machine learning force fields (MLFFs) promise ab initio accuracy at a fraction of the computational cost of first-principles simulation, yet their fidelity for aqueous ion hydration across chemically diverse cation series remains systematically underexplored. Here, we benchmark an on-the-fly MLFF (OT-MLFF) framework, implemented in VASP via kernel-based Bayesian regression with adaptive DFT calls triggered when the estimated force error exceeds a set threshold, together with the pretrained, equivariant MACE foundation model applied off-the-shelf, against ab initio molecular dynamics (AIMD; CP2K, PBE-D3) and classical MD (CMD; Madrid-2019\/TIP4P-2005) for aqueous solutions of Li+, Na+, K+, Cs+, Mg2+, and Ca2+. Across all six ions, the OT-MLFF reproduces a bulk water structure and the systematic increase of first-shell M\u2013O distances down both cation series with near-AIMD accuracy, outperforming CMD. Coordination-number distributions reveal a mild OT-MLFF overcoordination of Li+ (modal CN 5 versus 4 in both AIMD and MACE) and Cs+, whereas the two divalent shells, including the previously problematic Ca2+, are reproduced by both machine-learned potentials, all three methods placing the Ca2+ coordination number at \u22486. MACE tracks AIMD most closely overall, its principal bias being a residual overcoordination of K+ and undercoordination of Cs+ in the diffuse monovalent shells. Angular distribution functions confirm accurate reproduction of the rigid octahedral geometry of Mg2+ but reveal systematic OT-MLFF smoothing of three-body features for more labile shells, including the O\u2013Na\u2013O shoulder near 65\u201370\u00b0 and the O\u2013Ca\u2013O peak angle. The largest failures are kinetic: the OT-MLFF generates spurious first-shell water exchange for Mg2+, absent in AIMD, and completely suppresses the exchange of the dynamic Ca2+ shell, even though it reproduces the equilibrium coordination number of both ions, a clear dissociation between structural and dynamical fidelity. Velocity autocorrelation functions reveal a related failure, the OT-MLFF underestimating the cooperative cage confinement of the large monovalent ions Cs+ and K+. In each of these cases, the pretrained MACE model recovers the AIMD behavior that the on-the-fly potential misses. Collectively, these results establish that the OT-MLFF is robust for an equilibrium solvation structure but fails for three-body angular sensitivity and exchange kinetics in chemically distinct edge cases and that a deeper, higher-body-order, pretrained model such as MACE systematically narrows these gaps even without system-specific training. Targeted improvements such as augmented transition-state sampling, higher angular-resolution descriptors, and long-range electrostatic corrections are identified as high-priority directions for kinetic fidelity in next-generation electrolyte force fields.<\/jats:p>","DOI":"10.1021\/acs.jpcb.6c02837","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T16:25:47Z","timestamp":1788452747000},"page":"9543-9560","source":"Crossref","is-referenced-by-count":0,"title":["Benchmarking on-the-Fly\nMachine Learning Force Fields\nfor Ion Hydration: Structure, Coordination, and Exchange Dynamics\nacross Monovalent and Divalent Cations"],"prefix":"10.1021","volume":"130","author":[{"given":"Mohammed S.","family":"Salha","sequence":"first","affiliation":[{"name":"Queen Mary University of London , , Mile End Road , ,","place":["London, U.K., E1 4NS"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wuyang","family":"Lin","sequence":"additional","affiliation":[{"name":"Queen Mary University of London , , Mile End Road , ,","place":["London, U.K., E1 4NS"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5265-6672","authenticated-orcid":true,"given":"Gregory","family":"Chass","sequence":"additional","affiliation":[{"name":"Queen Mary University of London , , Mile End Road , ,","place":["London, U.K., E1 4NS"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4485-4468","authenticated-orcid":true,"given":"Devis","family":"Di Tommaso","sequence":"additional","affiliation":[{"name":"Queen Mary University of London , , Mile End Road , ,","place":["London, U.K., E1 4NS"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,2]]},"reference":[{"issue":"1","key":"2026091708470098400_cit1","doi-asserted-by":"publisher","first-page":"014705","DOI":"10.1063\/1.5037679","article-title":"Hydration and Dehydration\nof Monovalent Cations near\nan Electrode Surface","volume":"149","author":"Kiyohara","year":"2018","journal-title":"J. Chem. Phys."},{"issue":"43","key":"2026091708470098400_cit2","doi-asserted-by":"publisher","first-page":"20169","DOI":"10.1080\/19443994.2015.1112982","article-title":"Molecular\nDynamics Simulation of\nSeawater Reverse Osmosis Desalination Using Carbon Nanotube Membranes","volume":"57","author":"Kim","year":"2016","journal-title":"Desalin. Water Treat"},{"issue":"42","key":"2026091708470098400_cit3","doi-asserted-by":"publisher","first-page":"12219","DOI":"10.1021\/jp0728306","article-title":"Molecular\nDynamics Study of the Solvation\nof Calcium Carbonate in Water","volume":"111","author":"Bruneval","year":"2007","journal-title":"J. Phys. Chem.\nB"},{"issue":"3","key":"2026091708470098400_cit4","doi-asserted-by":"publisher","first-page":"1346","DOI":"10.1021\/cr8003828","article-title":"Effect of\nIons on the Structure of Water: Structure Making and Breaking","volume":"109","author":"Marcus","year":"2009","journal-title":"Chem. Rev."},{"issue":"13","key":"2026091708470098400_cit5","doi-asserted-by":"publisher","first-page":"134504","DOI":"10.1063\/1.5121392","article-title":"Force Field\nof Li+, Na+, K+, Mg2+,\nCa2+, Cl\u2013, and SO42\u2013 in Aqueous Solution Based on the\nTIP4P\/2005 Water Model and Scaled Charges for the Ions","volume":"151","author":"Zeron","year":"2019","journal-title":"J. Chem. Phys."},{"issue":"10","key":"2026091708470098400_cit6","doi-asserted-by":"publisher","first-page":"3153","DOI":"10.1021\/ct1002048","article-title":"Electronic Polarizability and the Effective Pair Potentials\nof Water","volume":"6","author":"Leontyev","year":"2010","journal-title":"J. Chem. Theory Comput"},{"issue":"35","key":"2026091708470098400_cit7","doi-asserted-by":"publisher","first-page":"10786","DOI":"10.1021\/jp804694u","article-title":"Polarization of Water\nin the First Hydration Shell\nof K+ and Ca2+ Ions","volume":"112","author":"Bucher","year":"2008","journal-title":"J. Phys. Chem. B"},{"issue":"3","key":"2026091708470098400_cit8","doi-asserted-by":"publisher","first-page":"774","DOI":"10.1021\/ct900576a","article-title":"Simulating Monovalent and Divalent\nIons in Aqueous Solution Using\na Drude Polarizable Force Field","volume":"6","author":"Yu","year":"2010","journal-title":"J. Chem. Theory\nComput."},{"key":"2026091708470098400_cit9","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511609633","volume-title":"Ab Initio Molecular Dynamics:\nbasic Theory and Advanced Methods","author":"Marx","year":"2009"},{"issue":"20","key":"2026091708470098400_cit10","doi-asserted-by":"publisher","first-page":"2334","DOI":"10.1002\/cphc.202000498","article-title":"Hydrogen-Bond\nStructure and Low-Frequency\nDynamics of Electrolyte Solutions: Hydration Numbers from Ab Initio\nWater Reorientation Dynamics and Dielectric Relaxation Spectroscopy","volume":"21","author":"Kim","year":"2020","journal-title":"ChemPhyschem"},{"issue":"10","key":"2026091708470098400_cit11","doi-asserted-by":"publisher","first-page":"104113","DOI":"10.1063\/5.0022060","article-title":"Transferable Interactions\nof Li+\nand Mg2+ Ions in Polarizable Models","volume":"153","author":"Wineman-Fisher","year":"2020","journal-title":"J. Chem.\nPhys."},{"key":"2026091708470098400_cit12","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1127\/ejm\/2019\/0031-2815","article-title":"Interatomic\nPotentials of Mg Ions in Aqueous Solutions: Structure and Dehydration\nKinetics","volume":"31","author":"Zhang","year":"2019","journal-title":"Eur. J. Mineral"},{"issue":"17","key":"2026091708470098400_cit13","doi-asserted-by":"publisher","first-page":"7772","DOI":"10.1039\/C3CP54923B","article-title":"Modelling\nthe Effects of Salt Solutions on the Hydration of Calcium Ions","volume":"16","author":"Tommaso","year":"2014","journal-title":"Phys. Chem. Chem. Phys."},{"issue":"16","key":"2026091708470098400_cit14","doi-asserted-by":"publisher","first-page":"10142","DOI":"10.1021\/acs.chemrev.0c01111","article-title":"Machine Learning Force Fields","volume":"121","author":"Unke","year":"2021","journal-title":"Chem. 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Technol."},{"key":"2026091708470098400_cit17","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2604.13659","article-title":"Ion-Specific\nAnomalous Water Diffusion in Aqueous Electrolytes: A Machine-Learned\nMany-Body Force Field Study with MACE","author":"Ciacchi","year":"2026","journal-title":"arXiv"},{"key":"2026091708470098400_cit18","doi-asserted-by":"publisher","DOI":"10.1002\/cphc.70385","article-title":"Short-Range Machine-Learning\nPotentials for Aqueous\nElectrolyte Solutions","volume":"27","author":"Hetzel","year":"2026","journal-title":"ChemPhyschem"},{"key":"2026091708470098400_cit19","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2606.20105","article-title":"Can DFT-Trained Neural\nNetwork Potentials Reproduce Structure, Solvation, and Water-Exchange\nProperties in Aqueous Magnesium Solutions?","author":"Falkner","year":"2026","journal-title":"arXiv"},{"issue":"18","key":"2026091708470098400_cit20","doi-asserted-by":"crossref","first-page":"184110","DOI":"10.1063\/5.0297006","article-title":"A Foundation Model for\nAtomistic Materials Chemistry","volume":"163","author":"Batatia","year":"2025","journal-title":"J. Chem. Phys."},{"key":"2026091708470098400_cit21","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1038\/s41467-023-36329-y","article-title":"Learning Local Equivariant\nRepresentations\nfor Large-Scale Atomistic Dynamics","volume":"14","author":"Musaelian","year":"2023","journal-title":"Nat. Commun."},{"key":"2026091708470098400_cit22","doi-asserted-by":"publisher","first-page":"2453","DOI":"10.1038\/s41467-022-29939-5","article-title":"E(3)-Equivariant\nGraph Neural Networks for Data-Efficient and Accurate Interatomic\nPotentials","volume":"13","author":"Batzner","year":"2022","journal-title":"Nat. Commun."},{"issue":"16","key":"2026091708470098400_cit23","doi-asserted-by":"publisher","first-page":"11169","DOI":"10.1103\/PhysRevB.54.11169","article-title":"Efficient Iterative Schemes for Ab\nInitio Total-Energy\nCalculations Using a Plane-Wave Basis Set","volume":"54","author":"Kresse","year":"1996","journal-title":"Phys.\nRev. 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B"},{"key":"2026091708470098400_cit26","doi-asserted-by":"publisher","first-page":"145188","DOI":"10.1016\/j.electacta.2024.145188","article-title":"Impact of Amorphous Structure on\nCO2 Electrocatalysis\nwith Cu: A Combined Machine Learning Forcefield and DFT Modelling\nApproach","volume":"507","author":"Muthuperiyanayagam","year":"2024","journal-title":"Electrochim. Acta"},{"key":"2026091708470098400_cit27","doi-asserted-by":"publisher","first-page":"1014","DOI":"10.1016\/j.jechem.2025.08.089","article-title":"Optimized Selectivity\nin CO2 Electrochemical Reduction Using Amorphous CuNi Catalysts: Insights\nfrom Density Functional Theory and Machine Learning Simulations","volume":"112","author":"Muthuperiyanayagam","year":"2026","journal-title":"J. Energy Chem."},{"issue":"39","key":"2026091708470098400_cit28","doi-asserted-by":"publisher","first-page":"53231","DOI":"10.1021\/acsami.4c11398","article-title":"Unveiling\nCarbon Cluster Coating in Graphene CVD on MgO: Combining Machine Learning\nForce Field and DFT Modeling","volume":"16","author":"Zhao","year":"2024","journal-title":"ACS Appl. Mater.\nInterfaces"},{"issue":"5","key":"2026091708470098400_cit29","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1107\/S0567739476001551","article-title":"Revised\nEffective Ionic Radii and Systematic Studies of Interatomic Distances\nin Halides and Chalcogenides","volume":"32","author":"Shannon","year":"1976","journal-title":"Acta Crystallogr.\nSect. A"},{"key":"2026091708470098400_cit30","doi-asserted-by":"publisher","first-page":"2157","DOI":"10.1002\/jcc.21224","article-title":"PACKMOL:\nA package for building initial configurations for molecular dynamics\nsimulations","volume":"30","author":"Marti\u0301nez","year":"2009","journal-title":"J. Comput. Chem."},{"key":"2026091708470098400_cit31","doi-asserted-by":"publisher","first-page":"194103","DOI":"10.1063\/5.0007045","article-title":"CP2K: An electronic\nstructure and molecular dynamics software package - Quickstep: Efficient\nand accurate electronic structure calculations","volume":"152","author":"Ku\u0308hne","year":"2020","journal-title":"J. Chem. Phys."},{"issue":"18","key":"2026091708470098400_cit32","doi-asserted-by":"publisher","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","article-title":"Generalized\nGradient Approximation\nMade Simple","volume":"77","author":"Perdew","year":"1996","journal-title":"Phys. Rev. Lett."},{"issue":"15","key":"2026091708470098400_cit33","doi-asserted-by":"publisher","first-page":"154104","DOI":"10.1063\/1.3382344","article-title":"A Consistent and Accurate\nAb Initio Parametrization of Density Functional Dispersion Correction\n(DFT-D) for the 94 Elements H-Pu","volume":"132","author":"Grimme","year":"2010","journal-title":"J. Chem. Phys."},{"issue":"15","key":"2026091708470098400_cit34","doi-asserted-by":"publisher","first-page":"154503","DOI":"10.1063\/1.3651474","article-title":"Van Der Waals\nEffects in Ab Initio Water at Ambient and Supercritical Conditions","volume":"135","author":"Jonchiere","year":"2011","journal-title":"J. Chem. Phys."},{"issue":"3","key":"2026091708470098400_cit35","doi-asserted-by":"publisher","first-page":"1703","DOI":"10.1103\/PhysRevB.54.1703","article-title":"Separable Dual-Space Gaussian Pseudopotentials","volume":"54","author":"Goedecker","year":"1996","journal-title":"Phys. Rev. B"},{"issue":"28","key":"2026091708470098400_cit36","doi-asserted-by":"publisher","first-page":"16301","DOI":"10.1039\/D0CP01957G","article-title":"Density Functional\nTheory Based Molecular Dynamics\nStudy of Solution Composition Effects on the Solvation Shell of Metal\nIons","volume":"22","author":"Wang","year":"2020","journal-title":"Phys. Chem. Chem. Phys."},{"issue":"8","key":"2026091708470098400_cit37","doi-asserted-by":"publisher","first-page":"084504","DOI":"10.1063\/1.4975608","article-title":"Revisiting\nthe Hydration Structure of Aqueous Na+","volume":"146","author":"Galib","year":"2017","journal-title":"J. Chem.\nPhys."},{"issue":"10","key":"2026091708470098400_cit38","doi-asserted-by":"publisher","first-page":"3902","DOI":"10.1021\/ct3001848","article-title":"Structure\nand Dynamics of Liquid Water from Ab Initio Molecular Dynamics, Comparison\nof BLYP, PBE, and revPBE Density Functionals with and without van\nDer Waals Corrections","volume":"8","author":"Lin","year":"2012","journal-title":"J. Chem. Theory Comput."},{"issue":"41","key":"2026091708470098400_cit39","doi-asserted-by":"publisher","first-page":"10846","DOI":"10.1073\/pnas.1712499114","article-title":"Ab Initio Theory and\nModeling of Water","volume":"114","author":"Chen","year":"2017","journal-title":"Proc. Natl. Acad. Sci. U.\nS. A."},{"issue":"24","key":"2026091708470098400_cit40","doi-asserted-by":"publisher","first-page":"17953","DOI":"10.1103\/PhysRevB.50.17953","article-title":"Projector\nAugmented-Wave Method","volume":"50","author":"Blo\u0308chl","year":"1994","journal-title":"Phys. Rev. B"},{"issue":"23","key":"2026091708470098400_cit41","doi-asserted-by":"publisher","first-page":"234505","DOI":"10.1063\/1.2121687","article-title":"A General Purpose Model for the Condensed Phases of\nWater: TIP4P\/2005","volume":"123","author":"Abascal","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2026091708470098400_cit42","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1002\/jcc.20035","article-title":"Development\nand testing of a general amber force field","volume":"25","author":"Wang","year":"2004","journal-title":"J. Comput. Chem."},{"key":"2026091708470098400_cit43","doi-asserted-by":"publisher","first-page":"014101","DOI":"10.1063\/1.2408420","article-title":"Canonical\nSampling through Velocity\nRescaling","volume":"126","author":"Bussi","year":"2007","journal-title":"J. Chem. Phys."},{"key":"2026091708470098400_cit44","doi-asserted-by":"publisher","first-page":"7182","DOI":"10.1063\/1.328693","article-title":"Polymorphic\nTransitions in Single Crystals: A New Molecular\nDynamics Method","volume":"52","author":"Parrinello","year":"1981","journal-title":"J. Appl. Phys."},{"key":"2026091708470098400_cit45","doi-asserted-by":"publisher","first-page":"108171","DOI":"10.1016\/j.cpc.2021.108171","article-title":"LAMMPS,-\na Flexible Simulation Tool for Particle-Based Materials Modeling at\nthe Atomic, Meso, and Continuum Scales","volume":"271","author":"Thompson","year":"2022","journal-title":"Comput.\nPhys. Commun."},{"issue":"8","key":"2026091708470098400_cit46","doi-asserted-by":"publisher","first-page":"670","DOI":"10.1038\/s41592-019-0506-8","article-title":"The PLUMED consortium. Promoting Transparency\nand Reproducibility in Enhanced Molecular Simulations","volume":"16","author":"Bonomi","year":"2019","journal-title":"Nat. Methods"},{"issue":"43","key":"2026091708470098400_cit47","doi-asserted-by":"publisher","first-page":"24447","DOI":"10.1021\/acs.jpcc.5b07532","article-title":"Thermodynamically\nConsistent Force\nField for Molecular Dynamics Simulations of Alkaline-Earth Carbonates\nand Their Aqueous Speciation","volume":"119","author":"Raiteri","year":"2015","journal-title":"J. Phys. Chem.\nC"},{"issue":"5","key":"2026091708470098400_cit48","doi-asserted-by":"publisher","first-page":"3080","DOI":"10.1021\/acs.cgd.1c01525","article-title":"A Database\nof Solution Additives Promoting Mg2+ Dehydration and the Onset of\nMgCO3 Nucleation","volume":"22","author":"Toroz","year":"2022","journal-title":"Cryst. Growth Des."},{"issue":"24","key":"2026091708470098400_cit49","doi-asserted-by":"publisher","first-page":"2993","DOI":"10.1016\/j.ccr.2005.03.032","article-title":"Coordination and\nLigand Exchange Dynamics of Solvated Metal Ions","volume":"249","author":"Rode","year":"2005","journal-title":"Coord. Chem. Rev."}],"container-title":["The Journal of Physical\nChemistry B"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jpcb.6c02837","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article-pdf\/130\/37\/9543\/68203184\/acs.jpcb.6c02837.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article-pdf\/130\/37\/9543\/68203184\/acs.jpcb.6c02837.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T13:57:05Z","timestamp":1789653425000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jpcbfk\/article\/130\/37\/9543\/5405498\/Benchmarking-on-the-Fly-Machine-Learning-Force"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,2]]},"references-count":49,"journal-issue":{"issue":"37","published-online":{"date-parts":[[2026,9,2]]},"published-print":{"date-parts":[[2026,9,17]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jpcb.6c02837","relation":{},"ISSN":["1520-6106","1520-5207"],"issn-type":[{"value":"1520-6106","type":"print"},{"value":"1520-5207","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,2]]}}}