The discovery emerged from a high-dimensional, charge-recursive neural network force field, or QRNN, trained exclusively on quantum-chemical gas-phase cluster calculations. Traditional molecular mechanics force fields, the kind that have served protein simulation so well, struggle with the peculiar physics of concentrated polar organic electrolytes, while ab initio molecular dynamics is limited to tiny systems and short timescales. Machine-learning force fields promise the accuracy of quantum chemistry at a cost many orders of magnitude lower, and the team’s refined model delivered a picture that conventional force fields simply cannot see. In simulations of lithium hexafluorophosphate in ethylene carbonate, the QRNN trajectories showed a sharp peak in the lithium-lithium radial distribution function near three angstroms, a signature of cations sitting in close proximity. The widely used OPLS4 force field, run on the same systems, produced no such peak and placed more than ninety-nine percent of lithium ions in single-ion clusters.

The statistics are striking. At 1.2 molar salt concentration, roughly forty percent of lithium ions were found in multi-lithium clusters during the QRNN trajectories, corresponding to an average of about 1.3 lithium ions per complex. At 2 molar, that proportion climbed above sixty-eight percent, while at 0.5 molar it fell to around twenty-three percent, showing that clustering scales strongly with concentration. Some clusters contained two or three lithium ions, and at the highest concentrations a smaller number contained four or even five. Crucially, these aggregates consisted of lithium cations bridged by ethylene carbonate molecules through their carbonyl oxygens, with the hexafluorophosphate anions pushed away. The ethylene carbonate molecules act as molecular glue, their high dielectric constant and polarizability stabilizing the otherwise repulsive approach of multiple positive charges, something that would be impossible in the gas phase or in an ordinary organic solvent.

Because such a radical departure from accepted solvation pictures demands extraordinary evidence, the team subjected their model to a battery of validation tests. Association energies computed with the QRNN force field agreed with density functional theory calculations at the ωB97X-D3BJ/def2-TZVPD level to within chemical accuracy, meaning errors below one kilocalorie per mole, for structures drawn from both QRNN and OPLS4 trajectories. The OPLS4 force field, by contrast, erred by ten to one hundred times more, and performed especially poorly on the multi-lithium clusters. Lithium-lithium distance scans in the presence of solvent molecules revealed a clear energy minimum between 2.4 and 3.0 angstroms, which the QRNN model reproduced faithfully, and an ab initio molecular dynamics simulation of a nearly five-hundred-atom system confirmed that a di-lithium cluster remains stable in that minimum region over the course of the simulation.

The model also passed demanding condensed-phase tests without ever having seen experimental data during training. Predicted densities for seven common electrolyte solvents, including ethylene carbonate, propylene carbonate, vinylene carbonate, fluoroethylene carbonate and three linear carbonates, matched measured values closely, and viscosity predictions for lithium hexafluorophosphate in a three-to-seven ethylene carbonate and dimethyl carbonate mixture were accurate up to the highest practical salt concentrations, a marked improvement over the team’s earlier work. Ionic conductivities from the simulations agreed strongly with experimental values at working temperatures. Because the potential energy surface was parameterized purely against quantum-chemical calculations, these comparisons constitute a fully independent test, and the results make a compelling case that first-principles machine-learning force fields can represent a complex chemical system to atomic resolution.

Experimental corroboration came from solid-state nuclear magnetic resonance spectroscopy performed on flash-frozen electrolyte samples. Freezing the liquid preserves the local solvation structures that fast molecular exchange would otherwise blur at room temperature. Direct-polarization lithium-7 spectra captured the full lithium population, while proton-to-lithium cross-polarization experiments showed attenuated signal consistent with lithium binding to carbonyl oxygens with protons facing away. Most tellingly, fluorine-to-lithium cross-polarization produced almost no signal, even after fivefold amplification. Both contact ion pairs and anion-containing aggregates would place lithium and fluorine atoms close enough to generate strong dipolar couplings and enhance such transfer. The absence of that spectroscopic signature indicates that the frozen samples contain predominantly solvent-separated species, exactly the single- and multi-lithium clusters the simulations predicted.

Simulated carbon-13 spectra built from clusters extracted from the QRNN trajectories matched the experimental line shapes across three salt concentrations, reproducing both the spread in chemical shifts of ethylene carbonate molecules bound in lithium clusters and the gradual growth of a shoulder on the carbonyl peak as concentration increased. When the identical protocol was applied to OPLS4 trajectories, the simulation adequately predicted spectra for dilute samples dominated by single-lithium structures but deviated from experiment once multi-lithium clusters became prevalent, particularly at carbon sites closest to the lithium ions. The agreement between a purely computational prediction and cryogenic solid-state NMR measurements provides some of the strongest evidence yet that these unusual cation aggregates are real features of the working electrolyte, not artifacts of a neural network’s imagination.

Why does this matter for the battery itself? The reduction potentials of electrolyte species determine what happens when the cell is first charged, when the anode draws electrons and the solid electrolyte interphase begins to form. Quantum-chemical calculations of one-electron reduction potentials, referenced to the lithium/lithium-ion couple through the ferrocenium/ferrocene standard, showed that the most common single-lithium complex, LiEC4, reduces at a much lower voltage than the family of di-lithium complexes such as Li2EC7. Experimentally, interphase formation begins at approximately 0.8 volts versus lithium/lithium-ion on both graphite and silicon anodes. The single-lithium clusters would not be spontaneously reduced at that voltage, but the di-lithium species fall within a tenth of a volt of it, and they appear to undergo even more favorable second one-electron reductions afterward. In other words, the multi-lithium clusters may not merely participate in the initial formation of the interphase; they may govern it, with the excess electron localizing on a carbonate moiety of an ethylene carbonate ligand shared between two lithium centers.

The finding finally offers a mechanistic explanation for one of battery chemistry’s oldest empirical choices: why ethylene carbonate has been indispensable in commercial electrolytes since the 1990s. Its unusual combination of high dielectric constant and polarizability in an aprotic solvent appears to be exactly what enables multiple lithium ions to co-complex around bridging carbonyl oxygens, creating the species that reduce at the right voltage to build a protective interphase. Beyond the specific chemistry, the work is a proof of concept that machine-learning force fields trained without any experimental input can uncover surprising phenomena in systems far more complex than liquid water, spanning elements across the periodic table. The team now plans to extend the platform to other solvents, salts and additives, and to add electrode models, reactive chemistry and applied voltage, aiming for an atomic-level picture of interphase formation. If successful, large-scale graphics-processing-unit-based simulation could become a genuine engineering tool, allowing electrolytes to be designed computationally rather than discovered by trial and error, with consequences for battery efficiency, cost and the broader electrification of transport and grid storage.

Subject of Research: Multi-lithium-ion clustering in lithium-ion battery electrolytes revealed by machine-learning molecular simulations and solid-state NMR spectroscopy

Article Title: Evidence for multi-Li+ clustering in lithium-ion battery electrolytes

Article References: Stevenson, J. M., Agarwal, G., Debnath, S., Goldsmith, Z. K., Mondal, M., Svirinovsky-Arbeli, A., Yeu, I. W., Metlay, A. S., Kwon, Y., Bhai, L., Guha, R. D., Keeler, E. G., Weber, J. L., Steingart, D. A., Marbella, L. E., Urban, A., Jacobson, L. D., Halls, M. D., & Friesner, R. A. (2026). Evidence for multi-Li+ clustering in lithium-ion battery electrolytes. Nature, 658(8136), 636-642. https://doi.org/10.1038/s41586-026-11138-7

Image Credits: AI Generated

DOI: 10.1038/s41586-026-11138-7

Keywords: lithium-ion batteries, electrolytes, machine-learning force fields, molecular dynamics, solid-state NMR, solvation structure, solid electrolyte interphase, ethylene carbonate, quantum chemistry, reduction potentials, computational chemistry, energy storage

The study, led by Haibing Zhang, Bichuan Cao, Lei Huang, Xiaogang Peng, and Linjun Wang of the Department of Chemistry at Zhejiang University, was published in Nano Research. Its central achievement is a machine learning force field, or MLFF, built on the DeePMD framework, that makes molecular dynamics simulations of realistically sized quantum dots computationally feasible without sacrificing the accuracy of quantum mechanical calculations. The work addresses a stubborn bottleneck in computational nanoscience: quantum dots large enough to matter experimentally contain thousands of atoms, far beyond the reach of conventional first-principles molecular dynamics, while classical force fields lack the flexibility to describe the messy, fluxional chemistry of a ligand-capped nanocrystal surface.

Machine learning force fields have emerged over the past decade as a way to split the difference. The underlying idea, traceable to the landmark neural network approach of Behler and Parrinello in 2007, is to train a neural network on a library of quantum mechanical calculations so that the network learns to predict the energy of each atom from its local atomic environment. Once trained, the model evaluates energies and forces at a tiny fraction of the cost of a density functional theory calculation, yet reproduces the quantum mechanical potential energy surface with remarkable fidelity. The DeePMD framework extends this idea with deep learning architectures that respect the symmetries of physics, ensuring that the predicted energy does not depend on how the molecule is rotated or translated in space.

What makes the Zhejiang team’s approach distinctive is the way they constructed the training data. Building a reliable force field for quantum dots requires examples that capture every relevant bonding motif, coordination environment, and surface reconstruction the simulation might encounter. Rather than laboriously hand-picking configurations, the researchers devised an effective strategy to generate a diverse dataset of small quantum dots, where quantum mechanical reference calculations remain affordable. Small clusters of zinc-blende CdSe, capped with carboxylate ligands, were sampled across a broad range of structural distortions and binding scenarios. Using the DP-GEN concurrent learning platform, the dataset was iteratively expanded to cover regions of configuration space where the model’s predictions were least certain, a technique that concentrates computational effort precisely where the force field needs more training.

The resulting model, which the authors call the QD force field, or QDFF, expresses the energy of each atom based purely on its local atomic structure. This locality assumption is what allows the force field, trained on small quantum dots, to be transferred to much larger ones. Once validated, the team deployed QDFF to run molecular dynamics simulations of large zinc-blende CdSe quantum dots passivated with carboxylate ligands, the workhorse ligand class used in colloidal synthesis. Carboxylates, with their negatively charged head group anchoring to surface cadmium ions and their hydrocarbon tails extending into solution, are the molecules that keep quantum dots dispersed, stable, and processable. Their arrangement on the surface, however, has been notoriously difficult to pin down.

The simulations revealed a surprisingly rich picture. The researchers identified four major binding geometries for carboxylate ligands on the CdSe surface: bridging, in which the ligand’s two oxygen atoms attach to two different cadmium sites; tilted, in which the carboxylate group leans away from a perpendicular orientation; chelating, in which both oxygens bind to a single cadmium atom; and claw, a more intricate arrangement in which the ligand appears to grip the surface in a pincer-like fashion. None of these geometries is static. Over the course of the simulations, ligands were observed migrating between binding modes, and the frequency of each geometry depended strongly on the length of the alkyl chain attached to the carboxylate head. Longer chains, it turns out, do more than just push neighboring dots apart in solution; they reshape the local binding landscape on the surface itself.

To go beyond a static catalog of geometries, the team turned to Markov state models, a statistical framework borrowed largely from protein folding studies that dissects long molecular dynamics trajectories into discrete states and the transition pathways connecting them. Applied to the ligand dynamics on the quantum dot surface, the Markov analysis exposed the detailed channels through which carboxylate ligands transform from one geometry to another, effectively producing a kinetic map of the surface chemistry. This level of detail matters because ligand geometry is not merely structural trivia. The way a ligand binds influences the electronic structure of the nanocrystal, its optical spectra, and its exciton dynamics, including the notorious blinking behavior and hole trapping processes that plague quantum dot emitters. Prior experimental work from the same group had already shown that carboxylate coordination structures on CdSe nanocrystals depend on the crystal facet, and that facet-ligand pairing can drive reversible surface reconstruction.

The significance of the new work lies in the marriage of scale and fidelity. Earlier computational studies of quantum dot surfaces were restricted to small clusters or short timescales, or relied on classical potentials that could not describe the breaking and reforming of coordination bonds. Ab initio molecular dynamics, the gold standard for accuracy, becomes prohibitively expensive for systems containing several thousand atoms and trajectories long enough to capture rare events. QDFF sidesteps both limitations, offering near-quantum accuracy at a computational cost that makes extended simulations of large, fully ligand-passivated quantum dots routine. The authors note that the high performance of the force field makes the approach promising for systematic studies of large quantum dots decorated with the many different ligand chemistries that can be synthesized in the laboratory.

The implications reach across the quantum dot field. Device engineers have long known that surface passivation quality governs the performance of quantum dot light-emitting diodes and solar cells; charge leakage, trap formation, and non-radiative recombination all trace back to imperfect surface chemistry. Ligand-related surface traps have been shown to be mobile on nanocrystal surfaces, and the mobility observed in the new simulations provides a dynamic, atomistic picture of exactly how such traps might form, migrate, and heal. By identifying which ligand geometries dominate and how they interconvert, the study gives synthetic chemists a concrete target: if particular binding modes correlate with electronic traps or degraded luminescence, ligand design can aim to suppress those modes, whether by adjusting chain length, branching, or anchoring chemistry.

There is also a methodological lesson in the work. The strategy of training on small, fully quantum mechanically characterized systems and transferring to large ones could be generalized well beyond CdSe carboxylate systems. Core-shell nanocrystals, alloyed quantum dots, perovskite nanocrystals, and other ligand-capped semiconductor systems all face the same computational wall. A validated QDFF-style force field, retrained for a new material system, could open similar windows onto surface dynamics that have remained opaque. The combination of machine learning force fields with Markov state modeling, in particular, offers a general recipe for extracting kinetic information, not just structural snapshots, from large-scale simulations of nanomaterials.

The research, supported by the National Natural Science Foundation of China, reflects a broader convergence of artificial intelligence and molecular simulation that is reshaping computational chemistry. As neural network potentials grow more accurate and the platforms for generating their training data more automated, the class of systems amenable to realistic atomistic simulation keeps expanding. For quantum dots, whose commercial success rests on exquisite control of surfaces, the arrival of a tool that finally renders those surfaces visible in motion may prove to be a turning point. The tiny ligands draped over a nanocrystal, once invisible to theory, are now coming into sharp focus, and with them the atomic-scale levers that determine whether a quantum dot shines brightly or flickers uselessly in a device.