In the electrolyte of a lithium-ion battery, positively charged lithium ions () move through the liquid surrounded by solvent molecules. In the standard models, each lithium ion is depicted as an independent structure enclosed by solvent. Because ions of the same positive charge repel each other through the Coulomb force, it seemed unlikely that lithium ions would approach one another without an anion in between and form a stable assembly. New research, however, suggests that solvation structures exist that this conventional picture cannot explain.
On October 14, 2026, a joint research team published the result in the journal Nature. The team included Professor Richard Friesner, Associate Professor Alexander Urban, Associate Professor Lauren Marbella, and Professor Daniel Steingart of Columbia University, together with researchers from Schrödinger. The researchers combined molecular dynamics simulations using a machine-learning force field with solid-state nuclear magnetic resonance (NMR) spectroscopy at cryogenic temperatures to analyze the structure of an electrolyte in which lithium hexafluorophosphate () is dissolved in ethylene carbonate (EC). The paper was first released on the preprint server ChemRxiv before being published in Nature.
The calculations showed that in a 1.2 M (mol/L) electrolyte, about 40% of lithium ions belong to "multi- clusters" that share solvent molecules without directly involving a counter-anion. Under these conditions, the average number of lithium ions across all lithium complexes, including single-ion complexes, is 1.3. The team also suggested that this structure may be involved in the initial formation of the solid electrolyte interphase (SEI), the protective film that forms on the surface of the negative electrode. However, the proportion of clusters was derived from simulations, and the NMR results only indirectly support the structure. The researchers did not observe the clusters directly inside an operating battery, and the study does not demonstrate improvements in battery capacity or lifetime.
Solvation structures that conventional computational models missed
In a battery electrolyte, the solvation structure, meaning which molecules surround a lithium ion and how closely the ions approach one another, greatly affects performance. The internal structure of the electrolyte relates to ionic conductivity, viscosity, and the degree of salt dissociation, as well as to electrochemical stability at the electrode interface and the composition of the electric double layer. Particularly important is the SEI, a nanometer-scale protective film formed when the electrolyte is reductively decomposed on the negative electrode surface during early charge-discharge cycles. A suitable SEI suppresses further excessive decomposition of the electrolyte and contributes to longer battery life and improved safety. In systems using lithium metal, it is also important for suppressing the growth of dendrites, the tree-like deposits that can form.
However, identifying at the atomic level the solvation structures involved in SEI formation has not been easy. Earlier studies have reported differing results for the "coordination number," the number of solvent molecules directly coordinated to a single lithium ion, depending on the experimental method and conditions. Some reported values as low as about 2.3 molecules per , lower than generally assumed for solvation structures. Known cases also existed in which comparing the Stokes radius, estimated from viscosity and mobility, with the van der Waals radius based on molecular size made the solvation structure hard to interpret. The team focused on the existence of clusters in which multiple lithium ions share solvent molecules as a possible clue to these discrepancies in measurements.
In the team's machine-learning force field calculations, the higher the concentration, the larger the fraction of lithium ions belonging to multinuclear clusters. The fraction was about 23% at 0.5 M, about 40% at 1.2 M, and more than 68% at 2.0 M, showing that the internal structure of the electrolyte changes substantially with concentration.
- 多核クラスター内Li+比率
- 単独Li+比率
データを表で見る
| 多核クラスター内Li+比率 (%) | 単独Li+比率 (%) | |
|---|---|---|
| 0.5 M | 23 | 77 |
| 1.2 M | 40 | 60 |
| 2.0 M | 68 | 32 |
Notably, classical fixed-charge force fields such as OPLS4, widely used in conventional computational chemistry, hardly reproduced these multinuclear clusters. Fixed-charge force fields treat the partial charges of atoms as constant, so they may not adequately represent changes in electron distribution, polarization, and screening by surrounding solvent when ions come close together. As a result, they cannot accurately reproduce the balance between the repulsion generated when lithium ions approach each other and the solvent-mediated stabilization, and mononuclear solvation structures come to dominate. The fact that past simulations found almost no multinuclear clusters may reflect not their absence in real electrolytes but a limit in the expressive power of the computational models.
What the machine-learning force field revealed: an electrolyte structure unlike earlier models
To tackle this problem, the team adopted Schrödinger's Charge-Recursive Neural Network Force Field (QRNN). QRNN uses machine learning to reproduce the energy relationships between atoms obtained from quantum chemical calculations, and applies them in molecular dynamics simulations. It aims to handle complex interionic interactions that conventional fixed-charge models cannot adequately represent, while analyzing larger systems over longer times than first-principles calculations allow.
An important point in this study is that no experimental data on the liquid state of the electrolyte were used to train QRNN. The model was trained on energy data for gas-phase molecular clusters calculated with density functional theory (DFT). The calculation conditions were B97X-D3BJ/def2-TZVPD, and the model was built from information on intermolecular interactions from quantum chemical calculations. Therefore, the agreement with experimental values for the density, viscosity, and diffusion coefficients of the liquid electrolyte was not obtained by directly training the model on those measurements. The team validated the model's predictive ability using condensed-phase experimental data not used in training.
| Evaluation item | QRNN machine-learning force field (this study) | OPLS4 classical fixed-charge force field (comparison) | Data used for validation |
|---|---|---|---|
| Association energy of gas-phase complexes | Mean absolute error below 1 kcal/mol relative to DFT values | Larger errors, especially for multinuclear clusters, in some cases 10 to 100 times those of QRNN | DFT reference calculations |
| Multinuclear clusters in 1.2 M electrolyte | About 40% of belong to multinuclear clusters | About 99% or more of complexes are mononuclear | No direct measurement of cluster fraction |
| Li–Li radial distribution function (RDF) | Clear close-contact peak at about 3 Å | No close-contact peak corresponding to about 3 Å | Indirect support from cryogenic solid-state NMR |
| Liquid properties (density, viscosity, diffusion coefficient, etc.) | Good agreement with experimental values for many items | Larger errors than QRNN for some items | Previously reported measurements of electrolyte properties |
| Computational cost (per energy evaluation) | 2 to 3 orders of magnitude higher than OPLS4 | Low computational load, suited to large, long simulations | Comparison of computational methods reported in the paper |
QRNN's accuracy was also confirmed by direct comparison with quantum chemical calculations. The team extracted representative molecular clusters from the QRNN and OPLS4 simulations and compared their association energies with those obtained by DFT. The mean absolute error of QRNN fell below 1 kcal/mol (about 4.184 kJ/mol) for structures extracted from either model, a level known as chemical accuracy. OPLS4, by contrast, showed larger errors, particularly in energy evaluation of complexes containing multiple lithium ions, making the difference from QRNN clear.
Using QRNN, the team ran molecular dynamics simulations of /EC electrolytes at 0.5 M, 1.2 M, and 2.0 M. QRNN performed a 1-nanosecond equilibration followed by a 5-nanosecond production run, tracking how the arrangement of ions and solvent molecules changes over time. Here, a multinuclear lithium cluster is defined as a structure in which another lies within 4.5 Å (angstroms; 1 Å = $10^{-10}$ m) of a given $\mathrm{Li}^+$. In the analysis, the radial distribution function (RDF) between lithium ions showed a clear peak at the short distance of about 3 Å. This means that structures in which multiple lithium ions come close through EC molecules form at a certain rate during the simulation.
This accuracy comes at a considerable computational cost, however. According to the paper, the cost per QRNN energy evaluation is 2 to 3 orders of magnitude higher than that of classical force fields such as OPLS4. Absolute figures for runtime or floating-point operations are not given, but the difference in computational load is not negligible. On the other hand, with first-principles molecular dynamics (ab initio MD), which evaluates interatomic interactions by quantum chemical calculation each time, running large systems for long times is itself difficult. QRNN was adopted as a method that combines energy accuracy close to quantum chemical calculation with the computational speed needed to statistically examine molecular arrangements in a liquid.
Experimental validation by cryogenic solid-state NMR
Even if calculations predict multinuclear clusters, that does not guarantee that such structures exist in the actual electrolyte. The experimental group at Columbia University therefore used solid-state NMR (ssNMR) spectroscopy to check whether the solvation structures predicted by the simulations match the measurements. Because NMR reflects the environment of electrons and atoms around a nucleus, it provides clues for analyzing interactions among lithium ions, solvent molecules, and anions.
The experimental challenge was that solvent molecules and ions move constantly in the liquid, and solvation structures interchange in a short time. In the liquid state at 313 K (about 40°C), such fast exchange time-averages the NMR signal, making it hard to distinguish different local structures. The team therefore flash-froze the samples and performed solid-state NMR measurements at low temperature. For carbon-13 () measurements they used a magnetic field of 14.1 T (tesla) and a temperature of 116 K, and for lithium-7 () measurements 9.32 T and 210 K. By suppressing molecular motion in the samples, they sought to probe the local solvation environments thought to exist in the liquid.
The first measurement examined was the fluorine-19 to lithium-7 cross-polarization ( CP) signal. In this measurement, the closer fluorine and lithium atoms are, the more readily a signal from magnetization transfer appears. If ion pairs or aggregates with direct contact between and the counter-anion were abundant, a strong signal reflecting that proximity would be expected. In practice, the signal was very weak, and the intensity had to be magnified fivefold to see the spectrum. This result supports the interpretation that most lithium ions in the frozen sample are not in direct contact with anions but are separated from them by solvent molecules. However, this alone cannot determine the ratio of mononuclear complexes to multinuclear clusters.
The team also examined the local environment of EC molecules by proton-to-carbon-13 cross-polarization magic-angle spinning ( CPMAS) measurements. As the concentration was raised from 0.5 M to 1.2 M and then 2.0 M, the NMR peak corresponding to the carbonyl group of EC broadened, and a shoulder on the peak became progressively clearer. This suggests that the coordination environments of EC molecules diversify as salt concentration increases, changing their interactions with lithium ions.
When NMR spectra were calculated using molecular structures extracted from the QRNN simulations, they reproduced well the broadening of the measured peak and the trend of the shoulder developing with rising concentration. Spectra calculated from OPLS4 structures, on the other hand, explained the experimental results to some extent at 0.5 M, where mononuclear complexes predominate, but agreement fell at 1.2 M and 2.0 M. Differences in chemical shift and peak shape were especially large for carbonyl carbons located near lithium ions. These comparisons support the view that the complex solvation structures predicted by QRNN explain the experimental results better than conventional models.
NMR validation does, however, have important limits. What was measured were flash-frozen samples, not the structure of the liquid electrolyte flowing inside a battery. It must also be considered how far changes in local structure or phase separation during freezing alter the molecular arrangement of the liquid state. The team used solid-state NMR as an indirect means of inferring solvation structures in the liquid, and the agreement between calculation and experiment does not by itself demonstrate the abundance or dynamic behavior of multinuclear clusters.
Multinuclear clusters as a possible trigger of SEI formation
Why can lithium ions of the same positive charge approach each other against strong repulsion? The team points to the high dielectric constant and polarizability of EC. The oxygen atoms in EC's carbonyl groups coordinate to multiple lithium ions and bridge them, which is thought to effectively screen the electrostatic repulsion between the cations. Such local solvation-based stabilization may enable association of lithium ions that would not normally approach one another. The team suggests that this property may be one reason EC-containing electrolytes have been widely used in lithium-ion batteries.
To investigate what reactions multinuclear clusters might undergo at the electrode interface, the team also calculated the reduction potentials of various lithium complexes by quantum chemical calculation. The calculations used the implicit solvent model SMD with B97X-D3BJ/def2-TZVPD, with potentials referenced to the ferrocene/ferrocenium redox couple and converted to the scale. During the first charge of a battery, as the negative electrode potential falls, components of the electrolyte are reduced and SEI formation begins. What the team examined was which species are most prone to this initial reduction reaction.
The calculations showed that, compared with the representative mononuclear lithium complex , complexes containing two lithium ions, ($x=4$ to $7$), are more susceptible to one-electron reduction. In particular, the reduction potential of the dinuclear complex $[\mathrm{Li}_2(\mathrm{EC})_7]^{2+}$, which was relatively abundant in the simulations, agreed within 0.1 V with the onset potential of SEI formation of about 0.8 V (vs. $\mathrm{Li}/\mathrm{Li}^+$) reported for EC-based electrolytes with graphite and silicon negative electrodes. This result suggests that multinuclear clusters are reduced earlier than mononuclear complexes and may be involved in SEI formation.
In the paper, the authors put forward the hypothesis that multinuclear lithium complexes "participate in, if not govern" initial SEI formation. One conceivable reaction pathway is that multinuclear clusters are drawn to the negatively charged electrode surface, accept electrons at a higher potential than mononuclear complexes, and undergo reductive decomposition, starting formation of the protective film. In addition, the paper's supplementary material (Supplementary Table 13) showed that for some dinuclear complexes, a second reduction following the first one-electron reduction is also thermodynamically favorable. This raises the possibility that further reductive decomposition proceeds, triggered by the first electron transfer.
However, the agreement of the calculated reduction potentials with experimentally reported SEI onset potentials does not mean the actual reaction pathway has been proven. This study did not directly trace the process by which multinuclear clusters accept electrons on an operating electrode surface and are incorporated into the SEI while their chemical bonds change. Whether a thermodynamically easily reduced structure also becomes a main reactant at a real electrode interface depends as well on reaction rates and abundance at the interface. The explanation that multinuclear clusters govern SEI formation is a promising hypothesis based on consistency between calculations and existing electrochemical experiments, not an established reaction mechanism.
Whether battery performance improves depends on further validation
This study advances the fundamental understanding of battery electrolytes, but it does not immediately lead to higher capacity, faster charging, or longer life. Some media reports and university press materials emphasize expectations for future improvements in battery performance. The paper, however, contains no charge-discharge cycling tests of prototype batteries developed using these findings, nor measured data showing improved capacity or lifetime. The core of the research is to elucidate the structure of molecular assemblies in the electrolyte and their possible involvement in SEI formation.
There are also constraints on the electrolyte compositions studied. Analysis of the abundance of multinuclear clusters and the main solvation structures focused on systems of dissolved in EC as the sole solvent at 0.5 M, 1.2 M, and 2.0 M. Commercial batteries, by contrast, widely use electrolytes in which EC is mixed with low-viscosity solvents such as dimethyl carbonate (DMC) and ethyl methyl carbonate (EMC). Additives such as fluoroethylene carbonate (FEC) are also sometimes used to tune electrode interface reactions and SEI properties.
During model validation, the team also examined the properties and intermolecular interactions of systems such as EC/DMC mixtures. However, they did not confirm that multinuclear lithium clusters form at the same proportions in practical mixed solvents. Whether similar structures form in electrolytes using lithium salts other than , such as , , and , also needs to be tested. If EC's high dielectric constant and polarizability are important for stabilizing the clusters, changes in solvent composition may alter how readily clusters form and what structures they take.
In addition, the main molecular dynamics simulations in this study did not include real electrodes. They also incorporated no reaction model that directly handles the voltage applied to the electrode, electron transfer between electrode and electrolyte, or bond breaking and formation. It is therefore unknown how the clusters found in the calculations move to the electrode interface and whether they dissociate there or are reduced while keeping their assembly intact. The team lists extending the simulations to include electrode models, reaction chemistry, and applied voltage as future challenges.
The effect of multinuclear clusters on lithium-ion transport is also unresolved. The authors discuss the possibility that multiple lithium ions move through the electrolyte as clusters and release ions at the electrode interface. However, how the presence of clusters affects the lithium-ion transference number or battery charging speed cannot be concluded from this study. The existence of multinuclear clusters and whether their structure works in favor of better battery performance need to be considered separately.
The research funding and ties to industry also deserve mention. The study was funded by Gates Ventures, and part of the experiments was carried out with support from the Energy Storage Research Alliance (ESRA), supported by the U.S. Department of Energy (DOE). Professor Richard Friesner is a co-founder of Schrödinger, which developed and commercializes the QRNN technology central to the study, and serves on its board of directors and as a scientific advisor. According to the paper's conflict-of-interest disclosure, he holds a financial interest in Schrödinger, and the coauthors include current employees of the company and people who were employees at the time of the research. Such industry-academia collaboration is important for applying advanced computational technology to basic research, but when judging the effectiveness of a computational method, confirmation of reproducibility by independent research groups is also important.
The result shows that it is not enough to view the electrolyte of a lithium-ion battery simply as a liquid in which independent ions and solvent molecules are gathered. A machine-learning force field predicted multinuclear lithium clusters that conventional fixed-charge models hardly reproduced, and cryogenic NMR measurements indirectly supported that structure. A new hypothesis also emerged that such clusters are involved in the initial formation of the SEI. However, it remains unclear whether the same structures form in the mixed solvents used in real batteries and at electrode interfaces, and how much they influence battery performance. If cluster formation and reactions can be verified under conditions closer to those of operating batteries, it could become an important clue for rationally designing electrolyte compositions from the molecular level.