A structure-preserving neural density functional for the ions of a polymer electrolyte

Liyao Lyu

cond-mat.softOct 8, 2026

A structure-preserving neural density functional for the ions of a polymer electrolyte

Authors: Liyao Lyu

Organizations: School of Artificial Intelligence and Data Science, University of Science and Technology of China, Hefei, Anhui, China · Suzhou Institute for Advanced Research, University of Science and Technology of China, Suzhou, Jiangsu, China · Suzhou Big Data & AI Research and Engineering Center, Suzhou, Jiangsu, China

Abstract

Predicting the structure and response of inhomogeneous polymer electrolytes requires a description of ion correlations that retains molecular-scale accuracy while remaining transferable across spatial scales and geometries. We develop a neural density functional for electrolytes that preserves spatial symmetries, thermodynamic integrability and the Noether identities, with perfect screening recovered in stable, noncritical bulk states. Its nonlinear density dependence captures the concentration-dependent correlations missed by a pair closure, including a crossover from enhanced to suppressed long-wavelength number fluctuations at strong coupling. The functional describes density profiles at an untrained salt concentration and predicts bulk structure factors and the long-wavelength number response. Trained solely on planar density and internal-force profiles from molecular dynamics, the functional predicts ionic structure in larger domains and in two-dimensional external fields. On the same ion data, it is more accurate than three other neural density-functional architectures and keeps its accuracy with a quarter of the training runs, where the errors of the best alternative grow by about two thirds. The spatial transferability provides a necessary foundation for connecting molecular correlations to continuum predictions at larger scales.

Figures & tables

Property	Sammüller et al. [ 24 ]	Bui–Cox [ 25 ]	Dijkman et al. [ 26 ]	Cheng [ 29 ]	This work
	Learned $c^{(1)}$		Learned $F_{\rm ex}$
Integrability	N	✗	✓	✓	✓
Spatial symmetries	G	G	✗	G	✓
Noether force/torque identities	N	✗	✗	✗	✓
Long-range electrostatics	✗	✓	✗	✗	✓
Larger domains	✓	✓	✗	✓	✓

Table 1: Structural guarantees and transferability of the learned functionals compared in this work, in their original formulations. ✓, guaranteed by construction (first four rows) or demonstrated without retraining (last three rows); N, verified numerically but not built in; G, holds only for the symmetry operations of the grid; ✗, neither built in nor reported.

Figure 1: A learned density functional for the ions of a salt-doped polymer melt. ( A ) Molecular dynamics under a planar external potential provides ion densities

n_{\pm}(z)

and internal force densities

f^{\rm int}_{\pm}(z)

. ( B ) The excess free energy is parameterized by radial kernels and a pointwise neural network and trained by matching internal force densities to MD; the ideal-gas and Coulomb contributions are included analytically. ( C ) Predicted density profiles for a held-out run, bulk charge structure, and number response at the smallest nonzero wavenumber, compared with MD.

Figure 2: Density profiles predicted for runs excluded from parameter fitting, at two coupling strengths. Top row:

\varepsilon_{r}=7.5

(

l_{B}=7.96\sigma

); bottom row:

\varepsilon_{r}=2

(

l_{B}=29.8\sigma

). Columns: a periodic array of neutral Gaussian wells at

c=0.02

, the strongest well at the untrained concentration

c=0.05

, and a periodic array of Gaussian wells at

c=0.06

. Cation densities relative to the mean; black curves and bands show MD averages and

\pm 2

standard errors estimated from eight blocks. Poisson–Boltzmann theory (dotted), the pair closure (dashed) and the neural functional (solid) are obtained by solving the canonical Euler–Lagrange equation under the applied potential. Numbers give the relative

L_{2}

error of each profile, averaged over cations and anions.

Figure 3: Generalization to larger boxes and nonplanar density fields at $c=0.04$ . Rows correspond to $\varepsilon_{r}=7.5$ and 2. ( A ) Cation density profiles in a box twice the training length under an aperiodic potential. Black curves and gray bands show MD averages and $\pm 2$ standard errors; blue dashed curves show the neural-functional prediction. ( B , C ) MD and predicted cation densities under an aperiodic two-dimensional potential of oblique plane waves and irregularly placed Gaussian wells and barriers, using a shared color scale within each row. All predictions use parameters trained on planar profiles in the original box.

Figure 4: Bulk structure and long-wavelength number response. ( A , B ) Normalized charge and number structure factors at

\varepsilon_{r}=7.5

and

c=0.02

0.08

. Points show zero-field MD results averaged over

k

-shells; curves show predictions from Eq. 7 . ( C , D ) Finite-wavenumber response factor

\Gamma(k_{1})=2\bar{n}/S_{NN}(k_{1})

\varepsilon_{r}=7.5

and

2

. Solid curves show the neural functional and dashed curves the pair closure. The dotted line marks the ideal value

\Gamma=1

. Neither quantity enters the force-matching loss.

Figure 5: Concentration dependence of effective correlations. Combined correlation kernel

\mathbf{q}^{\mathsf{T}}W(k_{1})\mathbf{q}

versus concentration at

\varepsilon_{r}=7.5

( A ) and 2 ( B ). Points show estimates from zero-field MD ( Supplementary Information , section S3.2); solid curves show the neural functional and dashed curves the pair closure.

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Quantum Chemistry Materials Science Molecular Property Prediction Lithium-Ion Batteries Computational Materials Science

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Electrolyte reactivity in lithium batteries is shaped by molecular functional groups, Li

^{+}

solvation and salt-anion participation. Conventional quantum chemistry is too computationally expensive for systematic analysis of diverse electrolyte molecules and their local solvation environments. Here we present EMolStudio, a density-matrix-centered AI platform for electronic-structure prediction and analysis. Its workflow integrates molecular functionalization, explicit Li

^{+}

first-shell assembly, density-matrix prediction, and electronic-structure parsing. Applied to 163,655 functionalized molecules and 22,500 first-shell clusters across four lithium salts, we find that 1) functionalization separates CO

_{2}

Me, CN, F/CF

_{3}

, and sulfonyl groups by distinct shifts in frontier levels, electrostatic potential, and Li

^{+}

-donor contact; 2) anion identity reshapes frontier-orbital localization, with LiTDI anchoring the highest occupied orbital on the anion across the library. By carrying a unified density-matrix representation from molecular functionalization to salt-resolved solvation shells, EMolStudio provides a general platform for understanding and designing battery electrolytes.

Abstract

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