Quadruplet-Conditioned Green–Kubo Analysis of Correlated Charge Transport in Reciprocal KF–NaF–AlF3–Al2O3 Melts

Abstract Understanding the relationship between transient local structure and correlated charge transport is essential for designing low-temperature electrolytes. Here, a physically constrained quadruplet-conditioned Green–Kubo (GK) framework is developed to establish a quantitative connection between transient local topology and correlated charge transport in reciprocal KF–NaF–AlF3–Al2O3 melts. The framework conservatively decomposes GK cross-correlation terms into element-resolved apparent transport contributions and assigns them to chemically interpretable quadruplet local environments. Molecular dynamics simulations reproduce the experimental density, viscosity, and ionic conductivity with mean relative errors of 1.32%, 6.18%, and 4.19%, respectively. Structural analysis reveals that compositional variation reconstructs both the first Al coordination shell and the surrounding second-neighbor chemical environment through the redistribution of free fluoride, fluoroaluminate, and oxygen-containing local motifs. The Nernst–Einstein approximation systematically overestimates the GK conductivity by a factor of 1.34–1.73, highlighting the essential role of interelement cross-current correlations in collective charge transport. Element-resolved decomposition further shows that alkali cations dominate the positive apparent transport contributions, whereas Al exhibits a negative apparent contribution and O contributes negligibly to the net charge current. The quadruplet-conditioned analysis further reveals that composition-driven local topological reconstruction continuously redistributes GK cross-correlation terms among transient local environments, thereby governing correlated charge transport. The proposed framework quantitatively links composition, transient local topology, and GK correlated transport, providing a physically constrained interpretation of ionic conductivity and a general framework for analyzing correlated transport in compositionally complex molten electrolytes.