Graph Theory of Deep Eutectic Solvents: From Typed Interaction Networks to Property Prediction

Deep eutectic solvents (DES) present a formidable challenge for property prediction due to the complex interplay of hydrogen bonding, Coulombic, dispersion, and coordination interactions that define their macroscopic behavior. Existing approaches─group contribution methods, COSMO-RS, and brute-force molecular dynamics─either lack transferability, require prohibitive computational cost, or obscure the physical origins of observed trends. Here we propose a graph-theoretic framework in which a DES mixture is represented as a directed, weighted, typed multigraph whose nodes are mixture components (or interaction sites) and whose edges encode pairwise interaction affinities categorized by physical type. We define a set of 11 physically interpretable graph invariants─comprising three interaction loads (S_HB, S_C, S_vdW), hydrogen-bond directionality (Δ_HB), weighted clustering coefficient (C_w), spectral radius (ρ(A)), algebraic connectivity (μ2), modularity (Q*), global efficiency (E_g), size asymmetry (Φ_V), and interaction entropy (H_int)─11 scalar descriptors that reduce to approximately four-five independent invariants for the two-node graphs used to represent binary DES (Section 9.5)─and propose closed-form equations (property closures) mapping these invariants to six thermophysical properties (density, viscosity, surface tension, melting point depression, conductivity, and refractive index) cross-validated against experimental data for 15 choline chloride-based DES, plus a heat-capacity closure that is proposed but not yet cross-validated owing to insufficient experimental data. Cross-validated performance meets the predefined target benchmark for density (R2 = 0.94, MAPE = 1.65%); performance for the other five properties falls below target at the current, heuristic level of parametrization, so the framework's primary demonstrated contribution at this stage is a physically transparent, mechanistically interpretable descriptor set rather than uniformly accurate prediction. The framework is designed to be parametrized from COSMO-RS interaction energies, quantum-mechanical cluster calculations, or molecular dynamics simulations, and its modular architecture enables systematic extension to ternary and higher-order systems, hydrated DES, and natural deep eutectic solvents (NADES). We discuss thermodynamic consistency constraints, uncertainty quantification strategies, and a cross-validation protocol for fitting the closure coefficients. This framework provides a computationally efficient, physically transparent bridge between molecular-level interaction data and engineering-scale property prediction for the rational design of task-specific DES.