A Hybrid Green–Kubo (hGK) Framework for Calculating Viscosity from Short MD Simulations

Viscosity calculation from equilibrium molecular dynamics (MD) simulations relies on the traditional Green-Kubo (GK) framework, which integrates the stress autocorrelation function (SACF) over time. While the formalism is exact in the linear response regime, the traditional approach often suffers from poor convergence and requires extensive phase space sampling, which is computationally demanding for soft matter and polymer systems. In this Letter, we introduce a hybrid Green-Kubo (hGK) framework that alleviates these limitations by partitioning the SACF into two physically meaningful regimes: (i) a short time ballistic component extracted directly from short MD simulations and (ii) a long time relaxation tail represented using analytically motivated functions, ϕ(τ), fitted only to short trajectories such that η = (<i>V/k</i>_B<i>T</i>)[¹/₆∑_αβ∫₀^τ_<i>l</i>⟨<i>P</i>_αβ(<i>t</i>) <i>P</i>_αβ(<i>t</i> + τ )⟩ dτ + ∫_{τ_<i>l</i>}^∞ϕ(τ) dτ]. This strategy bypasses the need for extensive sampling while preserving the exact GK framework in short times. Benchmarking against SPC/E water confirms excellent agreement with established results, and we further demonstrate the efficacy of the method for challenging electrolyte systems (EC-LiTFSI and PEO-LiTFSI), for which the GK framework fails to converge. The computational savings are substantial, with reductions of several orders of magnitude in required sampling achieved without compromising predictive accuracy. We also discuss the limitations of the hGK framework and outline clear avenues for refinement, including optimal tail selection and robust identification of relaxation regimes in noisy stress data. The hGK framework presented in this Letter provides a conceptually simple, broadly applicable, and computationally efficient route for viscosity prediction in molecular liquids, polymer melts, and ionically conducting soft materials.