Cross-correlation corrected friction in generalized Langevin models: Application to the continuous Asakura–Oosawa model

Abstract

The development of dynamically consistent coarse-grained models for molecular simulations is often based on generalized Langevin equations, motivated by the application of the projection operator formalism (Mori–Zwanzig theory). While Mori’s projection operator yields linear generalized Langevin equations that can be computationally efficiently implemented in numerical simulations, the downside is that Mori’s generalized Langevin equation does not encompass the multi-body potential of mean force required to correctly encode structural and thermodynamic properties in coarse-grained many-body systems. Zwanzig’s projection operator yields nonlinear generalized Langevin equations including the multi-body potential of mean force, while the remaining force contributions are not as cheap to implement in molecular simulation without making it formally hard to justify approximations. For many-particle coarse-grained models, due to computational and conceptual simplicity, an often used approach is to combine nonlinear conservative interactions with linear expressions to model dissipation. In a previous study [V. Klippenstein and N. F. A. van der Vegt, J. Chem. Phys. 154, 191102 (2021)], we proposed a method to parameterize such models to achieve dynamic consistency in coarse-grained models, allowing us to reconcile Mori’s and Zwanzig’s approach for practical purposes. In the current study, by applying the same strategy, we develop coarse-grained implicit solvent models for the continuous Asakura–Oosawa model, which under certain conditions allows us to develop very accurate coarse-grained potentials. By developing coarse-grained models for different reference systems with varying parameters, we test the broader applicability of the proposed procedure and demonstrate the relevance of accurate coarse-grained potentials in bottom-up derived dissipative models. We study how different system parameters affect the dynamic representability of the coarse-grained models. In particular, we find that the quality of the coarse-grained potential is crucial to correctly model the backscattering effect due to collisions on the coarse-grained scale. As hydrodynamic interactions are not explicitly modeled in the presented coarse-graining approach, deviations are observed in the long-time dynamics. The Asakura–Oosawa model allows for the tuning of system parameters to gain an improved understanding of this limitation. We also propose three new iterative optimization schemes to fine-tune the generalized Langevin thermostat to exactly match the reference velocity-autocorrelation function.