Klippenstein Viktor, van der Vegt Nico F A
Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, 64287 Darmstadt, Germany.
J Chem Phys. 2022 Jul 28;157(4):044103. doi: 10.1063/5.0093056.
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.
用于分子模拟的动态一致粗粒化模型的开发通常基于广义朗之万方程，其动机来自投影算符形式理论（森-茨万齐格理论）的应用。虽然森的投影算符产生的线性广义朗之万方程可以在数值模拟中高效地进行计算实现，但缺点是森的广义朗之万方程不包含在粗粒化多体系统中正确编码结构和热力学性质所需的多体平均力势。茨万齐格的投影算符产生包括多体平均力势的非线性广义朗之万方程，而在分子模拟中实现其余的力贡献成本较高，且难以从形式上证明近似的合理性。对于多粒子粗粒化模型，由于计算和概念上的简单性，一种常用的方法是将非线性保守相互作用与线性表达式相结合来模拟耗散。在之前的一项研究[V. Klippenstein和N. F. A. van der Vegt，《化学物理杂志》154, 191102 (2021)]中，我们提出了一种对这类模型进行参数化的方法，以实现粗粒化模型中的动态一致性，从而使我们能够在实际应用中协调森和茨万齐格的方法。在当前的研究中，通过应用相同的策略，我们为连续的朝仓-大泽模型开发了粗粒化隐式溶剂模型，在某些条件下这使我们能够开发出非常精确的粗粒化势。通过为具有不同参数的不同参考系统开发粗粒化模型，我们测试了所提出程序的更广泛适用性，并证明了精确的粗粒化势在自底向上推导的耗散模型中的相关性。我们研究了不同的系统参数如何影响粗粒化模型的动态可表示性。特别是，我们发现粗粒化势的质量对于在粗粒化尺度上正确模拟由于碰撞引起的反向散射效应至关重要。由于在所提出的粗粒化方法中没有明确模拟流体动力学相互作用，因此在长时间动力学中观察到了偏差。朝仓-大泽模型允许调整系统参数，以更好地理解这一局限性。我们还提出了三种新的迭代优化方案，以微调广义朗之万恒温器，使其与参考速度自相关函数精确匹配。
