Predicting energetic and entropic driving forces with coarse-grained models

Low resolution coarse-grained (CG) models provide exceptional computational efficiency for simulating soft materials. Consequently, many studies employ CG models to determine free energy surfaces along order parameters or reaction coordinates of interest. However, because CG models average over atomic details, it is challenging to determine the energetic and entropic contributions to the resulting free energy surfaces. In this work, we present a rigorous and predictive CG framework for computing these energetic and entropic driving forces based upon simulations at a single temperature. This dual approach employs distinct variational principles to independently approximate the exact CG interaction potential, W(R), and its energetic component, E_W(R). This dual approach determines the free energy surface, a_φ(x), along an order parameter, φ(x), via simulations with W(R). The dual approach then determines the energetic driving force, u_φ(x), by evaluating E_W(R) for the sampled configurations. The entropic driving force, s_φ(x), is indirectly inferred, s_φ(x) = (u_φ(x)−a_φ(x)) /T. Importantly, this entropic contribution reflects both the CG configuration distribution and the atomic details that have been eliminated from the CG model. We demonstrate that the dual approach reasonably describes the energetic and entropic driving forces between a pair of nonpolar solutes in a polar solvent. In contrast, naıvely estimating energetics with the CG interaction potential provides a qualitatively incorrect description for these driving forces.

低分辨率粗粒度（coarse-grained, CG）模型为软物质模拟提供了卓越的计算效率。因此，诸多研究采用CG模型沿目标序参量（order parameter）或反应坐标（reaction coordinate）计算自由能面（free energy surface）。然而，由于CG模型会对原子细节进行平均化处理，确定所得自由能面的能量与熵贡献颇具挑战。在本工作中，我们提出了一种严谨且具有预测性的CG框架，可基于单温度下的模拟计算上述能量与熵驱动力。该双路径方法借助不同的变分原理（variational principle），分别近似精确的CG相互作用势W(R)及其能量分量E_W(R)。首先，该方法通过基于W(R)的模拟，沿序参量φ(x)得到自由能面a_φ(x)；随后，通过对采样构型计算E_W(R)，得到能量驱动力u_φ(x)；而熵驱动力s_φ(x)则可通过下式间接推得：s_φ(x) = (u_φ(x)−a_φ(x))/T。值得注意的是，该熵贡献同时反映了CG构型分布与已从CG模型中剔除的原子细节。我们证实，该双路径方法可合理描述极性溶剂中一对非极性溶质间的能量与熵驱动力。与之相反，直接采用CG相互作用势简单估算能量，会对这类驱动力给出定性错误的描述。