Theoretische Physik and CENIDE, Universität Duisburg-Essen, D-47048 Duisburg, Germany.
J Phys Chem A. 2023 Mar 9;127(9):2176-2193. doi: 10.1021/acs.jpca.2c08763. Epub 2023 Feb 28.
The lack of a procedure to determine equilibrium thermodynamic properties of a small system interacting with a bath is frequently seen as a weakness of conventional statistical mechanics. A typical example for such a small system is a solute surrounded by an explicit solvation shell. One way to approach this problem is to enclose the small system of interest in a large bath of explicit solvent molecules, considerably larger than the system itself. The explicit inclusion of the solvent degrees of freedom is obviously limited by the available computational resources. A potential remedy to this problem is a microsolvation approach where only a few explicit solvent molecules are considered and surrounded by an implicit solvent bath. Still, the sampling of the solvent degrees of freedom is challenging with conventional grand canonical Monte Carlo methods, since no single chemical potential for the solvent molecules can be defined in the realm of small-system thermodynamics. In this work, a statistical thermodynamic model based on the grand canonical ensemble is proposed that avoids the conventional system size limitations and accurately characterizes the properties of the system of interest subject to the thermodynamic constraints of the bath. We extend an existing microsolvation approach to a generalized multibath "microstatistical" model and show that the previously derived approaches result as a limit of our model. The framework described here is universal and we validate our method numerically for a Lennard-Jones model fluid.
缺乏一种确定与浴相互作用的小系统平衡热力学性质的方法，这在传统统计力学中经常被视为一种弱点。这种小系统的一个典型例子是被明确定义的溶剂壳包围的溶质。解决这个问题的一种方法是将感兴趣的小系统封闭在大量的明溶剂分子浴中，这个浴比系统本身大得多。溶剂自由度的明确包含显然受到可用计算资源的限制。一种潜在的补救方法是微溶剂化方法，其中只考虑少数几个明溶剂分子，并被一个隐式溶剂浴包围。然而，用传统的巨正则蒙特卡罗方法对溶剂自由度进行采样具有挑战性，因为在小系统热力学的范围内，无法为溶剂分子定义单一的化学势。在这项工作中，提出了一种基于巨正则系综的统计热力学模型，该模型避免了传统的系统尺寸限制，并在浴的热力学约束下准确地描述了感兴趣系统的性质。我们将现有的微溶剂化方法扩展到广义多浴“微统计”模型，并表明以前推导的方法是我们模型的一个极限。这里描述的框架是通用的，我们使用 Lennard-Jones 模型流体对我们的方法进行了数值验证。
