Engineering Thermodynamics, Process & Energy Department, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology , Leeghwaterstraat 39, 2628CB Delft, The Netherlands.
Van't Hoff Institute for Molecular Sciences, University of Amsterdam , Science Park 904, 1098XH Amsterdam, The Netherlands.
J Chem Theory Comput. 2016 Apr 12;12(4):1481-90. doi: 10.1021/acs.jctc.5b01230. Epub 2016 Mar 9.
A new formulation of the Gibbs ensemble (GE) combined with the continuous fractional component Monte Carlo method is presented. In the proposed formulation, only a single fractional molecule per component is used instead of two in the original formulation by Shi and Maginn ( J. Comput. Chem. 2008 , 29 , 2520 - 2530 ). This has the following advantages: (1) one directly obtains chemical potentials, without using test particles. We show analytically that the expressions for the chemical potential are identical to those in the conventional Gibbs ensemble; (2) biasing is applied to each simulation box independently; (3) maximum allowed changes in the scaling parameter of intermolecular interactions can be chosen differently in each simulation box. Obtaining chemical potentials directly facilitates thermodynamic modeling using equations of state, and it can be used as an independent check to ensure that chemical equilibrium is achieved. As a proof of principle, our method is tested for Lennard-Jones (LJ) particles and the TIP3P-Ew water model. Results are compared with the conventional GE. Excellent agreement was found both for average densities and chemical potentials. In our new approach, the acceptance probability for molecule exchanges between the boxes is much higher (typically larger than 40% for LJ particles) than for the conventional GE (typically lower than 2% for LJ particles). It is also shown that the contribution of the fractional molecule should be disregarded when computing ensemble averages such as the average energy per molecule and the average densities. The algorithm can be easily extended to mixtures and molecules with intramolecular interactions.
提出了一种新的吉布斯系综（GE）与连续分数组分蒙特卡罗方法的组合。在所提出的配方中，与 Shi 和 Maginn 的原始配方（J. Comput. Chem. 2008, 29, 2520-2530）相比，每个组分仅使用单个分数分子，而不是两个。这具有以下优点：（1）直接获得化学势，而无需使用测试粒子。我们分析表明，化学势的表达式与传统吉布斯系综中的表达式相同；（2）每个模拟箱独立施加偏压；（3）每个模拟箱中可以选择不同的最大允许改变分子间相互作用的标度参数。直接获得化学势有助于使用状态方程进行热力学建模，并且可以用作独立检查以确保达到化学平衡。作为原理证明，我们的方法已针对 Lennard-Jones（LJ）粒子和 TIP3P-Ew 水模型进行了测试。结果与传统的 GE 进行了比较。发现平均密度和化学势的结果都非常吻合。在我们的新方法中，分子在盒子之间交换的接受概率要高得多（对于 LJ 粒子通常大于 40％），而对于传统的 GE 通常低于 2％（对于 LJ 粒子）。还表明，在计算平均能量每个分子和平均密度等总体平均值时，应忽略分数分子的贡献。该算法可以轻松扩展到混合物和具有分子内相互作用的分子。
