基于神经网络势与增强采样的气相水团簇成核过程研究※

doi:10.6023/A22010003

摘要/Abstract

由于气相分子密度低, 对气相成核过程的理论模拟往往需要很大的计算量. 为了提高模拟效率, 本工作将神经网络势与增强采样技术结合, 并以水团簇成核为例进行了研究. 采用密度泛函理论方法对不同尺寸的水团簇进行了能量和力的计算, 并由此训练出一套能较好描述水团簇体系相互作用的神经网络势. 将这个势应用于蒙特卡洛模拟并结合多种增强采样方法, 实现了在不同尺寸水团簇之间的随机行走, 由此可得到水团簇在特定条件下的概率分布以及吉布斯自由能. 通过后续的蒙特卡洛模拟结合伞形采样和变分过渡态理论, 可以进一步计算出不同水团簇的水分子蒸发速率. 观察到了四聚体到五聚体的自由能和蒸发速率的突变现象. 结构分析表明虽然五聚体的最低能量构型是二维环状结构, 但是在有限温度下五聚体中三维氢键网络已经开始形成. 这导致了在四聚体过渡到五聚体时的异常. 本工作提供的第一性原理精度下对气相水团簇成核进行研究的方法可以推广到更为复杂的多组分体系, 为研究大气颗粒物形成机理奠定了基础.

关键词: 神经网络, 蒙特卡洛, 水, 成核, 增强采样

Due to their low density in atmosphere, theoretical simulations of the nucleation of gas-phase molecules are computationally very expensive. In this study, neural network potential (NNP) is combined with enhanced sampling techniques to effectively investigate the nucleation of water clusters in gas phase. The neural network potential is trained based on water-cluster energies and forces from density functional theory (DFT). The problem that the binding between water molecules is too weak in the previous empirical force field model has been solved in the NNP. This NNP potential is then applied to Monte Carlo simulations in grand canonical ensemble with enhanced sampling methods such as aggregation-volume-bias Monte Carlo (AVBMC) and transition-matrix Monte Carlo (TMMC) to realize a random walk among different cluster sizes. Probability distribution of water cluster sizes and the corresponding Gibbs free energies can then be obtained. Subsequently, the evaporation rates of water clusters can be calculated via umbrella sampling Monte Carlo simulations in canonical ensemble combined with variational transition state theory (VTST). We observe a big change of free energy and evaporation rate from tetramer to pentamer. A statistical analysis of the number of hydrogen bonds suggests that more hydrogen bonds are required to be broken in the evaporation reaction of tetramer compared to that of trimer and pentamer. Structure analysis indicates that, although the ground state of the pentamer has a two-dimensional ring structure, three-dimensional hydrogen bond network begins to form in pentamer at finite temperature. Therefore, it is a two-dimensional to three-dimensional transition from tetramer to pentamer. The fact that the most probable configuration of pentamer is different from the lowest energy configuration demonstrates the importance of molecular simulations. Simply finding the lowest energy configuration via global geometry optimization and then calculating the free energy within a harmonic approximation of vibrations are not a universal protocol for cluster systems. Methods used in this study are expected to be applicable for more complicated multicomponent systems, which opens an avenue for the research of particulate matter formation in atmosphere.

Key words: neural network, Monte Carlo, water, nucleation, enhanced sampling

引用此文

徐森, 吴丽铃, 李震宇. 基于神经网络势与增强采样的气相水团簇成核过程研究^※[J]. 化学学报, 2022, 80(5): 598-606.

Sen Xu, Liling Wu, Zhenyu Li. Nucleation of Water Clusters in Gas Phase: A Computational Study Based on Neural Network Potential and Enhanced Sampling^※[J]. Acta Chimica Sinica, 2022, 80(5): 598-606.

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图/表 7

图1. 十个水分子组成的团簇神经网络势与第一性原理能量与力的对比图

Figure 1. Comparison of (a) energies and (b~d) forces from neural network potential (NNP) and DFT for the cluster with ten water molecules

图2. (a) 自由能随着水团簇尺寸的变化. (b) 巨正则系综平均增长和衰减概率随团簇尺寸的变化

Figure 2. (a) Gibbs free-energy and (b) grand canonical average growth and decay probabilities as a function of cluster size

Cluster	(H₂O)₂	(H₂O)₃	(H₂O)₄	(H₂O)₅	(H₂O)₆	(H₂O)₁₀
r_cut/Å	2.56	4.10	5.03	5.45	6.11	7.530
Rate constant/ (×10⁹ s^-1)	159.70	25.52	2.86	9.56	7.39	1.965

表1. 300 K下水团簇截断半径与蒸发速率常数

Table 1. Cutoff radii and evaporation rate constants of water clusters at 300 K

图3. 300 K下水团簇(H2O)n (n=2~6, 10)的(a) O—O径向分布函数和(b) OH—O角度分布函数

Figure 3. (a) Oxygen-oxygen distance and (b) OH—O angle distributions of (H2O)n (n=2~6, 10) at 300 K

图4. 300 K下(H2O)n (n=2~6, 10)不同氢键数目构型能量分布

Figure 4. Energy distribution of (H2O)n (n=2~6, 10) configurations with different numbers of hydrogen bonds at 300 K

Hbond number	2	3	4	5	6	10
IS	0.5	1.9	3.7	4.7	6.0	12.0
TS	0.0	0.6	1.8	3.6	4.6	10.0
Break Hbond	0.5	1.3	1.9	1.1	1.4	2.0

表2. 300 K下(H2O)n (n=2~6, 10)团簇蒸发反应物(IS)、过渡态(TS)氢键平均数目和蒸发过程打破氢键数目

Table 2. Average number of hydrogen bonds in reactants (IS), transition state (TS) and break hydrogen bond number of the evaporation reaction in (H2O)n (n=2~6, 10) at 300 K

图5. 300 K下(H2O)n的最概然结构. (a) n=3, (b) n=4, (c) n=5, (d) n=6

Figure 5. Most probable conformers of (H2O)n cluster at 300 K. (a) n=3, (b) n=4, (c) n=5, (d) n=6

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