Nucleation of Water Clusters in Gas Phase: A Computational Study Based on Neural Network Potential and Enhanced Sampling※

doi:10.6023/A22010003

Abstract

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

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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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Fig. & Tab. 7

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

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

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

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

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

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

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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