沿着熵路径的晶体成核：教导液体如何转变
Crystal nucleation along an entropic pathway: Teaching liquids how to transition
摘要：
我们结合机器学习（ML）和蒙特卡罗（MC）模拟来研究晶体成核过程。使用ML，我们评估了结晶过程中密度和温度范围内系统的正则配分函数。我们实现这一点的例子中的Lennard-Jones系统通过训练人工神经网络使用，作为参考数据集，状态方程的亥姆霍兹自由能的液相和固相。ML预测的准确性进行了测试，在很宽的范围内的热力学条件下，结果显示，提供一个准确的估计为典型的配分函数，当从平面直方图模拟的结果相比。然后，ML预测被用来计算系统的熵在MC模拟等温等压系综。这种方法所产生的结果与氩的液相和固相的实验数据非常吻合。最后，以熵为反应坐标，利用伞形取样技术，我们能够确定晶体成核过程的吉布斯自由能分布。特别是，我们得到了一个自由能垒非常好的协议，从以前的模拟研究的结果。这里开发的方法可以很容易地扩展到分子系统和复杂的流体，是特别有前途的熵驱动过程的研究。
英文摘要：
We combine machine learning (ML) with Monte Carlo (MC) simulations to study the crystal nucleation process. Using ML, we evaluate the canonical partition function of the system over the range of densities and temperatures spanned during crystallization. We achieve this on the example of the Lennard-Jones system by training an artificial neural network using, as a reference dataset, equations of state for the Helmholtz free energy for the liquid and solid phases. The accuracy of the ML predictions is tested over a wide range of thermodynamic conditions, and results are shown to provide an accurate estimate for the canonical partition function, when compared to the results from flat-histogram simulations. Then, the ML predictions are used to calculate the entropy of the system during MC simulations in the isothermal-isobaric ensemble. This approach is shown to yield results in very good agreement with the experimental data for both the liquid and solid phases of Argon. Finally, taking entropy as a reaction coordinate and using the umbrella sampling technique, we are able to determine the Gibbs free energy profile for the crystal nucleation process. In particular, we obtain a free energy barrier in very good agreement with the results from previous simulation studies. The approach developed here can be readily extended to molecular systems and complex fluids, and is especially promising for the study of entropy-driven processes.
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