Yu Tang-Qing, Chen Pei-Yang, Chen Ming, Samanta Amit, Vanden-Eijnden Eric, Tuckerman Mark
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
Department of Chemistry, New York University, New York, New York 10003, USA.
J Chem Phys. 2014 Jun 7;140(21):214109. doi: 10.1063/1.4878665.
The problem of predicting polymorphism in atomic and molecular crystals constitutes a significant challenge both experimentally and theoretically. From the theoretical viewpoint, polymorphism prediction falls into the general class of problems characterized by an underlying rough energy landscape, and consequently, free energy based enhanced sampling approaches can be brought to bear on the problem. In this paper, we build on a scheme previously introduced by two of the authors in which the lengths and angles of the supercell are targeted for enhanced sampling via temperature accelerated adiabatic free energy dynamics [T. Q. Yu and M. E. Tuckerman, Phys. Rev. Lett. 107, 015701 (2011)]. Here, that framework is expanded to include general order parameters that distinguish different crystalline arrangements as target collective variables for enhanced sampling. The resulting free energy surface, being of quite high dimension, is nontrivial to reconstruct, and we discuss one particular strategy for performing the free energy analysis. The method is applied to the study of polymorphism in xenon crystals at high pressure and temperature using the Steinhardt order parameters without and with the supercell included in the set of collective variables. The expected fcc and bcc structures are obtained, and when the supercell parameters are included as collective variables, we also find several new structures, including fcc states with hcp stacking faults. We also apply the new method to the solid-liquid phase transition in copper at 1300 K using the same Steinhardt order parameters. Our method is able to melt and refreeze the system repeatedly, and the free energy profile can be obtained with high efficiency.
预测原子晶体和分子晶体中的多晶型问题在实验和理论方面都构成了重大挑战。从理论角度来看，多晶型预测属于一类以潜在粗糙能量景观为特征的普遍问题，因此基于自由能的增强采样方法可用于解决该问题。在本文中，我们基于两位作者之前提出的一种方案进行构建，在该方案中，通过温度加速绝热自由能动力学 [T. Q. 于和 M. E. 塔克曼，《物理评论快报》107, 015701 (2011)] 对超胞的长度和角度进行增强采样。在此，该框架得到扩展，将区分不同晶体排列的一般序参量作为增强采样的目标集体变量。所得的自由能面维度相当高，重建起来并不简单，我们讨论了一种进行自由能分析的特定策略。该方法应用于使用施泰因哈特序参量研究高压和高温下氙晶体的多晶型，集体变量集里分别包含和不包含超胞。得到了预期的面心立方（fcc）和体心立方（bcc）结构，并且当将超胞参数作为集体变量包含在内时，我们还发现了几种新结构，包括具有六方密堆积（hcp）堆垛层错的面心立方态。我们还使用相同的施泰因哈特序参量将新方法应用于1300 K下铜的固液相变。我们的方法能够使系统反复熔化和重新冻结，并且可以高效地获得自由能分布。
