用爱因斯坦分子方法计算分子固体的自由能：冰XIII和XIV，硬哑铃和蛋白质的斑块模型
Computing the free energy of molecular solids by the Einstein molecule approach: Ices XIII and XIV, hard-dumbbells and a patchy model of proteins
摘要：
将最近提出的爱因斯坦分子方法推广到计算分子固体的自由能。该方法是Frenkel和Ladd的爱因斯坦晶体方法的变体[J. Chem. Phys. 81，3188（1984）]。为了证明其适用性，我们计算了硬哑铃固体的自由能，最近发现的两种水的固相，即冰XIII和冰XIV，其中水分子之间的相互作用由刚性不可极化的TIP 4P/2005模型势描述，和几个固体相，是结晶稳定的各向异性斑块模型与八面体对称的模仿蛋白质。我们的计算表明，在统计不确定性范围内，爱因斯坦晶体方法和爱因斯坦分子方法得到了相同的结果，另外，我们还详细地研究了分子固体自由能计算中的一些微妙问题。首先，对于具有非立方对称性的固体，我们研究了模拟盒的形状对自由能的影响。我们的结果表明，必须使用模拟盒的平衡形状来计算自由能，以避免在系统中出现人为应力，这将导致自由能的增加。在复杂的固体中，例如水的固相，另一个困难与参考结构的选择有关。由于在某些情况下，分子没有明显的取向，因此不清楚如何产生参考结构。我们的结果将表明，只要结构不是太远的平衡结构，计算的自由能是不变的自由能计算中使用的参考结构。最后，还研究了固体自由能的强尺寸依赖性。
英文摘要：
The recently proposed Einstein molecule approach is extended to compute the free energy of molecular solids. This method is a variant of the Einstein crystal method of Frenkel and Ladd[J. Chem. Phys. 81,3188 (1984)]. In order to show its applicability, we have computed the free energy of a hard-dumbbells solid, of two recently discovered solid phases of water, namely, ice XIII and ice XIV, where the interactions between water molecules are described by the rigid non-polarizable TIP4P/2005 model potential, and of several solid phases that are thermodynamically stable for an anisotropic patchy model with octahedral symmetry which mimics proteins.Our calculations show that both the Einstein crystal method and the Einstein molecule approach yield the same results within statistical uncertainty.In addition, we have studied in detail some subtle issues concerning the calculation of the free energy of molecular solids. First, for solids with non-cubic symmetry, we have studied the effect of the shape of the simulation box on the free energy. Our results show that the equilibrium shape of the simulation box must be used to compute the free energy in order to avoid the appearance of artificial stress in the system that will result in an increase of the free energy. In complex solids, such as the solid phases of water, another difficulty is related to the choice of the reference structure. As in some cases there is not an obvious orientation of the molecules, it is not clear how to generate the reference structure. Our results will show that,as long as the structure is not too far from the equilibrium structure,the calculated free energy is invariant to the reference structure used in the free energy calculations. Finally, the strong size dependence of the free energy of solids is also studied.
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