标题： 冰 Ih、II 和 III 的相图：准谐波研究 显示英文标题

标题： The phase diagram of ice Ih, II, and III: a quasi-harmonic study

摘要： 冰 Ih、II 和 III 的相图通过准谐波近似进行研究。 这种方法的结果与之前通过路径积分和经典模拟的热力学积分得出的相图以及实验数据进行了比较。 所研究的模型基于水分子的柔性（q-TIP4P/F）和刚性（TIP4P/2005，TIP4PQ/2005）描述。 准谐波近似能够合理地再现模拟相图的许多方面。 这种简单方法的优势在于它不受计算机模拟固有的统计误差的影响，同时经典和量子极限都易于访问，并且该近似的误差预计在零温度极限下会减小。 我们发现，计算得到的冰 Ih、II 和 III 的相图强烈依赖于冰 III 的氢无序，至少对于相共存模拟中通常使用的晶胞大小而言。 根据冰 III 中质子无序的情况，冰 II （在经典极限下）或冰 III（在量子极限下）可能会变得不稳定。 量子和经典极限的比较表明，冰 II 的稳定化是相图中最重要的量子效应。 与冰 Ih 或 III 相比，冰 II 的较低振动零点能是这种稳定化的微观原因。 讨论了对冰 III 的质子无序进行晶格能量平均的必要性。 显示英文摘要

摘要： The phase diagram of ice Ih, II, and III is studied by a quasi-harmonic approximation. The results of this approach are compared to phase diagrams previously derived by thermodynamic integration using path integral and classical simulations, as well as to experimental data. The studied models are based on both flexible (q-TIP4P/F) and rigid (TIP4P/2005, TIP4PQ/2005) descriptions of the water molecule. Many aspects of the simulated phase diagrams are reasonably reproduced by the quasi-harmonic approximation. Advantages of this simple approach are that it is free from the statistical errors inherent to computer simulations, both classical and quantum limits are easily accessible, and the error of the approximation is expected to decrease in the zero temperature limit. We find that the calculated phase diagram of ice Ih, II, and III depends strongly on the hydrogen disorder of ice III, at least for cell sizes typically used in phase coexistence simulations. Either ice II (in the classical limit) or ice III (in the quantum one) may become unstable depending upon the proton disorder in ice III. The comparison of quantum and classical limits shows that the stabilization of ice II is the most important quantum effect in the phase diagram. The lower vibrational zero-point energy of ice II, compared to either ice Ih or III, is the microscopic origin of this stabilization. The necessity of performing an average of the lattice energy over the proton disorder of ice III is discussed.