Study of structural phase transitions by first-principles molecular dynamics simulations at constant temperature and constant pressure condition

结合Car-Parrinello方法和Parrinello和Rahman提出的恒压方法，发展了一种研究共价或金属体系结构相变的第一性原理分子动力学模拟方法.在8 Si原子和64 Si原子系统中对该方法进行了验证，并在模拟中直接观察到了压缩和解压过程中的相变。在该方法的发展过程中，我们主要做了以下两个方面的工作：1.在Car-Parrinello方法中，离子的总动量不再守恒。但是，如果包含与波函数有关的量，守恒定律仍然成立。还研究了引入恒温器所引起的影响.为了真实地表示金属状态，应该允许部分占据能级。对几种方法进行了比较，认为用能量的费米分布来表示权重因子的方法是最稳定的，适合于动力学模拟，而与定压法相结合则大大增加了电子态计算的计算量。目前，高精度的模拟是非常困难的，在我们的模拟中观察到与实验结果的一些分歧。金属相的晶胞形状发生轻微变形，晶体对称性发生改变。通过结构相变获得的结构并不总是与已知结构一致。我们证实了增加布里渊区k点采样数和考虑能级的部分占据可以减小单胞的形变。

A first-principles molecular dynamics simulation method which enables the study of structural phase transitions in covalent or metallic systems is developed combining electronic state calculations by Car-Parrinello method and a constant pressure method proposed by Parrinello and Rahman. The method is tested in 8 Si atom and 64 Si atom systems and phase transitions are observed directly in simulations during compression or decompression processes.During the developing process of the method, we studied on following two themes.1. The total momentum of ions is no longer conserved in the Car-Parrinello method. But a conservation law is still held if quantities relating to wave functions are included. An effect caused by introduction of thermostats is also investigated.2. To express metallic states realistically, the partial occupation of energy levels should be allowed. Several methods are tested and we concluded that a method in which the weighting factor is expressed by Fermi distribution of the energy is most stable and suited for dynamical simulations.Costs for computation of electronic state calculations increase considerably by combination with a constant pressure method. Simulations with high accuracy is very hard at present and several disagreement with experimental results are observed in our simulations. The shape of a unit cell in metallic phases deforms slightly and the crystal symmetry is changed. Structures obtained via structural phase transitions do not always agree with known structures. We confirmed that the deformation of the unit cell decreases by increasing the number of k point sampling in Brillouin zone and taking into consideration partial occupation of energy levels.