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

将Car-Parrinello方法的电子态计算与Parrinello和Rahman提出的恒压方法相结合，发展了一种能够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。该方法在8Si原子和硅原子系统中进行了测试，在模拟中直接观察到了压缩或解压缩过程中的相变。在Car-Parrinello方法中，离子的总动量不再守恒。但是，如果包括与波函数有关的量，守恒定律仍然成立。文中还研究了引入恒温器所引起的影响。为了真实地表达金属状态，应该允许部分占据能级。对几种方法进行了测试，结果表明，用能量的费米分布表示权因子的方法是最稳定的，适合于动态模拟。与恒压方法相结合，电子态计算的计算成本大大增加。目前，高精度的模拟是非常困难的，在我们的模拟中观察到了一些与实验结果不一致的情况。金属相中的晶胞形状略有变形，晶体对称性发生变化。通过结构相变获得的结构并不总是与已知结构一致。通过增加布里渊区的k点采样次数和考虑能级的部分占据，我们证实了晶胞的形变减小。

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.