Application of symplectic algorithms to QCT calculation:H+H_2 system

The basic theory of symplectic algorithm was introduced. A comparison between Runge-Kutta method and symplectic integration method was preformed in the simulation of the long time behavior of H + H2 system on BKMP potential energy surface. Our results reveal a dis-sipative behavior in the integral of ordinary differential equation by the fourth order Runge-Kutta method, which causes incorrect simulation results in QCT calculations. However, when the symplectic integration method is applied, the dissipative behavior is not found in the same system. When the initial state is the same, the energy deviation of fourth order symplectic integral method is almost one percent of that of fourth order Runge-Kutta method in a 60000-step simulation, and that of sixth order symplectic integral method is much less. These results show that the symplectic integral methods are always the better choice in the integral calculation of the long time behavior in maintaining energy conservation.     

辛算法在准经典轨迹计算中的应用: H+H2体系

采用辛算法模拟了H + H₂在BKMP势能面上的长时间动力学行为, 并和Runge-Kutta方法计算的结果进行了比较.结果表明,采用Runge-Kutta方法模拟长时动力学行为时体系中出现动力学耗散行为,导致无法真实的模拟体系的物理实际;而采用辛算法模拟精确度更高,四阶辛算法误差只有Runge-Kutta法的约百分之一,六阶辛算法的误差则更小,体系中也未见动力学耗散行为.这些结果说明,在进行长时动力学行为模拟的时候,在保持体系能量守恒性上,辛算法应当是一种更好的积分方法.