用辛格式计算水分子的经典运动轨迹

本文应用辛算法计算了水分子的经典运动.基于经典模型,采用J. N Murrell et al. 给出的水分子基态势能函数,在质心坐标系中推导了水分子的正则坐标与共轭正则动量和Hamilton正则方程,应用辛格式计算了水分子的经典轨迹和能量,并与Runge- Kutta法做了比较.结果显示,辛算法计算至10-9s仍能保持系统能量守恒,与理论和实验一致;Runge-Kutta法则不然,系统能量变化很快,与理论和实验不符.

Computing Classical Trajectories of H2 O Molecule by Symplectic Algorithm

Classical movement of H2O molecule is computed by simplectic algorithm in this paper. On the basis of classical model and H2O molecule potential function proposed by J. N. Murrell et al, the canonical coordinates and canonical moment as well as Hamilton canonical equations in mass center coordinates have been deduced, classical trajectories and energy of H2O molecule have been computed. The computed result is compared with the result computed by Runge - Kutta method . The computed results indicate that simplectic scheme can keep energy of H2O system conservative, which is consistent with theory and experiments, in 10^ -9 second ; but energy computed by Runge - Kutta method is changing quickly with time, which is not consistent with theory and experiments.