Application Of Symplectic Algorithm In MCTDH Method

MCTDH(Multiconfiguration time-dependent Hartree)is an efficient time-dependent approximate method in the study of the high-dimension molecular dynamic problems. The efficiency and accuracy of the MCTDH method strongly depends on the integration method used in solving the equations of the motion. Since the MCTDH equations of motion form a system of coupled non-linear differential equations of first order, the well-developed powerful integrators, such as the split-operator or the Chebyshev propagators, can't be used directly in MCTDH. It is quite important to search integration methods with high accuracy and stability for the improvement of the MCTDH method.Symplectic algorithm, which is widely used in classical mechanics, has been introduced to solve the time-dependent Schr?dinger equation. It has been proved to be a stable and highly efficient propagator, and easy to implement.In this work, symplectic algorithm was employed to solve the MCTDH equations of motion(symplectic MCTDH method for short), and was used to calculate the initial–state selected reaction probabilities of the H+H2,H+D2,Cl+H2 reactions. The results showed good performance on the accuracy and stability of long time propagation. Finally, brief discussions are presented on how to improve the efficiency of the symplectic MCTDH method.