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An Exact Propagator for Solving the Triatomic Reactive Schrödinger Equation
Xue-ming Li,Zhi-gang Sun*
Author NameAffiliationE-mail
Xue-ming Li State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China;University of Chinese Academy of Sciences, Beijing 100049, China  
Zhi-gang Sun* State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, China zsun@dicp.ac.cn 
Abstract:
The exact short time propagator, in a form similar to the Crank-Nicholson method but in the spirit of spectrally transformed Hamiltonian, was proposed to solve the triatomic reactive time-dependent schrödinger equation. This new propagator is exact and unconditionally convergent for calculating reactive scattering processes with large time step sizes. In order to improve the computational efficiency, the spectral difference method was applied. This resulted the Hamiltonian with elements confined in a narrow diagonal band. In contrast to our previous theoretical work, the discrete variable representation was applied and resulted in full Hamiltonian matrix. As examples, the collision energy-dependent probability of the triatomic H+H2 and O+O2 reaction are calculated. The numerical results demonstrate that this new propagator is numerically accurate and capable of propagating the wave packet with large time steps. However, the efficiency and accuracy of this new propagator strongly depend on the mathematical method for solving the involved linear equations and the choice of preconditioner.
Key words:  Time-dependent wavepacket method  Spectral difference  Spectrally transformed Hamiltonian  Exact short time propagator  Reactive scattering
FundProject:This work was supported by the National Natural Science Foundation of China (No.21222308, No.21103187, and No.21133006), the Chinese Academy of Sciences, and the Key Research Program of the Chinese Academy of Sciences.
一种精确求解三原子反应散射的传播子
李学明,孙志刚*
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DOI:10.1063/1674-0068/30/cjcp1711220
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