The Construction And Application Of Several Propagators Of Time-Dependent Wave Packet Method

In recent several decades, time-dependent quantum wave packet method has obtained rapid development. However, it still challenge when deal with complex atom-diatom reaction and polyatomic reaction. So, it's very necessary to develop new numerical methods, make time-dependent quantum wave packet method more powerful to handle more complex reac-tion types. In the propagation of time-dependent wave packet, the main counting amount can attribute to multiply the transformation matrix. So, develop new propagator, increase the time step in the propagation, reduce the number of matrix multiply, is one of most significant way to decrease counting amount and improve numerical precision. In strong-field physics, coulomb singularity is always a hard nut to crack. The split operator, Crank-Nicolson differ-ence method and so on, can't deal with the problem which is aroused by coulomb singularity effectively. Based on the above issues, several new propagators have been constructed in this paper. The specific content of this paper is as follows:?1? Several high-order split operators which was constructed by second order spilt op-erator of TVT?kinetic-potential-kinetic? form have been test on several typical reactions ?H +H₂, H+H₂⁺, H+NH, H+O₂, F+HD?. The results have been compared with the high-order split operators which was constructed by VTV?potential-kinetic-potential? form second order split operator. Results indicate that except for the direct type reaction, numer-ical efficiency of the fourth order propagator 4A6a is always better in other type reactions. So, in the dynamic calculation we do not need to do so many test calculations to determine the optimal higher-order operator. We can simply choose the 4A6a propagator for a real reaction scattering calculation.?2? We applied the 4A6a propagator into the dynamic calculation of Li+HF/DF reaction which with the initial state ?v= 0. j= 0,1?. The reaction probabilities, integral cross section, differential cross section, ro-vibrational distribution of product and thermal rate constant are calculated at the state-to-state level of theory. These results are compared with previous theoretical investigations and experimental data. The results indicate that our data are well agreement with the experimental data and the 4A6a propagator has higher numerical efficiency.?3? The 4A6a propagator is also applied into the dynamic calculation of N+H₂ and its isotopic variants reactions. The reaction probabilities, integral cross section, differential cross section are calculated at the state-to-state level of theory. The rotational distribution of product for N+H₂ and its isotopic variants are compared with the experimental data for the first time and the results are excellent agreement with the experimental data. The thermal rate constant of N+H₂ and its isotopic variants are also compared with the experimental values. In the temperature range from 200 to 333 K, our results reproduced the experimental data.?4? In order to handle the problem of coulomb singularity of strong-field physics, an new propagator MCNSO has been constructed. Comparison with previous split operator, Crank-Nicolson difference method, the MCNSO propagator can deal with the problem of coulomb singularity more effectively. This propagator has higher precision and fit long time propa-gation. We adopted the MCNSO propagator calculate the high-order harmonic spectrum of H₂⁺ system with different intensity of laser for ten and sixteen optical circle. Three different models ?dipole acceleration, dipole moment, dipole velocity? are applied in the calculation of high-order harmonic spectrum and the comparison between them are carried out in detail.