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 schrodinger 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.
We present photoelectron angular distribution of the aligned molecular ion H2^＋ by intense ultrashort attosecond extreme ultraviolet laser pulses from numerical solutions of timedependent Schrodinger equations. Photoionization from a superposition state of the ground 1sσg and the excited 2pσu states with pulses at photon energies above the ionization potential, hω〉Ip, and intensity 10^14 W/cm^2, yields pulse duration dependent asymmetry of photoelectron angular distributions. We attribute the asymmetry to the periodical oscillation of the coherent electron wave packets, resulting from the interference of the two electronic states. For the processes with long pulse durations, such duration dependence is absent and symmetric angular distributions are obtained.
