“…[15] To solve this problem, Patchkovskii et al have proposed a parallel method, [18] and achieved the spa-tial derivatives of the radial coordinate by using the finitedifference method (FDM), which leads to an increase in the grids for the larger sized problem, [17] and finally significantly increasing the amount of computation in the case of higher accuracy. [19] Guan et al solved TDSE of two-electron quantum system in spherical coordinates efficiently based on the finite-element (FE) discrete-variable-representation (DVR) and Short-Iteration-Lanczos (SIL) propagator, [20] because the FE-DVR can offer higher computing accuracy [21] and make the Hamiltonian matrix very sparse, whose effects are similar to those provided by the B-spline [22,23] and sine-DVR, [24] and the efficiency of the wave function evolution strongly relies on the sparsity of the Hamiltonian matrix for the SIL propagator. [25] The most ideal structure of the Hamiltonian matrix is expected to have diagonal or similarly sparse elements for the SIL propagator.…”