Efficient method for simulating quantum electron dynamics under the time-dependent Kohn-Sham equation

A numerical scheme for solving the time evolution of wave functions under the time-dependent Kohn-Sham (TDKS) equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective Hamiltonian should evolve consistently with each other. For this purpose, a self-consistent loop is required at every time step for solving the time evolution numerically, which is computationally expensive. However, in this paper, we develop a different approach, expressing a formal solution of the TDKS equation, and prove that it is possible to solve the TDKS equation efficiently and accurately by means of a simple numerical scheme without the use of any self-consistent loops.