Efficient high-order operator-splitting schemes for solving the time-dependent Schrödinger equation

Several fourth-order symmetric operator-splitting schemes with four and five stages for solving the time-dependent Schrödinger equation have been proposed. These schemes have been studied and compared with some optimal fourth- and sixth-order operator split schemes reported in the literature using a one-dimensional model and several realistic three-dimensional triatomic reactive scattering problems in Jacobi coordinates. Two new fourth-order operator-splitting schemes with four and five stages, which are more efficient than previously reported schemes, are recommended for the realistic numerical solution of the time-dependent Schrödinger equation in the field of molecular dynamics. It was found that the order-preserving method proposed by McLachlan works well for three-dimensional triatomic reactive scattering problems in Jacobi coordinates, despite the complicated form of the Hamiltonian.