Complex integration steps in decomposition of quantum exponential evolution operators

We generalize previous high-order exponential split operator methods for solving time-dependent Schroedinger equations [A.D. Bandrauk, H. Shen, Chem. Phys. Lett. 176 (1991) 428] by introducing complex integration steps (a + ib) with real positive part a. We show that this new procedure avoids real negative steps which occur generally in high-order split operator methods. New highly accurate splitting schemes are thus derived and the efficiency of these is demonstrated in the calculation of the eigenstates of the one-electron molecular ion H 2 + .