Time dependent quantum mechanics using picosecond time steps: Application to predissociation of HeI2

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Abstract
Time‐dependent quantum mechanics has proved to be a useful conceptual and calculational tool for a wide range of femtosecond time scale processes. In this paper we develop a method of extending time‐dependent methodology to processes taking many picoseconds, through use of the interaction representation of quantum mechanics. Two implementations are presented, one in the energy frame and one in the coordinate frame; both of these implementations scale as N2 with the number of basis functions, as opposed to N3 for a matrix diagonalization. The interaction representation approach allows the use of time steps much greater than those that can be used in the Schrödinger representation, and is expected to be useful for the broad class of problems where the Hamiltonian can be partitioned into H0+V, where V≪H0. Converged quantum mechanical results are presented for the predissociation of T‐shaped HeI2 from highly excited vibrational levels, for times up to 200 ps.