Resonance energies, lifetimes and complex energy potential curves from standard wave-packet calculations

We show here for a simple model system that the wavepacket dynamics in the interaction region can be described by a superposition of the non-Hermitian exponential divergent eigenfunctions of the physical Hamiltonian. We demonstrate how it is possible to obtain the complex eigenvalues and also the corresponding resonance eigenfunctions from the propagation of the wavepacket within the framework of the standard formalism of quantum mechanics. The general results demonstrated here for a simple model can lead to two different types of computational applications: (i) for systems where one can obtain the resonance energies and lifetimes as well as their corresponding eigenfunctions it is possible to study the evolution of the physical properties solely based on the initially populated resonance states without the need to propagate the wavepacket; (ii) for molecular systems where it is quite difficult to solve the non-Hermitian time-independent Schrdinger equation and obtain molecular resonance energies and functions. For this type of problem, the methods presented here enable one to evaluate the topology of complex potential energy surfaces from the wavepacket propagation and facilitate the study of the nuclear dynamics of ionizing molecular systems.