Non-Hermitian quantum mechanics: Wave packet propagation on autoionizing potential energy surfaces

The correspondence between the time-dependent and time-independent molecular dynamic formalisms is shown for autoionizing processes. We demonstrate that the definition of the inner product in non-Hermitian quantum mechanics plays a key role in the proof. When the final state of the process is dissociative, it is technically favorable to introduce a complex absorbing potential into the calculations. The conditions which this potential should fulfill are briefly discussed. An illustrative numerical example is presented involving three potential energy surfaces.