The predissociation dynamics of vibrational eigenstates in the A [formula omitted] state of HBr + ions: numerical solution of coupled time-dependent Schrödinger equations

Abstract

The predissociation dynamics of the vibrational eigenstates of hydrogen bromide ions (HBr +) in the first excited electronic state A 2 Σ + which occurs via coupling to three repulsive ( 4 Σ − , 2 Σ − , and 4 Π ) states has been investigated by direct solution of four coupled time-dependent Schrödinger equations. The analysis shows multi-exponential decay for most of the predissociating vibrational states. The lifetime of these states decreases by several orders of magnitude from τ v=2 ≫1 ns to τ v=5 ≈17 fs. For even higher vibrational states lifetimes are increasing again up to the order of 100 fs. The contribution of the individual repulsive states to the predissociation dynamics is found to change as a function of time and of the vibrational level. The competition between the contributions of the repulsive states is most important during the first ∼10 fs. Beyond this one repulsive state in general dominates. Finally the shifting of vibrational `eigenenergies' of the A 2 Σ + state by spin–orbit interaction and their broadening due to the fast predissociation are analyzed.