Lifetimes of local and hyperspherical vibrational resonances of ABA molecules

Abstract

The complete spectrum of vibrationally excited ABA* molecular resonance lifetimes is evaluated using the simple Rosen–Thiele–Wilson model of coupled Morse oscillators. Two complementary methods are used: First, unimolecular dissociative resonance wave functions are propagated in time by the Fourier method, where the initial wave functions are obtained as an approximation by linear combinations of symmetry-adapted products of Morse functions. Second, bimolecular reaction S matrices are propagated along the hyperspherical radius of the system giving the diagonalized lifetime matrix, which is analyzed for resonance lifetimes and energies. The resulting uni- and bimolecular resonance energies agree within ±0.002 eV and the lifetimes within ±30%. Uni- and bimolecular assignments of gerade (+) and ungerade (−) ABA* symmetries agree perfectly. On the average, the unimolecular decay times decrease as the resonance energies increase from the ABA*→A+BA to about 3/4 of the A+B+A dissociation threshold; even more highly excited resonances tend to be slightly more stabilized. Superimposed on this overall nonmonotonous energy dependence is a strong, 1–2 orders of magnitude variation of lifetimes, indicating substantial mode selectivity for the decay of individual resonances, irrespective of the excitation energy. The mode selectivity is investigated for hyperspherical mode resonances with lobes extending across the potential valleys, in contrast with local mode resonances with frontier lobes pointing towards the valleys. On the average, hyperspherical mode resonances decay at a slower rate than local mode resonances. This conclusion agrees with our previous analysis of low energy ABA* resonances, and with Hose and Taylor’s analysis of the Hénon–Heiles system. However, these correlations are also violated by several important exceptions: the ABA* system has many slowly, but also a few rapidly, decaying hyperspherical resonances.