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.

Observation of a transition state resonance in the integral cross section of the F+HD reaction

“…The resonance thus serves as a ''gatewaystate'' and, in fact, the only pathway through which all the reactive flux must pass. Such a reaction mechanism was implicit in the studies of collinear AϩBA model systems by Bisseling et al 52 In a resonance mediated reaction many of the characteristics of the reactive cross section can then be tied to the properties of the resonance. Specifically, the resonance energy, width, and partial widths can be used to characterize the full reaction dynamics at low energies.…”

State-Selective Control for Dissipative Vibrational Dynamics of HOD by Shaped Ultrashort Infrared Laser Pulses

“…As the target states for the ultrafast selective preparation, we choose, as in the previous work, the local OH state 23(5, 0), the local OD state 24(0, 7), and the symmetric state 26(3, 3), which have almost the same vibrational energies, see Figure . Selective preparation of local states is known to be important for mode- or bond-selective laser chemistry, while symmetric states are interesting from the viewpoint of developing strategies for selective preparation of high vibrational states with lifetimes different from those of the local states of similar energy. ,, …”

Time dependent wavepackets and periodic orbit assignment

“…The tick marks indicate the variationally determined eigenvalues, from which it is evident that all three wavepackets have significant overlap with the zeropoint energy state, but that they become more selective as the energy increases. For example, the type C wavepacket progressively selects only the lowest energy (most local [18,19]) component of each manifold and the type B wavepacket the highest energy (most normal [18,19]) or hyperspherical [26] component. The type A wavepacket, on the other hand, is less selective, a difference attributable to the unstable character of the type A orbit above E = 0-71, whereas the B and C type orbits are stable.…”