Effective Phase Space Representation of the Quantum Dynamics of Vibrational Predissociation of the ArBr₂(B,ν =16···25) Complex

Abstract

We perform trajectory-based simulations of the vibrational predissociation of the ArBr2(B,ν=16···25) van der Waals triatomic complex, constrained to the T-shape geometry. To this aim, we employ a 2-fold mapping of the quantum dynamics into classical-like dynamics in an extended phase space. The effective phase space comprises two distinct sets of degrees of freedom, namely a collection of coupled harmonic oscillators and an ensemble of quantum trajectories. The time evolution of these variables represent bound and unbound motions of the quantum system, respectively. Quantum trajectories are propagated within the interacting trajectory representation. The comparison between the lifetimes of the predissociating complexes computed using the trajectory-based approach and the experimental results available for the target systems indicates that the present method is competitive with wavepacket propagation techniques. The competition between several simultaneous vibrational relaxation pathways was found to have a direct impact on the time scales of vibrational predissociation. Likewise, the analysis of the time evolution of the trajectories reveals the existence of regions in the effective phase space where transitions to vibrational states of higher energy are more likely to occur. The size and location of these regions influence the transient vibrational distributions and therefore the computed lifetimes. Furthermore, the mechanisms of energy redistribution along the dissociation coordinate are analyzed.

Factorized Electron–Nuclear Dynamics with an Effective Complex Potential

“…The two definitions of V i , eqs 19 and 27 derived from the requirements on the probability densities of eqs 3 and 5, respectively, are equivalent if p p = (28) This means that (from eq 18) the trajectory evolves according to the nuclear momentum p t of the f ull wave function Ψ, averaged and normalized over the electronic DOF,…”

“…A multitude of trajectory-based or trajectory-inspired methods, incorporating the NQEs approximately, often through the trajectory interaction or dynamics in extended spaces, have been developed, such as semiclassical initial value representation, , ring-polymer molecular dynamics, − approximate quantum trajectory methods, and approximate path-integral methods . There are trajectory-based yet (in principle) exact methods such as guided Gaussian methods − and accurate implementations of the quantum trajectory dynamics. − …”

Interacting trajectory representation of quantum dynamics: influence of boundary conditions on the tunneling decay of resonant states

“…(8) These approximated quantum potential and quantum force were previously used to study some representative onedimensional problems, where important quantum effects such as zero point energy, barrier tunneling and scattering, intramolecular vibrational relaxation, were accurately described using a moderately large number of interacting trajectories (i.e. a few hundreds) [53,56]. In this contribution, we will solve the equations of motion (3) for the quantum trajectories, using the approximation (7) for the quantum potential, to study the decay of a state initially localized in one side of a double well potential (via tunneling of the intermediate barrier) and of a shape resonance in one-dimension.…”

“…This interacting trajectory representation (ITR) of the QTM has been successfully applied to model problems, and shown to accurately reproduce important quantum effects such as zero point energies on harmonic and anharmonic potentials, as well as the tunneling through a barrier, among other quantum-mechanical effects [51,[54][55][56]. Worthy to note, similar approaches, based on the propagation of ensembles of entangled or interdependent trajectories have been introduced for the solution of the quantum Liouville equation [57], and in the context of fractional dynamics [58].…”