Semiclassical modeling of Rydberg wave-packet dynamics in diatomic molecules: Average decoupling theory

Abstract

The semiclassical dynamics of Rydberg electronic wave packets in diatomic molecules is investigated using a sum over classical trajectories method, which is based on the semiclassical form of Feynman's path integral. Our approach allows us to calculate intramolecular energy redistribution rates based on averaging of coupling parameters over classical trajectories associated with time-dependent parts of the overall system that exhibit different periodicities. The accuracy of our method is tested against perturbation theory and good agreement is obtained. A resonance structure in the computed autocorrelation function has also been observed in the case of rotating nuclei, when the periods of the classical trajectories of the electron match an integer multiple of the rotational period. This has previously been called the ''stroboscopic'' effect.

The role of phase in molecular Rydberg wave packet dynamics

“…I. 21 In fact, it is possible to mimic the results of the semiclassical calculations using our wave packet calculation. In the limit of high n and high rotational quantum numbers, both the electronic motion and nuclear rotation are classical.…”

“…Altunata et al have included phase to some degree in a semiclassical model of electron wave packets in a homonuclear diatomic molecule, in which they employ a sum over classical trajectories method. 21 The measurable quantity in these calculations is the autocorrelation function of the system, which can be considered as a probe of the state of the system. For the rotation of the core, the autocorrelation function is expressed as a sum over planar rotations, in the limit of high angular momentum quantum number, J, where the…”

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states

“…Two variants of a two-center potential have been considered, a truncated form and a self-consistent form with a very long history, the first of which has previously been used in modeling quantum defects for a range of polar Rydberg diatomics. Multi-center potentials are useful for Rydberg states of polar molecules in the intermediate range where the core rotational structure cannot be averaged because of the presence of core-Kepler stroboscopic resonances, 33,90 and where the internal structure leads to shape resonances. 104 The difference between the truncated and the full two-center potentials is two-fold: molecular anisotropy predictions are larger in the full form, as in Table V for BaF + , and inferred atomic polarizabilities are smaller in the full model than in the truncated model.…”

“…Rotation of the core produces resonances, including scattering from the cation mixing , formal interaction with dipole-bound levels, and rotation-electronic stroboscopic effects. 33,90 Combinations that have the same value using any origin along the symmetry axis, and thus are translationally invariant, are a convenient representation of the electrostatic potential. II.…”

Rydberg wave packets in molecules

“…21,22 On the other hand, investigation of both electronic and nuclear motion in Rydberg molecules has only recently begun to receive attention. [23][24][25][26][27][28][29][30][31] Rydberg wave packets in small molecular systems exhibit many of the dynamical complications found in large ' chemical ' molecules, for example, the high density of rovibronic energy levels with combined non-adiabatic couplings and competing discrete-continuum interactions of various sorts. There are already excellent reviews of molecular Rydberg states, 32 and their importance in ZEKE spectroscopy.…”