Semiclassical Wave Packet Propagation Research Articles

Semiclassical wavepacket propagation in a hydrogen atom

A description of a new time dependent semiclassical theory for propagating wave packets is given in terms of Monodromy matrix elements. The nonlinear classical phase space aids in the obtainment of the semiclassical autocorrelation function, which for the case of a Coulomb potential is compared to its quantum analog.

Classical orbits and semiclassical wavepacket propagation in the Coulomb potential

A simple and elegant semiclassical theory for propagating wavepackets is presented. The development of the theory avoids the explicit use of the Green-function formalism. It involves expanding the potential to a quadratic time-dependent form and the use of multiple reference trajectories. The classical analogue in phase space predicts the accuracy of the results. The theory is applied to the calculation of the autocorrelation function in a Coulomb field in one dimension. Remarkable agreement with an exact quantum calculation is obtained in many circumstances in spite of the Coulomb singularity. All the detailed quantum behaviour, including the long-time recurrences and the spectrum, is reproduced.

Improved semiclassical propagation of wave packets

The time-dependent variational method is applied to develop a potentially exact wave packet propagation technique that systematically improves the semiclassical Gaussian treatment of Heller. Difficulties encountered in previous applications of the variational method are avoided. Numerical examples are presented which demonstrate the accuracy and convergence of the present approach.

Electron-stimulated desorption and surface species conversion: The observation of a desorption resonance for atomic oxygen on the Pd(111) surface

The influence of electron bombardment on an oxygen-covered Pd(111) surface at 87 and at 300 K has been studied by temperature programmed desorption. It is found that electron bombardment of an O2(a) adlayer at 87 K leads to the depletion of O2(a) and the conversion to O(a) with about the same cross sections, ∼1×10−17cm2 (Ve =200 eV). The O2(a)-depletion process is preferred at higher O2(a) coverage as the availability of open sites limits the O2(a) conversion. The new channel for conversion to O(a) due to electron bombardment results in a maximum increase of O(a) coverage by 88% and an additional desorption feature at 704 K compared to the usual temperature programmed desorption behavior due to O(a) recombination. The cross sections for desorption and conversion of O2(a) exhibit different electron energy dependence, suggesting that different primary electron excitations are involved in the two processes. The cross section for the electron-stimulated desorption of atomic oxygen is observed to be strongly dependent on electron energy, with its maximum value being ∼1.2×10−17 cm2 at an electron energy of 10±2 eV. The behavior of the cross section as a function of electron energy suggests the involvement of a surface resonance near 10 eV. A possible mechanism for resonance enhanced desorption is suggested, based on semiclassical wave packet propagation over potential energy curves which are consistent with the excitation spectrum of oxygen negative ions.

Exact time-dependent wave packet propagation: Application to the photodissociation of methyl iodide

We propose a technique for exact wave packet propagation by a straightforward extension of the semiclassical wave packet propagation procedure. This is an efficient method to calculate photodissociation, Raman, and resonance Raman scattering cross sections. It is applied to the photodissociation of CH3I. The potential surfaces for CH3I are those suggested by Shapiro and Bersohn [J. Chem. Phys. 73, 3810 (1980)]. The results that we obtained by this time-dependent approach differs significantly from those of Shapiro and Bersohn, where a time-independent technique is used to calculate the cross sections.

Classical trajectory approach to photodissociation: The Wigner method

A time-dependent semiclassical method for generating energy-dependent photodissociation partial cross sections is presented. The method is based on the Wigner equivalent formulation of quantum mechanics with the semiclassical limit arising from one dynamical approximation: the replacement of the quantum Liouville operator by its h/→0 limit. The results of the present scheme for the collinear dissociation of ICN on a single dissociative surface are compared to those obtained from a distorted-wave analysis and a semiclassical wave packet propagation. A model calculation employing standard trajectory techniques indicates that the present method has several distinct advantages over the traditional quasiclassical approach.