Eduardo Vilallonga

Calculation of scattering wave functions by a numerical procedure based on the Mo/ller wave operator

We present a procedure that numerically evaluates the scattering wave function. The solution to the time‐independent Schrodinger equation is calculated by a novel combination of: (a) the Mo/ller operator of scattering theory, (b) time‐dependent wave packets whose shape is unconstrained, and (c) efficient wave packet propagation on a dynamically‐adapted grid. The superposition of packets appropriate to the scattering boundary conditions yields the full wave function, from which scattering amplitudes are then obtained. Since the procedure does not make use of basis‐set expansions, its computational cost is independent of the number of open channels. It explicitly calculates the wave function not only in the asymptotic region but also within the interaction region, so it allows one to evaluate additional information beyond the scattering amplitude, as well as the functional sensitivity of transition probabilities with respect to changes in the potential. Applications here are illustrated by two simple exampl...

Vibrational energy transfer at the gas–solid interface: The role of collective and of localized vibrational modes

We present a study of energy transfer (kinetic to vibrational) in collisions of atoms with diatomic molecules adsorbed on the surface of a metal substrate, for hyperthermal collision energies (0.1 to 1.0 eV). In order to make the many‐body problem computationally tractable, atomic motions are restricted to one spatial dimension and the combined diatomic‐metal target is modeled by a linear chain of coupled harmonic oscillators, so that vibrations of the target can be solved analytically for any arbitrary number of atoms. The collision is described in the semiclassical limit appropriate for hyperthermal velocities: translation of the projectile is obtained from a classical trajectory, while vibration of the target is treated quantum mechanically. The intensity of scattered atoms is obtained from the time‐correlation function of the semiclassical transition operator. As a result, the intensity is evaluated analytically without need of internal‐state expansions, and it includes the quantum‐statistical average...

A hybrid model for vibrational energy transfer at the gas–solid interface: Discrete surface atoms plus a continuous elastic bulk

We introduce a discrete‐continuum hybrid treatment of solid vibrations in order to describe the collisional excitation of adsorbate and defect modes by atom impacts. The inhomogeneous surface is represented by: (a) one or more atom clusters corresponding to the defect sites and their immediate neighbors, which are harmonically coupled to (b) an elastic continuous bulk. The model thus aims at reproducing the long‐wavelength spectrum of the lattice as well as the high‐frequency localized modes contributed by adsorbates and surface defects. The hybrid model is tested against lattice results in one‐dimensional simulations that allow for analytic solution of the surface motion (which would be unfeasible for three‐dimensional imperfect lattices); hybrid and lattice results are thus compared in detail under identical conditions. The model is also evaluated under the worst possible conditions for the continuum approximation, since collinear collisions correspond to three‐dimensional situations in which the transf...

Multiquantum vibrational energy transfer into adsorbates on solid surfaces by atomic collisions: A semiclassical treatment based on dynamical correlations

A semiclassical treatment for vibrational excitation of adsorbates on surfaces by atomic collisions in the superthermal energy regime (0.5≲E≲5 eV), which was introduced previously in one dimension [Vilallonga and Rabitz, J. Chem. Phys. 85, 2300 (1986)], is here extended to three dimensions. The projectile motion is represented in the limit of short de Broglie wavelengths, i.e., by classical trajectories and their associated phases, whereas adsorbate–surface vibrations are treated quantum mechanically. Using the Feynman‐path integral representation of the transition operator, this limit is approached in a flexible way that does not require a priori assumptions about the gas–surface potential and allows for strong surface corrugation, e.g., due to molecules adsorbed at low surface coverage. Distributions of transferred energies are approximated nonperturbatively by algebraic methods using time‐correlation functions of the semiclassical transition operator. A large number of energetically open states are thu...

Multiquantum vibrational energy transfer into surface Rayleigh, bulk shear, and pressure waves by atom–solid‐surface collisions: A discrete‐continuum hybrid treatment with applications to He–Pt(111)

A discrete‐continuum hybrid treatment is developed for energy transfer into solid‐surface vibrations by atomic collisions. Surface vibrations are described in terms of the displacement field of a three‐dimensional elastic continuum with a stress‐free boundary. The displacement field is evaluated discretely at the surface lattice sites and it is quantized by the standard methods for harmonic vibrations. This hybrid approach can extend classical Debye models to incorporate surface corrugation, lattice structure, and the Bose–Einstein statistics of phonons. The treatment is illustrated on He scattering from Pt(111) at superthermal collision energies, e.g., E=0.5 eV, to probe the repulsive cores of the gas–surface potential. Accordingly, the projectile motion is approximated by classical trajectories, whereas all vibrational modes are treated quantum mechanically. The differential (in final angles and transferred energy) scattered intensity is obtained from time‐correlation functions of the semiclassical tran...

Sensitivity of elastic gas–surface scattering to the potential: A functional sensitivity approach based on wave packet dynamics

Functional sensitivity analysis is used to study the effect of potential structure upon the elastic scattering of He atoms from a one‐dimensional surface. The calculations are implemented by computing the total scattering wave functions from a wave packet calculation by a Mo/ller wave operator method. The functional sensitivities of the various diffraction probabilities for several angles of incidence and surface corrugation are studied. The method is extended to examine the role of potential structure for a surface with adsorbed impurities. It was observed that the various diffraction processes draw from local regions of the potential in very different ways. At high angles of incidence for back scattering and particularly for strong surface corrugation, the large protruding portions of the surface cast a ‘‘shadow’’ of lower dynamical sensitivity. Results of this type should ultimately be insightful for the inversion of experimental data to obtain the interaction potential.

The calculation of time-correlation functions for molecular collisions

Abstract A general formalism relating cross sections to collisional time-correlation functions is applied to the calculation of energy transfer in molecular collisions. Basic aspects of the formalism are reviewed, followed by a detailed description of methods suitable for the calculation of quantal state-to-state cross sections. These methods are particularly useful in the description of scattering by large systems, or of systems with high total energies where expansions in target basis sets are unsuitable. We review applications of quantal time-correlation functions (TCFs) to vibrational-rotational energy transfer in molecular collisions. Doubly differential cross sections (in scattering angles and transferred energy) are obtained from Fourier transforms of TCFs of the transition operator by means of two complementary treatments: multiple-scattering expansions for impulsive energy transfer, and a semiclassical limit for short translational wavelengths. The TCFs are evaluated by operator algebra, yielding efficient computational procedures that incorporate large numbers of vibrational-rotational transitions. The treatments are thus well suited to scattering by complex polyatomic targets. Examples are given for inelastic scattering of atoms from diatomic and linear triatomic molecules at hyperthermal collision energies, and the calculated results are compared with experimental measurements. These methods are also applicable to scattering by solid surfaces and by adsorbates, and can include temperature effects. The review lists 140 references to related work on the formalism, methods of calculation and applications.

Mechanisms of collision-induced desorption of a physisorbed atom at superthermal energy: a multiple scattering study

Abstract A Faddeev-Watson multiple scattering approach to gas-surface collision-induced desorption is presented. The computational procedure is practical, yet allowing a fully quantum-mechanical treatment of gas-solid reactive scattering problems. The single plus double collision terms of the multiple collision series are included in the calculation, which provides a detailed description of the collision dynamics. The present study focuses on a simple model collision system: a heavy adsorbate on a rigid surface is ejected by a sufficiently energetic light projectile. Large differential cross sections are found when the amount of kinetic energy transferred from the projectile to the adsorbate coincides with that of a classical head-on elastic collision between two particles of the corresponding masses. In addition, when this energy transfer is a little over the binding energy of the bound state, double collisions analogous to classical off-center collisions, contribute significantly to the differential cross sections. Our results also show that qualitatively the differential cross sections reach their maxima when the incident energy is about twice the binding energy of the adsorbate, then stay approximately the same when the incident energy increases even further. In this work, the role of the form factor, which is the bound state wavefunction in momentum space, is investigated. It is found that the angular distributions of the scattered projectile and the ejected absorbate are very sensitive to the adsorbate form factor. Finally, a detailed comparison among the contributions to the differential cross sections from each of the multiple collision terms provides information about the relative importance of various collision-induced desorption mechanisms.

Sensitivity analysis of the potential for elastic gas-solid scattering from surface defects

Abstract The role of surface defects in elastic gas-solid collisions is investigated by means of a recently developed numerical procedure based on the Moller operator and wavepackets. Since the procedure explicitly evaluates the scattering wavefunction, it yields the probabilities for scattering from the given initial state into all possible final states as well as the sensitivity of the probabilities with respect to variations in the gas-surface potential. Probabilities and their functional sensitivities are calculated for a simulated Pt surface exhibiting various configurations of vacancies: isolated sites, “interacting” di-vacancies and closely-packed tri-vacancies. The functional sensitivities indicate which regions of the gas-defect-solid potential are most relevant to the scattering dynamics. The resultant physical insight should be ultimately helpful for inverting experimental data to obtain the interaction potential.

Atomic collisions with inhomogeneous solid surfaces: multiple scattering from surface defects and mixed overlayers

We employ the multiple-scattering expansion of the transition operator to evaluate the role of multiple collisions in elastic scattering of atoms from adsorbates on solid surfaces at superthermal energies (E ≳ 0.1 eV). The adsorbatesurface system is treated as a rigid-body model in the present work. Mixed-species periodic overlayers are considered as well as two-layer systems simultaneously involving periodic and non-periodic configurations. The calculated scattering patterns show rich structure due to the interference between waves scattered from different adsorbates. The enhanced sensitivity provided by wavevectors k ≳ 10 A−1 could be exploited for surface characterization by scattering experiments. We find that the single-collision approximation qualitatively reproduces the trends of the intensity with respect to final angles. Double-collision terms are evaluated with the pole approximation and found to play an important role in large transfers of parallel momentum.