Classical theory for scattering of rigid molecules from surfaces

Abstract

A theoretical model is presented for the scattering of molecules from surfaces under conditions in which the major modes of energy transfer are multiple phonon excitation at the surface and rotational excitations of the molecule. Beginning from a completely quantum mechanical formalism, the classical limit is obtained for large mass molecules and large energies and in this limit the result is a closed-form expression for the scattering intensities. Results of calculations are compared with recent measurements for the scattering of hyperthermal beams of C 2 H 2 from a LiF(0 0 1) surface. The results of these comparisons indicate that a classical theoretical treatment of translational and rotational motion is adequate for describing this system. Ó 2002 Elsevier Science B.V. All rights reserved.In this paper a theoretical model is developed for the scattering of rigid molecules from surfaces where the modes of energy exchange are multiphonon excitation of the surface and rotational excitation of the molecule and both are treated in the classical mechanical limit. Classical mechanics has been shown adequate to explain the scattering of heavier atoms from surfaces [1,2] where large numbers of phonon transfers is the means of energy exchange. Classical mechanics even gives good descriptions of the energy transfer for the surface collisions of small mass projectiles such as He and D 2 at incident energies over 100 meV [3]. For molecules with masses substantially larger than hydrogen or deuterium, such as CO, CO 2 or C 2 H 2 , rotational quantum numbers even at temperatures as low as 100 K are of order 10 or larger and in a typical surface collision the rotational excitation can involve quantum numbers even larger than that. Thus for such molecules, a classical treatment of the rotational excitations, combined with a classical treatment of the phonon exchange should be adequate.An earlier treatment of this same problem has been presented based on treating the rotational interactions of a molecular beam incident on the surface as interactions with a surface of discrete scattering centers [4]. This earlier treatment obtained very good agreement with recent measurements of the angular distributions of C 2 H 2 [5] scattering from a LiF(0 0 1) surface at incident energies above 100 meV. Qualitative agreement was obtained with further experimental measurements of the scattered intensities as a function of final rotational energies. The work described here extends this earlier theoretical model to include a better model of the surface interaction, one in which the rotational interaction is with a surface having a smoothly varying repulsive barrier. In this case, the correct conservation of angular momentum perpendicular to the surface is included,

Theoretical Studies of Energy and Momentum Exchange in Atomic and Molecular Scattering from Surfaces

“…The most important advance achieved during this grant period is our development of the theory of molecule scattering from surfaces under conditions in which the translational and rotational motions of the molecule are treated classically (which is valid for almost all molecules except hydrogen) while treating the internal vibrational modes of the molecule with quantum semiclassical theory [5,9,10,11,14]. Thus, the theory includes the three major modes of energy and momentum exchange with the surface, i.e, phonon excitation (surface vibrations), rotational excitation of the molecules, and excitation of internal mode vibrations of the molecule.…”