Molecule-surface scattering theory

An interesting alternative is the semigroup theory of Lindblad, Davies, and Kossakowski [162,165,163]. This and similar theories have been used in molecule surface scattering by Kosloff [164] and Jackson [166]. 

A type of molecular resonance scattering can also occur from the formation of short-lived negative ions due to electron capture by molecules on surfrices. While this is frequently observed for molecules in the gas phase, it is not so important for chemisorbed molecules on metal surfaces because of extremely rapid quenching (electron transfer to the substrate) of the negative ion. Observations have been made for this scattering mechanism in several chemisorbed systems and in phys-isorbed layers, with the effects usually observed as smaU deviations of the cross section for inelastic scattering from that predicted from dipole scattering theory. 

LEED does not only reveal the relative periodicities of the adsorbate mesh with respect to the substrate lattice. Applying dynamical scattering theory, i.e., modeling the scattering intensity of diffracted beams versus electron energy (so-called I-V curves), allows determination of absolute positions of atoms on the surface [20]. Unfortunately, the complexity of the method limits the number of atoms per unit cell and makes it applicable only to atomic or small-molecule lattices. 

Finally, in a recent paper, Yeganeh et al. suggest that the large asymmetries seen in polarized electron transmission are partly due to a combination of the presence of a molecule with axial chirality, surface orientation, and cooperative effects in the monolayer [129]. They use scattering theory to show that differences in transmitted intensity arise from the preferential transmission of electrons whose polarization is oriented in the same direction as the sense of advance of the helix. 

For completeness, we should mention that inclusion of single-phonon events can be accomplished within a time-independent scattering theory simply by using a first-order Taylor series expansion of the interaetion potential between the gas molecule and the solid surface ... 

A. Otto, Theory of First Layer and SmgJe Molecule Surface Enhanced Raman Scattering (SERS), Phys. Status Solidi A-Appl. Res. 188, 1455 (2001)... 

The basic question posed in reactive scattering theory today is simple. Given a potential energy surface for the interacting molecules, what will be the outcome of a collision between them. The outcome is described in various terms such as a reaction probability, distribution of final states, differential cross section, rate constant etc. All of these quantities depend on the initial state of the colliders. 

Both difficulties can be overcome by the method originally introduced in the quantum field theory (Popov 1983) and applied later to the quasiclassical theory of molecule-molecule and gas-surface scattering (Dubrovskiy and Bogdanov 1979a Bogdainov 1980 Bogdanov et al. 1989). 

According to the molecular scattering theory, a particle incident to the surface has a certain probability for a certain amount to stay on the surface, and the rest is scattered back into the gas phase, a is an initial attaching probability and is a parameter to be determined through a molecular dynamics simulation based on quantum chemistry. Although in surface chemistry, a thermal accommodation coefficient is also used, in atmospheric chemistry a mass accommodation coefficient is solely used so that here it is simply called an accommodation coefficient. In general a cannot be determined directly by experiments, and the experimentally determined parameter of intake of a gaseous molecule to the particle surface is an uptake coefficient y defined by... 

We first briefly describe the problems in constructing potential energy surfaces for the reactions of polyatomic molecules, we then go on to outline transition state theory, classical trajectory calculations, and mixed quantum classical methods for polyatomic molecules. After this we describe the various quantum scattering theories that have been developed for treating state-selected and state-to-state chemical reactions involving four or more atoms. We also refer to the reactions that have been studied using these treatments. 

Gersten, J. and Nitzan, A. (1980) Electromagnetic theory of enhanced Raman scattering by molecules adsorbed on rough surfaces. J. Chem. Phys., 73, 3023-3037. 

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