Short-range repulsion

Such attractive forces are relatively weak in comparison to chemisorption energies, and it appears that in chemisorption, repulsion effects may be more important. These can be of two kinds. First, there may be a short-range repulsion affecting nearest-neighbor molecules only, as if the spacing between sites is uncomfortably small for the adsorbate species. A repulsion between the electron clouds of adjacent adsorbed molecules would then give rise to a short-range repulsion, usually represented by an exponential term of the type employed... 

The existence of intennolecular interactions is apparent from elementary experimental observations. There must be attractive forces because otherwise condensed phases would not fomi, gases would not liquefy, and liquids would not solidify. There must be short-range repulsive interactions because otherwise solids and liquids could be compressed to much smaller volumes with ease. The kernel of these notions was fomuilated in the late eighteenth century, and Clausius made a clear statement along the lines of this paragraph as early as 1857 [1]. 

The above potential is referred to as a Lennard-Jones or 6-12 potential and is summed over all nonbonded pairs of atoms ij. The first positive term is the short range repulsion and the second negative term is the long range attraction. The parameters of the interaction are Aj and B... The convenient analytical form of the 6-12 potential means that it is often used, although an exponential repulsion term is usually considered to be a more accurate representation of the repulsive forces (as used in MM-t). 

The forces which bring about adsorption always include dispersion forces, which are attractive, together with short-range repulsive forces. In addition, there will be electrostatic (coulombic) forces if either the solid or the gas is polar in nature. Dispersion forces derive their name from the close connection between their origin and the cause of optical dispersion. First... 

An expression for the short-range repulsive force (which arises from the interpenetration of the electron clouds of the two atoms) can also be derived from quantum-mechanical considerations" as... 

When two or more molecular species involved in a separation are both adsorbed, selectivity effects become important because of interaction between the 2eobte and the adsorbate molecule. These interaction energies include dispersion and short-range repulsion energies (( ) and ( )j ), polarization energy (( )p), and components attributed to electrostatic interactions. 

FIG. 16-4 Depictio ns of surface excess F- Top The force field of the sohd concentrates component near the surface the concentration C is low at the surface because of short-range repulsive forces between adsorbate and surface. Bottom Surface excess for an imagined homogeneous surface layer of thickness Axf... 

Nevertheless, previous developments and some of our results prove that the structural properties of several systems with short-range repulsive forces are straightforwardly and sufficiently accurately given by ROZ integral equations. Thermodynamic properties are much more difficult to describe. Reliable tools exist to obtain thermodynamics at high temperatures or for states far from phase transitions. Of particular importance, and far from being solved, are the issues related to phase transitions in partly quenched systems, even for simple models with attractive interactions. It seems that the results obtained by Kierlik et al. [27], may serve as a helpful reference in this direction. 

As an example of a multilayer system we reproduce, in Fig. 3, experimental TPD spectra of Cs/Ru(0001) [34,35] and theoretical spectra [36] calculated from Eq. (4) with 6, T) calculated by the transfer matrix method with M = 6 on a hexagonal lattice. In the lattice gas Hamiltonian we have short-ranged repulsions in the first layer to reproduce the (V X a/3) and p 2 x 2) structures in addition to a long-ranged mean field repulsion. Second and third layers have attractive interactions to account for condensation in layer-by-layer growth. The calculations not only successfully account for the gross features of the TPD spectra but also explain a subtle feature of delayed desorption between third and second layers. As well, the lattice gas parameters obtained by this fit reproduce the bulk sublimation energy of cesium in the third layer. 

Physically the independence reflects the fact that dephasing is performed by weak long-range interactions, and rotational relaxation results mainly from short-range, repulsive forces. In other words the rotational state is changed solely when the distance between molecules becomes rather short, while the phase is frustrated in all cases and the contribution of frontal collisions is not so significant. 

FIG. 2 Energy of elastically coupled charges with an additional short-range repulsion term. Copyright 2001 Marcel Dekker, Inc. 

Which denotes respectively the short-range penetration corrected electrostatic multipolar (EMTP ) energy, short-range repulsion (Erep ), polarization (Epoi), charge-transfer (Ed), and dispersion (EdiSp) contributions. In presence of an open-shell cation, a ligand field correction is introduced (Elf)-... 

The height of the potential barrier decreases with the decrease of the transfer distance. Therefore, the contribution of the transitions between excited vibrational states increases and so does the transition probability. However, short-range repulsion between the reactants increases with a decrease of R, and the reaction occurs at an optimum distance R which is determined by the competition of these two factors. In principle, we may imagine the situation when the optimum distance R corresponds to the absence of a potential barrier for the proton. However, we should keep in mind that the transitions between certain excited states may become entirely adiabatic at short distances.40,41 In this case, the further increase of the transition probability with the decrease of R becomes quite weak, and it cannot compensate for the increased repulsion between the reactants, so that even for the adiabatic transition, the optimum distance R may correspond to sub-barrier proton transfer. 

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