Short-range repulsion energy

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 summations are over all atoms i and / with separations and C,y, and Pij are the adjustable parameters of the model. The interaction energy of the system as a whole is then the sum of the Coulombic energies, short-range repulsive energies, and the weakly attractive energy components for all constituents. As we shall see, the individual components are typically the atomic centers and the points representing the polarization centers of the system. The successes of the simple ionic models introduced by Born and coworkers have been well documented and cover a wide range of applications. 

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... 

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. 

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. 

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

The three parameters in the Morse function D, B, re are positive and are usually chosen to fit the bond dissociation energy, the harmonic vibrational frequency and the equilibrium bond length. At r = re, the Morse function V = 0. As r — D, V approaches D. For r re, V is large and positive, corresponding to short range repulsion. Although the Morse function has been used extensively, its representation of the potential away from re is not satisfactory. Several modifications have been proposed in Morse function. 

While Debye and HUckel recognized the short-range repulsive forces between ions by assuming a hard-core model, the statistical mechanical methods then available did not allow a full treatment of the effects of this hard core. Only the effect on the electrostatic energy was included—not the direct effect of the hard core on thermodynamic properties. 

Much of this book is concerned with the properties of narrow bands to which the tight-binding approximation is appropriate. In this case, if the band is half full or nearly so, the short-range repulsion between the electrons may have very important effects on the properties of the electrons in the bands, producing magnetic moments and non-conducting properties. These are a major theme of this book. At this point we introduce the Hubbard intra-atomic energy ... 

In actuality, molecules in a gas interact via long-ranged attractions and short-range repulsive forces. An interaction potential energy function is used to describe these forces as a function of intermolecular distance and orientation. This section introduces two commonly used interaction potential energy functions. 

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