Repulsive range parameter

TABLE 21.6 Madelnngconstants and repulsive range parameters of some ionic crystals... 

The lattice energy for potassium iodide, Kl, is 627.2 kJ/mol. If the ionic separation is 3.533 A, what is the repulsive range parameter p for Kl You will have to determine which Madelung constant to use. 

If the various parameters 0)2 were to scale as the repulsive force contributions have been assumed, Eq. (4.45), then this formula Eq. (4.49) would vanish. But the same scaling for attractive force parameters as for repulsive force parameters is not as reasonable. The attractive force contributions derive from longer-range interactions and relative strengths of those interactions may display additional variety. The calculation leading to Eq. (4.49) does, however, show that the slightly more general relation... 

In the physics literature, the model invented to go beyond the severely truncated electron-repulsion range of the Hubbard model has been the extended Hubbard Hamiltonian or the U-V model. Here, the intersite interactions are introduced between bonded sites through another independent phenomenological interaction parameter V [26] from which the model derives its name. The Hamiltonian is given... 

It follows that the short-range repulsive force F(K) between real molecules is not infinitely hard, i.e., the potential V(R) is not a vertical wall at some critical value of the center-to-center separation Ji of the colUding particles (e.g., R = d). Rather, there is a steeply increasing repulsion that is often approximated by an exponential form with a range parameter p and strength A ... 

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). 

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. 

Monte Carlo simulations [17, 18], the valence bond approach [19, 20], and g-ology [21-24] indicate that the Peierls instability in half-filled chains survives the presence of electron-electron interactions (at least, for some range of interaction parameters). This holds for a variety of different models, such as the Peierls-Hubbard model with the onsite Coulomb repulsion, or the Pariser-Parr-Pople model, where also long-range Coulomb interactions are taken into account ]2]. As the dimerization persists in the presence of electron-electron interactions, also the soliton concept survives. An important difference with the SSH model is that neu-... 

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