Coulomb nearest-neighbor repulsion

In crystal NaCl, each Na+ or Cl- ion is surrounded by 6 nearest neighbors of opposite charge and 12 nearest neighbors of the same charge. Two sets of forces oppose each other the coulombic attraction and the hard-core repulsion. The potential energy u(r) of the crystal is given by the Lennard-Jones potential expression,... 

After Pedersen and Carneiro, it is mostly the magnitude of the nearest-neighbor Coulomb repulsion energy, V, which is responsible for the difference between TEA(TCNQ)2 and MEM(TCNQ)2. The magnitude of V is determined largely by the shape and polarizability of the cations, and the cation TEA+ is believed to screen more efficiently than the cation MEM+, the intermolecular Coulomb repulsion represented by V [36]. 

We have seen that the nearest-neighbor distance jn ionic solids is determined by the joint action of the Coulomb interaction and the predominantly repulsive overlap interaction that we approximate with the Lennard-Jones form. First, let us explore the properties of KCI, an ionic solid with ion charge Z = 1. We have seen that the Coulomb energy per ion pair in the face-centered cubic structure is... 

Equation (6.13) was derived on a model of covalent bonds between nearest neighbors. It is not strictly applicable to ionic solids. The repulsion part of the potential energy must be similar for ionic and covalent cases, but the attraction part for ionic solids must also include the sum of the coulombic interactions with the remainder of the lattice. In effect, the number of bonds is increased. To see the magnitude of this effort, compare Equations (6.7) and (6.8) with their counterparts for a diatomic molecule, or ion-pair. 

Finally, as noted earlier, ratio n) v = 6)/ n) v = 4) equals 3/2 exactly for the case of the unbiased, nearest-neighbor random walk. As is seen in Table 1V.4, for attractive Coulombic interactions there is a systematic convergence to the exact limiting value of 3/2 with an increase in system size. Interestingly, the value 1.500 is realized for repulsive Coulombic interactions, even for the smallest system size reported. 

The principal effects of the electron-electron interaction can be embodied in a disordered Hubbard model containing three parameters t, the nearest-neighbor electron transfer matrix element assumed constant U, the Coulomb repulsion between electrons of... 

One should also mention that a more realistic modeling of a quarter-filled system would require the inclusion of at least the nearest-neighbor Coulomb repulsion terms in addition to the on-site ones. That means switching from the original Hubbard to the extended Hubbard model Hamiltonian ... 

Theoretical calculation based on a polaronic model [145] elaborated by Daikhin and Levi may give an explanation for the separation of the proton and anion transports. In this model Coulomb interactions between species with opposite signs have been taken into account. Owing to the very high repulsion forces between the nearest-neighbor sites in the polymer chain, it is unfavorable that protons on the... 

In eq. (41), d(/)fg destri s (creates) a d(/) electron with spin o on site i. The hq)ping is restricted to the nearest neighbors and scaled as t=t l2y/D. Ug is the screened onsite Coulomb repulsion for the localized f states and V is the hybridization between d and f states. This model retains the features of the impurity problem, including moment formation and screening, but is further complicated by the lattice effects. 

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