Coulomb repulsion parameter

Hmo+Vj+Vj is used the coefficient U, should be just Yo while U2=y,-Y2> where Y2 is a typical (or reference) next-neighbor PPP Coulomb repulsion parameter. Evidently the model could be further extended to include third or farther neighbor Coulomb interactions, possibly while still using a single new Coulomb interaction parameter Uj referenced against a typical PPP Coulomb repulsion parameter Y3 ... 

I have included the arbitrary parameter X in order to keep track of orders of magnitude. I will later set it to unity. In the case of the helium problem above, the perturbation would be just the Coulomb repulsion between the electrons. 

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-... 

In aqueous suspension, the stability is discussed in reference to the DLVO (Deryaguin-Landau-Verway-Overbeek) theory. Within this framework, all solid substances have a tendency to coagulate due to their large van der Waals attractive force. The coulombic repulsive force among colloidal particles more or less prevents this tendency. These two opposite tendencies determine the stability of suspensions. What kind of parameters are concerned in the present nonaqueous system, for which little is known about the stability This is an interest in this section. 

Auerbach et al. (101) used a variant of the TST model of diffusion to characterize the motion of benzene in NaY zeolite. The computational efficiency of this method, as already discussed for the diffusion of Xe in NaY zeolite (72), means that long-time-scale motions such as intercage jumps can be investigated. Auerbach et al. used a zeolite-hydrocarbon potential energy surface that they recently developed themselves. A Si/Al ratio of 3.0 was assumed and the potential parameters were fitted to reproduce crystallographic and thermodynamic data for the benzene-NaY zeolite system. The functional form of the potential was similar to all others, including a Lennard-Jones function to describe the short-range interactions and a Coulombic repulsion term calculated by Ewald summation. 

In equation (7), Kc is the pair-transfer interaction originated in the Coulomb repulsion and its value is the same as Jc Although J and K have the same value, it is noteworthy that these interactions represent different physical processes. Furthermore, it should be noted that the equation Vintra = Vinter + 2K still holds due to the equation (7intra = (/inter + 27c Consequently, the independent parameters of the effective interaction are two. In the present study, we employ yintra and K as two independent parameters. It is found that Vintra is about 0.2 eV, Vjnter is about 0.4 eV, and both J and K are about — 0.1 eV owing to the estimation already given. Of great importance here is the... 

Likewise the Hubbard model the periodic Anderson model (PAM) is a basic model in the theory of strongly correlated electron systems. It is destined for the description of the transition metals, lanthanides, actinides and their compositions including the heavy-fermion compounds. The model consists of two groups of electrons itinerant and localized ones (s and d electrons), the hybridization between them is admitted. The model is described by the following parameters the width of the s-electron band W, the energy of the atomic level e, the on-site Coulomb repulsion U of d-electrons with opposite spins, the parameter V of the... 

The energies of the d-d-excitations in this model are obtained by diagonalizing the matrix of the Hamiltonian constructed in the basis of rid-electronic wave functions (nd is the number of d-electrons). Matrix elements of the Hamiltonian are expressed through the parameters describing the crystal field and those of the Coulomb repulsion of d-electrons, which are Slater-Condon parameters Fk, k = 0,2,4, or the Racah parameters A, B, and C. In the simplest version of the CFT these quantities are considered empirical parameters and determined by fitting the calculated excitation energies to the experimental ones. 

---