Correlation models Coulomb integral

Table I. The calculated Coulomb integrals (eV). AO(p), AO(c), MO, MO(CC) denote the values calculated by the Cr-3d AOs in the point charge model (p), by the Cr-3d AOs in the cluster model (c), by the MOs of the impurity states and by the MOs of the impurity states with the correlation correction (CC), respectively, e and t represent the 6g and tag states in the octahedral notation, while (a) and (e) specify the states split by the trigonal crystal field.

It is well known that it is difficult to solve numerically integral equations for models with Coulomb interaction [69,70]. One needs to develop a renormalization scheme for the long-range terms of ion-ion correlations. Here we must do that for ROZ equations. 

Kohn-Sham orbitals (18)), Vn is the external, nuclear potential, and p is the electronic momentum operator. Hence, the first integral represents the kinetic and potential energy of a model system with the same density but without electron-electron interaction. The second term is the classical Coulomb interaction of the electron density with itself. Exc> the exchange-correlation (XC) energy, and ENR are functionals of the density. The exact functional form for Exc is unknown it is defined through equation 1 (79), and some suitable approximation has to be chosen in any practical application of... 

The results were analysed using HNC calculations described in another chapter of this book. The ion-ion correlations in the electrolyte and the ionic profiles in the vicinity of the water-air interface were calculated within the HNC integral equation approximation at the Primitive Model level of description (ionic spheres immersed in a continuous dielectric solvent). The (solvent-averaged) ion-ion interaction potential y(r) is the sum of a hard-sphere contribution (radii ), a generic Coulombic Contribution ZiZje / 47T oer) (valency Z, dielectric constant e = 78) and a specific dispersion contribution. ... 

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