Coulomb correlation integral

In addition Freeman and KoelUng stressed the importance of the relationship between bandwidth and the Coulomb correlation integral. 

Quantitatively the Coulomb repulsion integral of SCF-calculations for SEM correlates linearly with Ig Ksem Equation (3)... 

Fig. 6. Correlation between Ig Ksem of different vinylogous redox systems and the Coulomb repulsion integral...

In an electronic system it is essential to distinguish between the correlation of electrons with identical spin, Fermi correlation, from that of electrons with opposite spins. Coulomb correlation. The correlation term/(ri,r2) as defined in eqn (E7.10) will measure both types of correlation (McWeeny 1960). However, the limiting value of the correlation hole as expressed in eqn (E7.11) arises only from the correlation between electrons of the same spin, the Fermi hole. That part of/(r, r2) that refers to the correlation between electrons of opposite spin contributes zero when integrated over all space. If the co-... 

As in atomic spectra, the form of Eq. (128) shows why the semi-empirical parameters of w-electron theory tend to include correlation. Zero differential overlap allows the Jif integrals in the H.F. part of Eq. (128) to be broken down into one- and two-center Coulomb integrals. The large difference between the non-and semi-empirical values of these is accounted for by introduc-ingi >i correlation into (2 J . This is justified because the "zero differential overlap can equally well be made in the e fs, reducing them to one- and two-center Coulomb correlation energies. 

The advantage of using electron density is that the integrals for Coulomb repulsion need be done only over the electron density, which is a three-dimensional function, thus scaling as. Furthermore, at least some electron correlation can be included in the calculation. This results in faster calculations than FIF calculations (which scale as and computations that are a bit more accurate as well. The better DFT functionals give results with an accuracy similar to that of an MP2 calculation. 

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. 

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