Coulomb correlation energy

Weighted-Density Exchange and Local-Density Coulomb Correlation Energy Functionals for Finite Systems—Applications to Atoms. Phys. Rev. A 48, 4197. 

From the experimental viewpoint 1. the analysis of the variation of photoionization cross sections (affecting the intensities of photoelectron spectroscopy), gives an insight into the orbital composition of the bands of the solid 2. the combination of direct and inverse photoemission provides a powerful tool to assess the structure of occupied and of empty states, and, in the case of localized 5 f states, permits the determination of a fundamental quantity, the Coulomb correlation energy, governing the physical properties of narrow bands. 

Coulomb correlation energy, U. The energy gain due to band formation is of the order of the bandwidth, W. Provided U can be calculated Table 1 can be used to examine the criterion UAV = 1 for Mott-localization ... 

Coulomb correlation energy, I/44, and thereby showed how the cationic and anionic energy levels were both equally important. These workers calculated the gap arising in the charge excitation spectrum of a single transition-metal impurity hybridizing with a... 

Table 4.3 Coulomb correlation energies of the helium isoelectronic series Eq (OPM) versus CS (Colie and Salvetti 1975), LDA (Vosko et al 1980), GGA (Perdew et al 1992), MP2 (Ishikawa and Koc 1994) and exact results (Davidson et al 1991). Both the nonrelativistic values Ecnr and the difference between the relativistic numbers and aj-e given (all energies...

Responsible for this unique behavior is the large intra-atomic 4f Coulomb correlation energy, The properties of this parameter in the difficult case of 3d... 

Coulomb correlation energies of the Helium isoelectronic series versus CS [166], LDA... 

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. 

Owing to its small size, the dominant correlation corrections to the Breit interaction are those associated with one Breit and many Coulomb terms. As mentioned earlier, these dominant corrections can be obtained from MBPT formulas such as those in Eqs. (102) and (103) by substituting Vijki —> Uyw - - hijki and linearizing in hijki- The second-order (one Breit-one Coulomb) correlation energy from Eq. (92) is... 

Fig. 2. XPS and BIS spectra of GD (Lang et al. 1981). The sum of the 4f ionization potential and the 4f electron affinity d+ is equal to the 4f intrashell Coulomb correlation energy U.

Uc Coulomb correlation energy X mean free path... 

Fig, 9. XPS spectrum of intermediate-valent SmBj. Also shown is the ladder like structure of the 4f final state. The Coulomb correlation energy UC can be taken to be about 7eV. (After Campagna et al. 1979.)... 

Baer Y, Schoenes J. Electronic structure and Coulomb correlation energy in UO2 single crystal. Solid State Commun. 1980 33 885-888. 

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