Intra-atomic Coulomb energy

At this point, we have reached the stage where we can describe the adatom-substrate system in terms of the ANG Hamiltonian (Muscat and Newns 1978, Grimley 1983). We consider the case of anionic chemisorption ( 1.2.2), where a j-spin electron in the substrate level e, below the Fermi level (FL) eF, hops over into the affinity level (A) of the adatom, whose j-spin electron resides in the lower ionization level (I), as in Fig. 4.1. Thus, the intra-atomic electron Coulomb repulsion energy on the adatom (a) is... 

In Chap. E, photoelectron spectroscopic methods, in recent times more and more employed to the study of actinide solids, are reviewed. Results on metals and on oxides, which are representative of two types of bonds, the metallic and ionic, opposite with respect to the problem itineracy vs. localization of 5f states, are discussed. In metals photoemission gives a photographic picture of the Mott transition between Pu and Am. In oxides, the use of photoelectron spectroscopy (direct and inverse photoemission) permits a measurement of the intra-atomic Coulomb interaction energy Uh. 

The distance between two electrons at a given site is given as ri2. The electron wave function for one of the electrons is given as (p(ri) and the wave function for the second electron, with antiparallel spin, is Hubbard intra-atomic energy and it is not accounted for in conventional band theory, in which the independent electron approximation is invoked. Finally, it should also be noted that the Coulomb repulsion interaction had been introduced earlier in the Anderson model describing a magnetic impurity coupled to a conduction band (Anderson, 1961). In fact, it has been shown that the Hubbard Hamiltonian reduces to the Anderson model in the limit of infinite-dimensional (Hilbert) space (Izyumov, 1995). Hence, Eq. 7.3 is sometimes referred to as the Anderson-Hubbard repulsion term. 

In a category of materials known as Mott insulators, like MnO, CoO or NiO, with band gaps of 4.8, 3.4, and 1.8 eV, respectively ([2], and references therein), the upper energy band made from 3d states is partially occupied resulting in metallic conduction. The insulating behaviour of these compounds is attributed to a strong intra-atomic Coulomb interaction, which results in the formation of a gap between the filled and empty 3d states [35]. 

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... 

Internuclear distance. See Bond length Inert gas solids Simple metals Transition metals Intra-atomic Coulomb energy, 431, 527ff Intrinsic semiconductors, 152 Ion, 33, 289-338 Ion distortion, 190f Ion polarizability, 326f... 

Independent electronic structure calculations on YbPtBi were performed by Oppeneer et al, (1997) on the basis of density-functional theory in the local-spin-density approximation (LSDA), generalized with additional intra-atomic Coulomb correlations between 4f electrons. These calculations show that the Yb 4f level is pinned at the Fermi energy. This pinning is a generic property. Furthermore the hybridized 4f level is split into two van Hove-like side maxima. 

Coulomb repulsion between the electrons in the f shell and are much more sensitive to changes in the local environment than the spin-orbit transitions. They are therefore a useful probe of the way intra-atomic correlations are affected by the metallic state, particularly in the actinides. Nevertheless, there are relatively few investigations of Coulomb transitions in metals since their energies all exceed 500 meV and most exceed 1 eV, as can be seen in fig. 1. The lowest energies are found in Pr, Sm " and Tm, all of which have now been studied by neutrons (Taylor et al. 1988, Needham 1989, Osborn et al. 1990). Although Coulomb transitions are non-dipolar, they can have appreciable cross-sections at intermediate values of momentum transfer, and are, in many cases, stronger than the dipolar (i.e., J—>J 1) cross-sections at the same k. 

Hail coefficient T = temperature in kelvin U = intra-atomic Coulomb repulsion energy y = electronic specific heat constant A = band width... 

Here, denotes the energy of the orbital a (a = s, p, d) at atomic site i and hiao are the corresponding occupation-number operators. The are the hopping integrals describing electronic transitions between atoms i and j. The third term in Eq. (1) approximates the electron-electron interactions [30, 31]. The prime in the sum indicates that the terms with a = P and a = a are to be excluded. is the effective on-site interaction between electrons with spin a and a in the orbitals a and P of atom i. In Eq. (1) only the Coulomb and exchange intra-atomic integrals Uafi = otP /r 2 otP) and J fi = otP lr 2 Pot) are... 

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