The One-Electron Picture

G. Wendin, Structure and Bonding 45 Breakdown of the One-electron Pictures in Photoelectron Spectru, Springer, Berlin 1981. 

Wendin G (1981) Breakdown of the One-Electron Pictures in Photoelectron Spectra. 45 1-130... 

Note that the exchange term is of the form / y(r,r ) h(r )dr instead of the y (r) (r) type. Equation (1.12), known as the Hartree-Fock equation, is intractable except for the free-electron gas case. Hence the interest in sticking to the conceptually simple free-electron case as the basis for solving the more realistic case of electrons in periodic potentials. The question is how far can this approximation be driven. Landau s approach, known as the Fermi liquid theory, establishes that the electron-electron interactions do not appear to invalidate the one-electron picture, even when such interactions are strong, provided that the levels involved are located within kBT of Ep. For metals, electrons are distributed close to Ep according to the Fermi function f E) ... 

Wen81] Wendin G 1981 Breakdown of the one-electron pictures in photoelectron spectra, Structure and bonding 45 (Springer, Berlin). 

In the one-electron picture the photoelectron spectrum thus consists of a number of sharp peaks (Fig. 4 d), one for each core level, with the binding energy given by the negative of the HF eigenvalue (Koopmans theorem261). 

Table I. Overview of cases with strong perturbations and breakdown of the one-electron picture for core holes in free atoms...

The behaviour of the 4s, 4 p core levels around Xe is based on the existence of four subshells, basically three (4s, 4p, 4d) filled and one (4f) empty. In order to see further examples of complete breakdown of the one-electron picture one has to go to higher Z, to the n = 5 shell in the 5 f group and preceding elements (Fig. 16 Table 1, entry I). In... 

It is worth remembering that we are still working with the one-electron picture, and that we have applied the Boltzmann relation in order to approximate Fermi and quasi-Fermi distribution functions, assuming the quasi-free electron and hole densities of states in the bands. 

In most organic semiconductors the presence of charges modifies the local structure of the network by deformation of the particular site. This so-called polaron formation thus creates scattering centres for other charges. Moreover these locally trapped carriers commonly alter the energy conditions because of their Coulomb interaction. In combination with the polaron energy, the latter may be attractive or repulsive. These effects, as they involve more than one electron, force us to give up the one-electron picture and hence to use the correlated-electron description. 

Absorption of the X-ray makes two particles in the solid the hole in the core level and the extra electron in the conduction band. After they are created, the hole and the electron can interact with each other, which is an exciton process. Many-body corrections to the one-electron picture, including relaxation of the valence electrons in response to the core-hole and excited-electron-core-hole interaction, alter the one-electron picture and play a role in some parts of the absorption spectrum. Mahan (179-181) has predicted enhanced absorption to occur over and above that of the one-electron theory near an edge on the basis of core-hole-electron interaction. Contributions of many-body effects are usually invoked in case unambiguous discrepancies between experiment and the one-electron model theory cannot be explained otherwise. Final-state effects may considerably alter the position and strength of features associated with the band structure. 

The degree of bond length alternation is closely related to the magnitude of the forbidden energy gap, E, which in turn affeqts electrical, optical and other physical properties of the system. Within the one-electron picture (Huckel-model) one can show, that E = 2 I lo where 0 and are... 

It is worthwhile mentioning at this point that all properties of a subsystem defined in real space, including its energy, necessarily require the definition of corresponding three-dimensional density distribution functions. Thus, all the properties of an atom in a molecule are determined by averages over effective single-particle densities or dressed operators and the one-electron picture is an appropriate on ] [y)... 

The one-electron picture of ionization is confirmed for detachments from the 5h and 9h,., levels as the corresponding OVGF PS values are high. No IEs for these levels are found by the ADC(3) calculations. 

The above approach leans heavily however upon the supposed dominance of the one-electron core terms (which may well not be justified as far as the f-orbital — ligand interactions are concerned), and also provides only a little help in predicting the energetic ordering of the f-levels in D8h symmetry. Clearly if the one-electron picture is assumed with... 

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