Selfenergy electronic

Labzowsky, L., Goidenko, I., Tokman, M. and Pyykko, P. (1999) Calculated selfenergy contributions for an ns valence electron using the multiple-commutator method. Physical Review A, 59, 2707-2711. 

For many ionization energies and electron affinities, diagonal selfenergy approximations are inappropriate. Methods with nondiagonal self-energies allow Dyson orbitals to be written as linear combinations of reference-state orbitals. In most of these approximations, combinations of canonical, Hartree-Fock orbitals are used for this purpose, i.e. 

Because second order is the first nonvanishing contribution, zero and first order electron propagator calculations correspond to KT results. In the diagonal, P3 selfenergy, terms with three virtual indices, such as... 

In this subsection, we describe a method where the electron propagator machinery developed for quantum chemical calculations of single molecules is applied [9-21]. We use a so-called noncrossing approximation where a selfenergy for interacting bridge electrons is divided into two independent parts [55-57] ... 

Most of these diagrams contain two intermediate electron propagators and, therefore, double summations over the whole spectrum of the Dirac equation in the external nuclear field. This makes their computation numerically intensive. Both the selfenergy and vacuum-polarization screening corrections are ultraviolet divergent and require renormalization to yield a finite result. 

RPA theory. The usual quantity used in phonon theories is the phonon self--energy defined here by Equ. (8). This exact phonon selfenergy can easily be expressed in terms of the electron-electron vertex by eliminating the Green function D between Equs. (8) and (9). Introducing further the RPA and g %7 - 87 sim plifications, we find immediately that... 

The effect of aU interactions is now included in the electron (.S) and phonon (77) selfenergies. Formal expressions for the self-energies are obtained by comparing Eqs. (33) and (41) with Eq. (44)... 

Diagram the third-order contributions to the electron propagator selfenergy listed in Appendix D. 

When the Hartree-Fock method is used for the ionic calculation, the error due to the neglect of electron correlation is significant ifthe number of electrons in the crystal ion is different from that in the reference gas phase ion (this occurs for oxides, where the crystal ion is O2- and the reference gas phase ion is 0-). Earlier electron gas calculations estimated the selfenergy due to electron correlation [24], but in more recent calculations an... 

P. IndeHcato, P. J. Mohr. Coordinate-space approach to the botmd-electron selfenergy Self-energy screening calculation. Phys. Rev. A, 63(5) (2001) 052507. 

The energy terms of order two result from emission and absorption of one photon by one electron. These terms represent part of the selfenergy of the electrons and the photons. Since they do not depend on the separation of particles 1 and 2, we may cancel them by renormalization. Expanding the energy denominators in Eq. (8.12) with respect to E-Eo, we put... 

With this physical model in mind one can visualize the formation of an electronic polaron according to equations (54) and (55) in two steps. Initially, the extra particle put into the HF conduction band state 4>c must establish its new correlation bonds with the other N particles present in the (Af -F I) particle system < >( , giving rise to the electronic selfenergy correction E (e). At the same time, owing to the occupation of the previously empty state 0 - correlations Su I C, y C) are reduced in compared... 

Before explicitly calculating these quantities, some of their qualitative trends can be observed. For the bottom of the conduction band the denominators of rj in equation (59) are always negative (see Figure 1), therefore the electron selfenergy shifts this state downward. Also, since the values of rff in equation (60) are negative, the hole self-energy produces a positive (upward) shift. (We note that in the... 

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