Self energy correction term evaluation

The most important part of Suhai s calculations on the correlation energy of trans-VPS is the evaluation of the self-energy corrections to the HF band energies using equations (5.60) and (5.61). These quantities are collected in Table 5.4 for basis sets a, c, and e. (The results obtained for b and d are very similar to c and e, respectively, therefore they are not shown here.) The values of 2c are calculated at the bottom of the lowest conduction band, while the values of 2j refer to the top of the highest valence band. The shifts for both bands are seen to result from a positive and a negative term, but as a net effect the conduction band is shifted downward and the valence band upward. 

The decomposition of the irreducible part of the self-energy wave-function correction term is depicted in Fig. 2. The divergent terms are these with zero and one interaction in the binding potential present, below referred to as zero-potential term and one-potential term , respectively. The charge divergences cancel between both terms. In addition, a mass connter term Sm has to be subtracted to obtain proper mass renormalization similar to the case of the free self energy [47] (for onr schemes see also [44]). The zero- and one-potential terms are then semianalytically evaluated in momentum space (for details cf. 

In this paper, we investigate the correction terms obtained when applying a covariant Pauli-Villars regulator [16] when formulating the PWR procedure. In Section II we consider the first-order self energy and the Coulomb screened self energy is discussed in Section III. Finally, we derive an expression suitable for numerical evaluation of the correction term in the Coulomb screened case. 

Another disadvantage of the LDA is that the Hartree Coulomb potential includes interactions of each electron with itself, and the spurious term is not cancelled exactly by the LDA self-exchange energy, in contrast to the HF method (see A1.3I. where the self-interaction is cancelled exactly. Perdew and Zunger proposed methods to evaluate the self-interaction correction (SIC) for any energy density functional [40]. However, full SIC calculations for solids are extremely complicated (see, for example [41. 42 and 43]). As an alternative to the very expensive GW calculations, Pollmann et al have developed a pseudopotential built with self-interaction and relaxation corrections (SIRC) [44]. 

The second-order contribution to the self-energy is the lowest order nonvanishing correction to the electron binding energies as given by the orbital energies in the geometric approximation. In order to evaluate this correction term,... 

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