Green’s function, bare

Since in the FHCF(L) the effective crystal field is given in terms of the l-system Green s function, the natural way to go further with this technique is to apply the perturbation theory to obtain estimates of the /-system Green s function entering Fqs. (22) and/or (25). It was assumed and reasoned in [29] that the bare Green s function for the /-system has a block-diagonal form ... 

The bare Green s function for the /-system in the state when the metal is taken out has the block-diagonal form ... 

Now, let us come back to the bare Green s function. We know that... 

Let us now return to the bare Green s function, which we need to invert the Laplace-de Gennes transformation. First, we remark that for large values of according to (13.1.79) and (13.1.88), we have... 

In the derivation of (5.38) we have extracted the <5-function term from the phonon Green s function which, in turn, renormalized the bare potential V to the adiabatic one An expression similar to (5.37) can be obtained for an arbitrary bath whenever the coupling is suflSciently weak and the functional Z[Q(t)] can be expanded into the series... 

Fig. 1 (a) Self-energy in diagrammatic representation, (b) Expansion series for the vertex E up to g. Thick solid, thick dashed, and thin dashed lines indicate, respectively, the electron Green s function, the dressed phonon, and the bare phonon propagators... 

Head and Silva used occupation numbers obtained from a periodic HF density matrix for the substrate to define localized orbitals in the chemisorption region, which then defines a cluster subspace on which to carry out HF calculations [181]. Contributions from the surroundings also only come from the bare slab, as in the Green s matrix approach. Increases in computational power and improvements in minimization techniques have made it easier to obtain the electronic properties of adsorbates by supercell slab techniques, leading to the Green s function methods becoming less popular [182]. 

In this chapter, we have barely scratched the surface of the Green s function approach. This technique has been widely used, and with sufficient effort (i.e., using sophisticated self-energies) it provides an excellent description of both valence and core ionization potentials of a large class of molecules. We hope that our introduction will help the interested reader penetrate the literature. 

Green s function of the bare electrode system and SV is the difference between the potential of the full system containing an atomic or a molecular spacer and that of the bare electrodes. In atomic units ( g, r].m = 1), it is... 

We now have equations of motion for the one- and two-particle Green s functions. They depend on the Hartree-exchange-correlation self-energy. Its Hartree part is trivial, but a practical way of calculating its exchange-correlation part is needed. Hedin [36] proposed a scheme that yields to a set of coupled equations and allows in principle for the calculation of the exact self-energy. This scheme can be seen as a perturbation theory in terms of the screened interaction W instead of the bare Coulomb interaction v. We show a generalization of this derivation for the case of a nonlocal potential. 

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