Quasi-particle energies

As noticed from this expression, the CP calculation has to be basically carried out on the quasi-particle picture. Formally, quasi-particle energies and wave functions have to be evaluated by solving... 

This way we take the quasi-particle energies which are described by an effective mass and a self-energy shift and solve the Schrodinger equation for the separable Yamaguchi potential. Separating the center of mass motion, with energy p2/2 from the relative motion, with reduced mass M M /(M +... 

Note that the quasi-particle energy is independent of color and flavor in this case, since we have assumed a singlet pair in flavor and color. 

An immediate consequence of symmetry is the nature of the quasiparticle spectrum. The density of states p(co) can be calculated from the knowledge of the quasi-particle energies. For singlet states Ek,+ = Ek, with... 

Beyond the HF approximation, the band energies are defined as ionization potentials for occupied or valence bands, and as electron affinites for unoccupied or conduction bands, respectively [44], They are no longer one-electron energies, but are quasi-particle energies, which can be calculated via MBPT [26,44-48], CC [4(d),5,49-51], and propagator [6-9] or Green s function methods (GFM) [10-14]. 

The propagator [6-9] or Green s function method (GFM) [10-14] provides another approach to calculate the quasi-particle energy bands. The Dyson equation provides the exact E(N 1) energies in a formally one-particle picture, but the equation can only be solved approximately in real applications [57], With the irreducible self-energy part in the diagonal approximation being correct to second-order, the inverse Dyson equation can be written as [26]... 

Table 4 lists the MBPT(2) band gaps of polyacetylene calculated with basis set 6-31G and DZP at three different geometries by us [36]. The cutoffs N and K are both 21. The geometries used in the calculations are listed in Table 5. The first two were given by Suhai [53,55] and the last one was an experimentally estimated geometry [97], The band gaps obtained are 4.033, 3.744, and 3.222 eV, respectively. There is no direct measurement of the band gap, defined as a quasi-particle energy difference of the lowest unoccupied and highest occupied orbitals. Instead, the absorption spectrum of polyacetylene crystalline films rises sharply at 1.4 eV and has a peak around 2.0 eV [97]. To explain this measured spectrum, one needs to calculate the density of the system s excited states and the absorption coefficients of the states.

A partial justihcation for the interpretation of the KS eigenvalues as starting point for approximations to quasi-particle energies, common in band-structure calculations, can be given by comparing the KS equation with other self-consistent equations of many-body physics. Among the simplest such equations are the Hartree equation... 

Ek quasi-particle energy N degeneracy of 4f ground state... 

The° irst-order correction in eq. (2.17) is real, and gives in first-order perturbation theory the difference between quasi-particle energies E and LDA eigenvalues proportional to the distance from the Permi energy, (E-y). The Towest-order imaginary part of (2.17) can be shown to be of the form -ic(p)(E-y), with c > 0. 

The Quasi-Particle Energy Gap of AHemating (rans-Polyacetylene... 

TABLE 5.4. Different Physical Quantities Contributing to the Formation of the Quasi-Particle Energy-Band Gap in the Alternating trans PA One-Particle Energies e(HF), Electron and Hole Self-Energies, 2(e) and 2(h), Respectively, and Quasi-Particle Energies e(QP)<2 > ... 

TABLE 5.5. Single-Particle Energies (e[HF]) and Self-Energy Correlations (2) Contributing to the Quasi-Particle Energies (el pol) in the Valence and Conduction Bands of PolyC ... 

Application of the above-described method to different poly-mers " has yielded reasonably good agreement with experiment only (see the next section) if one employs a good basis set and substitutes into the Green matrix elements (8.22) not the HF one-electron eneigies, but rather the quasi-particle energies, which contain also correlation contributions at least in the second order of many-body perturbation theory (see Section 5.3). 

In the diagonal approximation this can be derived from the Dyson equation and provides directly the quasi particle energies. 

A many-electron method to calculate excitation energies in semiconductors and insulators. It uses a Green s function (G) and a screened Coulomb potential (denoted W) to express the so-called self-energy operator. The self-consistent solution of quasi-particle equations containing the self-energy operator gives quasi-particle energies which can be interpreted as... 

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