Second-order quasiparticle electron

Quasiparticle Second order Dilated Electron Propagator /42/ 124.98 0.05... 

The proposals found here can be seen as the result of a two-way strategy for the treatment of large molecules. First, we improve on the accuracy of the very efficient second order approximation. In addition, we introduce approximations that lower considerably the required computer resources for the use of higher-order approximations to the electron propagator within the quasiparticle approach. 

Figure. 6. Theta trajectories for the e-Ca 2P shape resonance from the zeroth (inset), second order ( 2), quasiparticle second order ( 2), diagonal Zph-TDA (E2pfc TDA) and quasiparticle diagonal ZphrTDA ( 2ph TDA) decouplings of Idle dilated electron propagator.

Zeroth order, Quasiparticle Second order and Quasiparticle Diagonal 2ph-TDA Bi-orthogonal Dilated Electron Propagator /45/ 1.71 0.10... 

The problem of the searching for the optimal one-electron representation is one of the oldest in the theory of multielectron atoms. Three decades ago, Davidson had pointed the principal disadvantages of the traditional representation based on the self-consistent field approach and suggested the optimal natural orbitals representation. Nevertheless, there remain insurmountable calculational difficulties in the realization of the Davidson program (see, e.g. Ref. [12]). One of the simplified recipes represents, for example, the DPT method [18,19]. Unfortunately, this method does not provide a regular refinement procedure in the case of the complicated atom with few quasiparticles (electrons or vacancies above a core of the closed electronic shells). For simplicity, let us consider now the one-quasiparticle atomic system (i.e., atomic system with one electron or vacancy above a core of the closed electronic shells). The multi-quasiparticle case does not contain principally new moments. In the lowest second order of the QED PT for the A , there is the only one-quasiparticle Feynman diagram a (Fig. 12.1), contributing the ImAZ (the radiation decay width). 

Here 7, is the total angular moment of the initial target state indices and are the incident and discrete state energies, respectively to the incident and captured muons. Further it is convenient to use the second quantization representation. In particular, the initial state of the system atom plus free muon can be written as a l final state is that of an atom with the discrete state electron, removed electron and captured muon in further 7 > represents one-particle (IQP) state, and F > represents the three-quasiparticle (3QP) state. The imaginary (scattering) part of the energy shift ImAE in the atomic PT second order (fourth order of the QED PT) is as follows [27,31] ... 

As a second example, we compare in O Table 24-2 first-order transitions calculated using the hybrid TPSSh and HSE functionals (Barone et al. 2005a), and calculations considering GW plus electron-hole interactions (GW + e-h) (Spataru et al. 2008), with experimental values. Here, it is worth to point out the results obtained with hybrid functionals, that predict peak positions in agreement with more complex quasiparticle and excitonic effects approaches. An explanation for this behavior has been recently presented by Brothers et al. (2008). 

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