A simple derivation of the exact quasiparticle theory and its extension to arbitrary initial excited eigenstates

Abstract

The quasiparticle (QP) energies, which are minus of the energies required by removing or produced by adding one electron from/to the system, corresponding to the photoemission or inverse photoemission (PE/IPE) spectra, are determined together with the QP wave functions, which are not orthonormal and even not linearly independent but somewhat similar to the normal spin orbitals in the theory of the configuration interaction, by self-consistently solving the QP equation coupled with the equation for the self-energy. The electron density, kinetic and all interaction energies can be calculated using the QP wave functions. We prove in a simple way that the PE/IPE spectroscopy and therefore this QP theory can be applied to an arbitrary initial excited eigenstate. In this proof, we show that the energy-dependence of the self-energy is not an essential difficulty, and the QP picture holds exactly if there is no relaxation mechanism in the system. The validity of the present theory for some initial excited eigenstates is tested using the one-shot GW approximation for several atoms and molecules. * ohno@ynu.ac.jp

GW(Γ) method without the Bethe-Salpeter equation for photoabsorption energies of spin-polarized systems

“…In this section, we derive the GW(Γ) method without BSE to calculate PAEs and compare the method with the previous formalism. We apply the "extended" QP theory [18] to the (N − 1)-electron system to obtain PAEs of the N-electron system.…”

“…without introducing any further relaxation. The electron attachment energies ε ν (including ε 0 ) can be calculated by solving the "extended" quasiparticle equation (EQPE): [18] h (1) s…”

“…In the present paper, we propose a completely different and very tractable approach, which allows the rigorous one-to-one correspondence between the PA peaks and the ("extended") QP levels, [18] although each peak height (intensity or oscil-lator strength) is not obtained. Our idea is to treat a cationic system instead of a neutral system and to consider the following three processes:…”

“…But anyway this is a simple and transparent task on the basis of the "extended QP theory." [18]) It allows one to identify the rigorous one-to-one correspondence between the PA peaks and the ("extended") QP levels. Since our new method requires the GW calculation only and does not require the BSE, we named this as the "GW(Γ) method without BSE."…”

Ab initio simulations of x-ray emission spectroscopy with the GW+ Bethe-Salpeter equation method

“…The success of the Green's-function approach in XPS and XAS simulations results from the accurate descriprtion of the screening ef-fect due to the core hole state within the GW approximation (GWA) [41][42][43][44] . The second property is that the Green's-function approach can treat an arbitrary excited state as an initial state, which was recently established as extended quasiparticle theory 45 . This property allows one to make the initial state with a core hole the input electronic configuration and offer a powerful justification to apply the Green's-function method to XES simulations.…”