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

## TL;DR

This paper presents a straightforward derivation of the exact quasiparticle theory, extending its applicability to arbitrary initial excited eigenstates, and validates it using the GW approximation on atoms and molecules.

## Contribution

It provides a simple derivation of the quasiparticle theory and extends its validity to excited states, demonstrating its applicability beyond ground states.

## Key findings

- QP energies and wave functions can be self-consistently determined.
- The theory applies to arbitrary initial excited eigenstates.
- Validation with GW approximation confirms the theory's accuracy.

## 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.