Theory of electronic resonances: fundamental aspects and recent advances

Abstract

Electronic resonances are states that are unstable towards loss of electrons. They play critical roles in high-energy environments across chemistry, physics, and biology but are also relevant to processes under...

Channel-specific core-valence projectors for determining partial Auger decay widths

“…General overviews of complex scaling can be found, for example, in Refs. [2,27]. Our approach to molecular Auger decay is based on the method of complex basis functions [32,33,36], which is a variant of complex scaling suitable for molecular electronic resonances.…”

“…In this way, the decay is quenched and the imaginary part of the energy stays zero apart from contributions resulting from the representation of the wave function in a finite basis set. [2,28] The CVS projector can be thought of as a sum of projectors representing individual Auger decay channels, which we will call Auger channel projectors (ACPs). We now determine the wave function under the constraint that only the amplitudes leading to certain Auger final states are zero.…”

“…Consequently, core-ionized states and Auger decay have attracted considerable interest in molecular electronic-structure theory. A fundamental challenge is that core-ionized states are electronic resonances embedded in the ionization continuum [2]; their lifetime is finite precisely because of Auger decay. To model only the energy levels of the species involved in X-ray absorption or Auger spectra, that is, to reproduce the positions of the signals, it has been shown that the decay process can often be neglected.…”

“…These approaches have the advantage that electronic-structure methods for bound states can be used to describe the initial and final states of Auger decay, but modeling the wave function of the outgoing electron correctly can be challenging [22,26]. Complex-variable techniques based on non-Hermitian quantum chemistry [2,27,28] offer an alternative framework for the treatment of Auger decay [29]. Here, electronic resonances are described as discrete L 2 integrable solutions of the Schrödinger equation with complex energy E res = E − iΓ/2, where E is the physical energy of the state and Γ its decay width.…”

“…In our earlier work [29], we used complex scaling of the Hamiltonian [30,31] and of the exponents of the basis functions [32,33] to describe molecular Auger decay. This allows a more black-box approach in the sense that no explicit treatment of the continuum is necessary but the computational cost is increased because of unphysical parameter dependencies [2,28]. A special interest in the context of Auger decay lies in determining the probability with which a core-ionized state decays into a certain final state.…”