Partial Auger Decay Widths from Complex-Valued Density Matrices

TL;DR

This paper introduces a new method to compute partial Auger decay widths using complex-valued density matrices within non-Hermitian quantum mechanics, providing accurate results for various molecules and comparing favorably with existing methods.

Contribution

The authors propose a novel approach to calculate partial Auger decay widths directly from two-electron density matrices, avoiding the need for channel-specific wave function convergence.

Findings

Method yields spectra that agree well with existing approaches.

Successfully computed spectra for molecules like methane, ethane, and hydrogen sulfide.

First reported spectrum for cyanide anion.

Abstract

We discuss a new strategy to compute partial Auger decay widths with equation-of-motion ionisation-potential coupled-cluster (EOMIP-CCSD) wave functions in the framework of non-Hermitian quantum mechanics, where the decaying character of the metastable states is described via complex-scaled basis functions. While the total decay width can generally be obtained from the energy eigenvalues, the computation of partial decay widths, i. e. the contributions of channels to the total decay rate, governing their probability distribution, is less trivial. In the past, methods where channels are projected out during the EOMIP-CCSD iteration have been developed (Auger Channel Projector), but such a procedure requires to establish convergence of the excitation vector for each separately. Furthermore, they suffer from interaction between the channels upon perturbation of the wave function. In contrast, we suggest to compute the contribution of the two-electron transition that Auger decay implies, where two valence electrons are involved, one refilling the core hole and one emitted to the continuum, from the respective entries in the two-electron density matrix that describe the extent of this transition in the wave function upon application of correlation and excitation operator. In this way, we obtain all partial decay widths from wave functions determined in the full excitation manifold. The results from this approach compare very well to the Auger Channel Projector results: we compute spectra for K-edge ionised states of methane, ethane, hydrogen sulfide, and the cyanide anion, as well as Coster-Kronig spectra of L1-edge ionised hydrogen sulfide, which differ only negligibly between the two methods. A spectrum of the cyanide anion has not been reported before -- we discuss the selectivity of the decay process with respect to the initial state and the possibility of interatomic Auger decay.