Molecular Auger decay rates from complex-variable coupled-cluster theory

Abstract

The emission of an Auger electron is the predominant relaxation mechanism of core-vacant states in molecules composed of light nuclei. In this non-radiative decay process, one valence electron fills the core vacancy while a second valence electron is emitted into the ionization continuum. Because of this coupling to the continuum, core-vacant states represent electronic resonances that can be tackled with standard quantum-chemical methods only if they are approximated as bound states, meaning that Auger decay is neglected. Here, we present an approach to compute Auger decay rates of core-vacant states from coupled-cluster and equation-of-motion coupled-cluster wave functions combined with complex scaling of the Hamiltonian or, alternatively, complex-scaled basis functions. Through energy decomposition analysis, we illustrate how complex-scaled methods are capable of describing the coupling to the ionization continuum without the need to model the wave function of the Auger electron explicitly. In addition, we introduce in this work several approaches for the determination of partial decay widths and Auger branching ratios from complex-scaled coupled-cluster wave functions. We demonstrate the capabilities of our new approach by computations on core-ionized states of neon, water, dinitrogen, and benzene. Coupled-cluster and equation-of-motion coupled-cluster theory in the singles and doubles approximation both deliver excellent results for total decay widths, whereas we find partial widths more straightforward to evaluate with the former method. We also observe that the requirements towards the basis set are less arduous for Auger decay than for other types of resonances so that extensions to larger molecules are readily possible.

Theory of electronic resonances: Fundamental aspects and recent advances

“…in typical calculations in Gaussian basis sets. 67,92,136 θ-dependence entails the need to find an optimal value, θopt, which is usually done using the criterion 52,123,124 min…”

“…Further reasons are the use of complex algebra and the need to include additional diffuse functions in the basis set; standard bases typically yield bad results. 17,67,92,136 While there are basis sets that have been designed specifically for resonances, [137][138][139] the addition of a few shells of even-tempered diffuse functions to a standard basis usually works as well. 17,67…”

“…For example, CBF-HF determinants for a core-vacant state or a molecule in a static electric field can be easily constructed using maximumoverlap techniques 210 starting from a real-valued core-vacant HF determinant or a field-free HF determinant, respectively. 92,104,136 It also needs to be mentioned here that the strengths and weaknesses that have been established for a particular electronicstructure method in the context of bound states, are still relevant for resonances. For example, many resonances have open-shell character, a spin-complete description as afforded by multistate methods such as EOM-CC and ADC is advantageous.…”

“…( 7) is best applied to energy differences here. 104,136,157 For CAP calculations, the differences are usually negligible.…”

“…208 A core-ionized H2O molecule with electronic configuration (1a1) 1 (2a1) 2 (1b2) 2 (3a1) 2 (1b1) 2 can decay into 16 states of H2O 2+ where shake-up processes and double Auger decay have not even been considered yet. 136,263 In a molecule exposed to a static electric field, electrons from all orbitals can undergo tunnel ionization giving rise to a multitude of decay channels but the relative ease with which ionization from a particular orbital happens greatly depends on the orientation of the field and the molecule. 104,106 Partial decay widths describing the contributions of different channels are thus of great importance for the chemistry and physics of electronic resonances.…”