  Fano-ADC is a family of ab initio methods for prediction of electronic decay
widths in excited, singly- and doubly-ionized systems. It has been particularly
successful in elucidating the geometry dependence of the inter-atomic decay
widths in clusters and facilitated prediction of new electronic decay
phenomena. However, the available Fano-ADC schemes are limited to the second
order treatment of the initial state and fist-order treatment of the final
states of the decay. This confines the applicability of the Fano-ADC approach
to first-order decay processes, e.g. normal but not double Auger decay, and
compromises the numerical accuracy of the schemes through the unbalanced
treatment of electronic correlation. Here we introduce the ADC(2,2)
approximation for singly ionized states which describes both initial and final
states of the decay up to second order. We use the new scheme to construct the
Fano-ADC(2,2) approximation for the decay widths and show that it provides
superior accuracy for the decay widths of a series of processes. Moreover, the
Fano-ADC(2,2) method provides access to second-order decay processed, such as
double Auger decay, which are qualitatively beyond reach of the previously
available Fano-ADC implementations.
