Resonances are a fundamental concept in physics, yet their calculation is by far not a matter of routine. The electronic decay of an excited molecule is investigated in terms of decay processes and the decay width is calculated in two ways with Wigner-Weisskopf theory and non-degenerate non-Hermitian Rayleigh-Schrödinger perturbation theory employing complex absorbing potentials. A general non-Hermitian multireference perturbation theory is devised, and tested on a model problem, to improve on the accuracy of the two former approaches. The molecular Auger decay of an initial Xe 4d core hole is studied in the xenon fluorides (XeFn, n = 2, 4, 6) with electron propagator methods, and the electronic decay processes are identified by comparing the ionization spectra of the singly ionized molecule with its double ionization spectra. Electronic decay processes of interatomic character are found to have considerable impact on the electronic decay width in the xenon fluorides, due to a relation between the final state population and the decay width that is derived. The electron density in the valence shell of the xenon atom is low due to the fluorine atoms. The increase in decay width is, therefore, in contrast to the leading opinion that a low electron density on the atom that carries the initial core hole, leads to a low decay width.