A matrix eigenvalue formulation is presented for the pole search probl
em occurring in the renormalized two-particle Green's function method.
Emphasis is on the method's suitability for calculations on large mol
ecules. Thus it employs a first-order irreducible vertex part. The ref
ormulation is achieved by a transformation from the doubly-occupied or
bital space to a space spanned by orbital and satellite indices. The m
ethod is applied to the calculation of the Auger spectrum of octatetra
ene. Evaluation of the average hole-hole separation for every state sh
ows that the Auger spectrum of octatetraene should in general already
provide a model for the Auger spectrum of polyacetylene. However, the
results also predict that several single-state peaks at low binding en
ergy can be expected in the Auger spectrum of octatetraene. These shou
ld be due to delocalized states which are characteristic for long fini
te polyenes. (C) 1996 American Institute of Physics.