Electronically metastable states can efficiently be investigted using L-2 t
echniques, such as the complex absorbing potential (CAP) or the stabilizati
on method; but, the study of autodetaching systems is nonetheless far more
expensive than the investigation of comparable bound states. The costly ste
p of the L-2 methods for resonances involves the repeated diagonalization o
f a parameterized Hamilton operator, and in this communication we investiga
te representations of the needed operators in very small basis set consisti
ng of a few eigenstates of the physical Hamiltonian. It is shown that CAP c
alculations can indeed be performed using a very small eigenstate basis set
, whereas basis sets of comparable size are unsuitable for stabilization ca
lculations. Our results allow us to study the frequently employed energy se
lection procedure in the context of Siegert energies. (C) 2001 John Wiley &
Sons, Inc.