Electronic Resonances
If a molecule can bind an additional electron, it is said to possess a
positive electron affinity, and the corresponding anion is a stable
entity. If however the electron cannot be permanently bound, the
corresponding metastable or temporary state is called a resonance.
A resonance has by definition a negative electron affinity,
and the anion (or more general the (N+1)electron system)
shows a characteristic autodetachment lifetime. Examples for
resonance states that decay by electron emission include:
 radical anions such as CO_{2}^{} or the benzene anion
 doubly charged molecules such as CO_{3}^{2}
 highly excited states (coreionized, doubly excited, ...)
 molecules in external fields (e.g. Stark field ionization)
As these examples show, resonance states pop up in many
contexts. One particular field I would like to emphasize are
electron induced reactions. Here the energy
of the incoming electron is channeled into the nuclear degrees of freedom initiating a
rearrangement or dissociation reaction, and the resonance state plays
the role of a reactive intermediate.
From the computational quantum chemist's viewpoint it is important to
note that owing to the possible decay, metastable states are
associated with nonsquareintegrable wavefunctions, and consequently,
standard (bound state) ab initio methods are inappropriate for these systems.
Ab initio methods for resonances
I am interested in ab initio methods that account for the
autodetachment in a framework analogous with standard electronic
structure methods (in contrast to electron scattering methods).
In particular, we have combined the multireference
CI and the electron propagator based ADC(2) methods with
complex absorbing potentials as well as with variants of Taylorstyle
stabilization techniques (both are L^{2} continuum approaches).
These methods extend the application range of quantum chemistry into the metastable regime.
(I have also played with complex coordinates and StieltjesImaginglike
approaches. Yet, apart from some highly special cases, I could not make these
methods work for me in any convincing way.)

This figure shows the results of a complex absorbing potential calculation
for the ^{2}Pi_{u} resonance of CO_{2}^{}.
Starting out from the real energy axis, the discretized continuum states move
into the complex energy plane as the absorption strength is
increased. The trajectory associated with the resonance can be identified by
its "stabilization" close to 4 eV / 0.18 eV.

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