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 CO₂^- or the benzene anion
doubly charged molecules such as CO₃^2-
highly excited states (core-ionized, 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 non-square-integrable 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 multi-reference CI and the electron propagator based ADC(2) methods with complex absorbing potentials as well as with variants of Taylor-style stabilization techniques (both are L² continuum approaches). These methods extend the application range of quantum chemistry into the metastable regime. (I have also played with complex coordinates and Stieltjes-Imaging-like 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 ²Pi_u resonance of CO₂^-. 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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