  We present the theory for the evaluation of non-adiabatic couplings (NACs)
involving resonance states within the complex absorbing potential
equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within
the singles and doubles approximation. Resonance states are embedded in the
continuum and undergo rapid decay through autodetachment. In addition, nuclear
motions can facilitate transitions between different resonances and between
resonances and bound states. These non-adiabatic transitions affect the
chemical fate of resonances and have distinct spectroscopic signatures. The NAC
vector is a central quantity needed to model such effects.
  In the CAP-EOM-CC framework, resonance states are treated on the same footing
as bound states. Using the example of fumaronitrile, which supports a bound
radical anion and several anionic resonances, we analyze the non-adiabatic
coupling between bound states and pseudocontinuum states, between bound states
and resonances and between two resonances. We find that the NAC between a bound
state and a resonance is nearly independent of the CAP strength and thus
straightforward to evaluate whereas the NAC between two resonance states or
between a bound state and a pseudocontinuum state is more difficult to
evaluate.
