Despite the continuous development of theoretical methodologies for describing nonadiabatic dynamics of molecular systems, there is a lack of approaches for processes where the norm of the wave function is not conserved, i.e., when an imaginary potential accounts for some irreversible decaying mechanism. Current approaches rely on building potential energy surfaces of reduced dimensionality, which is not optimal for more involving and realistic multidimensional problems. Here, we present a novel methodology for describing the dynamics of complex-valued molecular Hamiltonians, which is a generalisation of the trajectory surface hopping method. As a first application, the complex surface fewest switches surface hopping (CS-FSSH) method was employed to survey the relaxation mechanisms of the shape resonant anions of iodoethene. We have provided the first detailed and dynamical picture of the π*/σ* mechanism of dissociative electron attachment in halogenated unsaturated compounds, which is believed to underlie electron-induced reactions of several molecules of interest. Electron capture into the π* orbital promotes C[double bond, length as m-dash]C stretching and out-of-plane vibrations, followed by charge transfer from the double bond into the σ* orbital at the C-I bond, and, finally, release of the iodine ion, all within only 15 fs. On-the-fly dynamics simulations of a vast class of processes can be envisioned with the CS-FSSH methodology, including autoionisation from transient anions, core-ionised and superexcited states, Auger and interatomic coulombic decay, and time-dependent luminescence.
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