We present a general two-dimensional model of conical intersection between metastable states that are vibronically coupled not only directly but also indirectly through a virtual electron in the autodetachment continuum. This model is used as a test ground for the design and comparison of iterative solvers for resonance dynamics in low-energy electron-molecule collisions. Two Krylov-subspace methods with various preconditioning schemes are compared. To demonstrate the applicability of the proposed methods on even larger models, we also test the performance of one of the methods on a recent model of vibrational excitation of CO2 by electron impact based on three vibronically coupled discrete states in continuum (Renner-Teller doublet of shape resonances coupled to a sigma virtual state) including four vibrational degrees of freedom. Two-dimensional electron energy-loss spectra resulting from electron-molecule scattering within the models are briefly discussed.

Faculty of Mathematics and Physics Institute of Theoretical Physics Charles University 5 Holešovičkách 2 180 00 Prague Czech Republic

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