An accurate calculation of bound and resonance spectra of the non-rotating odd O2 exchange symmetry HO2 radical is presented. The calculation has been carried out by a recently developed iterative technique which uses filter diagonalization of a sparse matrix of the system Hamiltonian with absorbing boundary conditions. We were able to obtain 361 bound states and some 232 isolatable resonances (Γ<0.01 eV) in a wide energy range corresponding to the HO2→H+O2 unimolecular decomposition reaction. It is shown that all resonances found have the same nature as the bound states in that they all are localized in the same region of space over the deep potential well, and moreover the extrapolated smoothed density of the bound states merges easily with the smoothed density of the resonance states. The level statistics for both bound and resonance states indicates a highly chaotic regime consistent with the random matrix theory. Strong mode mixing makes assignments of most bound and resonance states impossible because the corresponding wave functions do not show any simple pattern. Interestingly, the randomly fluctuating high resolution density of states after smoothing shows a structure resembling two basic frequencies corresponding to the O2 stretch and HOO bend motion of the HO2 molecule.

We observe the formation in a single-photon transition of two core holes, each at a different carbon atom of the C2H2 molecule. At a photon energy of 770.5 eV, the probability of this 2-site core double ionization amounts to 1.6 ± 0.4% of the 1-site core double ionization. A simple theoretical model based on the knockout mechanism gives reasonable agreement with experiment. Spectroscopy and Auger decays of the associated double core hole states are also investigated.

A simple recursion polynomial expansion of the Green's function with absorbing boundary conditions. Application to the reactive scattering An iterative method for calculating resonance positions and widths is developed. The system Hamiltonian with an asymptotic complex absorbing potential is represented by a large and sparse matrix. A small set of ''good'' basis functions suitable for diagonalizing the Hamiltonian matrix in a given energy window is generated by acting with a polynomial expansion of the imaginary part of the system Green's function onto a generic initial wave packet. As an application to a realistic three-dimensional system, the calculation of 65 resonances of the nonrotating HCO molecule up to the energy 9000 cm Ϫ1 is presented. The method is shown to be rapidly convergent and accurate, especially for narrow resonances.

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