Recursion polynomial expansion of the Green’s function with absorbing boundary conditions: Calculations of resonances of HCO by filter diagonalization

Abstract

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−1 is presented. The method is shown to be rapidly convergent and accurate, especially for narrow resonances.