Resonance transition probabilities by the complex Lanczos recursion method

Resonance transition probabilities are obtained without the need to compute eigenvectors of the complex scaled Hamiltonian matrix. The new computational approach is a combination of the complex Lanczos recursion method, the complex coordinate method, and the extension of the Wyatt and Scott modified QL algorithm to complex matrices. To illustrate the method, the coupling strength between a resonance state and different scattering channels of HD from a flat Ag surface are calculated.