Computing resonance energies, widths, and wave functions using a Lanczos method in real arithmetic

We introduce new ideas for calculating resonance energies and widths. It is shown that a non-Hermitian-Lanczos approach can be used to compute eigenvalues of H+W, where H is the Hamiltonian and W is a complex absorbing potential (CAP), without evaluating complex matrix-vector products. This is done by exploiting the link between a CAP-modified Hamiltonian matrix and a real but nonsymmetric matrix U suggested by Mandelshtam and Neumaier [J. Theor. Comput. Chem. 1, 1 (2002)] and using a coupled-two-term Lanczos procedure. We use approximate resonance eigenvectors obtained from the non-Hermitian-Lanczos algorithm and a very good CAP to obtain very accurate energies and widths without solving eigenvalue problems for many values of the CAP strength parameter and searching for cusps. The method is applied to the resonances of HCO. We compare properties of the method with those of established approaches.