Calculation of quantum resonance energies and lifetimes via quasi-minimum residual filter diagonalization

The quasi-minimum residual (QMR) method of Freund [SIAM J. Sci. Stat. Comput. 13 (1992) 425] is applied to the problem of calculating quantum resonance energies and lifetimes via a filter diagonalization (FD) scheme. Using the HO2 molecule as a test case, the resulting quasi-minimum residual filter diagonalization (QMRFD) algorithm is shown to be capable of accurately computing complex eigenvalues throughout the spectrum from a single Lanczos subspace. The algorithm is efficient, and requires the storage of only two complex vectors in the primary DVR representation. The quality of the FD results is verified by a comparison with resonance energies and linewidths obtained by fitting the spectral density profile.