Lanczos methods for hamiltonian spectra: Hilbert-space approximations to interaction-prepared states

Abstract

Recent progress is reported in applications of iterative methods for calculations of molecular electronic continuum states. Vectors constructed in an appropriate Lanczos basis are seen to provide directly approximations to the interaction-prepared states of Fano and Cooper. Nondegenerate point-group-symmetry electronic continuum wave functions are constructed recursively in this way for complex molecules without explicit enforcement of the S-matrix, K-matrix or other asymptotic boundary conditions required in conventional scattering developments. A multi-channel Feshbach-Fano version of the approach employing an appropriately selected Q space of zeroth-order states provides a Lanczos formulation of complex photoionization spectra based on eigenfunctions of molecular point-group-symmetry type. Computational applications of the methods described are reported for the partial cross sections of selected (N 2, CO 2, C 2H 2) molecules.