Lanczos Approach to Molecular Spectroscopy without Explicit Calculation of Eigenfunctions

Abstract

The Lanczos algorithm is a simple and accurate recursive scheme to determine eigenvalues of a large real-symmetric or Hermitian matrix. Because of its reliance on a three-term recursion relation based on matrix-vector multiplication, the Lanczos algorithm does not alter the Hamiltonian matrix and scales favorably with the dimension of the problem. It is, however, more difficult to obtain the corresponding eigenfunctions, particularly for large dimensional problems. In this review, we discuss several efficient Lanczos-based schemes to directly obtain useful scalar spectroscopic properties without explicitly calculating eigenfunctions.