The Lanczos Algorithm in Molecular Dynamics: Calculation of Spectral DensitiesLarge Scale Eigenvalue Problems, Proceedings of the IBM Europe Institute Workshop on Large Scale Eigenvalue Problems

In the past the Lanczos algorithm has proven to be a very useful tool in the study of molecular dynamics. It enables efficient calculation of the spectral densities which are essential in the interpretation of spectroscopic or scattering experiments. In the present work, the use of the Lanczos algorithm in the calculation of the spectral densities is analyzed in a general fashion. Its application to problems characterized by complex symmetric matrices, which are normally encountered in the analysis of magnetic resonance experiments, is then recovered as a particular case. After a discussion of the factors influencing the convergence in the calculation of spectral densities, the implementation of the Lanczos algorithm with non-orthogonal basis functions is considered in relation to molecular systems having hindered degrees of freedom.