Lanczos algorithms and cross correlation functions C-if(E)
2003 (English)In: Journal of Theoretical and Computational Chemistry, ISSN 0219-6336, E-ISSN 1793-6888, Vol. 2, no 4, 523-535 p.Article in journal (Refereed) Published
Cross correlation (CC) functions C-if(E) play an important role in chemical physics. They appear in the description of reactive scattering, photo-dissociation, photo-electron spectroscopy and electron transfer to mention a few. In this paper, we discuss two methods based on the Lanczos algorithm to compute the CC function for several initial and final states at the same time, without diagonalization. The property of the coupled two-term recursions variant of the Lanczos algorithm that yields a decomposition T = U-k(T) Delta(k)U(k) of the tridiagonal Lanczos matrix is crucial. The first method, the quasi minimal-recursive residue generation method (QM-RRGM) is based on solving a set of linear equations whereas the second method is based on a band-Lanczos method. The computational cost is of the same order of magnitude for both methods and is given by the number of matrix-vector multiplications in the underlying Lanczos method. Only a small set of scalars needs to be updated each recursion. The methods are compared for a model problem, the continuum resonance Raman cross section for a collinear model of CH2IBr. Both methods shows similar convergence properties. By adding a pre-conditioner, the rate of convergence can be increased dramatically.
Place, publisher, year, edition, pages
2003. Vol. 2, no 4, 523-535 p.
IdentifiersURN: urn:nbn:se:uu:diva-144157ISI: 000220867400005OAI: oai:DiVA.org:uu-144157DiVA: diva2:392743