The calculation of absorption band shapes in dynamic Jahn-Teller systems by the use of the Lanczos algorithm

Abstract

An economical way of using the Lanczos algorithm on the very large sparse matrices associated with absorption band-shape calculations in dynamic Jahn-Teller and similar systems is described, and the sources of error are identified and discussed. Band shapes are calculated for a two-mode E(X)( epsilon ₁(+) epsilon ₂) system which show a remarkable similarity with those calculated using a single effective frequency. Band shapes are also calculated for T(X)( tau (+) epsilon ) with and without spin-orbit coupling, with the resolution of very narrow spikes in the band under favourable circumstances.