The theoretical investigation of mesoscopic objects requires new techniques which are particularly suited for the study of selected aspects of these systems. Vibrational spectroscopy is a main source for structural information on heterogeneous systems. We present an efficient quantum chemical method, which relies on a modified Davidson algorithm for targeting selected vibrations in infrared and Raman spectra. This approach is applied to the characteristic breathing modes of single-walled carbon nanotubes. (C) 2003 American Institute of Physics.