Localizing normal modes in large molecules.

We show how vibrational spectra obtained from quantum chemical calculations can be analyzed by transforming the calculated normal modes contributing to a certain band in the vibrational spectrum to a set of localized modes. This is achieved by determining the unitary transformation that leads to modes which are maximally localized with respect to a suitably defined criterion. We demonstrate that these localized modes are more appropriate for the analysis of calculated vibrational spectra of polypeptides and proteins than the normal modes, which are usually delocalized over the whole system. Both the frequencies at which the bands in the vibrational spectra appear and the total intensities of these bands can be interpreted in terms of the localized modes. Furthermore, we show how coupling constants for the interaction between the localized modes, which can be employed to rationalize the observed band shapes, can be extracted from the calculations.