Within the last eight years we have developed and investigated quantum chemical methods for the inverse solution of the vibrational problem within the harmonic approximation. In 2002, our starting point was the observation that the vibrational analysis of large molecules with standard quantum chemical methods becomes unfeasible even in the harmonic approximation because of the time consuming calculation of the entries in the Hessian matrix. Considering also the fact that one would calculate in this standard approach many spectral features that are often not needed for assigning a molecular structure, we developed a subspace iteration protocol called Mode-Tracking that allows us to converge pre-defined molecular vibrations to normal modes relevant for answering a scientific question. Since this yields only a very limited part of the vibrational spectrum, a fingerprint identification is not possible. To overcome this problem, we devised the Intensity-Tracking algorithm that distributes intensity within any type of vibrational spectroscopy to those normal modes that pick up intensity. In order to accomplish this it was necessary to rigorously define Intensity Carrying Modes.
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