New developments in the analysis of vibrational spectra On the use of adiabatic internal vibrational modes

Abstract

Depending on geometry, conformation, and electronic structure, each molecule has vibrational spectra that are measured with the help of infrared or Raman spectroscopy. Conclusions can be drawn from the measured vibrational spectra with regard to the structure of a compound. Vibrational frequencies and force constants in the harmonic approximation can be calculated and these values are used for the analyses of measured vibrational spectra. This chapter presents a way of analyzing calculated vibrational spectra in terms of internal vibrational modes associated with the internal coordinates used to describe geometry and conformation of a molecule. An internal mode is localized in a molecular fragment by describing the rest of the molecule as a collection of massless points that just define molecular geometry. Alternatively, the new fragment motions can be considered as motions that are obtained after relaxing all parts of the vibrating molecule but the fragment under consideration. The new modes are suited to analyze the vibrational spectra of a molecule in terms of internal coordinate modes, to correlate the vibrational spectra of different molecules, and to extract chemically useful information directly from vibrational spectra. The chapter discusses the concept of localized internal vibrational modes, the basic equations of vibrational spectroscopy, previous attempts of defining internal vibrational modes, definitions of adiabatic internal modes, adiabatic internal force constant, mass, and frequency, characterization of normal modes in terms of internal vibrational modes, definition of internal mode amplitudes, and analysis of vibrational spectra in terms of adiabatic internal modes. There is the explanation of the correlation of vibrational spectra of different molecules, derivation of bond information from vibrational spectra, and adiabatic internal modes from experimental frequencies, and a generalization of Badger's rule. There are details on intensities of adiabatic internal modes and investigation of reaction mechanism with the help of the CNM analysis.