8 - Vibrational Frequencies and Intensities

Abstract

Methods of vibrational spectroscopy provide important information about the molecular structure, nature of chemical bond, intramolecular forces acting between the atoms in a molecule, and intermolecular forces in condensed phase. There has been considerable interest among theoretical chemists to use the classical (normal coordinate) and quantum mechanical methods to study vibrations of molecules. These methods have been put to different uses such as for the determination of accurate force fields (quadratic, cubic, quartic, etc.), prediction of the frequency and intensity of rotational–vibrational bands of molecules in harmonic and anharmonic approximations, evaluation of vibrationally averaged properties and thermodynamic functions, determination of many-body potentials etc. All these aspects of classical and quantum mechanical methods have been discussed in detail in this chapter with suitable examples. Selection rules for vibrational transitions in polyatomic molecules, origin of fundamental bands, overtones and combination tones, and scaling procedures to correct the vibrational frequencies of errors due to the neglect of electron correlation and anharmonicity have been given due attention. A brief account of the second-order perturbation theory of anharmonic oscillators and the calculation of anharmonicity and vibration–rotation interaction constants of polyatomic molecules have been given with illustrative examples.