2. Scaling Procedures in Vibrational Spectroscopy

This chapter contains a brief review of the up-to-date scaling procedures that are used in the computational vibrational spectroscopy to improve agreement between the calculated harmonic frequencies and the observed fundamentals. Initially, the basics of vibrational spectroscopy are reminded. This includes the concept of potential energy surface, harmonic approximation, and a basic quantum chemistry treatment of the anharmonicity for a diatomic molecule. Brief description of the Wilson–Decius–Cross method for polyatomic molecules is also presented. Then the commonly used scaling procedures are discussed. The distinction between single- and multi-parameter scaling procedures is made. Four scaling procedures are reviewed. First, Pople’s uniform scaling is presented. Second, Yoshida’s wavenumber linear scaling method is discussed. Both methods are simple single-parameter frequency scaling methods. Then basics of two multi-parameter scaling methods, which are much more accurate but less straightforward to use, are given. Thus, Pulay’s scaled quantum mechanical force field method, in which scaling factors are applied directly to the calculated force constants is reviewed. Finally, introduction to quite recently proposed multi-parameter frequency scaling method, called effective scaling frequency factor method, is provided. The relevant sections start with a short description of the theory for a given method. Then a brief literature review on the historical background of methodology development is given.