Introduction to Quantum Vibrational Spectroscopy

In this chapter, the quantum mechanical basis for computational studies of near-infrared spectra (NIR) is discussed. Since this topic is rarely covered in detail in the literature, the necessary prerequisites are provided as well, which include (i) the coordinate frame for the description of molecular vibrations, (ii) methods for the determination of the vibrational potential, (iii) the principles of the harmonic approximation, and (iv) its role as the foundation for methods taking anharmonic effects into account. The details of various anharmonic approaches in quantum vibrational spectroscopy are discussed, including methods based on the vibrational self-consistent field (VSCF) approach, vibrational perturbation theory (VPT) as well as one- and multidimensional grid-based methods. The merits and pitfalls of these approaches are critically assessed from the perspective of applications in NIR spectroscopy. Selected examples from recent literature are included to demonstrate how these methods can be applied to solve practical problems in spectroscopy. The aim of this chapter is to provide a comprehensive presentation of the topic aimed at a spectroscopic audience, while remaining accessible and focused on the key details. Although primarily intended for readers interested in NIR spectroscopy, the essential information provided in this chapter represents a fundamental perspective on quantum vibrational absorption spectroscopy and is useful for a more general readership as well.