Chapter 5
Introduction to Quantum Vibrational
Spectroscopy
Krzysztof B. Be´ c, Justyna Grabska, and Thomas S. Hofer
Abstract 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.
Keywords Quantum vibrational spectroscopy · Harmonic approximation ·
Overtone and combination transitions · Anharmonic methods
K. B. Be´ c · J. Grabska
CCB-Center for Chemistry and Biomedicine, Institute of Analytical Chemistry and
Radiochemistry, Leopold-Franzens University, Innrain 80/82, 6020 Innsbruck, Austria
e-mail: Krzysztof.Bec@uibk.ac.at
J. Grabska
e-mail: Justyna.Grabska@uibk.ac.at
T. S. Hofer (B)
CCB-Center for Chemistry and Biomedicine, Institute of General, Inorganic and Theoretical
Chemistry, Leopold-Franzens University, Innrain 80/82, 6020 Innsbruck, Austria
e-mail: t.hofer@uibk.ac.at
© Springer Nature Singapore Pte Ltd. 2021
Y. Ozaki et al. (eds.), Near-Infrared Spectroscopy,
https://doi.org/10.1007/978-981-15-8648-4_5
83
Introduction to Quantum Vibrational
Spectroscopy
Krzysztof B. Be´ c, Justyna Grabska, and Thomas S. Hofer
Abstract 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.
Keywords Quantum vibrational spectroscopy · Harmonic approximation ·
Overtone and combination transitions · Anharmonic methods
K. B. Be´ c · J. Grabska
CCB-Center for Chemistry and Biomedicine, Institute of Analytical Chemistry and
Radiochemistry, Leopold-Franzens University, Innrain 80/82, 6020 Innsbruck, Austria
e-mail: Krzysztof.Bec@uibk.ac.at
J. Grabska
e-mail: Justyna.Grabska@uibk.ac.at
T. S. Hofer (B)
CCB-Center for Chemistry and Biomedicine, Institute of General, Inorganic and Theoretical
Chemistry, Leopold-Franzens University, Innrain 80/82, 6020 Innsbruck, Austria
e-mail: t.hofer@uibk.ac.at
© Springer Nature Singapore Pte Ltd. 2021
Y. Ozaki et al. (eds.), Near-Infrared Spectroscopy,
https://doi.org/10.1007/978-981-15-8648-4_5
83