Chapter 2
Scaling Procedures in Vibrational
Spectroscopy
Olga Bąk and Piotr Borowski
Abstract 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.
List of Acronyms
ARPE
Average relative percentage error
ESF
Effective scaling factor
ESFF
Effective scaling frequency factor method
FC
Force constant
FF
Force field
IC
Internal coordinate
O. Bąk Á P. Borowski (&)
Faculty of Chemistry, Maria Curie-Skłodowska University,
Maria Curie-Skłodowska Sq. 3, 20-031 Lublin, Poland
e-mail: piotr.borowski@poczta.umcs.lublin.pl
© Springer Nature Switzerland AG 2019
A. Koleżyński and M. Król (eds.), Molecular Spectroscopy—Experiment
and Theory, Challenges and Advances in Computational Chemistry
and Physics 26, https://doi.org/10.1007/978-3-030-01355-4_2
49
Scaling Procedures in Vibrational
Spectroscopy
Olga Bąk and Piotr Borowski
Abstract 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.
List of Acronyms
ARPE
Average relative percentage error
ESF
Effective scaling factor
ESFF
Effective scaling frequency factor method
FC
Force constant
FF
Force field
IC
Internal coordinate
O. Bąk Á P. Borowski (&)
Faculty of Chemistry, Maria Curie-Skłodowska University,
Maria Curie-Skłodowska Sq. 3, 20-031 Lublin, Poland
e-mail: piotr.borowski@poczta.umcs.lublin.pl
© Springer Nature Switzerland AG 2019
A. Koleżyński and M. Król (eds.), Molecular Spectroscopy—Experiment
and Theory, Challenges and Advances in Computational Chemistry
and Physics 26, https://doi.org/10.1007/978-3-030-01355-4_2
49