124
5 The Vibrations of Polyatomic Molecules
where δr α is the change in the angle between the two OH bonds.
To improve the force field, it may be helpful to add some central force terms
between non-bonded atoms. It is equivalent to take into account the van der Waals
forces between non-bonded atoms. This modified force field often called Urey–
Bradley force field. One might also add a bond stretching angle bending interaction
constant.
These additional terms ameliorate the force field but there are more force constants
to determine which complicates the problem.
5.8 Conclusion
One of the main difficulties of the vibrational analysis is to correctly take into account
the interactions between the vibrational states as explained in Sects. 5.5, 5.6, and 6.6.
If the molecule is quite small, the variational method can be used (Bowman et al.
2008; Császár et al. 2012; Tennyson 2016). However, the usual way is the band-byband analysis because it is faster and easier. Although it is widely used, it is not a good
method because the determined parameters are effective ones, i.e., the interactions
are empirically and partially taken into account. The so-called global analysis is much
better. The first step is to analyze the ground state, then the first lowest excited state,
and so on, climbing the ladder. At each step, if an interaction is possible, it is taken
into account and the interesting parts of the spectra permitting to determine it are
analyzed. The difficulty is obvious: the infrared spectra are needed in the whole range.
Furthermore, the rotational spectra have to be measured from the centimeterwaves
to the submillimeterwaves. Finally, the help of an ab initio anharmonic force field is
very useful. But, at the end, a collection of reliable parameters is obtained. A typical
example is the global rovibrational analysis of carbonyl sulfide, OCS (Lahaye et al.
1987).
References
Bowman JM, Carrington T, Meyer H-D (2008) Variational quantum approaches for computing
vibrational energies of polyatomic molecules. Mol Phys 106:2145–2182
Bunker PR, Jensen P (1998) Molecular symmetry and spectroscopy. NRC Research Press, Ottawa
Califano S (1976) Vibrational states. Wiley, New York
Császár AG, Fábri C, Szidarovszky T, Mátyus E, Furtenbacher T, Czakó G (2012) Fourth age of
quantum chemistry: molecules in motion. Phys Chem Chem Phys 14:1085–1106
Demaison J, Herman M, Liévin J (2007) Anharmonic force field of cis- and trans-formic acid from
high-level ab initio calculations, and analysis of resonance polyads. J Chem Phys 126:164305
Herman M, Liévin J, Vander Auwera J, Campague A (1999) Advances in chemical physics: global
and accurate vibration Hamiltonians from high-resolution molecular spectroscopy, vol 108. Wiley,
Hoboken, NJ
Jahn HA (1939) Note on the Coriolis coupling terms in polyatomic molecules. Phys Rev 56:680–683
5 The Vibrations of Polyatomic Molecules
where δr α is the change in the angle between the two OH bonds.
To improve the force field, it may be helpful to add some central force terms
between non-bonded atoms. It is equivalent to take into account the van der Waals
forces between non-bonded atoms. This modified force field often called Urey–
Bradley force field. One might also add a bond stretching angle bending interaction
constant.
These additional terms ameliorate the force field but there are more force constants
to determine which complicates the problem.
5.8 Conclusion
One of the main difficulties of the vibrational analysis is to correctly take into account
the interactions between the vibrational states as explained in Sects. 5.5, 5.6, and 6.6.
If the molecule is quite small, the variational method can be used (Bowman et al.
2008; Császár et al. 2012; Tennyson 2016). However, the usual way is the band-byband analysis because it is faster and easier. Although it is widely used, it is not a good
method because the determined parameters are effective ones, i.e., the interactions
are empirically and partially taken into account. The so-called global analysis is much
better. The first step is to analyze the ground state, then the first lowest excited state,
and so on, climbing the ladder. At each step, if an interaction is possible, it is taken
into account and the interesting parts of the spectra permitting to determine it are
analyzed. The difficulty is obvious: the infrared spectra are needed in the whole range.
Furthermore, the rotational spectra have to be measured from the centimeterwaves
to the submillimeterwaves. Finally, the help of an ab initio anharmonic force field is
very useful. But, at the end, a collection of reliable parameters is obtained. A typical
example is the global rovibrational analysis of carbonyl sulfide, OCS (Lahaye et al.
1987).
References
Bowman JM, Carrington T, Meyer H-D (2008) Variational quantum approaches for computing
vibrational energies of polyatomic molecules. Mol Phys 106:2145–2182
Bunker PR, Jensen P (1998) Molecular symmetry and spectroscopy. NRC Research Press, Ottawa
Califano S (1976) Vibrational states. Wiley, New York
Császár AG, Fábri C, Szidarovszky T, Mátyus E, Furtenbacher T, Czakó G (2012) Fourth age of
quantum chemistry: molecules in motion. Phys Chem Chem Phys 14:1085–1106
Demaison J, Herman M, Liévin J (2007) Anharmonic force field of cis- and trans-formic acid from
high-level ab initio calculations, and analysis of resonance polyads. J Chem Phys 126:164305
Herman M, Liévin J, Vander Auwera J, Campague A (1999) Advances in chemical physics: global
and accurate vibration Hamiltonians from high-resolution molecular spectroscopy, vol 108. Wiley,
Hoboken, NJ
Jahn HA (1939) Note on the Coriolis coupling terms in polyatomic molecules. Phys Rev 56:680–683