frequencies (could be accidental, due to the complications that follow from, e.g., the
Fermi resonance in this range). In the high-frequency range, even small increase in
the relative error in the calculated frequency leads to the significant increase in the
frequency deviations (which are transferred to the RMS value). This is compensated
by better description in the middle range of a spectrum by the ESFF method. It is
evident when the ARPE values are analyzed. In this test, the ESFF procedure
surpasses SQM even more (602–92).
The main shortcoming of the ESFF procedure, alike any other frequency scaling
ones (the Pople’s US, or the WLS), is the lack of consistency between the calculated frequencies and the final molecular FF. In the case of SQM, the FCs and the
final frequencies are obviously consistent, as the latter are obtained from the scaled
(effective) FFs. It has the advantage, in particular if further analysis on the FCs is
required. In addition, apart from obtaining reliable frequencies, improved eigenvectors (normal modes) can be used in the transformation of the dipole moment
derivatives to obtain more reliable IR and/or Raman intensities.
2.3.6.2 Numerical Stability
Optimization of the SFs within the ESFF procedure is numerically stable. It consists
in solving a set of linear equations. In contrast, a search for SQM optimal SFs is an
iterative procedure and may fail occasionally (which we found a few times). In
addition, SQM sometimes becomes problematic in the case of factors’ optimization
for the third-row elements [70]. Namely, the successive increase of the YY factor
value with the decreasing quality of the VTZ-type basis set was observed; in the
case of 6-311G*, the value above 1.6 was found for that factor, at the expense of
another, which was significantly lower than 1. The FF SFs significantly larger than
unity for the structural motifs including the third-row atoms have been already
found before in earlier works [67]. However, the main idea behind the scaling
procedures consists in using the SFs that are close to unity. Thus in spite of
providing reasonable frequencies, the conclusions related to the SQM-scaled FFs
may be wrong when one, or a few SFs significantly deviate from unity. This is not
the case of the ESFF factors. Regardless of the reason of such a behavior, it seems
that the ESFF scaling procedure is more stable, in particular in the case of the
systems for which strong coupling of local modes is observed.
2.3.6.3 Possible Future Applications
The ESFF method is well suited to the description of the macromolecular compounds, better than SQM. Obviously, we do not have in mind the simulations of
spectra, like those presented in [77], as the SQM method can be used in conjunction
with the methodology presented there with equal success. However, when
attempting to describe really large systems in the restricted frequency range at the
levels of the mode-tracking [78, 79] and/or intensity-tracking [80, 81] procedures,
90
O. Bąk and P. Borowski
Fermi resonance in this range). In the high-frequency range, even small increase in
the relative error in the calculated frequency leads to the significant increase in the
frequency deviations (which are transferred to the RMS value). This is compensated
by better description in the middle range of a spectrum by the ESFF method. It is
evident when the ARPE values are analyzed. In this test, the ESFF procedure
surpasses SQM even more (602–92).
The main shortcoming of the ESFF procedure, alike any other frequency scaling
ones (the Pople’s US, or the WLS), is the lack of consistency between the calculated frequencies and the final molecular FF. In the case of SQM, the FCs and the
final frequencies are obviously consistent, as the latter are obtained from the scaled
(effective) FFs. It has the advantage, in particular if further analysis on the FCs is
required. In addition, apart from obtaining reliable frequencies, improved eigenvectors (normal modes) can be used in the transformation of the dipole moment
derivatives to obtain more reliable IR and/or Raman intensities.
2.3.6.2 Numerical Stability
Optimization of the SFs within the ESFF procedure is numerically stable. It consists
in solving a set of linear equations. In contrast, a search for SQM optimal SFs is an
iterative procedure and may fail occasionally (which we found a few times). In
addition, SQM sometimes becomes problematic in the case of factors’ optimization
for the third-row elements [70]. Namely, the successive increase of the YY factor
value with the decreasing quality of the VTZ-type basis set was observed; in the
case of 6-311G*, the value above 1.6 was found for that factor, at the expense of
another, which was significantly lower than 1. The FF SFs significantly larger than
unity for the structural motifs including the third-row atoms have been already
found before in earlier works [67]. However, the main idea behind the scaling
procedures consists in using the SFs that are close to unity. Thus in spite of
providing reasonable frequencies, the conclusions related to the SQM-scaled FFs
may be wrong when one, or a few SFs significantly deviate from unity. This is not
the case of the ESFF factors. Regardless of the reason of such a behavior, it seems
that the ESFF scaling procedure is more stable, in particular in the case of the
systems for which strong coupling of local modes is observed.
2.3.6.3 Possible Future Applications
The ESFF method is well suited to the description of the macromolecular compounds, better than SQM. Obviously, we do not have in mind the simulations of
spectra, like those presented in [77], as the SQM method can be used in conjunction
with the methodology presented there with equal success. However, when
attempting to describe really large systems in the restricted frequency range at the
levels of the mode-tracking [78, 79] and/or intensity-tracking [80, 81] procedures,
90
O. Bąk and P. Borowski