frequently of the order of 0.1–0.2%) unless the factors’ optimization was based on
merely a few fundamentals. In passing the authors noticed that numerous scaling
factors for types involving the third-row atoms are greater than unity.
Further development of the SQM scaling procedure consisted in continuous
development of the SFs’ database. One of the authors of this chapter
(PB) developed an alternative, multi-parameter frequency scaling method, the
so-called effective scaling frequency factor (ESFF) method. To properly investigate
its predictive capabilities, the development of ESFF was accompanied by the
analogous SQM calculations, which were always considered as benchmark. The
methodological aspects will be provided in the next section, in which the ESFF
procedure is described in detail. Here we merely mention the fundamental things
concerning the FF SFs’ database development. First, the SFs for subsequent use
with B3LYP/6-311G** FFs were reported in 2008 as a consequence of verifying
the transferability of the ESFF SFs [68]. Baker’s training set of 30 molecules [54]
was used. The calculations were based on 660 fundamentals (3 less than originally),
and the original 11-parameter scaling frame [54] based on redundant PICs was
adopted. Second, a new, reduced set of FF SFs was proposed in 2010 [69]. With
this set of factors, the scaling procedure will be referred to as a “9-parameter scaling
frame”. The main difference between the standard, 11-parameter set, and a new,
9-parameter set is the splitting of the type composed of all XX bonds into two types
corresponding to (i) XX single and CC conjugated bonds, the so-called XX(s,c)type, and (ii) the remaining double and triple XX bonds, the so-called XX(d,
t) + CN(c)-type, respectively, while joining a few distinct groups into one group
(CH, OH, and NH as well as HCH and HNH were combined into the common XH
and HXH groups, respectively). Note that the additional flexibility obtained by
proliferating of the factors in the range of XH vibrations is unnecessary, as the
interpretation of the spectra in the range above 2500 cm
−1 is fairly straightforward.
Moreover, in this range the largest deviations between the scaled and the experimental frequencies are observed anyway, inter alia on account of the frequency
shifts due to the Fermi resonance. As before B3LYP/6-311G**, computational
level and Baker’s training set were used. The proposed, new set of factors seems to
be more flexible in the middle range of a vibrational spectrum, in that it is capable
of reproducing the vibrational spectra with higher accuracy in the region where XX
stretching vibrations occur. The obvious advantage of using the 11-parameter frame
is that the user does not have to assign a formal bond type or distinguish between,
say, a CC double bond or a conjugated bond, which is not always obvious, as all
XX bonds form one group. Thus, it can be still recommended in a large number of
cases. Third, a series of FF SFs within the 9-parameter scaling frame for subsequent
use with B3LYP FFs computed with a variety of Pople’s basis sets were reported in
2012 [70]. In addition to structural motifs spanned by molecules of Baker’s training
set (i.e., motifs derived from C-, H-, O-, N-, and Cl-containing molecules), for
which the FF SFs were also calculated, motifs obtained for silicon- and sulfur(II)containing compounds were considered, and FF SFs for new types of redundant
PICs (HY, XY, YY, XXY, and XYX+YYX) were determined (VDZ basis sets
80
O. Bąk and P. Borowski
merely a few fundamentals. In passing the authors noticed that numerous scaling
factors for types involving the third-row atoms are greater than unity.
Further development of the SQM scaling procedure consisted in continuous
development of the SFs’ database. One of the authors of this chapter
(PB) developed an alternative, multi-parameter frequency scaling method, the
so-called effective scaling frequency factor (ESFF) method. To properly investigate
its predictive capabilities, the development of ESFF was accompanied by the
analogous SQM calculations, which were always considered as benchmark. The
methodological aspects will be provided in the next section, in which the ESFF
procedure is described in detail. Here we merely mention the fundamental things
concerning the FF SFs’ database development. First, the SFs for subsequent use
with B3LYP/6-311G** FFs were reported in 2008 as a consequence of verifying
the transferability of the ESFF SFs [68]. Baker’s training set of 30 molecules [54]
was used. The calculations were based on 660 fundamentals (3 less than originally),
and the original 11-parameter scaling frame [54] based on redundant PICs was
adopted. Second, a new, reduced set of FF SFs was proposed in 2010 [69]. With
this set of factors, the scaling procedure will be referred to as a “9-parameter scaling
frame”. The main difference between the standard, 11-parameter set, and a new,
9-parameter set is the splitting of the type composed of all XX bonds into two types
corresponding to (i) XX single and CC conjugated bonds, the so-called XX(s,c)type, and (ii) the remaining double and triple XX bonds, the so-called XX(d,
t) + CN(c)-type, respectively, while joining a few distinct groups into one group
(CH, OH, and NH as well as HCH and HNH were combined into the common XH
and HXH groups, respectively). Note that the additional flexibility obtained by
proliferating of the factors in the range of XH vibrations is unnecessary, as the
interpretation of the spectra in the range above 2500 cm
−1 is fairly straightforward.
Moreover, in this range the largest deviations between the scaled and the experimental frequencies are observed anyway, inter alia on account of the frequency
shifts due to the Fermi resonance. As before B3LYP/6-311G**, computational
level and Baker’s training set were used. The proposed, new set of factors seems to
be more flexible in the middle range of a vibrational spectrum, in that it is capable
of reproducing the vibrational spectra with higher accuracy in the region where XX
stretching vibrations occur. The obvious advantage of using the 11-parameter frame
is that the user does not have to assign a formal bond type or distinguish between,
say, a CC double bond or a conjugated bond, which is not always obvious, as all
XX bonds form one group. Thus, it can be still recommended in a large number of
cases. Third, a series of FF SFs within the 9-parameter scaling frame for subsequent
use with B3LYP FFs computed with a variety of Pople’s basis sets were reported in
2012 [70]. In addition to structural motifs spanned by molecules of Baker’s training
set (i.e., motifs derived from C-, H-, O-, N-, and Cl-containing molecules), for
which the FF SFs were also calculated, motifs obtained for silicon- and sulfur(II)containing compounds were considered, and FF SFs for new types of redundant
PICs (HY, XY, YY, XXY, and XYX+YYX) were determined (VDZ basis sets
80
O. Bąk and P. Borowski