PICs-based SQM formalism were determined using the standard implementation of
the procedure; LSFs for non-redundant NICs-based ESFF procedure were found
using the homemade program. 11-parameter scaling frame (vide infra) was used.
The RMS value of 11.66 cm
−1 for ESFF was observed and was slightly lower than
in the case of SQM, in spite of using less flexible, NICs basis. The ARPE was also
lower in the case of ESFF. The low value of the RMS deviation obtained for a very
diversified set of molecules allowed to conclude that LSFs are well transferable, at
least as well as FF SFs.
At the same time, transferability of the SFs among the related molecules (see
Sect. 2.3.1) was investigated [13]. A set of three related molecules: toluene, styrene,
and p-methylstyrene was used. As before, the FFs were computed at the B3LYP/
6-311G** level. Two sets of experimental frequencies were considered. The first
set included 66 well-resolved fundamentals in the range of 3000–400 cm
−1 (the
ArH and =C–H stretching vibrations were not considered) unambiguously assigned
to the normal modes. The second comprised 39 fundamentals corresponding to the
“pure” modes (i.e., 60% contribution or more from one NIC). Very low RMS
(3.30 cm
−1 ) was obtained for all 66 frequencies. This showed that local SFs are
well transferable among the related molecules. It has to be emphasized that such a
good performance of ESFF follows from classification of NICs into types specific
for the three molecules considered (eight LSFs overall, out of which three were
designed specifically to describe the vinyl group modes). The confirmation of good
transferability of LSFs “within the molecule” follows from the test, in which the
factors were first optimized based on a set of 39 “pure” vibrations, and then applied
to scale all 66 frequencies. Only minor differences in the values of LSFs were
observed, and, in addition, the RMS value increased only slightly, up to 3.35 cm
−1 .
The ESFF calculations described above revealed that the SF attributed to the
C=C stretching vibration in styrene and p-methylstyrene was significantly lower
than that obtained for the ring stretching. This may constitute an evidence of
different anharmonicity of the stretching vibrations of bonds of different order, or of
their different sensitivity to the neglect of a part of correlation effects in the FFs
determination. The other research carried out roughly at the same time but published somewhat later (see [71]) confirmed this observation suggesting the necessity
of some modifications within the standard, 11-parameter scaling frame [54], at least
in some applications. Utilization of the 11-parameter set of the SFs may lead to
errors in the assignment of bands to the normal modes, in particular, in the congested region of a spectrum. Thus, a new, 9-parameter set [69], described in more
details in Sect. 2.3.4.2, was proposed and the LSFs (as well as FF SFs) were found
for Baker’s training set of molecules and at the B3LYP/6-311G** computational
level. The results obtained with the aid of this set are of comparable quality to those,
obtained in the 11-parameter calculations (the RMS values are similar, i.e.,
11.77 cm
−1 for SQM and 11.62 cm
−1 for ESFF), in spite of reducing the number of
factors by 2. It follows directly from the significant lowering of the RMS value in
the middle range of the spectrum, i.e., 1000–2500 cm
−1 , from 10.29 to 9.20 cm
−1 ,
when going from the 11- to 9-parameter calculations, which compensates for the
2 Scaling Procedures in Vibrational Spectroscopy
85
the procedure; LSFs for non-redundant NICs-based ESFF procedure were found
using the homemade program. 11-parameter scaling frame (vide infra) was used.
The RMS value of 11.66 cm
−1 for ESFF was observed and was slightly lower than
in the case of SQM, in spite of using less flexible, NICs basis. The ARPE was also
lower in the case of ESFF. The low value of the RMS deviation obtained for a very
diversified set of molecules allowed to conclude that LSFs are well transferable, at
least as well as FF SFs.
At the same time, transferability of the SFs among the related molecules (see
Sect. 2.3.1) was investigated [13]. A set of three related molecules: toluene, styrene,
and p-methylstyrene was used. As before, the FFs were computed at the B3LYP/
6-311G** level. Two sets of experimental frequencies were considered. The first
set included 66 well-resolved fundamentals in the range of 3000–400 cm
−1 (the
ArH and =C–H stretching vibrations were not considered) unambiguously assigned
to the normal modes. The second comprised 39 fundamentals corresponding to the
“pure” modes (i.e., 60% contribution or more from one NIC). Very low RMS
(3.30 cm
−1 ) was obtained for all 66 frequencies. This showed that local SFs are
well transferable among the related molecules. It has to be emphasized that such a
good performance of ESFF follows from classification of NICs into types specific
for the three molecules considered (eight LSFs overall, out of which three were
designed specifically to describe the vinyl group modes). The confirmation of good
transferability of LSFs “within the molecule” follows from the test, in which the
factors were first optimized based on a set of 39 “pure” vibrations, and then applied
to scale all 66 frequencies. Only minor differences in the values of LSFs were
observed, and, in addition, the RMS value increased only slightly, up to 3.35 cm
−1 .
The ESFF calculations described above revealed that the SF attributed to the
C=C stretching vibration in styrene and p-methylstyrene was significantly lower
than that obtained for the ring stretching. This may constitute an evidence of
different anharmonicity of the stretching vibrations of bonds of different order, or of
their different sensitivity to the neglect of a part of correlation effects in the FFs
determination. The other research carried out roughly at the same time but published somewhat later (see [71]) confirmed this observation suggesting the necessity
of some modifications within the standard, 11-parameter scaling frame [54], at least
in some applications. Utilization of the 11-parameter set of the SFs may lead to
errors in the assignment of bands to the normal modes, in particular, in the congested region of a spectrum. Thus, a new, 9-parameter set [69], described in more
details in Sect. 2.3.4.2, was proposed and the LSFs (as well as FF SFs) were found
for Baker’s training set of molecules and at the B3LYP/6-311G** computational
level. The results obtained with the aid of this set are of comparable quality to those,
obtained in the 11-parameter calculations (the RMS values are similar, i.e.,
11.77 cm
−1 for SQM and 11.62 cm
−1 for ESFF), in spite of reducing the number of
factors by 2. It follows directly from the significant lowering of the RMS value in
the middle range of the spectrum, i.e., 1000–2500 cm
−1 , from 10.29 to 9.20 cm
−1 ,
when going from the 11- to 9-parameter calculations, which compensates for the
2 Scaling Procedures in Vibrational Spectroscopy
85