that the obtained results were supposed to be as consistent with those available in
the literature as possible. It is difficult to summarize that paper and all the recommendations that follow from it in a few sentences, so the reader interested in
scaling procedures is encouraged to go through the details by reading the reference
in the free time. At this point, we only mention that we recalculated standard
deviations for LSFs
5 which are closely related to uncertainties described in
Sect. 2.3.2.2. They turned out to be on average by an order of magnitude lower than
those reported for US [44, 45, 47].
2.3.6 Comparison of Multi-parameter Scaling Procedures
The US procedure is the simplest one of all described, and for this reason, it is the
most frequently used in various applications. However, its obvious disadvantage is
lowest quality of the scaled frequencies. In this section, comparison of the two most
powerful scaling techniques: SQM and ESFF will be presented.
2.3.6.1 Quality of the Scaled Frequencies
First applications of the ESFF technique [13, 68, 69, 71, 74], although successful
could not be directly compared to those of SQM. First, they were carried out using
non-redundant NICs-based algorithm, while the SQM calculations carried out at the
same time for comparison used more flexible, redundant PICs basis. Second,
slightly different classifications of ICs were adopted. For example, in the first
methodological paper [74] only five SFs were optimized in the case of ESFF, eight
FF SFs were used in the case of SQM. In addition, in the paper devoted to toluene,
styrene, and 4-methylstyrene [13] three specific ICs were used to treat the vinyl
group motions in the ESFF scaling. Third, in the case of ESFF weights used in the
optimization procedure were always equal to unity. Nevertheless in an overwhelming majority of cases, ESFF turned out to provide slightly better results than
SQM in that the RMS and ARPE values were lower. Results before the modification of the ESFF procedure consisting in utilization of the redundant PICs
appeared [75] are summarized in Table 2.9.
Full comparison of SQM and ESFF method was given in Ref. [66]. This time
both approaches used the same, redundant PICs-based algorithms. From the statistical point of view, the ESFF method is noticeably better than SQM—in most
(524–207) out of 740 cases (370 computational levels  2 scaling frame, i.e., 9and 11-parameter), the ESFF RMS values were lower than those obtained with
SQM. The SQM method predicts somewhat more accurate XH stretching
5
They were calculated in earlier works devoted to ESFF procedure, but due to a mistake in data
handling they were incorrect.
2 Scaling Procedures in Vibrational Spectroscopy
89
the literature as possible. It is difficult to summarize that paper and all the recommendations that follow from it in a few sentences, so the reader interested in
scaling procedures is encouraged to go through the details by reading the reference
in the free time. At this point, we only mention that we recalculated standard
deviations for LSFs
5 which are closely related to uncertainties described in
Sect. 2.3.2.2. They turned out to be on average by an order of magnitude lower than
those reported for US [44, 45, 47].
2.3.6 Comparison of Multi-parameter Scaling Procedures
The US procedure is the simplest one of all described, and for this reason, it is the
most frequently used in various applications. However, its obvious disadvantage is
lowest quality of the scaled frequencies. In this section, comparison of the two most
powerful scaling techniques: SQM and ESFF will be presented.
2.3.6.1 Quality of the Scaled Frequencies
First applications of the ESFF technique [13, 68, 69, 71, 74], although successful
could not be directly compared to those of SQM. First, they were carried out using
non-redundant NICs-based algorithm, while the SQM calculations carried out at the
same time for comparison used more flexible, redundant PICs basis. Second,
slightly different classifications of ICs were adopted. For example, in the first
methodological paper [74] only five SFs were optimized in the case of ESFF, eight
FF SFs were used in the case of SQM. In addition, in the paper devoted to toluene,
styrene, and 4-methylstyrene [13] three specific ICs were used to treat the vinyl
group motions in the ESFF scaling. Third, in the case of ESFF weights used in the
optimization procedure were always equal to unity. Nevertheless in an overwhelming majority of cases, ESFF turned out to provide slightly better results than
SQM in that the RMS and ARPE values were lower. Results before the modification of the ESFF procedure consisting in utilization of the redundant PICs
appeared [75] are summarized in Table 2.9.
Full comparison of SQM and ESFF method was given in Ref. [66]. This time
both approaches used the same, redundant PICs-based algorithms. From the statistical point of view, the ESFF method is noticeably better than SQM—in most
(524–207) out of 740 cases (370 computational levels  2 scaling frame, i.e., 9and 11-parameter), the ESFF RMS values were lower than those obtained with
SQM. The SQM method predicts somewhat more accurate XH stretching
5
They were calculated in earlier works devoted to ESFF procedure, but due to a mistake in data
handling they were incorrect.
2 Scaling Procedures in Vibrational Spectroscopy
89