some of which contain sulfur(II) atoms was chosen. The number of bands was
carefully selected from their IR and Raman spectra and assigned. In contrast to the
previous calculations, spectra were obtained for the compounds in the liquid phase;
as was already pointed out the already known SFs are expected to be highly
transferable from the gas to condensed phase, provided they refer to the structural
motifs exhibiting weak intermolecular interactions. The considered molecules
contain a great variety of new structural motifs. To increase the population of the
sulfur(II)-containing motifs, the so-called auxiliary molecules were added to the set.
Thus, the set of bands was assigned to an overall number of over 600 normal
modes. This time redundant PICs-based formalism of the ESFF procedure was
used. The B3LYP calculations using a series of basis sets: 6-31xxx (VDZ) and
6-311xxx (VTZ), where xxx=++G**, +G**, +G*, G**, G*, and G, were carried
out. In addition, the LSFs and FF SFs within the 9-parameter scaling frame using
Baker’s training set were calculated for all basis sets listed above. These are the
recommended factors; thus, extension of the applicability of the scaling procedures
to the subsequent use with the common basis sets and in conjunction with the
B3LYP density functional (already mentioned in Sect. 2.3.4.2) was made. Since the
B3LYP computational level is one of the most popular in the vibrational frequency
determinations, LSFs (ESFF) and FF SFs (SQM) for subsequent use within the
redundant PICs formalism are presented in Tables 2.6 and 2.7.
In the calculations of the new SFs, the “old” ones were given the precomputed
values as they turn out to be highly transferable to the present set of molecules, as
expected. Initial calculations suggested the necessity of introducing five new SFs,
corresponding to HY, XY, YY, XXY, and XYX+YYX types, respectively. The
optimized factors are reported in Table 2.8. It should be noted that for the types
XX, XY, and YY an increase of the ESFF and FF SFs is observed in the reported
sequence, i.e., along with the increasing number of the third-row atoms, in which
case they adopt values greater than unity. This is also the case of CCl type and, as
already discussed, is due to the geometric effect.
Finally, an extended database of the SFs for ESFF and SQM calculations, which
is available through the files attached to the paper (supporting information) was
created [66] and a detailed analysis of the selected, the most important results was
given. The SFs for 26 typical density functionals, in conjunction with 14 typical
basis sets were determined. In particular, Pople’s (as before, apart from the smallest
ones, i.e., 6-311G and 6-31G), and Dunning’s cc-pVDZ, cc-pVTZ, aug-cc-pVDZ
and aug-cc-pVTZ basis sets were used. This gives, along with the MP2 calculations
carried out using all Dunning’s and the largest Pople’s basis sets
4 (i.e., 6-311++G**
and 6-31++G**), an overall number of 370 typical computational levels and 1480
sets of SFs, i.e., ESFF and SQM SFs within the 11- and 9-parameter scaling frames.
Again the calculations were carried out using Baker’s training set. The reason is
4
Note that the requirements of the MP2 and other correlated ab initio approaches with respect to
the basis set are higher as compared with DFT, due to the necessity of the adequate description of
the correlating orbitals, not only the electron density.
2 Scaling Procedures in Vibrational Spectroscopy
87
carefully selected from their IR and Raman spectra and assigned. In contrast to the
previous calculations, spectra were obtained for the compounds in the liquid phase;
as was already pointed out the already known SFs are expected to be highly
transferable from the gas to condensed phase, provided they refer to the structural
motifs exhibiting weak intermolecular interactions. The considered molecules
contain a great variety of new structural motifs. To increase the population of the
sulfur(II)-containing motifs, the so-called auxiliary molecules were added to the set.
Thus, the set of bands was assigned to an overall number of over 600 normal
modes. This time redundant PICs-based formalism of the ESFF procedure was
used. The B3LYP calculations using a series of basis sets: 6-31xxx (VDZ) and
6-311xxx (VTZ), where xxx=++G**, +G**, +G*, G**, G*, and G, were carried
out. In addition, the LSFs and FF SFs within the 9-parameter scaling frame using
Baker’s training set were calculated for all basis sets listed above. These are the
recommended factors; thus, extension of the applicability of the scaling procedures
to the subsequent use with the common basis sets and in conjunction with the
B3LYP density functional (already mentioned in Sect. 2.3.4.2) was made. Since the
B3LYP computational level is one of the most popular in the vibrational frequency
determinations, LSFs (ESFF) and FF SFs (SQM) for subsequent use within the
redundant PICs formalism are presented in Tables 2.6 and 2.7.
In the calculations of the new SFs, the “old” ones were given the precomputed
values as they turn out to be highly transferable to the present set of molecules, as
expected. Initial calculations suggested the necessity of introducing five new SFs,
corresponding to HY, XY, YY, XXY, and XYX+YYX types, respectively. The
optimized factors are reported in Table 2.8. It should be noted that for the types
XX, XY, and YY an increase of the ESFF and FF SFs is observed in the reported
sequence, i.e., along with the increasing number of the third-row atoms, in which
case they adopt values greater than unity. This is also the case of CCl type and, as
already discussed, is due to the geometric effect.
Finally, an extended database of the SFs for ESFF and SQM calculations, which
is available through the files attached to the paper (supporting information) was
created [66] and a detailed analysis of the selected, the most important results was
given. The SFs for 26 typical density functionals, in conjunction with 14 typical
basis sets were determined. In particular, Pople’s (as before, apart from the smallest
ones, i.e., 6-311G and 6-31G), and Dunning’s cc-pVDZ, cc-pVTZ, aug-cc-pVDZ
and aug-cc-pVTZ basis sets were used. This gives, along with the MP2 calculations
carried out using all Dunning’s and the largest Pople’s basis sets
4 (i.e., 6-311++G**
and 6-31++G**), an overall number of 370 typical computational levels and 1480
sets of SFs, i.e., ESFF and SQM SFs within the 11- and 9-parameter scaling frames.
Again the calculations were carried out using Baker’s training set. The reason is
4
Note that the requirements of the MP2 and other correlated ab initio approaches with respect to
the basis set are higher as compared with DFT, due to the necessity of the adequate description of
the correlating orbitals, not only the electron density.
2 Scaling Procedures in Vibrational Spectroscopy
87