splitting of 81 cm
À1 resulting in the ω 18 (A 1 ) frequency of 2,118 cm
À1 and the two
degenerate ω 16, 17 (E) frequencies of 2,037 cm
À1 . So the TEP is only redshifted by
116 cm
À1 compared to carbon monoxide, in line with the finding that TEP values are
generally higher in value than their local mode counterparts. The lowering of the
local CO stretching frequency is the result of σ-donation and π-back donation
involving both e g and t 2g symmetrical 3d(Ni) orbitals (see Fig. 1). By using the
normal A 1 -symmetrical CO stretching frequency as a bond strength descriptor, the
full amount of CO weakening cannot be correctly described, because of the massdependent splitting of A 1 and E-symmetrical modes. Figure 6a suggests that for [Ni
(CO) 3 F]
À , the degenerate ω 16,17 (E) frequencies would have been a better choice as
bond strength descriptors.
The ACS analysis can be complemented by a decomposition of the 18 normal
modes of [Ni(CO) 3 F]
À into local mode contributions, as shown in Fig. 6b and
Table 1. All CO stretching modes including the TEP couple to some extend with
the NiC stretching modes, leading to a non-negligible admixture of about 4%. In
summary, the local mode analysis is an essential tool for the quantification of mode–
mode coupling, which depends on the nature of the ML bond, the symmetry of the
complex, and its geometry. If for a given complex all N vib normal vibrational
frequencies are known (measured or computed), one can easily determine the local
CO stretching frequencies and use these local, mode–mode coupling free frequencies, which we have coined LTEPs [274] instead of the TEPs as ML bond strength
descriptors.
4.2 Correlation Between CO and ML Bonding
However, even if mode–mode coupling free LTEPs would be used, there is still an
important open question, i.e., does the CO stretching frequency reflect ML bonding
as assumed by Tolman? This question can be answered by comparing the local mode
CO force constants k
a (CO) with the corresponding local NiL force constants k
a (NiL)
(as shown in Fig. 7) for the set of 181 [NiCO 3 L] complexes [274]. Since (1) the local
constants are independent of the choice of the coordinates used to describe the
molecule under consideration and (2) they are directly linked to the intrinsic bond
strength, we will use local mode force constants instead of local mode frequencies
throughout the remainder of this work.
Clearly, there is no general relationship between k
a (CO) and k
a (NiL) for this large
set of [NiCO 3 L] complexes calling Tolman’s assumption into question. Subsets of
data points belonging to a well-defined type of ligand show rather qualitative
relationships, indicated by the different dashed blue lines in Fig. 7. This can be
seen as an extension of Kühl’s findings that for each transition metal complex with a
different metal, i.e., V, Cr, Mo, W, Mn, Fe, or Rh, a different relationship has to be
used [134]. The results presented in Fig. 7 show that even within the Ni–phosphine
complexes, there is no unique relationship. One has to distinguish between normal
trialkyl phosphines (purple filled dots in Fig. 7), phosphines with electronegative
Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .
245
À1 resulting in the ω 18 (A 1 ) frequency of 2,118 cm
À1 and the two
degenerate ω 16, 17 (E) frequencies of 2,037 cm
À1 . So the TEP is only redshifted by
116 cm
À1 compared to carbon monoxide, in line with the finding that TEP values are
generally higher in value than their local mode counterparts. The lowering of the
local CO stretching frequency is the result of σ-donation and π-back donation
involving both e g and t 2g symmetrical 3d(Ni) orbitals (see Fig. 1). By using the
normal A 1 -symmetrical CO stretching frequency as a bond strength descriptor, the
full amount of CO weakening cannot be correctly described, because of the massdependent splitting of A 1 and E-symmetrical modes. Figure 6a suggests that for [Ni
(CO) 3 F]
À , the degenerate ω 16,17 (E) frequencies would have been a better choice as
bond strength descriptors.
The ACS analysis can be complemented by a decomposition of the 18 normal
modes of [Ni(CO) 3 F]
À into local mode contributions, as shown in Fig. 6b and
Table 1. All CO stretching modes including the TEP couple to some extend with
the NiC stretching modes, leading to a non-negligible admixture of about 4%. In
summary, the local mode analysis is an essential tool for the quantification of mode–
mode coupling, which depends on the nature of the ML bond, the symmetry of the
complex, and its geometry. If for a given complex all N vib normal vibrational
frequencies are known (measured or computed), one can easily determine the local
CO stretching frequencies and use these local, mode–mode coupling free frequencies, which we have coined LTEPs [274] instead of the TEPs as ML bond strength
descriptors.
4.2 Correlation Between CO and ML Bonding
However, even if mode–mode coupling free LTEPs would be used, there is still an
important open question, i.e., does the CO stretching frequency reflect ML bonding
as assumed by Tolman? This question can be answered by comparing the local mode
CO force constants k
a (CO) with the corresponding local NiL force constants k
a (NiL)
(as shown in Fig. 7) for the set of 181 [NiCO 3 L] complexes [274]. Since (1) the local
constants are independent of the choice of the coordinates used to describe the
molecule under consideration and (2) they are directly linked to the intrinsic bond
strength, we will use local mode force constants instead of local mode frequencies
throughout the remainder of this work.
Clearly, there is no general relationship between k
a (CO) and k
a (NiL) for this large
set of [NiCO 3 L] complexes calling Tolman’s assumption into question. Subsets of
data points belonging to a well-defined type of ligand show rather qualitative
relationships, indicated by the different dashed blue lines in Fig. 7. This can be
seen as an extension of Kühl’s findings that for each transition metal complex with a
different metal, i.e., V, Cr, Mo, W, Mn, Fe, or Rh, a different relationship has to be
used [134]. The results presented in Fig. 7 show that even within the Ni–phosphine
complexes, there is no unique relationship. One has to distinguish between normal
trialkyl phosphines (purple filled dots in Fig. 7), phosphines with electronegative
Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .
245