complexes [Ni(CO) 3 L]. However, their attempt to eliminate mode–mode coupling
by manipulating the Hessian of calculated second energy derivatives failed to
remove the kinematic coupling between the CO stretching vibrations and other
vibrations, as was pointed out by Kalescky and co-workers in their local mode
study of Crabtree’s 66 nickel–tricarbonyl complexes. This work led for the first time
to decoupled, local CO stretching modes [145]. Setiawan and co-workers extended
the original set of 66 nickel–tricarbonyl complexes to a more comprehensive set of
181 nickel–tricarbonyl complexes [Ni(CO) 3 L], shown in Figs. 3 and 4, including
besides phosphine ligands also nitrogen and cyano, amines, arsines, stilbines,
bismuthines, boron compounds, carbonyl, thiocarbonyl, carbenes, water and ethers,
thioethers, haptic ligands, and anions [274].
In Fig. 5a, the normal mode frequencies ω(CO, A 1 ) are correlated with the
corresponding local mode frequencies ω
a (CO) for both experimental and calculated
frequencies. If the TEP would be without any coupling errors, i.e., the normal mode
ω(CO, A 1 ) stretching frequencies would be completely local as assumed by Tolman,
all data points should be found along the dashed line, which defines modedecoupled, i.e., local TEP values. Instead data points (experimental, brown color;
calculated, green color, Fig. 5a) suggest more positive TEP values in particular with
decreasing local CO stretching frequency. In other words, a lower CO stretching
frequency does not necessarily indicate a stronger Ni–CO π-back bonding but a
larger mode–mode coupling. It also seems that the ω(CO, A 1 ) stretching mode,
chosen by Tolman, does not necessarily reflect the total red shift of the CO stretching
as indicated in Fig. 1e–f. These findings hold for both measured and calculated TEP
values (CEPs) excluding that the harmonic approximation used for the CEPs causes
the deviation between normal and local mode frequencies.
The mode–mode coupling can also directly be assessed by the coupling frequencies ω coup (CO) shown in Fig. 5b as function of ω
a (CO). They are defined as the
difference between the local mode frequency and the corresponding normal mode
frequency being connected via an ACS, i.e., ω coup ¼ ω(λ ¼ 1) À ω(λ ¼ 0), which
reflects the changes in the local mode frequency ω
a
¼ (λ ¼ 0) caused by mode–mode
coupling. Large coupling frequencies are obtained when the starting local mode
frequencies are close or identical (degeneracy caused by symmetry) and the mass
ratio of the vibrating atoms is comparable. The sum of local mode and coupling
frequency is always identical to the corresponding normal mode frequency. When
adding the sum of coupling frequencies to the sum of local mode frequencies, the
zero-point energy (ZPE) is recovered [85]. Fig. 5b suggests qualitatively an inverse
relationship between coupling frequencies and the local CO stretching frequencies,
i.e., a smaller CO stretching frequency ω
a
(CO) implies a larger mode–mode coupling. Anionic ligands with strong σ- and/or π-donor capacity lead to the largest
errors as Ni–CO π-back bonding is connected with a change in the Ni–C bond and an
increased Ni–C and CO coupling. This means that for neutral and anionic ligands,
TEP errors of 40–100 cm
À1 can be expected making the use of the uncorrected TEP
highly questionable. Overall more electronegative ligands lead to higher TEP errors,
whereas cationic ligands such as NO
+ or HC
+ give more reliable TEP values.
Detailed insight into mode–mode coupling can be obtained by two special
features of the local mode analysis, which allow the comprehensive analysis of a
Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .
241
by manipulating the Hessian of calculated second energy derivatives failed to
remove the kinematic coupling between the CO stretching vibrations and other
vibrations, as was pointed out by Kalescky and co-workers in their local mode
study of Crabtree’s 66 nickel–tricarbonyl complexes. This work led for the first time
to decoupled, local CO stretching modes [145]. Setiawan and co-workers extended
the original set of 66 nickel–tricarbonyl complexes to a more comprehensive set of
181 nickel–tricarbonyl complexes [Ni(CO) 3 L], shown in Figs. 3 and 4, including
besides phosphine ligands also nitrogen and cyano, amines, arsines, stilbines,
bismuthines, boron compounds, carbonyl, thiocarbonyl, carbenes, water and ethers,
thioethers, haptic ligands, and anions [274].
In Fig. 5a, the normal mode frequencies ω(CO, A 1 ) are correlated with the
corresponding local mode frequencies ω
a (CO) for both experimental and calculated
frequencies. If the TEP would be without any coupling errors, i.e., the normal mode
ω(CO, A 1 ) stretching frequencies would be completely local as assumed by Tolman,
all data points should be found along the dashed line, which defines modedecoupled, i.e., local TEP values. Instead data points (experimental, brown color;
calculated, green color, Fig. 5a) suggest more positive TEP values in particular with
decreasing local CO stretching frequency. In other words, a lower CO stretching
frequency does not necessarily indicate a stronger Ni–CO π-back bonding but a
larger mode–mode coupling. It also seems that the ω(CO, A 1 ) stretching mode,
chosen by Tolman, does not necessarily reflect the total red shift of the CO stretching
as indicated in Fig. 1e–f. These findings hold for both measured and calculated TEP
values (CEPs) excluding that the harmonic approximation used for the CEPs causes
the deviation between normal and local mode frequencies.
The mode–mode coupling can also directly be assessed by the coupling frequencies ω coup (CO) shown in Fig. 5b as function of ω
a (CO). They are defined as the
difference between the local mode frequency and the corresponding normal mode
frequency being connected via an ACS, i.e., ω coup ¼ ω(λ ¼ 1) À ω(λ ¼ 0), which
reflects the changes in the local mode frequency ω
a
¼ (λ ¼ 0) caused by mode–mode
coupling. Large coupling frequencies are obtained when the starting local mode
frequencies are close or identical (degeneracy caused by symmetry) and the mass
ratio of the vibrating atoms is comparable. The sum of local mode and coupling
frequency is always identical to the corresponding normal mode frequency. When
adding the sum of coupling frequencies to the sum of local mode frequencies, the
zero-point energy (ZPE) is recovered [85]. Fig. 5b suggests qualitatively an inverse
relationship between coupling frequencies and the local CO stretching frequencies,
i.e., a smaller CO stretching frequency ω
a
(CO) implies a larger mode–mode coupling. Anionic ligands with strong σ- and/or π-donor capacity lead to the largest
errors as Ni–CO π-back bonding is connected with a change in the Ni–C bond and an
increased Ni–C and CO coupling. This means that for neutral and anionic ligands,
TEP errors of 40–100 cm
À1 can be expected making the use of the uncorrected TEP
highly questionable. Overall more electronegative ligands lead to higher TEP errors,
whereas cationic ligands such as NO
+ or HC
+ give more reliable TEP values.
Detailed insight into mode–mode coupling can be obtained by two special
features of the local mode analysis, which allow the comprehensive analysis of a
Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .
241