422
P. P. Roma´ nczyk and S. S. Kurek
Note that directly correlating K c , for systems with two identical redox sites, with
the degree of electronic coupling between the diabatic states for electron donor and
acceptor (H ab parameter) without other evidences (spectroscopic, QC calculations)
for the extent of an extra-electron delocalisation may be wrong. However, it is routinely employed in the literature (see, e.g., [66, 67]). Only a qualitative relationship
may exist, and, as demonstrated in an excellent review by Winter [68], a large redox
potential splitting is not a necessary condition for appreciable degree of groundstate delocalisation in the MV state. Below, we will show two examples of entirely
valence-trapped Mo
I Mo
II systems (class I in Robin–Day classification) despite it
showing substantial to very large potential splittings for two consecutive 1e reductions, demonstrating suitability of DFT modelling of their properties.
Mixed-valence complexes based on di-{Mo
II/I (NO)}
2+/1+ fragments stabilised
by κ
3 -hydrotris(3,5-dimethylpyrazol-1-yl)borate) (=scorpionate), discussed above,
demonstrate a wide range of behaviour, from fully delocalised to valence-trapped.
Their amazing electronic and magnetic properties have been described in the literature, mainly of those with π-coupled bridges [32, 57]. Generally, much less work has
been devoted to species (this class and other classes) containing saturated alkylene
ligand systems. Aside from the examples below, we should mention here a study
by Ding et al. [69] who analysed the extent of delocalisation (H ab ) in Fc-bridge-Fc
systems with various bridging ligands, including saturated C–C single bonds, by
conventional and constrained [70] DFT methods. The latter approach consists in
constructing charge-localised states by imposing an external constraint, i.e. adding
an effective potential to the Hamiltonian. They concluded that only constrained DFT
is capable to predict quantitatively the strength of electronic coupling for systems,
which are incorrectly described by conventional DFT as delocalised owing to the
significant self-interaction error in common approximate DFT functionals.
Let us now return to dimolybdenum species. The separation of the reduction
potentials, red E 1/2 , for the complexes based on di-{Mo
II (NO)Tp
Me2 }
2+ fragments
incorporating single or double [OCH 2 (CZ 2 ) n CH 2 O]
2− bridges (n 0–3, Z H or F)
ranges between 70 and 360 mV, which reflects modest to substantial electrochemical
interactions transmitted through the σ-framework and corresponds to the K c value up
to ca. 10
6 [71, 72]. This can be compared with complexes with unsaturated bridges
allowing a strong electronic coupling, like the [(PY5Me 2 ) 2 V 2 (μ-5,6-dmbzim)]
3+
cation ( ox E 1/2 376 mV in MeCN [73]) and the Creutz−Taube ion ( ox E 1/2
390 mV in water [56]),
6 or with Fc-CH 2 -CH 2 -Fc for which ox E 1/2 (in CH 2 Cl 2 )
is unmeasurable [74], which agrees well with the small H ab value predicted by
constrained DFT for the 1e oxidised form of the latter complex [69].
The redox potential splitting ( red E 1/2 ) measured for a di-Mo
II complex with a
single ethane-1,2-diolate bridge equals 310 mV in CH 2 Cl 2 , and the IR spectrum
of the Mo
I Mo
II form shows two NO stretching vibrations instead of one, as in the
neutral Mo
II Mo
II , pointing to valence-trapped behaviour [75]. As can be seen in
Fig. 4, both electrochemical and spectral features are excellently reproduced by
computations. Again, the IEF-PCM/B3LYP/LACV3P+/6-311++G(2d,2p) level of
6 Note, however, that for these species, E 1/2 might be larger in a less polar solvent.
P. P. Roma´ nczyk and S. S. Kurek
Note that directly correlating K c , for systems with two identical redox sites, with
the degree of electronic coupling between the diabatic states for electron donor and
acceptor (H ab parameter) without other evidences (spectroscopic, QC calculations)
for the extent of an extra-electron delocalisation may be wrong. However, it is routinely employed in the literature (see, e.g., [66, 67]). Only a qualitative relationship
may exist, and, as demonstrated in an excellent review by Winter [68], a large redox
potential splitting is not a necessary condition for appreciable degree of groundstate delocalisation in the MV state. Below, we will show two examples of entirely
valence-trapped Mo
I Mo
II systems (class I in Robin–Day classification) despite it
showing substantial to very large potential splittings for two consecutive 1e reductions, demonstrating suitability of DFT modelling of their properties.
Mixed-valence complexes based on di-{Mo
II/I (NO)}
2+/1+ fragments stabilised
by κ
3 -hydrotris(3,5-dimethylpyrazol-1-yl)borate) (=scorpionate), discussed above,
demonstrate a wide range of behaviour, from fully delocalised to valence-trapped.
Their amazing electronic and magnetic properties have been described in the literature, mainly of those with π-coupled bridges [32, 57]. Generally, much less work has
been devoted to species (this class and other classes) containing saturated alkylene
ligand systems. Aside from the examples below, we should mention here a study
by Ding et al. [69] who analysed the extent of delocalisation (H ab ) in Fc-bridge-Fc
systems with various bridging ligands, including saturated C–C single bonds, by
conventional and constrained [70] DFT methods. The latter approach consists in
constructing charge-localised states by imposing an external constraint, i.e. adding
an effective potential to the Hamiltonian. They concluded that only constrained DFT
is capable to predict quantitatively the strength of electronic coupling for systems,
which are incorrectly described by conventional DFT as delocalised owing to the
significant self-interaction error in common approximate DFT functionals.
Let us now return to dimolybdenum species. The separation of the reduction
potentials, red E 1/2 , for the complexes based on di-{Mo
II (NO)Tp
Me2 }
2+ fragments
incorporating single or double [OCH 2 (CZ 2 ) n CH 2 O]
2− bridges (n 0–3, Z H or F)
ranges between 70 and 360 mV, which reflects modest to substantial electrochemical
interactions transmitted through the σ-framework and corresponds to the K c value up
to ca. 10
6 [71, 72]. This can be compared with complexes with unsaturated bridges
allowing a strong electronic coupling, like the [(PY5Me 2 ) 2 V 2 (μ-5,6-dmbzim)]
3+
cation ( ox E 1/2 376 mV in MeCN [73]) and the Creutz−Taube ion ( ox E 1/2
390 mV in water [56]),
6 or with Fc-CH 2 -CH 2 -Fc for which ox E 1/2 (in CH 2 Cl 2 )
is unmeasurable [74], which agrees well with the small H ab value predicted by
constrained DFT for the 1e oxidised form of the latter complex [69].
The redox potential splitting ( red E 1/2 ) measured for a di-Mo
II complex with a
single ethane-1,2-diolate bridge equals 310 mV in CH 2 Cl 2 , and the IR spectrum
of the Mo
I Mo
II form shows two NO stretching vibrations instead of one, as in the
neutral Mo
II Mo
II , pointing to valence-trapped behaviour [75]. As can be seen in
Fig. 4, both electrochemical and spectral features are excellently reproduced by
computations. Again, the IEF-PCM/B3LYP/LACV3P+/6-311++G(2d,2p) level of
6 Note, however, that for these species, E 1/2 might be larger in a less polar solvent.