1.1 Mixed-Valence Compounds
1.1.3 Factors affecting intramolecular electronic coupling in mixed-
It is important to understand the factors influencing the communication between redox sites in a mixed-valence compound if we are to design molecules for prede- fined applications. Essentially, we are interested in how the electronic coupling Vda depends on the structural and electronic properties of the molecule.
Class II and III mixed-valence compounds almost always consist of redox groups linked by a conjugated bridge; few examples of appreciable electronic communication through saturated bonds exist, and in those few the end groups are usually held at very close distances.52,53The dependence of the electronic cou-
pling on the distance between the end groups and upon the degree of conjugation in the linker was demonstrated nicely for a series of diferrocenyl complexes. Two ferrocenyl (Fc) groups were joined by alkane, alkene and alkyne chains of var- ious lengths, and the mixed-valence character of the resulting compounds were measured electrochemically and by analysis of the IVCT bands. The simplest diferrocenyl compound, biferrocene, consists of two Fc groups linked by a sin- gle bond between one of the cyclopentadiene (Cp) rings of each, and is a Class II mixed-valence compound.54 The insertion of even a single saturated carbon
(Fc−CH2−Fc) between the the two Fc groups is sufficient to kill the electronic coupling between the redox units, resulting in a class I molecule.55Alkenyl bridges
facilitate electronic coupling between the Fc groups, since they are conjugated, and class II behaviour is observed even through a 12-membered alkene chain.56
However, the magnitude of the coupling decreases exponentially, as expected, as the linker length increases. A similar trend is observed for alkynyl bridges.57,58
This implies that anything that reduces the conjugation in the bridge will reduce the communication between the end groups. Chemical factors, such as the bond order, are not the only factors which affect conjugation; geometrical factors such as rotation around a C−C bond or bending of the π-system both
reduce the overlap between orbitals, which in turn reduces the degree of conju- gation.59 The effect of rotation was demonstrated by calculating the resistance
through a biphenyl molecule, attached to two gold electrodes via S···Au bonds, as a function of the angle between the planes defined by each phenyl ring.60 The
resistance was found to increase with the angle between the planes, reaching a maximum at 90°. This explains why interactions between redox sites are greater for molecules in which the various conjugated components are rigidly fixed in rel- ative orientations approaching planarity, and, to a lesser extent, those in which rotations are inhibited by steric hindrance.43
The effect of conformation on the degree of electronic coupling between redox groups can be advantageous. If we can alter the conformation of the bridge using some external stimulus, the electronic coupling, and hence electron transport properties, can be altered. The class of molecules where this is possible are known as conformational switches.61
Since conjugated groups facilitate efficient electronic coupling between redox groups, aromatic rings and π-conjugated macrocycles are often used as bridg- ing structures. However care must be taken when using cyclical bridges since structural isomers can have different coupling parameters. One of the simplest demonstrations of this is the mixed-valence behaviour of the ortho, meta and para isomers of a diferrocenylbenzene.62 Upon analysis of the IVCT bands, the
para isomer was found to exhibit the strongest electronic coupling between the ferrocenyl groups, followed by the ortho and, finally, meta isomers. The differ- ence in coupling strength was attributed to quantum interference effects between different tunnelling channels. However, this effect is not always observed. No significant difference in coupling strength was observed for the structural isomers of a diferrocenyl cyclobutadiene-CoCp sandwich structure where the ferrocenyl groups are bound to either adjacent, or opposite, vertices of the cyclobutadiene.58
The electronic coupling also depends on the difference between the orbital energies on the end groups and bridge, and, as a result, the same bridge may lead to a different distance-coupling relationship between different end groups. The effect of varying the bridge energy was demonstrated using symmetric di- ferrocenyl molecules where the ferrocenyl groups are bridged by five-membered heterocycles.63 A series of heterogroups with varying electron donating ability
were inserted on the bridge, and the IVCT bands were analysed. The more elec- tron donating the group on the bridge the higher the mixed-valence character of the molecule, as expected for better orbital matching.
The energy of the redox groups can be similarly tuned by substitution of electron donating or withdrawing groups. Indeed, this has already been exploited to break the symmetry between ferrocenyl end groups in a diferrocenyl mixed-
valence complex to fix the order in which the oxidations occur.64
Generally, the distance between the redox active elements of the molecule should be5Å or less to ensure class II or III mixed-valence behaviour. However, longer-range coupling (10Å to 12Å) is possible through the π-system of some linkers, particularly conjugated macrocycles.65
In summary, in order to maximise electronic coupling between redox groups, they should be connected at close range through conjugated linkers whose orbital energies align with those of the redox groups. Molecules with large separations, saturated linkers, and/or large energy barriers to electron transport through the linker will tend to exhibit Robin-Day class I mixed-valence behaviour. Care must be taken to ensure a mixed-valence compound, designed for a given application, possesses the properties intended. This is non-trivial given the interplay between the various factors which determine the degree of electronic communication be- tween redox centres in a molecule, and cannot be guaranteed by assembling sev- eral well-characterised building blocks.