2.66.5.1 Comproportionation Equilibrium
The stability of a mixed-valence complex is measured by the free energy of comproportionation, Gc, according to the comproportionation equilibrium:
ẵRuII-RuII ỵ ẵRuIII-RuIII Kc
$2ẵRuIII-RuII ð4ị
which also defines the comproportionation constant, Kc. Gc may be determined electrochem- ically by using cyclic voltammetry, where the difference between metal-centered redox couple potentials,EẳEoM2EoM1:
ẵRuII-RuII EoM1
$ỵ ẵRuIII-RuIIE
o
$M2ẵRuIII-RuIII ð5ị
Figure 3 Solvent dependence of the LMCT band of [{Ru(NH3)5}2(-1)]4þ in nitromethane (NM), acetonitrile (AN), acetone (AC), and DMSO (reproduced with permission from ref. 4; # 1998, American
Chemical Society).
can be related to the free energy of comproportionation via the Nernst equation. The magnitude ofKcis determined by the sum of all energetic factors relating to the stability of the reactant and product complexes. For the dinuclear ruthenium complexes incorporating the 1,4-dicyanamido- benzene bridging ligand, five distinct factors contribute to the magnitude ofGc:
GcẳGsỵGeỵGiỵGrỵGex ð6ị where Gs reflects the statistical distributionof the comproportionationequilibrium; Ge
accounts for the electrostatic repulsion of the two like-charged metal centers;Giis aninductive factor dealing with competitive coordination of the bridging ligand by the metal ions;Gr is the free energy of resonance exchange, the only component ofGcwhich represents ‘‘actual’’ metal–
metal coupling; and finally, Gex is the free energy of antiferromagnetic exchange. Unlike the other four terms, which all favor the mixed-valence product ofEquation(4), Gexmeasures a stabilizing influence upon a reactant complex, and thus is of opposite sign to the remaining terms ofEquation(6). It is not appropriate to relate the magnitude of the comproportionation constant to the extent of metal–metal coupling for weakly coupled mixed-valence complexes, because of the relatively important contribution of the other terms in Equation(6). However, for strongly coupled systems, the resonance term Gr makes the dominant contribution to Gc, and the other terms are of minor importance. Finally, the free energy of comproportionation results from the formationof two mixed-valence complexes (Equation(4)). To be congruent with theory, we must consider the free energy of comproportionation per mixed-valence complex, or Gc0ẳ0.5Gc. By analogy, we define the free energy of resonance exchange per mixed-valence complex asGr0ẳ0.5Gr.
In Section2.66.4.2, the effect of solvent on the LMCT bands of [{Ru(NH3)5}2(-1)]4þ (Figure 3) clearly indicated a change in the electronic structure of the complex and, as a result, the extent of antiferromagnetic exchange was dramatically perturbed. It should not be surprising that the degree of metal–metal coupling in the mixed-valence complexes, and hence their compro- portionation constants, should also show a considerable solvent dependence. Figure 4 shows the cyclic voltammograms of the RuIII/IIcouples of [{Ru(NH3)5}2(-1)]4þinwater (a) and acetone (b).
Inwater, the RuIII/IIcouples are nearly superimposed on each other, indicating that the extent of metal–metal coupling (Gr) is very weak. However inacetone, the RuIII/IIcouples have become completely separated, indicating that the extent of metal–metal coupling has dramatically increased.
In aprotic solvents, the magnitude of the comproportionation constant decreases with increasing solvent donor properties, and is due to the donor–acceptor interaction between solvent and ammine protons (Section2.66.1). In water, protonation of the cyanamide groups provides another mechan- ism by which metal–metal coupling can be disrupted. The solvent-dependent cyclic voltammetry of all the ammine complexes has been performed and the data compiled.4,15
(a) (b)
Figure 4 Cyclic voltammograms of the RuIII/II couples of [{Ru(NH3)5}2(-1)]4þ in(a) water and (b) acetone.
Case Study of the Dicyanamidebenzene System 791
Inorder to extract the value of Gr from the free energy of comproportionation, the free energy termsGs,Ge,Gi, an dGexmust be evaluated. The antiferromagnetic exchange term Gexmay be estimated from room-temperature magnetic moments, as discussed in Chapter 2.45.
Comprehensive estimates of Gex(or one-half the separation between singlet ground and triplet excited states) are available for the pentaammine complexes, and to a lesser extent for the tetraammine complexes.4 The nonexchange contributions to Gc, i.e., GneẳGsỵGeỵGi, were estimated from theGcof the most weakly coupled mixed-valence complex and corrected for the change inGewith solvent.4
Because both free energy values for antiferromagnetic exchange and nonexchange contributions to Gc can be determined, it is now possible to extract an experimental value for the free energy of resonance exchange in the mixed-valence complexes. Theory, together with electronic absorption data, provides a route toGrthat can be used for comparison, and that is the subject of the next section.
2.66.5.2 Spectroelectrochemistry 2.66.5.2.1 UV–vis NIR Studies
A mixed-valence complex will fall into one of three categories, as proposed by Robin and Day,16 depending upon the degree of coupling between the metal centers. Completely valence-trapped complexes (no coupling between the metal centers) are termed Class I, while complexes in which the valence electrons are fully delocalized (very strong coupling between the metal centers) are termed Class III. All complexes whose behavior falls betweenthese extremes constitute Class II.
For symmetric Class II mixed-valence complexes, the relationship betweenGr0and the metal–
metal coupling element is given by:17
G0rẳHMM2 =EIT ð7ị where, EIT and HMM are the intervalence band energy and metal–metal coupling element, respectively. The derivation of the general equation for the effective (i.e., indirect) coupling of the metal centers is discussed in detail in Chapter 2.44. Its general form is:4,13
HMM0ẳHMLHM0L
2EMLeff þHLMHLM0
ELMeff ð8ị The coupling element HMM0 of Equation(8) is the effective metal–metal coupling, while the coupling elements in the two terms on the right ofEquation(8)are associated with metal–ligand interactions of the electron-transfer and hole-transfer pathways, respectively. The denominators are reduced energy gaps between metal and ligand orbitals. For the complexes of this study, only the hole-transfer pathway, and thus the second term of Equation(8), need be considered: and giventhe approximationHLMẳHLM0, Equation(8) simplifies to:
HMM0ẳ HLM2
ELMeff ð9ị HLM values were evaluated using Equation(3) and the electronic absorbance data of the low- energy LMCT band of the polyaammineruthenium dinuclear complexes, assuming a value of rẳ6:5A˚, which is the distance between RuIII and the center of the 1,4-dicyanamidobenzene bridging ligand. The experimental LMCT oscillator strength should be divided by a factor of two inorder to compensate for the absorptionof two RuIII-cyanamide chromophores. The reduced energy gap for the hole-transfer case is given by:13
ELMeff ẳ 0:5 1
ELMCTþ 1 ELMCTEIT
1
ð10ị
where ELMCT is the energy of the LMCT band atlmax.
The electronic absorption data for the polyaammineruthenium dinuclear complexes were obtained by spectroelectrochemical studies, using an optically transparent, thin-layer electro- chemical (OTTLE) cell.15,18 It is important that the effect of electrochemical titration on the
absorption spectrum of the complex be consistent with the stepwise, reversible reduction of the complex. Specifically, isosbestic points must be maintained during a single redox process and, upon reversing the applied potential, the original spectrum is obtained. The electronic absorption data required to calculate theoretical values ofHMM0 and hence, by usingEquation(7), theoretical values ofGr0, have beenpublished, but the final result for all the polyammineruthenium dinuclear complexes is showninFigure 5.
The success ofEquation(9)in predicting metal–metal coupling for the complexes of this study is shownby the good correlationbetweenHMM2 0/EITandGr0for the pentaammine, tetraammine, and triammine complexes inFigure 5. Inaddition, these results strongly support the realizationthat metal–ligand and metal–metal coupling elements are related to charge-transfer band oscillator strengths. The curvature in the data may be real, since it may result from the breakdown inEquation (7)as strong coupling or Class III mixed-valence properties are obtained. The examination of the Class II/Class III boundary is the subject of the IR spectroelectrochemical studies discussed below.
2.66.5.2.2 Infrared Studies
It would be of some theoretical and practical importance to know the magnitude of resonance exchange energy required to achieve a delocalized state in a mixed-valence complex. In this regard, infrared spectroscopy has been recognized as a powerful means of examining electron transfer in mixed-valence complexes, as its time scale (1013s) gives an almost instantaneous view of the state of a fluxional molecule.19
For the dinuclear ruthenium complexes incorporating 1,4-dicyanamidobenzene ligands, the cyanamide stretch(NCN) provides an excellent marker, as it absorbs strongly and normally appears between2,100 cm1and 2,200 cm1, a region that is free of most solvent interference.
It has beenshownthat reductionof the mononuclear complex, mer-[Ru(NH3)3(bpy)- (2,3-dichlorophenylcyanamide)]2þ, results ina shift of(NCN) from 2,120 cm1to 2,180 cm1for cyanamide bound to RuIIIand RuIIrespectively.19This shift to higher energies is unexpected, but it canbe explained by the polarizationof the cyanamide group as shownin Scheme 3.
N C N
Cl Ru(III) Cl
Cl N Cl Ru(II)
+ 1e–
N C
Scheme 3 HMM′2EIT (cm–1)
∆G′r (cm–1)
1,600
1,400
1,200
1,000
800
400
200
100
0 200 400 600 800 1,000 1,200 1,400 1,600
Figure 5 Plot of Gr0 vs. HMM2 0/EIT for the pentaammine ( &), tetraammine ( ) and triammine (~) complexes (reproduced with permissionfrom ref.4; # 1998, AmericanChemical Society).
Case Study of the Dicyanamidebenzene System 793
The presence of both these resonance forms is seen in the IR spectroelectrochemical reduction of [{Ru(NH3)5}2(-4)]4þ inDMSO (Figure 6). In Figure 6a, the reductionof [III,III] to [III,II]
results inthe loss of the single (NCN) band at 2,110 cm1and the growth of two new (NCN) bands at 2,040 cm1and 2,150 cm1that are assigned to cyanamide groups bound to RuIII and RuII, respectively. Complete reductionto [II,II] (Figure 6b) gives only a single band at 2,140 cm1. These results are entirely consistent with Class II behavior in which there are identifiable RuIIIand RuIIions in the mixed-valence state.
Figure 7 shows the IR spectroelectrochemical reductionof trans,trans-[{Ru(NH3)4- (pyridine)}2(-3)]4þ inDMSO. Uponreductionof [III,III] to [III,II] in Figure 7a, the single (NCN) band at 2,090 cm1 simply reduces intensity. Further reduction to the [II,II] complex (Figure 7b) results in the appearance of a new band at 2,140 cm1. These results are consistent with Class III behavior in the mixed-valence state in which the metal ions are indistinguishable.
As canbe seeninFigure 6a, the average energy of the(NCN) bands in the [III,II] complex is approximately the same as that of the single(NCN) band of the [III,III] complex. InFigure 7a, it is therefore coincidence that the (NCN) energy of the Class III mixed-valence complex is the same as that of the [III,III] complex.
By examining a number of complexes that spanned the range of Class II to Class III behavior, it was possible to show that the properties of the complex, trans,trans- [{Ru(NH3)4(py)}2(-3)]3þ in acetonitrile can be regarded as benchmarks for delocalization for polyammineruthenium dinuclear complexes incorporating 1,4-dicyanamidobenzene bridging
(a)
(b) 100
90
Transmittance (%)
Wave number (cm–1) 80
2,200 2,100 2,000 1,900
100
90
Transmittance (%)
Wave number (cm–1) 80
2,200 2,100 2,000 1,900
Figure 6 (a) IR spectra showing the reduction of the [III,III] complex, [{Ru(NH3)5}2(-Me2dicyd)][PF6]4to the [III,II] complex; (b) IR spectra showing the reduction of the mixed-valence complex to the [II,II]
complex, inDMSO solution(reproduced with permissionfrom ref.19; # 2001, AmericanChemical Society).
ligands.19 It was shown that this complex obeys the general condition for delocalization in symmetric mixed-valence complexes, 2Hẳl, and possesses an experimental free energy of reson- ance exchangeGr0ẳ1,250 cm1and resonance exchange integral Hẳ3,740 cm1.