Table 1 A collection ofPLvalues.5,27,33,35–38
Ligand PLa
Ligand PL
NOþ þ1.40 Py 0.59
CCH2Ph þ0.27 NH3 0.77
CNH2 þ0.09 CF3CO2 0.78
CO 0 o-CN(H)C6H4C(PR3) 0.83
N2 0.07 NCNH2 0.85
P(OPh)3 0.18 NCNC(NH2)2 0.86
Vinylidenes 0.25 0.28 NCNHCN 0.88
o-3PCH2C6H4NC 0.32 NCS 0.88
2,6-Cl2PhNC 0.33 o-NẳC(H)C(PR3)(C6H4) 0.96
PPh3 0.35 CN 1.00
4-ClPhNC 0.37 (0.11) NCO 1.16
PhNC 0.38 (0.12) C CPh 1.22
2-MePhNC 0.38 NCNC(NH)NH2 1.22
4-MePhNC 0.39 (0.13) H 1.22
PhCN 0.40 NCNCN 1.14
4-MeOPhNC 0.40 (0.14) I 1.15
CH3NC 0.43 (0.17) Br 1.17
tBuNC 0.44 (0.18) Cl 1.19
Protonated indoles 0.53 N3 1.26
Protonated carbenes 0.55 OH 1.55
CH3CN 0.58 carbynes ca 0.27
a Quoted values for isocyanides are for linear MCNR bonding. Values for bent MCNR are given in parentheses.
Table 2 Core Esand polarizability Lvalues for a selection of species.1,5,27,28,33,39–43
Msa
[MYX4] Es(V) vs. SCE bL
Mo(CO)5 1.44 0.86
W(CO)5 1.52 0.90
Tc(tBu-NC)(dppe)2 1.34 0.99
Re(N2)(dppe)2 1.20 0.74
Re(CNMe)(dppe)2 1.19 0.93
Fe(H)(dppe)2 1.04 1.0
Mo(NO)(dppe)2 0.91 0.51
TcH(dppe)2 0.34 4.0
Mo(CO)(dppe)2 0.11 0.72
Mo(N2)(dppe)2 0.13 0.84
Mo(PhCN)(dppe)2 0.40 0.82
Mo(N3)(dppe)2 1.00 1.0
Re(Cl)(dppe)2 0.41b 1.88b
[Re(Cl)(dppe)2]þ 1.42 1.30
Trans-[FeBr(depe)2]þ 1.32 1.10
Trans-[FeBr(depe)2]2þ 1.98 1.30
a dppe=1,2-diphenylphosphinoethane, depe=1,2-diethylphosphinoethane.
The EL(L) parameters are defined via the reversible E1/2[RuIII/RuII] couple such that for a general complex Ru(UVWXYZ) the observedE1/2[RuIII/RuII] potential versus NHE is given by
E1=2ẵRuIII=RuII ẳELðUị ỵELðVị ỵELðWị ỵELðXị ỵELðYị ỵELðZị ẳELðLị ð8ị Through a statistical analysis of the very large number ofE1/2[RuIII/RuII] redox couples which have been reported in the literature, and making use of Hammett relationships, vide infra,EL(L) values for many hundreds of ligands are available.EL(L) parameter value ranges are shown in Table 3 and detailed data are shown in1,44 and on the Lever website.46 Several authors have published tables of additional EL(L) data, including45,47. Relationships have been developed between Hammett substituent constants ((R)) and theELparameters such thatEL(L) parameters for substituted ligands can be extrapolated from the EL(L) value of the parent ligand via application of Hammett relationships, namely:48 (Table 4), viz: (Rp is the so-called reaction parameter) (Equation (9)):
ELðRLị ẳ2:303ðRTlnFịRpðRị ỵELðHLị ẳf0ðRị ỵELðHLị ð9ị
Table 3 Ligand electrochemical parameters for typical ligands, V. vs.
NHE.1,27,39,41,44,45
Alkyls, aryls, methyl, phenyl, NO, etc.
0.90 to 0.70
Most anions, including organic carboxylates, SiH3, MeO, MeS, etc.
0.70 to 0
Saturated amines and weakly-accepting amines, carbenes 0 toþ0.25
Unsaturated amines, pyridines, bipyridines, pyrazines, etc.
þ0.1 toþ0.4
Hard thioethers, softer phosphines, nitriles þ0.35 to þ0.5
Isocyanides,asofter phosphites, harder phosphines, arsines, stibines, vinylidenesa
þ0.4 toþ0.65 Harder phosphites þ0.65 to þ0.75
Dinitrogen, organic nitrites, PCl3, PF3, etc.
þ0.7 toþ0.95
Positively charged ligands,-acid olefins, carbon monoxidea
>þ0.9 Carbynes caþ1.2 Nitrosoniuma
>þ1.5
a Generally non-innocent and subject to some variation depending on the-donicity of the central metal ion.
Table 4 Ligand electrochemical parameters,EL(RL) and Hammett,, relationships.49
Ligand Group Reaction parameter, S0M Parent EL(LH) Ra
R-BQDIb 0.17 0.26 0.98
R-Phosphines,* 0.17 0.35 0.95
R-Pyridines,c 0.13 0.24 0.95
R-Bipyridines, 0.07 0.25 0.99
R-Diketones,þ 0.12 0.01 0.98
R-Salend 0.21 0.14 1.00
Direct,pe
0.62 0.37 0.95
a Regression coefficient b o-benzoquinonediimine c P
=pþmas necessary d Based on a limited data set in ref. 50 e for substituents acting directly as ligands, e.g., Cl, H, etc.
Ligand Electrochemical Parameters and Electrochemical–Optical Relationships 255
The Lever ligand electrochemical parameter theory can be applied to any metal couple via the following expression (10):
E1=2ẵMnỵ1=Mnỵ ẳSMELðLị ỵIM ð10ị Redox potentials are related to the ratio of the stability constants for binding of the ligands to the metal ions in the two oxidation states. TheSMfor agiven couple then reflects how the ratio for that couple compares with the ratio for theE1/2[RuIII/RuII] couple. As aconsequence theSM
value depends on the spin states associated with each oxidation state, and will also depend on the stereochemistry. Thus the SM value for E1/2[FeIII(hs)/FeII(hs)] is different from that for E1/2
[FeIII(ls)/FeII(ls)] or for E1/2[FeIII(hs)/FeII(ls)], etc. (hs=high spin, ls=low spin) and will differ for four- or five-coordinate versus six-coordinate species. The IMparameter is a function of the difference in free energy of solvation for the pair of ions concerned (differential solvation energy), of the gas phase redox potential for the free ions involved, and trivially from the reference electrode used. The differential solvation energy term also influences SM since, for example, the slopes for the RuIII/II couples in organic solvents and in water differ appreciably.
The net charge on the complexes, e.g., [Os(en)3]2þ versus Os(en)2Cl2 versus [Os(CN)6]4 appears not to be a factor when the reversible potentials are recorded in an organic solvent, i.e., all these species would have the same SMand IM values for a given couple. However, there are some exceptions where solvation effects are more important, e.g.,51–57 In general, solvato- chromic species (see Chapter 2.27) may show deviations whereby the redox potential will be dependent on the solvent employed.58–60
Solvation effects are crucially important for data recorded in water phase wherein we can certainly expect differentSM,IMvalues for different net charges for the same metal redox couple.
Thus, systems of different net charge, when studied in water, should be independently analyzed.
This model has proven very effective for a wide range of Werner-type classical and organomet- allic species.44Some problems arise in the latter class where stereochemistry can be a factor, i.e., isomers of different stereochemistry having rather different redox potentials. This appears to be particularly troublesome with certain strongly -bonding ligands such as carbonyls, isonitriles, carbenes, vinylidenes, etc.33,35,41,44
In these cases it is preferable to adopt a correction following the methodology of Bursten described above (Equation (5)).2,61
Thus, for a carbonyl species, one may writeEquation (11):
E1=2ẵMnỵ1=n ẳSMELðLị ỵIMỵcx ð11ị
where cx is as inEquation (2). (Unfortunately, this correction was termed ‘‘mx’’ in ref.44but with m being what is defined as ‘‘x’’ here and ‘‘x’’ being defined as chere. We have changed to the terminology used by Bursten to be consistent with Equation (2)). If acomplex contains two (or more) types of strongly -accepting ligand, such as isonitrile and carbonyl, then further correc- tions,m0x0can be added toEquation (11). The value of ‘‘x’’ (andx0, etc.) follows directly from the stereochemistry (see1,2,44) while the value of ‘‘c’’ was determined empirically as a best fit to sets of data for various Mnþ1/npotentials. Typically, such corrections are of the order of 0–0.3 V so that they can be significant (see footnote to Table 344).
Most studies have involved six-coordinate species where the electron being removed during oxidation has originated from thet2g(in Oh) non-bonding or pi-bonding set. There is no reason to suppose that the model would not also apply to complexes with other coordination numbers and indeed has been demonstrated to be valid for 4- and 5-coordinate rhodium(I) species.34
The model has also been extended to sandwich organometallic species1,47,62 M(-L)2 (e.g., -L=arenes, cyclopentadienyls, etc.), however with the difference that the scale is based on the FeIII/FeII couple due to the lack of a sufficient number of ruthenium sandwich species with reversible redox couples. The magnitudes of theEL(-L) values cover a wide range (Table 5) a nd depend critically on a simple net charge/atom calculation, i.e., (charge on-L)/(no. of coordinat- ing atoms) (Figure 11,63). An extensive range of substituted cyclopentadienes and arenes, etc. can be analyzed by adding a Hammett parameter correction (vide infra). Regression lines for a range of redox couples have been reported.1,62,63 For clarity in the discussion below, the slopes and intercepts of these correlations are defined asSMFe
andIMFe
because they are based on a FeIII/II standard and not a RuIII/II standard.
The redox potentials of half-sandwich species,62,64 e.g., M(-L)Xn, can be rationalized using acombination of EL(L) and EL(-L) values.
Thus, a large number of half-sandwich species can be written generally as (-L)MXn, e.g., CpFe(dppe)Br or (6-C6H6)Cr(CO)2(PPh3), etc. If one treats -LM as a ‘‘common core’’ for a series of species of the same metal center and oxidation state, e.g., (-L)M(XYZ) (vary X, Y, Z) then the ligand parameter model can be used in the classical fashion, plotting the redox potentials againstEL(XYZ), generating a slope SMLRu
and an intercept IMLRu. Since the stereochemistry differs from regular octahedral, the slopes and intercepts of these correlations will not be the same as those for the same redox process in an octahedral environment. Conversely one may have a series (-L) MXn in which MXnis the common constant core and the ligand is varied. In this case good linear correlations are obtained when plotting the redox energy againstEL(-L) with slope SMXFe
and interceptIMXFe62
(but differing in value from those obtained for M(-L)2sandwich species).
Combining these two observations, it is evident that a set of redox data for a general half- sandwich (-L)M(XYZ) species will obey:62
E1=2ẵMnỵ1=n ẳSMLRuELðXYZị ỵSMXFeELð-Lị ỵIMLX ð12ị A dataset forE1/2[Cr1/0] potentials exhibited by (-L)Cr(XYZ) species is shown in Figure 2.
Table 5 Ranges of sandwich ligandEL(-L) values, V vs. NHE.
4-C4Ph42 1.59
Substituted Cyclopentadienes 0.04 toþ0.75
Substituted Arenes þ1.6 toþ2.6
7-C7H7þ þ3.62
a For full listing see.1,62,63Useful additional values can be derived from the data reported in.65,66
Average charge density (electron/atom)
–0.6 –0.4 –0.2 0.0 0.2
–2 –1 0 1 2 3 4
EL(V VS. NHE)
C4H42–
R-Cylopentadienyls 1
R-Arenes C7H7+
Figure 1 EL(-L) plotted against average charge density being defined as formal charge divided by number of coordinating atoms. The numbered ligand 1 is a carborane [1,2-C2(Et)2B4H4]2.
Ligand Electrochemical Parameters and Electrochemical–Optical Relationships 257
2.19.4.1 Relationship BetweenEL(L)andPL
Since the PLparameter is based on the potential changes when a carbonyl ligand is replaced by another ligand L, it should be linearly related to the EL(L) parameter; indeed, the appropriate expression is found, experimentally, to be (but vide infra):1
PL ẳ 1:17ELðLị 0:86ðVị ẵ24 species;Rẳ0:996 ð13ị Equation (13) has been used fairly extensively27,34,39,41 as a means to derive EL(L) values of ligands in somewhat esoteric organometallic species where only the PL values can be directly derived. However, the relationship should be used with caution since a few ligands are known apparently to be ill-behaved in this correlation, carbonyl being one of them. Further,PLvalues tend to be quite small and the relative error in usingEquation (13)can be fairly high. It should also be evident that the Esvalues of a core [Ms] (e.g., Mo(CO)4Py) as described inSection 2.19.3can, in principle, be obtained by calculating the appropriate Mnþ1/noxidation potential in [Ms(CO)] (e.g., Mo(CO)5Py)) using the availableEL(L) parameters (plus appropriate corrections factors following Equation (11)). However, thePL=0 ‘‘point’’ (for L=CO) in agraph ofE[Msnþ1/n] vs.PLfor aseries [MsL] does not always lie on the best line through the other points (see, for example,34,67), possibly because of a need for the type of stabilization correction indicated inEquation (11). Thus, theEs
value (atPL=0) may not correspond precisely withE1/2[Ms(CO)]. Because of these uncertainties, neither Es nor L can be derived reliably from EL(L). Indeed the modus operandi of the PL
methodology is that it is extracting information out of more restricted sets of data than the usual EL(L) approach in order to look for more subtle variations in electronic structure. Thus, there should be no analytical relationship betweenELandPLandEquation (13)is an approximation.
2.19.4.2 EL(L) Parameters and Reduction Potentials
Many ligands such as the polypyridines, quinones and quinonediimines, porphyrins and phthalo- cyanines, etc. can be reduced sequentially. Often, other ligands are attached to the metal center.
These additional ligands influence the reduction potential at the reducible ligand in a systematic way that can be rationalized via the EL(L) parameter. For a reducible fragment Mn(LL) in a complex, M(LL)WXYZ: we can write
E1=2ẵLL0=ðMnỵị ẳSLELðWXYZị ỵIL ð14ị –1.0
–1.0
–0.5 –0.5
0.0 0.0
0.5 0.5
1.0 1.0
1.5
1.5 π-LCrX3
Cyclopentadienes
Arenes
E1/2(Calc.) (V vs.NHE)
E1/2(Expt.) (V vs.NHE)
Figure 2 Observed CrIII/II potentials for some chromium half-sandwich species plotted versus the value calculated usingEquation (12).
whereE1/2[LL0/(Mnþ)] is the reduction potential of LL0to LLwhen bound to Mnþ. Note tha t we refer to a specific oxidation state,nþ, and that the behavior of LL bound to say, Mnþ1þ, will be different.
SLis an important parameter.8For example, ifSLis ca. 0, the reduction potential at the M(LL) site is independent of the other ligands WXYZ, i.e., there is no net transfer of electron density from these ligands to the M(LL) site—an improbable event, it would seem, but one which is approximately true for the Mo(bpy)2XY series whereSLis very small (0.06).68IfSLis large, then one may suppose that the M(LL) site is very polarizable and susceptible to the influence of the other ligands. Thus,SLconveys information about coupling of the WXYZ ligands to the LL ligand via the metal center, or more precisely, therelativebinding of the WXYZ ligands to LL in the LL and LLoxidation states.
IL is also an interesting parameter. If binding of LL to the metal center has no effect upon its energy levels, SL=0, and IL is the reduction potential of the free ligand. Thus, bothSL and IL
provide information about the extent of mixing between metal orbitals and the ligand reduction orbital. We may question whetherEquation (14) is truly linear over a very wide range ofEL(L) values; data available suggest that it is, but a more detailed analysis could be profitable. One may wish to write a corresponding equation for ligand oxidation,E1/2[Lþ/0], but this is trivial, because it is equivalent to usingEquation (14)for acomplex of the oxidized ligand.
2.19.4.3 Reduction Potentials Vs. Oxidation Potentials
Given that both the oxidation and reduction potentials can be written in terms of EL(L) it should be true that within homologous series of complexes,Eoxand Ered must linearly correlate.
This relationship has indeed been known experimentally for quite some time.58,69–72The equation for this linear correlation can be written:
E1=2ẵLL0=ðMnị ẳ ðSL=SMịE1=2ẵMnỵ1=nðLLị ỵ ẵIL ðSL=SMịIMSLdELðLLị ð15ị InEquation (15), LL is the ligand being reduced, d is the denticity of that ligand, and the term in square brackets is a constant for the given reducible ligand, LL. A table of these data is presented elsewhere.1The slopes do indeed equal (SL/SM) to within experimental error.
2.19.4.4 Redox Processes of Homologous Series of Ligand Fragments
Studies with substituted ligands (homologous series of ligands) can be very useful to reveal subtle changes in electrochemical behavior as a function of substituent. Coupled with computational techniques, such studies can yield detailed insight into metal–ligand interactions.
2.19.4.4.1 Reduction
In ahomologous series of complexes such as Mn(RL)X5and Mn(RLL)X4maintaining X constant and varying R, and taking account ofEquations (9),(10), a nd(14)it is clear that we can writeEquation (15):
E1=2ẵRL0=ðMnị ẳdfðRị ỵE1=2ẵHL0=ðMnị ð16ị which may be recast asEquation (17):
E1=2ẵRL0=ðMnị ẳ ðdf=f0ịELðRLị ỵC ð17ị where E1/2[HL0/(Mn)] is the reduction potential of the parent ligand metal complex, in these examples, [M(HL)X5]n or [M(HLL)X4]n and will be a constant here, f and f0 are reaction parameters indicating the sensitivity of the function to the variation in Hammett substituent parameter, and(R) is an appropriate set of Hammett substituent constants.
There is an extensive literature pertaining to the observation that redox potentials in homologous series of complexes are linearly dependent upon a Hammett parameters(R)36,50,73–95(also seeTable 2).1 Species of the type [M(RLL)2X2]nþand [M(RLL)3]nþ also generally obey Equations (15)and (16) which is rather surprising on reflection. Arguments can be made as to whether reduction Ligand Electrochemical Parameters and Electrochemical–Optical Relationships 259
occurs at one RLL ligand site in a multi-RLL complex or whether the reduction process is delocalized over several RLL ligands. But the fact remains that the constant terms in Equations (15) and (16) should not be precisely constant in these multi-RLL (or multi-RL) species. With data currently available, they do appear to be essentially constant within the error of the experiment.
Similar correlations exist with metal-centered reduction processes as a function of ligand substituent.96,97
Compounds such as [M(LL)X4(RL)]nþare interesting because they raise the issue of how ‘tuning’
the RL ligand will affect reduction at another ligand (LL), i.e., tuning the intra-ligand interactions in the molecule, Few investigations of M(LL) reduction potentials as a function of RL and X have been reported. The relevant equation (from Equations (9) and(14)) would simply be: [for given X]
E1=2ẵLL0=ðMị ẳSLf0ðRị ỵCðvary RLị ð18ị
ẳSLf00ELðRLị ỵC00 ð19ị At first sight Equations (18) and (19) are independent of the X ligand provided X is kept constant. However, one might expectSLto vary with X, in practice, if X does mediate and modify the coupling between RL and LL. Systematic studies of this type are virtually unknown but the complexes [Re(bpy)(CO)3(R-Py)]þfall into this class.66
2.19.4.4.2 Oxidation
Tuning the metal-centered oxidation potentials of M(RL)xXy species is essentially trivial since EL(RL) can be varied through Equation (10).
2.19.4.5 EL(L) Relationships with Non-electrochemical Parameters
Clot and co-workers45 have explored relationships connecting the Tolman electronic parameters (TEP)98 with other kinds of parameters. Like the ligand electrochemical parameters, the TEP values are believed to be a measure of the net donor power, and, of the ligand. The Tolman parameters for a ligand L are based on the observedA1(CO) stretching frequency of the species LNi(CO)3. These researchers also used density functional theory to computationally obtain A1
(CO) values of LNi(CO)3species as means to determine if these parameters could be obtained by calculation instead of experiment, thereby expanding the range of possible structures to species not yet available in the laboratory. These computed electronic parameters (CEP) correlated extremely well with the experimental TEP values with the regression relationship:
TEPẳ0:9572 CEPỵ4:081ðcm1ị ð20ị
These authors then demonstrated a ‘full transferability’ between CEP/TEP andEL(L) through the relationships (21): (EL(L) in V vs. NHE, CEP/TEP in cm1)
ELðLị ẳ0:01302 TEP26:67
ẳ0:01246 CEP26:62 ð21ị
As shown in Table 545 these relationships provide a very useful means to extend further the database of EL(L) values especially to ligands less commonly used in classical coordination chemistry, e.g.,t-butyl (EL(L)=0.90 V), H2S (0.43 V), SiH3(0.56 V) and a series of carbenes with EL(L) ca0 þ0.2 V, etc.
However, these equations involve subtracting two relatively large numbers to obtain, in most cases, a rather small number forEL(L). Small errors are likely here but the final calculated redox potential may be seriously in error due to the need to multiply by 6 for an ML6 species (see Figure 245).
These authors also show how the Hammett parametermcan be linked toEL(L) viaEquation (22):
m ẳ 0:82ELðLị ỵ0:60ðELðLịin V vs:NHEị ð22ị expanding on an earlier relationship withp49
p ẳ 1:61ELðLị ỵ0:60ðELðLịin V vs:NHEị ð23ị These equations should be used with caution as the regression coefficients are not sufficiently close to unity for high accuracy.