Published: August 02, 2011
pubs.acs.org/IC
Nearest- and Next-Nearest-Neighbor Ru(II)/Ru(III) Electronic Coupling
in Cyanide-Bridged Tetra-Ruthenium Square Complexes.
Ju-Ling Lin,
†Chia-Nung Tsai,
†Sheng-Yi Huang,
†John F. Endicott,*
,‡Yuan-Jang Chen,*
,†and
Hsing-Yin Chen
§†Department of Chemistry, Fu-Jen Catholic University, New Taipei City 24205, Taiwan, R.O.C.
‡Department of Chemistry, Wayne State University, Detroit, Michigan 48202, United States
§Department of Medicinal and Applied Chemistry, Kaohsuing Medical University, Kaohsuing 807, Taiwan, R.O.C.
b
S Supporting Information’ INTRODUCTION
The electronic properties of complexes with an approximately square cyanide-bridged tetrametallic core have been of some
interest recently.17 When the metals can be oxidized or
reduced, the electronic mixing between metals in different formal oxidation states can in principle lead to delocalization of charge density in the mixed valence species generated, and this delocalization can alter the physical and chemical properties of the complexes.817However, it is generally difficult to evaluate the extent of electronic delocalization between the metal centers in these systems since (a) the best developed descriptions of mixed valence complexes were obtained for the weak coupling limit in which the delocalization is very small810,12,14and (b) most of these approaches are based on the properties of metal to metal charge transfer (MMCT) absorption bands, and the orbital compositions of the observed transitions are rarely well estab-lished for the electron-rich metals that are often used in such studies. Furthermore, electroabsorption studies have shown that the weak coupling approach can greatly underestimate the donoracceptor (D/A) mixing in complexes with large mixing matrix elements.1821
The cyanide linkage of D/A pairs of metals can be
“non-innocent”, and it can contribute to a variety of complex proper-ties even when there is a significant difference in the potentials for oxidizing and reducing the complexes and the D/A mixing is
relatively weak.22,23 When the difference between the donor
oxidation and acceptor reduction potentials, FΔE1/2(F is Faraday’s
constant), is small, much greater D/A mixing is expected, and there should be corresponding alterations in complex properties. Multimetallic complexes with the metals bridged by cyanide differ from their analogs with polypyridyl bridging ligands (such as pyrazine) in the high energies of their metal to or from cyanide
charge transfer (MLCT or LMCT, respectively) absorptions.23
As a consequence, the effects of D/A mixing between next nearest neighbor metals tend to be interpreted in terms of the mediation by the intermediate metal center rather than by the cyanide.1This approximation either ignores the contributions of the bridging cyanide or assumes that some molecular orbital of the intermediate (L)M(CN)2linker mediates the mixing of the
remote metals. While it is difficult to evaluate the validity of this assumption, it does point to a unique feature of the cyanide-bridged complexes.
The D/A couples generated by one-electron oxidation of the simple CN-bridged tetra-metallic square complexes reported in this study are linked by two (L)M(CN)2moieties, and this amplifies the
effects of NN mediated NNN mixing, thereby providing some unique insights into the issues related to strong D/A mixing.
Received: April 19, 2011
ABSTRACT:Electrochemical properties of cyanide-bridged metal squares, [Ru4]4+ and
[Rh2Ru2]6+, clearly demonstrate the role of the nearest (NN) metal moiety in mediating
the next-nearest neighbor (NNN) metal-to-metal electronic coupling. The differences in electrochemical potentials for successive oxidations of equivalent Ru(II) centers in [Ru4]4+
areΔE1/2= 217 mV and 256 mV and are related to intense, dual
metal-to-metal-charge-transfer (MMCT) absorption bands. This contrasts with a small value ofΔE1/2= 77 mV and
no MMCT absorption bands observed to accompany the oxidations of [Rh2Ru2]6+. These
observations demonstrate NN-mediated superexchange mixing by the linker Ru of NNN Ru(II) and Ru(III) moieties and that this mixing results in a NNN contribution to the ground state stabilization energy of about 90( 20 meV. In contrast, the classical Hush model for mixed valence complexes with the observed MMCT absorption parameters predicts a NNN stabilization energy of about 6 meV. The observations also indicate that the amount of charge delocalization per Ru(II)/Ru(III) pair is about 4 times greater for the NN than the
NNN couples in these CN-bridged complexes, which is consistent with DFT modeling. A simple fourth-order secular determinant model is used to describe the effects of donor/acceptor mixing in these complexes.
’ EXPERIMENTAL SECTION
1. Materials and Synthesis of Compounds. The following
commercial chemicals were used with no further purification: RuCl33 3H2O, Ru(bpy)2Cl23 2H2O, and NH4PF6 (STREM); RhCl33 3H2O (KOJUNDO); 2,20-bipyridine, 2,20:60,300-terpyridine, and trifluoro-methanesulfonic acid-d (DOTF) (Aldrich); and KPF6 (SHOWA). The syntheses of the following compounds have been reported elsewhere: cis-[Ru(bpy)2(CN)2](H2O)2,24 cis-[Rh(bpy)2Cl2](PF6),25 cis-[Rh(bpy)2(CN)2](PF6),26and [(bpy)2Ru{CNRu(tpy)(bpy)}2](PF6)4.27 [Ru4](PF6)4. A mixture of 49.65 mg (0.095 mmol) of [Ru(bpy)2Cl2 ]-(H2O)2and 50.10 mg (0.100 mmol) of [Ru(bpy)2(CN)2](H2O)2in 31 mL of H2O was refluxed for 4 days. Then, 2 mL of saturated aqueous NH4PF6 solution was injected into a round-bottom flask, and the mixture was chilled to precipitate the target complex, [Ru4](PF6)4. All steps of the synthesis were carried out in an argon atmosphere. The sample was chromatographically purified twice (with aluminum oxide 90 active neutral, purchased from Merck, as the stationary phase, and a 1:3 (v/v) mixture of CH3CN and toluene as the eluent). The second brown band contained the desired compound. The solvent was removed by rotary evaporation followed by drying in a vacuum. The typical yield was 82%. Anal. Calcd (found) for C84H64N20F24P4Ru4: C, 43.16 (42.69); H, 2.76 (2.82); N, 11.98 (12.05).
[Rh2Ru2](PF6)63 (H2O)4. This reaction was carried out in an argon atmosphere. A solution containing 101.62 mg (0.166 mol) of [Rh-(bpy)2(CN)2](PF6), 86.93 mg (0.167 mmol) of Ru(bpy)2Cl23 2 H2O, and 20 mL of a 1:1 (v/v) mixture of ethylene glycol/H2O was refluxed for 4 days. A saturated aqueous solution of KPF6(3 mL) was added to the solution, the mixture was cooled to room temperature, and the crude product was removed by filtration. The crude product was purified by chromatography using the above procedure. The typical yield of the bright red-orange product was 18%. Anal. Calcd (found) for C84H72N20 -F36O4P6Rh2Ru2: C, 37.32 (37.07); H, 2.68 (2.45); N, 10.36 (10.52).
Electrochemistry. Electrochemical measurements were performed using an Epsilon Electrochemical Workstation. Cyclic voltammograms (CV) and differential pulse voltammograms (DPV) were obtained in acetonitrile solution, which contained 103 M complex and 0.1 M n-tetrabutylammonium hexafluorophosphate (n-TBAH) at scan rates of 100 mV/s and 4 mV/s, respectively. A three-electrode system consisting of a Pt disk (1 mm) as a working electrode, polished with 0.10.3 μm Baikowski alumina suspension, a Pt wire as the counter electrode, and Ag/AgCl as the reference electrode was used. Ferrocene (0.437 V vs Ag/AgCl) was used as the internal standard.
Absorption Spectroscopy (UVvisNIR). UVvisNIR absorption spectra of these multimetal complexes in a solution of CH3CN/H2O = 1:1 (v/v) were determined with a Shimadzu UV-3101PC spectro-photometer at 298 K. The spectral changes that accompanied redox titrations were obtained with the target complexes dissolved in the [DOTF] = 0.03 M solution (CH3CN/D2O = 1:1 (v/v)) and 3 103M (NH3)2Ce(NO3)6, as the oxidant, or 1.5 103M ferrocene, as the reductant; the CH3CN/D2O = 1: 1 (v/v) solutions of both oxidant and reductant contained 0.03 M [DOTF].
Computational Methods. Density functional theory (DFT) calcula-tions with the Becke three-parameter hybrid functional B3LYP28 were used in this work. The atoms were represented with the LANL2DZ2830basis set implemented in the Gaussian 03 program.31 For [Ru4]
5+/6+
, only C2 constrained geometry optimizations were performed. Since all of the calculated electronic states were open-shell, spin-unrestricted wave functions were employed. The properties of electronically excited states were calculated by the time-dependent DFT (TD-DFT) approach with the Gaussian 03 package.31 The UV-vis absorption spectra were simulated by using the data of TD-DFT calculations with full width at half-height of 2000 cm1; this was achieved by using the GaussView program.32The calculated low-energy
absorption spectra, the composition of electronic transitions, the associated molecular orbitals, and the Mulliken spin densities and charges for the series of mixed-valence complexes are shown in the Supporting Information S1.
’ RESULTS
In this work, we have synthesized the square complexes [Ru4]4+
and [Rh2Ru2]4+, in which Ru(II)(bpy)2moieties are linked by
cyanide, see Figure 1. The oxidations of the chemically equivalent Ru(II)(bpy)2 moieties of the former occur in well separated,
electrochemically distinct steps, as shown in Figure 2, and they result in the low energy metal-to-metal charge transfer absorp-tions, which are shown in Figure 3 and summarized in Table 1. In contrast, the electrochemical oxidations of the [Rh2Ru2]6+
complex are not as well separated, and we have not detected any
absorption changes at energies less than 15 000 cm1
accom-panying the oxidations. These electrochemical observations are clear evidence for the mediation of next nearest neighbor (NNN)
Ru(II) and Ru(III) superexchange12,14 mixing by the nearest
neighbor (NN) (bpy)2Ru(CN)2linker, and this is discussed in
detail below.
The DFT modeling of the [Ru4]5+complex38 results in the
same spin and, by inference, charge densities on NNN metals, and this is not consistent with the unsymmetrical distribution of charge (about 90% on RuNand about 10% on RuN0) implicated
by the electrochemical observations on the doubly bridged NNN metals (see the Discussion section).38It is possible that this is a problem of a tendency of the DFT approach to give symmetrical
Figure 2. The cyclic voltammograms (gray curves) and differential pulse voltammograms (red curves) of [Rh2Ru2]6+and [Ru4]4+vs Ag/ AgCl in acetonitrile with 0.1 M TBAH.
Figure 1. Schematic representations of the square complexes. Since the M and Ru sites differ in their linkage to cyanide, they will be distinguished as Mc, Mc0, RuN, and RuN0.
charge distributions in chemically equivalent moieties39within a molecule, and this is being further investigated. In contrast,
the DFT calculations on the [Ru4]
6+
complex indicate about 16% charge delocalization between NN Ru centers, which is consistent with the inferences from the electrochemical measurements.
’ DISCUSSION
The absorption spectra of linked D/A complexes have tradi-tionally been interpreted in terms of models that assume single donor and acceptor orbitals that are weakly mixed.11,14,15,40,41 Such models are of limited value for electron-rich donors such as Ru(II), which have several potential donor orbitals that are similar in energy, and when the D/A mixing is very strong. Thus, each Ru center in the complexes considered here contains three dπ orbitals that do not differ much in energy, so that the orbital compositions of the observed absorption bands are often ambiguous. As a consequence, the experimental assessment of D/A mixing is much more straightforward when based on the
electrochemical properties of the relatively simple square complexes with cyanide-bridged RuIII,II(bpy)2D/A moieties,
and it demonstrates that there is much more electronic mixing between the remote centers than inferred from the weak mixing models.
The DFT modeling of the absorption spectra of the complexes reported here and for some related Ru-polypyridyl complexes discussed previously42,43indicates that the dominant observed absorption bands are often the convolution of several components that differ in their orbital composition and that the HOMOLUMO transitions, which generally correlate with the oxidation/reduction properties of the complexes, are often difficult to identify due to small oscillator strengths and/or very low energies.27,43 This is particularly a concern in the class of
complexes considered here because the NN Ru(bpy)2centers
differ only in their linkage to cyanide, and this should result in
small intrinsic values of FΔE1/2 while the electron-transfer
reorganizational energies of the Ru(bpy)2 moieties are also
expected to be relatively small.17As a result, there could be very low energy MMCT transitions. Such a low energy absorption band (∼4000 cm1) has been reported to result from oxidation
of the closely related [Fe4]4+complex.6
There are fewer ambiguities in the interpretation of our electrochemical observations. Thus, the lowest energy Rh(III) acceptor orbitals occur at such high energies that the NN Ru(II)/ Rh(III) mixing is effectively zero in [Rh2Ru2]6+, and a very
small value ofΔE1/2= 77 meV is observed for oxidations of the
chemically equivalent Ru(II) centers. The sum of contributions from through space Ru(II)/Ru(III) mixing,εNNNtp , and several
electrostatic factors37that accompany the NNN oxidation,εNNNel ,
are approximately 77 meV. However, the differences in solvating oxidized and reduced species are expected to dominateεNNNel ,
and replacing Rh(III) by Ru(III), which should not alter (εNNNtp +
εNNNel ), increases ΔE1/2 by 180 mV. This increase can be
attributed to twice the stabilization energy that results from NN Ru(III) mediation of NNN Ru(II)/Ru(III) coupling, 2εNNNspx , in the [Ru4]7+ complex. Since there are two bridging
linkages in the [Ru4]7+complex, this implies a superexchange
contribution ofεNNNspx /(bridging unit)≈ 45 meV (≈ 360 cm1);
if the contributions are approximately additive, this corresponds to the NNN stabilization energy in the comparable trimetallic Table 1. MMCT Absorption and Electrochemical Parameters of Some Mixed-Valence Multi-Metal Ions
E1/2(Ru(III/II)) FΔE1/2 MMCT absorption parameters
complexesa charge (n+) range V (DPV)b eV cm1 charge (n+) hνmax(low) (ε/103) [Δv 1/2]c hνmax(high) (ε/103) [Δv 1/2]c [Ru4]n+ (4+) to (6+) 0.717, 0.930 (0.692, 0.909) 217 1750 5+ 7.47 (9.6)[3.4] 11.6 (3.4) [3.4] (6+) to (8+) 1.687, 1.970 (1.680, 1.936) 256 2060 6+ 10.0 (23.0)[3.3]d
[Rh2Ru2]n+ (6+) to (8+) 1.449 (1.379, 1.456) 77 620 [all] (ε < 200 M1cm1between 10000 and 15000 cm1) cis-[Ru(bpy)2{CN-Ru(bpy)(tpy)}2]n+ d (4+) to (6+) 1.008, 1.137 (0.983, 1.117) 129 1040 5+ 7.63 (5.8) [4.0] 10.6 (1.4) [3.8]
(6+) to (7+) 1.820 6+ 8.90 (8.4) [4.4]
cis-[Ru(bpy)2{CN-RuA5}2]n+ e,f (4+) to (6+) 0.055, 0.125 70 560 5+ 9.5 (0.35) [4.2] 14.6 (3.3)[4.4]
(6+) to (7+) 6+ 15.3 (6.0)[5.7]
trans-[(Am)4Cr(CNRuA5)2]n+ f,g (5+) to (7+) 0.36 6+ 10.0 (0.14) [5.1]h 20.0 (8) [4.9]
aThis work except as indicated.bCyclic voltammograms of 0.1 M TBAH/CH
3CN with a Ag/AgCl reference electrode and ferrocene (E1/2= 0.437 V vs Ag/AgCl) as an internal reference except as indicated. vmax= absorption maxima in cm1/103;ε = molar absorptivity, M1cm1;Δv1/2= full bandwidth at half height in cm1/103; EMMCT=fitted Gaussian-maximum; in 0.03 M aqueous DOTF ([DOTF] = 0.03 M, except as indicated.cAbsorption spectra in mixed solvents (D2O/CH3CN, v/v = 1/1; in this work).dData from ref 22eReferences 23 and 33.fA = NH3.gReferences 3436; Am = 1,4,7,10-tetraazacyclotetradecane.hBased on spectral changes resulting from incremental Ce(IV) oxidations of the fully reduced complex in deaerated 0.1 M aqueous NaHSO4solutions with the absorbance maximum evaluated from a Job's plot described in ref 37.
Figure 3. Absorption changes that accompany Ce4+oxidations of the Ru centers of theCN-bridged complex, [Ru4]
4+
: black curve, [Ru4] 4+
; red curve, [Ru4]
5+
; and blue curve, [Ru4] 6+
complex. Although the contributions of εNNNtp are probably
comparable,εNNNel is likely to be smaller for thefirst two
oxida-tions of [Ru4] 4+, so by using (ε NNN tp +εNNN el ) ≈ 77 meV and
allowing for an experimental uncertainty of(5 mV in each electro-chemical determination we obtain, reasoning as above, 64 > εNNNspx /meV g 35 per bridging unit in the [Ru4]5+complex. Thus,
the estimates ofεNNNspx for the two NNN Ru(II)/Ru(III) couples
are small and comparable, with εNNNspx /bridging unit ≈
45 ( 10 meV. Similarly, we find 47 > εNNNspx /meV g 30 in
the trimetallic [Ru(CNRu)2]
4+
complex (with one bridging unit); this is based on the assumption that (εNNNtp +εNNNel )≈
3570 meV since the oxidations of equivalent Ru(tpy)(bpy) moieties of [Ru(CN-Ru)2]4+were indistinguishable.27These
electrochemistry-based observations put significant constraints on the magnitude of the NN mixing.
The relationship between the NN D/A mixing and the NN mediated NNN D/A mixing is commonly classified as “super-exchange” (spx), and it is usually formulated in terms of a
three-state LCAO-based model:12,14,44donor (D), acceptor (A), and
bridging ligand states (NN). This approach assumes that the NN and NNN mixings can be uniquely identified, for example, as expressed in terms of their respective stabilization energy con-tributions to the total ground state stabilization energy,εg(3)(for
a three-state model), that results from configurational mixing:
εgð3Þ≈ εNN þ εNNN ð1Þ
Equation 1 is expressed as a sum of distinct mixing perturba-tions which are based on the respective diabatic energies so that εNN= (HNN)2/[ENN(1 + (HNN/ENN)2)] andεNNN= (HNNN)2/
[ENNN(1 + (HNNN/ENNN)2)]. If one assumes that εNNNis a
linear combination of through space (tp) and bridging ligand mediated contributions, then a LCAO formalism leads to eq 2 with the limit thatRNN2 , ∼0.1.12,14
HspxNNN≈H
2
NNð2ENN ENNNÞ
2ENNðENN ENNNÞ
ð2Þ Equation 2 has singularities for the diabatic energies at ENN=
ENNNand at ENN= 0. Figure 3 suggests that ENN∼ ENNNfor
[Ru4]5+and that the NN mixing matrix elements are quite large
so that substantial errors would be expected if this equation were used (see Figure 4). Alternatively, one can use the third order secular determinant, to represent perturbational mixing in the three state system, but this raises some issues regarding the definition of “superexchange” mixing. The simplest definition is the difference between the stabilization energy of a mixed valent three center system of the DtAcAt0(subscripts t and t0for terminal
and c for central) type from that for the equivalent two center system, so that εNNN≈ εg(3) εg(2). This definition differs
somewhat from that in the weak coupling limit since some of the additional stabilization energy of a three center system can arise from an appreciable redistribution of charge among Dt, Ac, and
At0whenRDA2> 0.1; however, it is reasonably straightforward
and will be employed here.
In the weak coupling limit (forRNN2, 0.1), the spectroscopic
parameters for the MMCT absorption can be related to the mixing matrix element by8,9
HNN ¼ 0:0205 rDA ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εmaxΔν1=2νmaxðNNÞ q ð3Þ With the hνmax(low) parameters in Table 1 and rDA= 5.2 Å (the
distance between Ru(II) and Ru(III) centers), eq 3 results in
HNN ∼ 1950 cm1 and RNN(H)2 ≈ 0.07 . This value of
RNN(H) 2
in eq 2 leads toεNNN
spx ∼ 27 cm1 (∼ 3 meV) per
bridging moiety, which is far smaller than the 360 cm1
(45 meV) per bridging moiety that we observe. However, it is well documented18,19,21that inappropriately small values of
HNNare obtained from eq 3 based on the geometric distance
between D and A centers and MMCT absorption spectra when the absorptivities are very large; such underestimates are usually attributed to overestimates of the effective dipole lengths of the optical transitions.
We have used a fourth order secular determinant, eq 4, to model the lowest energy eigenvalues for the ground state,ξG, for
a [Ru4]n+,ξG(Ru), and for a reference system,ξG(ref),
1 ξ RNN0 RNN 0 RNN0 X ξ 0 RNN0 RNN 0 ξ RNN 0 RNN0 RNN 1 ξ ¼ 0 ð4ÞAll energies in eq 4 are relative to ENN = ENN(RuN) so that
1 = ENN/ENN,ξ = ε/ENN,RNN= HNN/ENN, and X = ENNN/ENN.
The distinction betweenRNNandRNN0is only for convenience
in defining the reference model used: (a) for [Ru4]n+ RNN =
RNN0; (b) for the equivalent reference systemRNN0= 0. Then, the
Figure 4. Comparison of perturbation theory models for contribution of a NNN center (e.g., RuN0) to the ground state stabilization,εg, per bridging moiety for different ratios of excited state energies. For [Ru4]5+, assuming HNNN(tp) ≈ 0 and with R2= 0.25, 0.2, 0.16, and 0.06 (dark red, dark blue, and purple curves, respectively): (a) with eigenvalues calculated using eq 4 for different ratios of X = ENNN/ENN(solid curves) or (b) based on eqs 2 and 6 (dashed lines). Red curves for [(Am)4Cr(CNRu(NH3)5)2]6+((Am)4= 1,4,7,77-tetraazacyclotetrade-cane (cyclam)) withRNN2= 0.028 (based on work in refs 23, 34, 36) and eigenvalues calculated from third order secular determinants (solid curves) or eq 2 (dashed lines). Note that the values ofξNNN=εNNN/ ENNgenerated from eq 2 are less than0.1 for RNN
2
= 0.16, 0.2, and 0.25 when X < 1. The gray rectangles correspond to plausible values of X for [(Am)4Cr(CNRu(NH3)5)2]
6+
, left, and [Ru4] 5+
lowest energy eigenvalues correspond toξG(Ru) andξG(ref),
respectively, and the superexchange contribution is then
ξGðspxÞ ¼ ξGðRuÞ ξGðrefÞ ð5Þ
For the comparisons in this paper, we have calculated values of the eigenvalues for increments 0.1 of 0 e X e 1.5 (using PSI-Plot).45
For the comparison in Figure 3, we have used the reduced energies in eq 2 to define ξGðspxwÞ ¼ εNNN=ENN ¼ ðHðspxÞNNNÞ2=ðENNNENNÞ ¼ R2NNð2 XÞ 2ð1 XÞ " #2 1 X ð6Þ
In order to estimate plausible values of RNN2, we have
calculated values of ξG(spx) for a range of values of X and
RNN2 using eqs 4 and 5. The results are compared to the
expectation based on the [Ru4]4+electrochemistry in Figure 5,
and they indicate thatRNN2= 0.20( 0.05 and X = 0.90 ( 0.15.
This value ofRNN2combined with ENN= 7500 cm1implies a
(normalized) value of HNN∼ 3400 cm1, which is similar to the
value inferred previously from a variety of observations on the [(bpy)2Ru(CNRu(NH3)5)2]
5+
complex.23
The estimated values ofRNN2 and X agree reasonably well
with those based on the relative energies that are observed for the different MMCT transitions and those based on the eigenvalues of eq 4 as illustrated in Figure 6.
The relative values ofεNNNspx obtained using eq 2 and a third
order secular determinant are reversed in their relative magni-tudes for the [(Am)4Cr(CNRu(NH3)5)2]6+ complexes
exam-ined by Watzky et al.23Thus, eq 3 and the NN spectroscopic
parameters (and other observations)23give HNN≈ 3400 cm1
andRNN2 ∼ 0.03, so that eq 2 gives HNNN∼ 900 cm1and
εNNNspx = (HNNN)2/ENNN≈ 75 cm1, butεNNNspx = 11 cm1using
the third order secular determinant with X = 0.5. These estimates of the superexchange stabilization energy for the Cr complex are both larger than the value of about 2.7 cm1implied by eq 3 and
the observed MMCT spectral parameters.23 Note that, even
excluding those regions where singularities dominate eq 2, Figure 3 shows that the secular determinant-perturbation theory approach leads to smaller values ofεNNNspx than found using eq 2
andRNN
2> 0.03 and that this difference decreases with R NN
2
. Although εNNNspx = 11 cm1, based on a third-order secular
determinant, is only about 4 times greater than that based on the observed spectra and eq 3, the observation that the values ofεNNN
are nearly identical for a series of [(Am)4M(CNRu(NH3)5)2]6+
complexes with different metal centers (M = Cr(III), Co(III) and Rh(III)) and very different values of ENNandRNN2suggests that a
different explanation is necessary, possibly a vibronic constraint as discussed previously.23,36In this sense, the [Ru4]5+system is very
similar to the trans-[(py)4Ru(CNRu(NH3)5)2] 5+
system in which X∼ 1 and configurational mixing between the electron-transfer excited states relaxes the constraints on NNN mixing.35
The mixing of diabatic states leads to small changes in state
energies only when RDA2 , 0.1. So, the use of observed
spectroscopic parameters in eqs 2 and 3 in the evaluation of the properties of mixed valence complexes in this limit should only lead to small discrepancies except in the regions of the singularities illustrated in Figure 3. However, sinceRDA2is much
larger than this for the complexes considered here, the observed electronic energies can be very different from those of the diabatic limit. When this is the case, the use of the observed spectroscopic parameters and eqs 2 and 3 will necessarily result in large errors in the evaluation of mixed valence complex proper-ties. Figure 5 illustrates the variations in the adiabatic energies of a four state system for several values ofRDA2.
Of course, any simple perturbation theory model can provide only a general guide to the interpretation of multimetal electron-rich systems such as discussed here, since there are a large
Figure 5. Reduced NNN superexchange energies calculated from the four-state model, eq 4, as a function ofRNN2and X. The values ofRNN2 used are entered in thefigure. The long dashed horizontal line is the value ofξNNN= 0.048 implied by the electrochemical observations, and the short dashed lines correspond to the estimated uncertainties in that value. The shaded box corresponds to the plausible range of values for X andRNN2.
Figure 6. Energies of adiabatic MMCT excited states based on a four-state model (eq 4) in which the diabatic four-states are assumed to be pairs of degenerate states that differ in their reduced energy by 1.0. The curves are constructed for different values of RNN
2and X using the differences between the eigenvalues of eq 4 and relative to the ground state energy of 0: curve colors as in Figure 4. The shaded square indicates the plausible ranges ofRNN
2 and X.
number of electronic excited states that differ little in energy and the coupling between them will alter the model’s predictions. For example, the successive oxidations of [Ru4]
4+
result in shifts of the energies of absorption bands assigned to MLCT transi-tions, which suggests that some of these excited states also mix with the MMCT states thereby altering the energy relations.
The above arguments overlook some complications that are intrinsic to these mixed valence systems. The most notable of these is that our DFT modeling of this class of complexes indicates that there are appreciable bridging cyanide contribu-tions to their HOMOs (Supporting Information S1).38This is at least partly a consequence of the strong oxidizing capacity of the Ru(III)(bpy)2centers, and the resulting delocalization of charge
onto the bridging ligand must contribute to the observed stabilization energies, but this is very difficult to model in a simple manner. The second notable issue is the nature of the observed transitions. Figures 4 and 5 indicate that 0.8 < X < 1.2 so that the observed absorption bands are likely to be mixtures of the NN and NNN MMCT transitions. However, Figure 5 also suggests that it is unlikely that there are relevant MMCT
transitions at energies lower than about 5000 cm1 in these
complexes.
’ CONCLUSIONS
The [Ru4]4+and [Rh2Ru2]6+square complexes discussed here
are unique in that it is possible to estimate ground state super-exchange stabilization energies of equivalent ruthenium centers based on well-defined and distinct electrochemical oxidations of [Ru4]2+and from this to infer thatRNN2∼ 0.2. This
demon-strates much stronger RuII/RuIIIelectronic mixing and greater electronic delocalization than is implied by the interpretation of the MMCT spectra using the conventional Hush treatment (eq 3). DFT modeling supports the inference of appreciable electronic delocalization in the mixed valence tetra-ruthenium complexes. The optical and electrochemical properties of these complexes illustrate how badly the conventional, superexchange treatment, eq 2, misrepresents the electronic coupling between a remote D/A pair when the energies of the diabatic MMCT and bridging ligand excited states are similar in energy and the donor/ bridging ligand mixing is appreciable. A simple secular determi-nant approach for introducing the electronic perturbations has been shown to provide a much more reasonable description of the mixed valence systems.
’ ASSOCIATED CONTENT
b
S Supporting Information. Computed MMCT absorptionspectra, selected SOMO structures, Mulliken-densities of [Ru4]5+
and [Ru4]6+, and visibleultraviolet region absorption spectra.
This material is available free of charge via the Internet at http:// pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected] (Y.-J.C.), [email protected]. edu (J.F.E).
’ ACKNOWLEDGMENT
This work was funded in part (Y.-J.C.) by the National Science Council of R.O.C through Grants NSC-95-2113-M-030-003 and
NSC-96-2113-M-030-006-MY2 and in part (J.F.E.) by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through Grant DE-FG02-09ER16120. We thank the National Center for High-Performance Computing (R.O.C.) for provid-ing computational resources. We are grateful for many helpful comments and suggestions from Dr. R. L. Lord.
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![Figure 2. The cyclic voltammograms (gray curves) and differential pulse voltammograms (red curves) of [Rh 2 Ru 2 ] 6+ and [Ru 4 ] 4+ vs Ag/ AgCl in acetonitrile with 0.1 M TBAH.](https://thumb-ap.123doks.com/thumbv2/9libinfo/7488041.114522/2.911.579.724.96.237/figure-cyclic-voltammograms-curves-differential-voltammograms-curves-acetonitrile.webp)
![Figure 3. Absorption changes that accompany Ce 4+ oxidations of the Ru centers of the CN-bridged complex, [Ru 4 ]](https://thumb-ap.123doks.com/thumbv2/9libinfo/7488041.114522/3.911.79.442.457.711/figure-absorption-changes-accompany-oxidations-centers-bridged-complex.webp)
