# CrIII as an alternative to RuII in metallo-supramolecular chemistry

Davood Zare, Benjamin Doistau, Homayoun Nozary, Céline Besnard, Laure

Guénée, Yan Suffren, Anne-Laure Pelé, Andreas Hauser, Claude Piguet

► To cite this version:

Davood Zare, Benjamin Doistau, Homayoun Nozary, Céline Besnard, Laure Guénée, et al. CrIII as an alternative to RuII in metallo-supramolecular chemistry. Dalton Transactions, 2017, 46 (28), pp.8992 - 9009. 10.1039/c7dt01747b. hal-01578431

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Cite this: *Dalton Trans.*, 2017, **46**,
8992

Received 12th May 2017,
Accepted 8th June 2017

DOI: 10.1039/c7dt01747b

rsc.li/dalton

Cr<sup>III</sup> as an alternative to Ru<sup>II</sup> in metallo-supramolecular chemistry†

Davood Zare,<sup>‡a</sup> Benjamin Doistau,<sup>*,‡a</sup> Homayoun Nozary,<sup>a</sup> Céline Besnard,<sup>b</sup>
Laure Guénée,<sup>b</sup> Yan Suffren,<sup>c</sup> Anne-Laure Pelé,<sup>c</sup> Andreas Hauser<sup>*c</sup> and
Claude Piguet<sup>ID *a</sup>

Compared to divalent ruthenium coordination complexes, which are widely exploited as parts of multi-component photonic devices, optically active trivalent chromium complexes are under-represented in multi-metallic supramolecular architectures performing energy conversion mainly because of the tricky preparation of stable heteroleptic Cr<sup>III</sup> building blocks. We herein propose some improvements with the synthesis of a novel family of kinetically inert heteroleptic bis-terdentate mononuclear complexes, which can be incorporated into dinuclear rod-like dyads as a proof-of-concept. The mechanism and magnitude of intermetallic Cr···Cr communication have been unraveled by a combination of magnetic, photophysical and thermodynamic investigations. Alternated aromatic/alkyne connectors provided by Sonogashira coupling reactions emerge as the most efficient wires for long-distance communication between two chromium centres bridged by Janus-type back-to-back bis-terdentate receptors.

Introduction

Since the discovery of chromium by Louis Nicolas Vauquelin in 1798, chromium derivatives, particularly in their most stable oxidation state Cr<sup>III</sup>, have been widely studied for their catalytic, 1⁻³ hole transfer ability in photo-cathodic solar cells, 4,5 magnetic, 6⁻¹² and optical properties. 13⁻¹⁵ The latter aspect culminated with the building of the first laser in 1960,¹⁶ which exploited the stimulated emission of electromagnetic radiation from the Cr<sup>III</sup>-centred excited levels found in ruby. Despite its appealing electronic properties, Cr<sup>III</sup> has been scarcely introduced into polymetallic supramolecular architectures working as photonic devices, 17,18 whereas hundreds, if not thousands of sophisticated structures built with luminescent divalent ruthenium complexes have been designed and tested so far. 19⁻²⁴ The main reason for this side-lining can be found in the Cr<sup>III</sup> coordination chemistry, which somehow mirrors that of trivalent cobalt with the formation of

kinetically inert complexes as exemplified by the very small
rate constants found for ligand exchange (e.g., k<sub>H₂O</sub> = 2.4 ×
10<sup>-6</sup> s<sup>-1</sup> for [Cr(H₂O)₆]<sup>3+</sup>)²⁵ and for hydrolysis (e.g., k<sub>hydrolysis</sub> =
3.5 × 10<sup>-4</sup> s<sup>-1</sup> for cis-[Cr(ethylenediamine)₂Cl₂]<sup>+</sup> under acidic
conditions).²⁶ Consequently, Cr<sup>III</sup> cannot be part of sophisti-
cated multi-component self-assembly processes, in which
structural self-healing under thermodynamic control is
crucial.²⁷ Some rare (but remarkable) exceptions arose with (i)
the serendipitous crystallization by Winpenny and coworkers
of poly-chromium wheels at high temperatures (210 °C to
400 °C) using thermally resistant ligands²⁸⁻³⁰ and (ii) the use
of preformed chromium complexes working as inert partners
for the preparation of hydroxo,³¹ oxalato,³²,³³⁻³⁶ and cyano
bridged architectures.⁷,⁹,³⁷ In this context, post-modifications
were recently shown to open novel pathways for the stepwise
building of multi-metallic assemblies including inert ruthe-
nium–polypyridine complexes³⁸⁻⁴⁰ or platinum–salen deriva-
tives,⁴¹,⁴² but the manipulation of related Cr<sup>III</sup>–polypyridine
entities remains scarce and elusive.⁴³⁻⁴⁵ Moreover, recent dem-
onstration that [Cr(2,2′:6′,2″-terpyridine)₂]<sup>3+</sup> (≡[Cr(tpy)₂]<sup>3+</sup>)
complexes rapidly dissociate under slightly alkaline con-
ditions,⁴⁶ a trend which confirms a previous observation
reported for [Cr(2,2'-bipyridine)₃]<sup>3+</sup> (≡[Cr(bpy)₃]<sup>3+</sup>),⁴⁷ prevents
post-treatment of these complexes for the design of organized
polynuclear assemblies. To the best of our knowledge, trivalent
chromium has thus never been used as a partner for thermo-
dynamic multi-component self-assembly processes occurring
in solution, but its labile divalent precursor Cr<sup>II</sup> was shown to
successfully promote the synthesis of heterometallic d–f triple-

<footnote><sup>a</sup>Department of Inorganic and Analytical Chemistry, University of Geneva, 30 quai E. Ansermet, CH-1211 Geneva 4, Switzerland. E-mail: Benjamin.Doistau@unige.ch, Claude.Piguet@unige.ch</footnote>

<footnote><sup>b</sup>Laboratory of Crystallography, University of Geneva, 24 quai E. Ansermet, CH-1211 Geneva 4, Switzerland</footnote>

<footnote><sup>c</sup>Department of Physical Chemistry, University of Geneva, 30 quai E. Ansermet, CH-1211 Geneva 4, Switzerland. E-mail: Andreas.Hauser@unige.ch</footnote>

<footnote>†Electronic supplementary information (ESI) available. CCDC 1542315–1542329.
For ESI and crystallographic data in CIF or other electronic format see DOI:
10.1039/c7dt01747b</footnote>

<footnote>‡These authors contributed equally to this research work.</footnote>
stranded helicates under thermodynamic control.⁴⁸,⁴⁹ Subsequent air oxidation led to inert luminescent Cr<sup>III</sup> sensitizers, which induced unprecedented lanthanide-centred molecular energy-transfer upconversion.⁵⁰⁻⁵³ Last but not least, the characterization of Cr<sup>III</sup> complexes in solution is severely hampered by the broad and poorly interpretable NMR signals produced by the long electronic relaxation times (about 0.5 ns) of their zero-field split Cr(<sup>4</sup>A<sub>2</sub>) ground state.⁵⁴ This drawback is overcome for diamagnetic Ru<sup>II</sup> complexes, which were thus selected for building well-defined photoactive polynuclear architectures useful for water splitting,⁵⁵ light-harvesting and energy conversion.⁵⁶⁻⁵⁸ Nevertheless, while trivalent chromium exhibits some shortcomings compared to divalent ruthenium, its photophysical properties in pseudo-octahedral complexes offer some unparalleled attractiveness since the visible window is dominated by a single spin-allowed absorption band corresponding to the Cr(<sup>4</sup>T<sub>2</sub> ↔ <sup>4</sup>A<sub>2</sub>) transition, the energy of which can be easily tuned by the ligand-field parameter Δ, whereas the near-infrared window is governed by efficient long-lived Cr(<sup>2</sup>E ↔ <sup>4</sup>A<sub>2</sub>) phosphorescence, the energy of which is controlled by the nephelauxetic effect tuned by the Racah parameters *B* and *C* (Fig. 1).¹³,⁵⁹,⁶⁰ It is thus trivial to switch from low-energy absorption combined with high-energy phosphorescence found in CrO<sub>6</sub> chromophores (small values of Δ and large values of *B*) toward the opposite situation found in CrN<sub>6</sub> chromophores.¹³ Furthermore, the almost spin-only behavior combined with negligible zero-field splitting parameters measured for the degenerate paramagnetic Cr(<sup>4</sup>A<sub>2</sub>) ground state (for instance *D* = 0.03 cm<sup>-1</sup> for [(tpy)CrCl<sub>3</sub>]<sup>61</sup> offers a simple approach for unravelling electronic intermetallic communications *via* the estimation of the isotropic exchange coupling constant operating between chromium centres.¹⁰,¹²,⁶²

In diamagnetic polynuclear Ru<sup>II</sup> architectures, for which the Creutz–Taube complex is the arch type (Fig. 2a),⁶³ the

<figure><img src="image_3.png" /><figcaption>**Fig. 1** Low-energy part of the energy level diagram for an octahedral Cr<sup>III</sup> sensitizer showing the energy levels modeled in terms of the ligand field strength Δ and the Racah parameters *B* and *C*.⁵⁹,⁶⁰ The upward green arrow stands for the lowest-energy spin-allowed absorption transition, while the downward red arrow refers to the lowest-energy phosphorescence.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Fig. 2** (a) Creutz–Taube complex, (b) [(tpy)Ru(L)(Ru(tpy))]<sup>m+</sup> complexes,⁶⁹⁻⁷¹ (c) [(tpy)Ru<sup>II</sup>(L)Co<sup>III</sup>(tpy)]<sup>5+</sup> complexes displaying directional electron transfer,⁷²,⁷³ (d) [(tpy)Ru<sup>II</sup>(L)Os<sup>III</sup>(tpy)]<sup>4+</sup> complexes displaying directional energy transfer.⁷⁴,⁷⁵</figcaption></figure>

magnitude of the intermetallic interaction is deduced from the envelope of the intervalence electronic absorption bands occurring in mixed valence Ru<sup>II</sup>–Ru<sup>III</sup> dimers.⁶⁴⁻⁶⁸ When applied to back-to-back bis-terpyridine bridging ligands *L* in [(tpy)Ru(L)(Ru(tpy))]<sup>5+</sup> (Fig. 2b), the associated theories successfully rationalized the exponential decrease of the electronic interaction parameter with increasing intermetallic separations⁶⁹⁻⁷¹ and the magnification of both through-bond electron transfer (Fig. 2c)⁷²,⁷³ and energy transfer (Fig. 2d)⁷⁴⁻⁷⁸ for short electron-rich aromatic bridges. Unfortunately, one-electron reductions of [Cr(bpy)<sub>3</sub>]<sup>3+</sup> and [Cr(tpy)<sub>2</sub>]<sup>3+</sup> occur on the bound ligands⁷⁹,⁸⁰ and no related approach can be envisioned for unravelling intermetallic coupling in analogous polypyridine Cr<sup>III</sup> complexes.

Altogether, the magnetic and photophysical properties of Ru<sup>II</sup> polypyridine and Cr<sup>III</sup> polypyridine complexes are complementary, with each series displaying specific advantages and shortcomings, but the paramagnetism associated with the three unpaired electrons in Cr<sup>III</sup> opens additional perspectives. However, the lack of easy accessible synthetic procedures for the preparation and characterization of pure heteroleptic polynuclear chromium complexes has up to now prevented Cr<sup>III</sup> polypyridines from being used as active building blocks in (supra)molecular optical devices. Recently, Barker *et al.*,⁸¹ Isaacs *et al.*⁸² and Housecroft and Constable *et al.*⁴⁶,⁸³,⁸⁴ tried to find a remedy for this frustrating limitation with the systematic exploration of the stability and lability of mononuclear
<figure><img src="image_5.png" /><figcaption>**Scheme 1** Structures and nomenclature of the investigated dinuclear chromium complexes. tppz = 2,3,5,6-tetra-2-pyridinylpyrazine, bbt = 4,4''''-bis(2,2':6,2''-terpyridine), and ebbt = 4,4''''-(ethynyl)-bis(2,2':6,2''-terpyridine). X₃ stands for Cl₃ or 2,2':6,2''-terpyridine.</figcaption></figure>

six-coordinate bis-terimine⁸³,⁸⁴ and ter-bisimine⁴⁶,⁸¹,⁸² Cr³⁺ complexes. Building on the identification of labile Cr³⁺-O(tri-flate) bonds and their easy formation from Cr-Cl bonds, we herein propose to extend this procedure for the synthesis of a series of novel back-to-back dinuclear [X₃Cr³⁺(L)Cr³⁺X₃] complexes (Scheme 1, X₃ = Cl₃ or X₃ = tpy), which are reminiscent of the well-known Ru¹¹ dyads. We also plan to unravel the inter-metallic electronic communication with the help of magnetic measurements (isotropic superexchange coupling constants), photophysical studies (ligand-field and Racah parameters and intermetallic energy transfer rate constants) and thermodynamic considerations (cooperative binding of labile Er³⁺ as a model for Cr³⁺).

## Results and discussion

### Synthesis and characterization of homoleptic and heteroleptic mononuclear [CrLCl₃], [CrL₂](PF₆)₃ (L = tpy, ebzpy, tppz) and dinuclear [Cl₃Cr(L)CrCl₃], [(tpy)Cr(L)Cr(tpy)](PF₆)₆ (L = tppz, bbt, ebbt) complexes

As a first step toward this goal, we used Ga³⁺ as a trivalent labile diamagnetic model cation for Cr³⁺ for the straightforward formation of a homoleptic [Ga(tpy)₂]³⁺ cation (Table S1, ESI†), which displayed the expected well-resolved D₂d-symmetrical ¹H NMR spectrum (6 signals observed for 22 available aromatic protons, Fig. S1, ESI†). The downfield shifts of the aromatic signal (Δδ = -1.01 ppm) observed for the hydrogen nuclei located at the *ortho*-positions of the nitrogen atoms of the distal pyridine rings are diagnostic for an ortho-

gonal arrangement of the two planar tridentate terpyridine ligands around the central cation as found in [Fe(tpy)₂]²⁺ (Δδ = -1.64 ppm), [Ru(tpy)₂]²⁺ (Δδ = -1.37 ppm) and [Os(tpy)₂]²⁺ (Δδ = -1.43 ppm).⁸⁵ The crystal structure of [Ga(tpy)₂](PF₆)₃·2CH₃CN (1, Fig. 3 left, Fig. S2 and Tables S2, S4 and S5†) confirmed this statement with an interplanar angle of 88.5° between the two tridentate N₃ chelates. Combined with the pincer effect brought by the two-fused 5-membered chelate rings in the terpyridine moieties (N<sub>distal</sub>-Cr-N<sub>distal</sub> = 156.6(1)° instead of 180° expected for octahedral geometry, see Fig. 3), the diamagnetic GaN₆ core adopts the expected compact and slightly distorted pseudo-octahedral geometry previously reported for other [M(tpy)₂]²⁺ (z = 2, 3) complexes.⁸⁶,⁸⁷ No specific close-packing interactions due to significant π-π aromatic interactions compatible with ‘terpyridine embrace’ supramolecular patterns⁸⁷ could be identified (the closest inter-aromatic distance amounts to 4.5 Å, far beyond the accepted cutoff of 3.8 Å for π-stacking interactions; Fig. S3†).⁸⁸,⁸⁹ We however note that [Ga(tpy)₂](PF₆)₃·2CH₃CN (1) crystallizes in the chiral P2₁₂₁₂₁ space group, the origin of which probably arises from packing effects since [Ga(tpy)₂]³⁺ cations are essentially achiral. In order to overcome the complications produced by the kinetic inertness of Cr³⁺ salts, the related homoleptic complex [Cr(tpy)₂]³⁺ is obtained by the reaction of the reduced labile precursor Cr(CF₃SO₃)₂·H₂O⁴⁸ with 2,2':6',2''-terpyridine (tpy), or with its extended analogue 2,6-bis(1-ethyl-benzimidazol-2-yl)pyridine (ebzpy),⁹⁰ to give saturated six-coordinated Cr¹¹ complexes.⁸⁰ Subsequent air oxidation (outer sphere mechanism)⁴⁸ provides [Cr(tpy)₂](PF₆)₃·2.5CH₃CN (2, Fig. S4 and Tables S2, S6 and S7, ESI†) and [Cr(ebzpy)₂](PF₆)₃·5.5CH₃CN (3, Fig. S5 and Tables S3, S8-S11, ESI†) in 70-80% yields after metathesis with PF₆⁻ (Fig. 3).

<figure><img src="image_6.png" /><figcaption>**Fig. 3** Synthesis of the homoleptic tricationic [Ga(tpy)₂]³⁺ [Cr(tpy)₂]³⁺ and [Cr(ebzpy)₂]³⁺ complexes. The molecular structures of the cations are those found in the crystal structures of [Ga(tpy)₂](PF₆)₃·2CH₃CN (1), [Cr(tpy)₂](PF₆)₃·2.5CH₃CN (2) and [Cr(ebzpy)₂](PF₆)₃·5.5CH₃CN (3). The hydrogen atoms have been omitted for clarity. Color code: C = grey, N = blue, Cr = orange, Ga = green.</figcaption></figure>
The molecular structures of the CrN₆ (2 and 3) and GaN₆ (1) moieties are almost superimposable and closely match that previously reported for [Cr(tpy)₂](ClO₄)₃·H₂O.⁹¹,⁹² Again, intermolecular packing interactions are very limited for these chromium complexes (Fig. S6 and S7, ESI†), a trend assigned to the combination of (i) the considerable inter-cation repulsions and (ii) the delicate accommodation of three counter-anions per cationic complex in the crystal structures.⁴⁶ We would like to stress here that the crystal structure of 2, monitored at 180 K in this work, is identical to that previously deposited for 2{[Cr(tpy)₂](PF₆)₃·5CH₃CN recorded at 123 K,⁴⁶ an observation which confirms the robustness of the packing process despite the lack of identifiable strong intermolecular interactions in the crystal structures of these [Cr(tpy)₂]X₂ complexes.

Since no high-resolution NMR signals could be recorded for the slow-relaxing Cr<sup>III</sup> complexes, their magnetic characterization in solution is restricted to the measurement of the effective magnetic moments in acetonitrile for [Cr(tpy)₂](PF₆)₃ (μ<sub>eff</sub> = 4.4(4) BM) and [Cr(ebzpy)₂](PF₆)₃ (μ<sub>eff</sub> = 4.2(4) BM), which only slightly deviate from the spin-only value (μ<sub>eff</sub> = 3.88 BM). Unfortunately, we were not able to record satisfying ESI-MS spectra for these mononuclear triply-charged complexes in solution, probably because of partial dissociation occurring during the vaporization process.⁴⁶

Higher structural complexity requires the rational synthesis of heteroleptic bis-terdentate CrN₆ chromophores following the strategy originally proposed by Barker *et al.* for bidentate phenanthroline ligands⁸¹ and adapted for tridentate terpyridines by Housecroft and Constable and coworkers (Fig. 4).⁴⁶,⁸⁴ Beyond [Cr(tpy)Cl₃], the structure of which was previously reported (Fig. 4 top centre),⁶¹,⁹³ we confirm that the three weakly bound THF molecules in CrCl₃(THF)₃ can be displaced by closely related tridentate ligands⁹⁴ to give [Cr(ebzpy)Cl₃]·DMF (5, Tables S12–S14 and Fig. S8 and S9†) and [Cr(tppz)Cl₃]·2DMF (6, Tables S12, S15, and S16 and Fig. S8 and S9†).⁹⁵ The three CrN₃ chelate units are almost superimposable showing similar bond distances (Cr–N = 2.05(3) Å) and bond angles (average pincer angle N<sub>distal</sub>–Cr–N<sub>distal</sub> = 156.5 (5)°). The crystal structure of [Cr(tppz)Cl₃] (6) reveals specific geometric distortions at the metal centre caused by the repulsion of the hydrogen atoms at the 3-position of the bound pyridine rings with the two unbound pyridine units. The result is a twisting of the bound part of the tppz ligand, in which the dihedral angles between the pyridine and pyrazine rings amount to 19.46°. The reaction of [Cr(L)Cl₃] with concentrated trifluoromethanesulfonic acid (CF₃SO₃H) displaces the three chloride anions to give [Cr(L)(CF₃SO₃)₃] (L = tpy, ttpz, Table S1†). The slightly more basic ebzpy ligand (compared with tpy and ttpz) did not resist protonation and only [H₂ebzpy](CF₃SO₃)₂ could be isolated (10, Fig. S10 and Tables S17 and S18†). Subsequent mixing of [Cr(L)(CF₃SO₃)₃] with a second tridentate ligand L' either restores the homoleptic complexes (L' = L) or provides (L' ≠ L) the heteroleptic complexes [Cr(tpy)(ebzpy)](PF₆)₃ (7, Fig. S11 and Tables S17, S19 and S20†) and [Cr(tpy)(tppz)](PF₆)₃ (8, Fig. S12 and Tables S21–S25†) in fair to good yields (Fig. 4 bottom). Their molecular

<figure><img src="image_7.png" /><figcaption>**Fig. 4** Synthesis of the heteroleptic mononuclear chromium complexes. The molecular structures are those found in the crystal structures of [Cr(ebzpy)Cl₃]·DMF (5), [Cr(tpy)Cl₃]·(CH₃)₂SO,⁹³ [Cr(tppz)Cl₃]·2DMF (6) [Cr(tpy)₂](PF₆)₃·2.5CH₃CN (2), [Cr(tpy)(ebzpy)](PF₆)₃·2CH₃CN (7), [Cr(tpy)(tppz)](PF₆)₃·3CH₃CN (8) and [H₂(ebzpy)](CF₃SO₃)₂ (10). The hydrogen atoms have been omitted for clarity. Color code: C = grey, N = blue, Cr = orange, Cl = green, H = yellow.</figcaption></figure>

structures show CrN₆ units almost superimposable with those found in the homoleptic model cations [Cr(tpy)₂]³⁺ and [Cr(ebzpy)₂]³⁺. Again, no remarkable intermolecular π-stacking interactions could be highlighted (Fig. S13 and S14†) and the structural distortion produced by steric congestion with the non-coordinated pyridine rings in the tppz ligand is retained in [Cr(tpy)(tppz)]³⁺ (the average dihedral angle between the pyridine and pyrazine rings in the tridentate bound unit amounts to 19(4)°).

With this strategy at hand, the synthesis of a series of six rod-like heteroleptic dinuclear Cr<sup>III</sup> complexes with three different bridging ligands (tppz, bbt, and ebbt) and two types of capping entities (Cl₃ or tpy) can be envisioned. Firstly, the reaction of an excess of CrCl₃·6H₂O with the appropriate bridging ligand⁹⁵ quantitatively yields [Cr₂Cl₆(tppz)] and [Cr₂Cl₆(bbt)], while [Cr₂Cl₆(ebbt)] is obtained with more difficulties because of the low solubility of the free ligand in common organic solvents (left part of Fig. 5 and Table S1†).
<figure><img src="image_8.png" /><figcaption>**Fig. 5** Synthesis of the heteroleptic dinuclear chromium complexes. The molecular structures are those found in the crystal structures of [Cr₂Cl₆(tppz)]·3C₅H₉NO (11), [Cr₂Cl₆(bbt)] (12), [Cr₂(tpy)₂(bbt)](PF₆)₆ and [Cr₂(tpy)₂(ebbt)](PF₆)₆, but we were unable to connect two triply charged [Cr(tpy)]³⁺ cations at the termini of the shorter tppz ligand (Fig. 5). The crystal structure of [Cr₂Cl₆(tppz)]·3C₅H₉NO (11), Fig. S15 and Tables S26–S28†), with its intermetallic distance 6.662(3) Å and interplanar angle of 25.5° between the two chelate N₃ planes, completes a collection of similar rod-like dyads reported for [Ru₂Cl₆(tppz)]⁻ (RuII···RuIII = 6.504 Å, interplanar angle = 26.38°),⁹⁶ [Ru₂(CH₃CN)₆(tppz)] (RuII···RuII = 6.56 Å, interplanar angle = 27.08°)⁹⁷ and for other [M₂X₆(tppz)] binuclear complexes.⁹⁸⁻¹⁰² The crystal structures involving the extended bbt bridging ligands [Cr₂Cl₆(bbt)] (12), Fig. S16 and Tables S26, S29 and S30†) and [Cr₂(tpy)₂(bbt)](PF₆)₆·8CH₃CN·(CH₃CH₂)₂O (13, Fig. S17 and Tables S31–S33†) have surprisingly no precedent for analogous ruthenium complexes despite the intense activity dedicated to these specific supramolecular</figcaption></figure>

Alternatively, stoichiometric reactions between the bridging ligand (1 eq.) and labile [Cr(tpy)(CF₃SO₃)₃] (2 eq.) lead to the targeted dinuclear complexes [Cr₂(tpy)₂(bbt)](PF₆)₆ and [Cr₂(tpy)₂(ebbt)](PF₆)₆, but we were unable to connect two triply charged [Cr(tpy)]³⁺ cations at the termini of the shorter tppz ligand (Fig. 5). The crystal structure of [Cr₂Cl₆(tppz)]·3C₅H₉NO (11, Fig. S15 and Tables S26–S28†), with its intermetallic distance 6.662(3) Å and interplanar angle of 25.5° between the two chelate N₃ planes, completes a collection of similar rod-like dyads reported for [Ru₂Cl₆(tppz)]⁻ (RuII···RuIII = 6.504 Å, interplanar angle = 26.38°),⁹⁶ [Ru₂(CH₃CN)₆(tppz)] (RuII···RuIII = 6.56 Å, interplanar angle = 27.08°)⁹⁷ and for other [M₂X₆(tppz)] binuclear complexes.⁹⁸⁻¹⁰² The crystal structures involving the extended bbt bridging ligands [Cr₂Cl₆(bbt)] (12, Fig. S16 and Tables S26, S29 and S30†) and [Cr₂(tpy)₂(bbt)](PF₆)₆·8CH₃CN·(CH₃CH₂)₂O (13, Fig. S17 and Tables S31–S33†) have surprisingly no precedent for analogous ruthenium complexes despite the intense activity dedicated to these specific supramolecular

architectures.¹⁹⁻²⁴,⁶⁹ The intermetallic separation is fixed to ca. 10.9 Å by the back-to-back bis(terpyridine) spacer (Fig. 5). The dihedral angle within the bridging 4,4'-bipyridine motif amounts to 36.5(4)° in [Cr₂Cl₆(bbt)] and to 83.0(1)° in [Cr₂(tpy)₂(bbt)](PF₆)₆. While the smaller angle matches the theoretically computed interplanar angle of 35–40°, which simultaneously minimizes the torsion energy and optimizes orbital overlap in 4,4'-bipyridine,¹⁰³⁻¹⁰⁵ the almost orthogonal arrangement of the two central pyridine rings found in [Cr₂(tpy)₂(bbt)](PF₆)₆ is unique for this spacer since the largest value reported so far reached 61(1)° for a dinuclear copper(II) complex.¹⁰⁶ Four PF₆⁻ counter-anions are located between the two CrN₆ units of the dinuclear complex. They are involved in twelve Cₐromatic⁻H···F···P hydrogen bonds (2.4 Å to 2.6 Å),¹⁰⁷,¹⁰⁸ which significantly stabilize the orthogonal arrangement of the central back-to-back bis(terpyridine) spacer (Fig. S18†). The crystal structure of [Cr₂(tpy)₂(ebbt)](PF₆)₆·10CH₃CN (14, Fig. S19 and Tables S31, S34 and S35†) obviously displays not only the longest intramolecular Cr···Cr distance (13.4669(6) Å, Fig. 5), but also the smallest dihedral angle between the two quasi-planar terpyridine units connected by the alkyne bridge (0.1(3)°). To the best of our knowledge, no molecular structure has been previously reported with this extended ebbt ligand.¹⁰⁹ We are now in a position to investigate the nature and magnitude of intramolecular intermetallic interactions operating between pseudo-octahedral Cr¹¹¹ metallic cations incorporated into rod-like heteroleptic dyads possessing variable lengths.

### Unravelling intermetallic communication in dinuclear [Cl₃Cr(L)CrCl₃], [(tpy)Cr(L)Cr(tpy)](PF₆)₆ complexes (L = tppz, bbt, ebbt): magnetic evidence

Two trivalent Cr¹¹¹ centres connected by short oxide bridges usually display strong anti-ferromagnetic interaction ($J_{ex} < 0$) operating between the two $S = 3/2$ spin carriers via a super-exchange mechanism.⁶² Application of the van Vleck equation to a coupled Cr¹¹¹ pair obeying the Heisenberg–Dirac–van Vleck spin Hamiltonian $\hat{H}_{HDVV} = -J_{ex}\hat{S}_A\hat{S}_B$ ($\hat{S}_A$ and $\hat{S}_B$ are the spin operators localized on each metallic centre and $J_{ex}$ is the phenomenological magnetic exchange coupling constant) provides a contribution to the paramagnetic susceptibility $\chi_{para}^{dimer}$ expressed in eqn (1), where $g$ is the Landé factor, $N_A = 6.022 \times 10^{23} \text{ mol}^{-1}$ is Avogadro's number, $\mu_B = 9.274 \times 10^{-24} \text{ J T}^{-1}$ is the Bohr magneton and $k_B = 1.3806 \times 10^{-23} \text{ J K}^{-1}$ is the Boltzmann constant.⁶²

$$ \chi_{para}^{\text{dimer}} = \frac{N_A g^2 \mu_B^2}{k_B T} \frac{2e^{J_{ex}/k_B T} + 10e^{3J_{ex}/k_B T} + 28e^{6J_{ex}/k_B T}}{1 + 3e^{J_{ex}/k_B T} + 5e^{3J_{ex}/k_B T} + 7e^{6J_{ex}/k_B T}} \quad (1) $$

Compared with $[J_{ex}]$ values expected in the 1–10 cm⁻¹ range for the [X₃Cr(L)CrX₃] dyads, the weak contribution of the zero-field splitting ($D = 0.03 \text{ cm}^{-1}$ for [Cr(tpy)Cl₃], $D = 0.2 \text{ cm}^{-1}$ for [Cr(tpy)₂]³⁺)¹²,⁶¹,⁸⁰ can be neglected and the magnetic susceptibilities recorded in the 2–300 K range for the five dimeric complexes (Fig. 6 plotted as $\chi T$ vs. $T$) could be satisfyingly fitted to eqn (2), where $\chi_{para}^{dimer}$ is given in eqn (1), $\chi_{dia}^{dimer}$ is the diamagnetic
<figure><img src="image_9.png" /><figcaption>Fig. 6 Dependence of $\chi_{tot}^{dimer} T$ on the applied temperature (2–300 K) for the dinuclear $Cr^{III}$ complexes showing the experimental data (colored crosses) and non-linear least-square fits with eqn (2) (black dotted traces).</figcaption></figure>

netic susceptibility of the dimer calculated by means of Pascal's constant¹¹⁰ and $\chi_{tot}^{dimer}$ is the temperature-independent paramagnetic contribution of the dimer (Table S36†).

$$ \chi_{tot}^{\text{dimer}} = \chi_{\text{para}}^{\text{dimer}} + \chi_{\text{dia}}^{\text{dimer}} + \chi_{\text{TIP}}^{\text{dimer}} \quad (2) $$

For temperatures larger than 150 K, the magnetic susceptibilities of all dinuclear complexes converge to a common constant value of $3.55 \le \chi T \le 3.67 \text{ cm}^3 \text{ mol}^{-1}$, which is close to $\chi T = 3.75 \text{ cm}^3 \text{ mol}^{-1}$ calculated for two independent spin-only $Cr^{III}$ centres ($S = 3/2$). At low temperature, the $\chi T$ versus $T$ curves abruptly decrease, which is diagnostic for weak intramolecular anti-ferromagnetic interactions, the magnitude of which can be estimated by the exchange constants $-5.4 \le J_{ex} \le -0.7 \text{ cm}^{-1}$ collected in Fig. 6 (Table S36†). The $J_{ex}$ values found for pairs of coupled $CrN_3Cl_3$ units in dinuclear $[Cl_3Cr(L)CrCl_3]$ dyads (orange, green and black traces in Fig. 6) show the expected reduction of the efficiency of the anti-ferromagnetic superexchange pathway with the increasing length of the molecular bridge separating the paramagnetic $Cr^{III}$ centres ($J_{ex}^{tppz} < J_{ex}^{bbt} < J_{ex}^{ebbt}$). Switching from $CrCl_3N_3$ to $CrN_6$ coordination spheres in going from $[Cl_3Cr(bbt)CrCl_3]$ ($J_{ex} = -1.36 \text{ cm}^{-1}$, orange trace) to $[(tpy)Cr(bbt)Cr(tpy)]^{6+}$ ($J_{ex} = -2.37 \text{ cm}^{-1}$, red trace) is accompanied by an almost doubling of the magnitude of the anti-ferromagnetic exchange interactions for a fixed intermetallic distance of 10.9 Å (Fig. 5 and Table S36†). This trend is particularly counter-intuitive since the largest anti-ferromagnetic communication is found for $[(tpy)Cr(bbt)Cr(tpy)]^{6+}$, in which the dihedral angle between the connected pyridine rings of the 4,4'-bipyridine bridge is close to 90° thus minimizing $\pi$-orbital overlap.¹¹¹,¹¹² We however note that related trends, previously observed for oxo bridged $Cr^{III}$ binuclear complexes, could be assigned to the relative energies of

the natural magnetic orbitals ($t_{2g}$ for a pseudo-octahedral $Cr^{III}$ complex) with respect to that of the HOMO orbital of the bridging ligand.¹¹³ Applying this reasoning to the replacement of three anionic $\pi$-donor chloride ligands in $[Cl_3Cr(bbt)CrCl_3]$ with three $\pi$-acceptor heterocyclic nitrogen atoms in the capping terpyridine units in $[(tpy)Cr(bbt)Cr(tpy)]^{6+}$ is expected to decrease the energy of the Cr-centred pseudo-$t_{2g}$ magnetic orbitals, thus favoring their mixing with the occupied molecular orbitals of the back-to-back bis(terpyridine) bridge. A thorough theoretical approach dealing with $Fe^{III}$-$Cu^{II}$ complexes recently confirmed the prospective dependence of the exchange interaction constant with the nature of the ligand field.¹¹⁴ Finally, the *a priori* surprising increase of the anti-ferromagnetic interaction accompanying the 24% increase of the intermetallic distance on going from $[(tpy)Cr(bbt)Cr(tpy)]^{6+}$ ($Cr \cdots Cr = 10.9 \text{ Å}$, $J_{ex} = -2.37 \text{ cm}^{-1}$, red trace) to $[(tpy)Cr(ebbt)Cr(tpy)]^{6+}$ ($Cr \cdots Cr = 13.5 \text{ Å}$, $J_{ex} = -2.78 \text{ cm}^{-1}$, violet trace) can be assigned to the beneficial effect of the bridging alkyne unit, which reduces the dihedral angle between the connected pyridine rings from 83.2(3)° in the bbt spacer to 0.1(3)° in the ebbt analogue and thus favors the overlap integral leading to detectable intramolecular anti-ferromagnetic interactions on the nanometric scale.

### Unravelling intermetallic communication in dinuclear $[Cl_3Cr(L)CrCl_3]$, $[(tpy)Cr(L)Cr(tpy)](PF_6)_6$ complexes ($L = tppz, bbt, ebbt$): optical evidence

The experimental energies of the $Cr^{III}$-centred excited states (with respect to that of the $Cr(^4A_2)$ ground state) are deduced from the combination of the absorption (Fig. 7a and b and Appendix 1 in the ESI†) and emission (Fig. 7c and Appendix 2 in the ESI†) spectra recorded for the dinuclear complexes in solution and in the solid state (Table 1 columns 7–9). At first sight, the energy of these levels can be roughly modeled by using the diagonal elements of the Tanabe–Sugano matrices assuming a pseudo-octahedral geometry for the $CrN_3Cl_3$ and $CrN_6$ chromophores found in $[Cl_3Cr(L)CrCl_3]$ ($L = tppz, bbt, ebbt$) and $[(tpy)Cr(L)Cr(tpy)](PF_6)_6$ ($L = bbt, ebbt$).¹¹⁵ However, this level of approximation implies that the $Cr(^2E)$ and $Cr(^2T_1)$ states are degenerate, which is clearly not the case in these dimeric complexes (Fig. 7 and Table 1).

The additional consideration of configuration interaction between the states of the same multiplicity and symmetry, but from different strong field configurations led Jorgensen⁵⁹ to introduce second-order corrections $\alpha B^2/\Delta$ in eqn (3)–(5), which are derived from the off-diagonal elements of the Tanabe–Sugano matrices.

$$ E(^4T_2) = \Delta \quad (3) $$

$$ E(^2T_1) = 9B + 3C - 24(B^2/\Delta) \quad (4) $$

$$ E(^2E) = 9B + 3C - 90(B^2/\Delta) \quad (5) $$

Although Jorgensen⁵⁹ fixed $C/B = 4$ for deriving eqn (3)–(5), there is no obvious reason for this assumption and a systematic and detailed ligand-field analysis of electronic spectra
<figure><img src="image_10.png" /><figcaption>Fig. 7 Absorption spectra recorded for [(tpy)Cr(bbt)Cr(tpy)](PF₆)₆ (a) in acetonitrile solution (2.5 × 10⁻⁵ mol dm⁻³, 295 K) and (b) in the solid state. (c) Corresponding solid state emission spectra collected at variable temperatures (λexc = 400 nm).</figcaption></figure>

recorded for Cr<sup>III</sup> compounds revealed that 3 ≤ C/B ≤ 8.<sup>115</sup> In his seminal textbook,<sup>60</sup> Lever replaced eqn (5) with eqn (6).

$$E(^{2}\mathrm{E}) = 9B + 3C - 50(B^{2}/\Delta) \quad (6)$$

This transforms the modelling of the $E(^{2}\mathrm{T}_{1}) - E(^{2}\mathrm{E})$ energy gap, for which Jorgensen's approach predicts $66B^{2}/\Delta$ (eqn (5)), to only $26B^{2}/\Delta$ (eqn (6)). Compared with the theoretical set of exact energies computed by Ferguson by means of full Eisenstein's matrices with $B = 680 \text{ cm}^{-1}$ and $C = 2720 \text{ cm}^{-1}$ (C/

$B = 4.0$),<sup>116,117</sup> the exact computed $E(^{2}\mathrm{T}_{1}) - E(^{2}\mathrm{E})$ energy gap amounts to $630 \text{ cm}^{-1}$ for $\Delta = 19940 \text{ cm}^{-1}$ in fair to good agreement with the prediction of the second-order correction $26B^{2}/\Delta = 603 \text{ cm}^{-1}$ (eqn (6)), but rather far from $1531 \text{ cm}^{-1}$ obtained with eqn (5). We conclude that only a complete ligand-field treatment is capable of extracting reliable Racah parameters $B$ and $C$ for Cr<sup>III</sup> complexes,<sup>119</sup> but eqn (6) seems superior to eqn (5) when a rough modeling of the energy of the lowest spin-flip <sup>2</sup>E excited state is foreseen. We therefore used eqn (3), (4) and (6) for estimating the ligand-field strength $\Delta$ and the Racah parameters $B$ and $C$ for each dimeric and monomeric complex (Table 1 and Fig. 8, Table S37 and Fig. S20 in the ESI†) together with eqn (7) and (8) for predicting the energy of the missing $Cr(^{2}\mathrm{T}_{2})$ and $Cr(^{4}\mathrm{T}_{1})$ levels.

$$E(^{2}\mathrm{T}_{2}) = 15B + 5C - 176(B^{2}/\Delta) \quad (7)$$

$$E(^{4}\mathrm{T}_{1}) = 1.5\Delta + 7.5B - 0.5\sqrt{225B^{2} + \Delta^{2} - 18B\Delta} \quad (8)$$

In agreement with both the spectrochemical and the nephe-laugetic series,<sup>118</sup> the ligand-field parameters in mononuclear complexes increase on going from $CrN_{3}Cl_{3}$ (16300 ≤ $\Delta$ ≤ 17000 cm<sup>-1</sup>) to $CrN_{6}$ (18750 ≤ $\Delta$ ≤ 19120 cm<sup>-1</sup>), whereas the Racah parameters $B = 682(19) \text{ cm}^{-1}$ are comparable for both types of chromophores. A narrow distribution of these com-plexes around $\Delta/B \approx 25$ results in the d<sup>3</sup> Tanabe–Sugano diagram (Fig. S21†). The latter $\Delta/B$ values are significantly smaller than $\Delta/B = 31.2$ reported for the well-known $[Cr(bpy)_{3}](PF_{6})_{3}$ complex ($\Delta = 23400 \text{ cm}^{-1}$, $B = 730 \text{ cm}^{-1}$ and $C = 2730 \text{ cm}^{-1}$, $C/B = 3.7$)<sup>119</sup> because the pincer effect produced by 5-membered chelate rings operates four times in $[Cr(L)_{2}]^{3+}$ (L = tpy, ebzpy) and only three times in $[Cr(bpy)_{3}]^{3+}$. This deleter-ious effect is not a fatality for tridentate ligands and it can be overcome by the use of six-membered chelate rings as found in $[Cr(ddpd)Cl_{3}]$ (15) (Fig. S22 and S23 and Tables S38–S40 in the ESI†) and in $[Cr(ddpd)_{2}][BF_{4}]_{3}$ complexes (ddpd = $N,N'$-dimethyl-$N,N'$-dipyridin-2-ylpyridine-2,6-diamine).<sup>120</sup> The larger $N_{distal}$–Cr–$N_{distal}$ angle of 172.0(9)° observed in $[Cr(ddpd)_{2}]^{3+}$ (compared with 156.5(5)° in $[Cr(tpy)_{2}]^{3+}$) indeed restores a large ligand field strength in bis-terdentate pseudo-octahedral complexes ($\Delta = 22990 \text{ cm}^{-1}$, Table S37†). Focusing now on the through-bridge effect produced by the connection of a second neutral $CrCl_{3}$ unit which transforms $[Cr(tppz)Cl_{3}]$ into its dinuclear $[Cl_{3}Cr(tppz)CrCl_{3}]$ analogue ($Cr \cdots Cr = 6.66 \AA$), we observe that $\Delta$ decreases by almost $500 \text{ cm}^{-1}$ (Fig. 8). This effect can be taken as an assessment of the mutual polarization (i.e. electronic communication) produced by the two Cr<sup>III</sup> centres connected to the bridging back-to-back bis-terdentate ligand. Taking now $[Cr(tpy)Cl_{3}]$ as the mono-nuclear reference, the same trend is monitored for $[Cl_{3}Cr(bbt)CrCl_{3}]$ ($\Delta$ decreases by $300 \text{ cm}^{-1}$ for $Cr \cdots Cr = 10.93 \AA$) and $[Cl_{3}Cr(ebbt)CrCl_{3}]$ ($\Delta$ decreases by $200 \text{ cm}^{-1}$ for $Cr \cdots Cr \ge 13 \AA$), but with an expected attenuation for longer intermetallic distances. For the charged $[CrN_{6}]^{3+}$ chromophore found in the mononuclear $[Cr(tpy)_{2}]^{3+}$ reference complex ($\Delta = 18750 \text{ cm}^{-1}$, Table 1), the latter effect is drastically amplified leading to a ca. 2000 cm<sup>-1</sup> reduction of the ligand-field parameter $\Delta$ in the

<figure><img src="image_11.png" /></figure>
<table><caption>**Table 1** Ligand-field energy Δ and Racah parameters (B and C) deduced with eqn (3), (4) and (6) by using the experimental energy of the excited Cr(²E), Cr(²T₁) and Cr(⁴T₂) levels observed for the dinuclear [Cl₃Cr(L)CrCl₃] and [(tpy)Cr(L)Cr(tpy)](PF₆)₆ complexes (L = tppz, bbt, ebbt) and for their mononuclear analogues [Cr(L)Cl₃] (L = tppz, tpy) and [Cr(tpy)₂](PF₆)₃</caption><thead><tr><th rowspan="2">Compound</th><th rowspan="2">Δ/cm<sup>-1</sup></th><th rowspan="2">B/cm<sup>-1</sup></th><th rowspan="2">C/cm<sup>-1</sup></th><th rowspan="2">Δ/B</th><th rowspan="2">C/B</th><th colspan="5">E/cm<sup>-1</sup> <sup>a</sup></th></tr><tr><th>²E</th><th>²T<sub>1</sub></th><th>⁴T<sub>2</sub></th><th>²T<sub>2</sub> <sup>b</sup></th><th>⁴T<sub>1</sub> <sup>c</sup></th></tr></thead><tbody><tr><td>[Cr<sub>2</sub>Cl<sub>6</sub>(tppz)]</td><td>16 000</td><td>708</td><td>2564</td><td>23</td><td>3.6</td><td>12 500</td><td>13 316</td><td>16 000</td><td>17 927</td><td>22 893</td></tr><tr><td>[Cr<sub>2</sub>Cl<sub>6</sub>(bbt)]</td><td>16 393</td><td>648</td><td>2785</td><td>25</td><td>4.3</td><td>12 903</td><td>13 569</td><td>16 393</td><td>19 134</td><td>21 980</td></tr><tr><td>[Cr<sub>2</sub>Cl<sub>6</sub>(ebbt)]</td><td>16 502</td><td>604</td><td>2863</td><td>27</td><td>4.7</td><td>12 920</td><td>13 495</td><td>16 502</td><td>19 482</td><td>22 671</td></tr><tr><td>[Cr<sub>2</sub>(tpy)<sub>2</sub>(bbt)](PF<sub>6</sub>)<sub>6</sub></td><td>16 722</td><td>720</td><td>2636</td><td>23</td><td>3.7</td><td>12 837</td><td>13 643</td><td>16 722</td><td>18 524</td><td>23 782</td></tr><tr><td>[Cr<sub>2</sub>(tpy)<sub>2</sub>(ebbt)](PF<sub>6</sub>)<sub>6</sub></td><td>16 474</td><td>668</td><td>2672</td><td>25</td><td>4<sup>d</sup></td><td>12 674</td><td>13 379<sup>d</sup></td><td>16 474</td><td>18 614</td><td>23 132</td></tr><tr><td>[Cr(tppz)Cl<sub>3</sub>]</td><td>16 474</td><td>693</td><td>2770</td><td>24</td><td>4<sup>d</sup></td><td>13 089</td><td>13 846<sup>d</sup></td><td>16 474</td><td>19 117</td><td>23 312</td></tr><tr><td>[Cr(tpy)Cl<sub>3</sub>]</td><td>16 694</td><td>697</td><td>2786</td><td>24</td><td>4<sup>d</sup></td><td>13 175</td><td>13 931<sup>d</sup></td><td>16 694</td><td>19 265</td><td>23 585</td></tr><tr><td>[Cr(tpy)<sub>2</sub>](PF<sub>6</sub>)<sub>3</sub></td><td>18 750</td><td>675</td><td>2698</td><td>28</td><td>4<sup>d</sup></td><td>12 953</td><td>13 584<sup>d</sup></td><td>18 750</td><td>19 340</td><td>25 663</td></tr></tbody></table>

<sup>a</sup> Energies are given with respect to that of the ground Cr(⁴A₂) level. <sup>b</sup> Computed with eqn (7). <sup>c</sup> Computed with eqn (8). <sup>d</sup> The Cr(²T₁ ← ⁴A₂) transition could not be unambiguously assigned and the associated Racah parameters were calculated assuming C = 4B. The energy of the Cr(²T₁) level was computed using eqn (4).

time-resolved emission spectroscopy performed on powder samples of the dinuclear complexes at cryogenic temperatures. The Cr(²E → ⁴A₂) phosphorescence signals showed double exponential decays for all complexes except for the unsolvated centrosymmetrical [Cr₂Cl₆(bbt)] complex, for which the kinetic decay trace is mono-exponential (Table 2 and Fig. A2-9-A2-13 in Appendix 2†).

Since (i) mono-exponential decay traces in the millisecond range are systematically recorded for the Cr(²E) phosphorescence occurring in related mononuclear chromium complexes (0.24 ≤ τCr(²E) ≤ 1.37 ms at 3 K, Table S37 and Table A2 I Appendix 2†) and (ii) the fast components of the multi-exponential Cr(²E → ⁴A₂) decay traces account for less than 20% of total intensities in the dinuclear complexes, we assume that the powder samples of [Cr₃Cr(L)CrCl₃] (L = tppz, ebbt) and [(tpy)Cr(L)Cr(tpy)](PF₆)₆ complexes (L = bbt, ebbt) possess two non-equivalent chromium sites as found in the crystal structures of [Cr₂Cl₆(tppz)]·3C₅H₉NO (11) and [Cr₂(tpy)₂(bbt)](PF₆)₆·8CH₃CN·(CH₃CH₂)₂O (13). The energies of the two Cr(²E) levels, referred to as D = donor and A = acceptor in the dinuclear complexes, are therefore slightly different and compatible with the operation of intramolecular intermetallic energy transfers characterized by their first-order rate constants W<sub>D→A</sub> and W<sub>A→D</sub> (Fig. 9a). This model was previously postulated by Castelli and Forster for rationalizing the multi-

<caption>**Fig. 8** Low-energy part of the energy level diagrams obtained for the dinuclear [Cr₃Cr(L)CrCl₃] and [(tpy)Cr(L)Cr(tpy)](PF₆)₆ complexes (L = tppz, bbt, ebbt, bold font) and for their mononuclear analogues [Cr(L)Cl₃] (L = tppz, tpy) and [Cr(tpy)₂](PF₆)₃ (normal font). The ligand-field Δ parameter is highlighted. Full traces are used for experimentally observed excited levels, whereas dotted traces correspond to calculated levels.</caption>

related charged dinuclear complexes [(tpy)Cr(L)Cr(tpy)]<sup>6+</sup> (L = bbt, ebbt, Fig. 8 and Table 1). The considerable reduction of Δ recorded for the longest ebbt bridging ligand in [(tpy)Cr(ebbt) Cr(tpy)]<sup>6+</sup> combined with the operation of the largest nephe lauxetic dispersion (i.e. the minimum B Racah parameter, Table 1) confirms that an alternation of alkyne/aromatic groups is particularly adapted for the design of electronic wires between Cr<sup>III</sup> centres, a result in line with the exceptional delocalization of the electronic density from the metal centres reported for analogous rod-like Ru(II)/Os(II) dyads.<sup>121-123</sup> Intermetallic communication can be alternatively probed by

<table><caption>**Table 2** Experimental lifetimes found for the dinuclear [Cl₃Cr(L)CrCl₃] and [(tpy)Cr(L)Cr(tpy)](PF₆)₆ complexes (L = tppz, bbt, ebbt) and intermetallic energy transfer rate constants W<sub>D→A</sub> estimated with eqn (9)</caption><thead><tr><th>Complex</th><th>T/K</th><th>τ<sub>1</sub>/μs</th><th>τ<sub>2</sub>/μs</th><th>W<sub>D→A</sub>/s<sup>-1</sup></th><th>Cr···Cr<sup>d</sup>/Å</th></tr></thead><tbody><tr><td>[Cr<sub>2</sub>Cl<sub>6</sub>(tppz)]</td><td>5</td><td>3.6(1)</td><td>0.9(1)</td><td>8(2) × 10<sup>5</sup></td><td>6.660(2)</td></tr><tr><td>[Cr<sub>2</sub>Cl<sub>6</sub>(bbt)]</td><td>5</td><td>21(1)<sup>b</sup></td><td>—</td><td>—</td><td>10.9261(8)</td></tr><tr><td>[Cr<sub>2</sub>Cl<sub>6</sub>(ebbt)]</td><td>3.5</td><td>3.6(1)</td><td>0.4(1)</td><td>2.2(4) × 10<sup>6</sup></td><td>—</td></tr><tr><td>[Cr<sub>2</sub>(tpy)<sub>2</sub>(bbt)](CF<sub>3</sub>SO<sub>3</sub>)<sub>6</sub></td><td>5</td><td>40.3(1)</td><td>2.3(1)</td><td>4.1(8) × 10<sup>5</sup></td><td>10.8957(5)</td></tr><tr><td>[Cr<sub>2</sub>(tpy)<sub>2</sub>(ebbt)](PF<sub>6</sub>)<sub>6</sub></td><td>3.5</td><td>0.24(1)</td><td>0.04(1)</td><td>2.1(4) × 10<sup>7</sup></td><td>13.4669(6)</td></tr></tbody></table>

<sup>a</sup> Intermetallic distance measured in the crystal structures. <sup>b</sup> Mono-exponential decay.

<figure><img src="image_12.png" /></figure>
<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 9** (a) Energy level diagram and (b) kinetic matrix equations for the relaxation of the Cr(²E) excited levels occurring in a dinuclear chromium complex with non-equivalent metallic sites (Cr<sub>D</sub>·Cr<sub>A</sub>). k<sub>A</sub> and k<sub>D</sub> are the first-order de-excitation rate constants (sum of radiative and non-radiative processes), whereas W<sub>D→A</sub> and W<sub>A→D</sub> are the intramolecular energy transfer rate constants.</figcaption></figure>

exponential decay observed in solid samples of [Cr(urea)<sub>6</sub>]<sup>3+</sup> chromophores.<sup>124</sup> It is further supported by the time-resolved luminescence spectra recorded for [(tpy)Cr(bbt)Cr(tpy)]X<sub>6</sub> (X = PF<sub>6</sub> in Fig. 7c and X = CF<sub>3</sub>SO<sub>3</sub> in Fig. A2-13 in Appendix 2†), which show a faster decay of the high energy part of the emission band (corresponding to the lifetime of Cr<sub>D</sub>(²E)) followed by a longer decay for the low energy part (corresponding to the lifetime of Cr<sub>A</sub>(²E)).

Although the time evolution of the population densities of the three states ($N^{1/2}$, i = 0, 1, 2) can be obtained by numerically solving the matrix kinetic equation shown in Fig. 9b with the help of projection operators and Lagrange–Sylvester formula,<sup>125</sup> reasonable approximations assume that (i) the back energy transfer is negligible ($W_{A→D} \approx 0$) for time-resolved measurements performed below 5 K, (ii) the long-lived component $\tau_1$ of the bi-exponential decay kinetic trace (Table 2, column 3) reflects the sum of radiative and non-radiative relaxation rate constants of the acceptor ($k_A \approx (\tau_1)^{-1}$ in Fig. 9) and (iii) $\tau_1$ can also be taken as an acceptable estimation for the relaxation rate constant of the donor in the absence of acceptor ($k_D \approx k_A \approx (\tau_1)^{-1}$ in Fig. 9). With this in mind, the short-lived component $\tau_2$ observed in the dinuclear complexes (Table 2, column 4) stands for the sum of the relaxation pathways affecting Cr<sub>D</sub>(²E) (eqn (9) left), from which the intramolecular intermetallic energy transfer rate constants $W_{D→A}$ can be easily deduced (eqn (9) and Table 2 column 5).

$$ \frac{1}{\tau_2} = k_D + W_{D \to A} \Rightarrow W_{D \to A} = \frac{1}{\tau_2} - \frac{1}{\tau_1} \quad (9) $$

The first striking results concern the rather short characteristic lifetimes $0.2 \le \tau_1 \le 40$ µs measured for the Cr(²E)

levels in the dinuclear complexes in the absence of energy transfer ($\tau_1 = (k_A)^{-1} \approx (k_D)^{-1}$, Table 2, column 3). The reduction by one to two orders of magnitude compared with related data recorded for the mononuclear analogues under the same experimental conditions (solid state, cryogenic temperatures, Table S37†) are reminiscent of the well-documented<sup>4,127</sup> effect of the reduction in ligand-field strength on the relaxation pathways affecting the Cr(²E) level. For a given chromophore (CrN<sub>3</sub>Cl<sub>3</sub> in [Cl<sub>3</sub>Cr(L)CrCl<sub>3</sub>] or CrN<sub>6</sub> in [(tpy)Cr(L)Cr(tpy)][PF<sub>6</sub>)<sub>6</sub>], we additionally detect a surprising counterintuitive increase of the intermetallic energy transfer rate constant for larger intramolecular Cr···Cr distances (Table 2). According to the Fermi's golden rule summarized in eqn (10), the rate of resonant intermetallic energy transfer depends on (i) the spectral overlap integral $\Omega_{DA}$ between the absorption spectrum of the acceptor A, and the emission spectrum of the donor D and (ii) the perturbation operator $H_P$ usually modelling the magnitude of through-space (multipolar electrostatic) and/or through-bond (double electronic exchange) communication.<sup>7,5,126</sup>

$$ W_{D \to A} \propto (2\pi/\hbar) |\langle DA^* | H_P | D^*A \rangle|^2 \Omega_{DA} \quad (10) $$

Since the energies of the narrow and weakly Stokes-shifted spin–flip Cr(²E $\leftrightarrow$ ⁴A<sub>2</sub>) transitions do not significantly depend on the ligand-field strength, the 810–1080 cm<sup>-1</sup> spectral widths measured for the Cr(²E $\rightarrow$ ⁴A<sub>2</sub>) phosphorescence band in the dinuclear complexes (Fig. A2-4 to A2-8 in Appendix 2†) are compatible with non-negligible and comparable spectral overlap integrals $\Omega_{DA}$ along the complete series. We therefore assign the unusually large energy transfer rate constants operating in the longest rod-like dyads [Cl<sub>3</sub>Cr(ebbt)CrCl<sub>3</sub>] ($W_{D→A} = 2.2(4) \times 10^6$ s<sup>-1</sup>) and [(tpy)Cr(ebbt)Cr(tpy)]<sup>6+</sup> ($W_{D→A} = 2.1(4) \times 10^7$ s<sup>-1</sup>) to the exceptional through-bond conducting character of alkyne-containing bridges doped with aromatic rings,<sup>121,122</sup> a trend in line with magnetic data (see the previous section). For unsolvated crystals of [Cr<sub>2</sub>Cl<sub>6</sub>(bbt)] (12), the center of symmetry found in the crystal structure is maintained in the powder sample and a mono-exponential decay is observed (Table 2, entry 2), in agreement with the kinetic model for which $k_A = k_D$ and $W_{D→A} = W_{A→D}$<sup>128</sup>.

### Unravelling intermetallic communication in dinuclear [Cl<sub>3</sub>Cr(L)CrCl<sub>3</sub>], [(tpy)Cr(L)Cr(tpy)][PF<sub>6</sub>)<sub>6</sub> complexes (L = tppz, bbt, ebbt): thermodynamic evidence

The failure to isolate the dinuclear [(tpy)Cr(tppz)Cr(tpy)][PF<sub>6</sub>)<sub>6</sub> complex from the reaction of [(tpy)Cr(CF<sub>3</sub>SO<sub>3</sub>)<sub>3</sub>] with tppz (Fig. 5) suggests the operation of a strong anti-cooperative protocol for the successive binding of two [Cr(tpy)]<sup>3+</sup> to the bridging tppz ligand. The spectrophotometric titrations of [(tpy)Cr(tppz)]<sup>3+</sup> with Er<sup>3+</sup> in acetonitrile (Er<sup>3+</sup> stands for a labile and non-hydrolyzable substitute of [Cr(tpy)]<sup>3+</sup>) confirms the lack of affinity of the available tridentate site of tppz in [(tpy)Cr(tppz)]<sup>3+</sup> for a second trivalent cation ($\beta_{11}^{Cr(tppz).Er} \ll 50$ in equilibrium (11), Fig. 10).<sup>129</sup> A quantitative assessment of the
<figure><img src="image_15.png" /><figcaption>Fig. 10 (a) Variation of absorption spectra, (b) corresponding variation of molar extinctions and (c) proposed modeling ($β_{1,1}^{Cr(tppz),Er} \ll 50$) for the titration of $[(tpy)Cr(tppz)]^{5+}$ ($2 \times 10^{-4}$ M) with Er(CF₃SO₃)₃ in acetonitrile (298 K).</figcaption></figure>

searched cooperative factors can be approached by the spectro-photometric titrations of the bridging ligand tppz (or bbt) with Er(CF₃SO₃)₃ in acetonitrile: chloroform = 65:35 (Fig. 11). The resulting changes in the absorption spectra are characterized by smooth end points occurring at Eu: L = 1:3, Eu: L = 1:2, Eu: L = 1:3 and Eu: L = 1:1 (Fig. 11a and b for L = tppz and Fig. S24a for L = bbt in the ESI†). Factor analysis (Fig. 11c and Fig. S24c†)¹³⁰ followed by non-linear least square fits¹³¹ to equilibria (12)–(15) (Fig. 11e) provide satisfying re-constructed individual absorption spectra (Fig. 11d and Fig. S24d†) together with macroscopic formation constants gathered in Table 3 (entries 1–4).

Monitoring these titrations using light-scattering techniques did not reveal any sign of aggregation due to the formation of two-dimensional and three-dimensional polymers as postulated by Long and coworkers for related reactions involving a back-to-back bis-terdentate ligand and Eu(NO₃)₃.¹³² Application of the site binding model (eqn (16))¹³³ to equilibria (12)–(15) leads to eqn (17)–(20), which model the complete complexation process with only four parameters. (1) $ω_{m,n}^{Er,L}$ stands for pure entropic contribution to the complexation reaction brought by the change in the rotational entropy when the reactants are transformed into products (Appendix 3 in the ESI†).¹³⁴ (2) $f_{N_3,L}^{Er}$ represents the intrinsic affinity of Er³⁺ for the tridentate binding unit of the bridging ligand (including desolvation processes). (3) $u_{Er}^{L,L} = \exp(-\Delta E_{Er}^{L,L}/RT)$, respectively (4) $u_{L}^{Er,Er} = \exp(-\Delta E_{L}^{Er,Er}/RT)$ are the cooperative effects, in terms of Boltzmann factors, which accompany the successive binding of ligands to the same metallic centre ($u_{Er}^{L,L}$), respectively, the successive binding of metals to the same bridging ligand ($u_{L}^{Er,Er}$). Multi-linear least-square fits of eqn (17)–(20) to the experimental stability constants

provided the thermodynamic descriptors collected in Table 3 (entries 5–7).

$$β_{m,n}^{Er,L} = ω_{m,n}^{Ln,L} \cdot \prod f_{N_3,L}^{Er} \cdot \prod u_{Er}^{L,L} \cdot \prod u_{L}^{Er,Er} \quad (16)$$

$$β_{1,1}^{Er,L} = ω_{1,1}^{Er,L} f_{N_3,L}^{Er} = 12 f_{N_3,L}^{Er} \quad (17)$$

$$β_{1,2}^{Er,L} = ω_{1,2}^{Er,L} (f_{N_3,L}^{Er})^2 u_{Er}^{L,L} = 48 (f_{N_3,L}^{Er})^2 u_{Er}^{L,L} \quad (18)$$

$$β_{1,3}^{Er,L} = ω_{1,3}^{Er,L} (f_{N_3,L}^{Er})^3 (u_{Er}^{L,L})^3 = 128 (f_{N_3,L}^{Er})^3 (u_{Er}^{L,L})^3 \quad (19)$$

$$β_{2,1}^{Er,L} = ω_{2,1}^{Er,L} (f_{N_3,L}^{Er})^2 u_{L}^{Er,Er} = 72 (f_{N_3,L}^{Er})^2 u_{L}^{Er,Er} \quad (20)$$

The intrinsic affinity of the tridentate N₃ binding units for the entering trivalent Er³⁺ cation in the bridging bbt ligand $\Delta G_{N_3,bbt}^{Er} = -2.303 \cdot RT \log(f_{N_3,bbt}^{Er}) = -40(2) \text{ kJ mol}^{-1}$ perfectly matches the one previously reported for the monomeric precursor terpyridine (tpy) ligand under similar conditions (acetonitrile, 298 K).¹³⁵ This implies that, beyond an obvious statistical factor of 2, the connection of a second tridentate binding unit in the back of the original terpyridine units to give bbt has little effect on the binding properties of the tridentate N₃ site taken separately. As expected, the successive binding of several tridentate N₃ units to the same trivalent Er³⁺ centre is accompanied by some minor anti-cooperative processes ($\Delta E_{Er}^{L,L} = 9(2) \text{ kJ mol}^{-1}$ for bbt and $6(2) \text{ kJ mol}^{-1}$ for tpy) resulting from the stepwise neutralization of the positive metallic charge by an increasing number of bound nitrogen donors.¹³⁵ With this in mind, it appears logical that the much less basic bridging pyrazine ring found in tppz ($pK_a = 0.37$),¹³⁶ compared with the 4,4'-bipyridine bridge in bbt ($pK_a = 4.8$),¹³⁷ leads to both a reduced affinity for Er³⁺ ($\Delta G_{N_3,tppz}^{Er} = -32(2) \text{ kJ mol}^{-1}$) and a smaller ligand–ligand interaction ($\Delta E_{Er}^{tppz,tppz} = 5(3)$
<figure><img src="image_16.png" /><figcaption>Fig. 11 (a) Variation of absorption spectra and (b) corresponding variation of observed molar extinctions at different wavelengths observed for the spectrophotometric titration of tppz with Er(CF₃SO₃)₃ (total ligand concentration: 8 × 10⁻⁵ mol dm⁻³ in CH₃CN: CHCl₃ = 65: 35, 298 K). (c) Evolving factor analysis using five absorbing eigenvectors,¹³⁰ (d) re-constructed individual electronic absorption spectra¹³¹ and (e) proposed thermodynamic model.</figcaption></figure>

kJ mol⁻¹). However, the most noteworthy thermodynamic result concerns the considerable anti-cooperative mechanism accompanying the successive fixation of two Er³⁺ cations onto the bridging ligand, which are diagnostic for the operation of intermetallic electrostatic communication on the nanometric scale in these polyaromatic dyads. The large value ΔE<sub>tppz</sub><sup>Er.Er</sup> =

18(5) kJ mol⁻¹ found for the short-bridging tppz ligand combined with its limited intrinsic affinity ΔG<sub>N<sub>3</sub>.tppz</sub><sup>Er</sup> explains the difficulties in isolating dinuclear [X<sub>3</sub>Cr(tppz)CrX<sub>3</sub>] complexes. The smaller anti-cooperative effect observed for bbt (ΔE<sub>bbt</sub><sup>Er.Er</sup> = 12(5) kJ mol⁻¹) restores sufficient affinity for the formation of dinuclear [X<sub>3</sub>Cr(bbt)CrX<sub>3</sub>] complexes.
<table><caption>**Table 3** Experimental stability constants (log($\beta_{m,n}^{Er,L}$)) and microscopic thermodynamic parameters fitted with eqn (17)–(20) for the reaction of tppz or bbt with Er(CF₃SO₃)₃ in acetonitrile/chloroform (65 : 35) at 298 K</caption><thead><tr><th>Ligand</th><th>tppz</th><th>bbt</th></tr></thead><tbody><tr><td>log($\beta_{1,1}^{Er,L}$)</td><td>6.42(2)</td><td>8.19(16)</td></tr><tr><td>log($\beta_{1,2}^{Er,L}$)</td><td>12.03(3)</td><td>13.76(32)</td></tr><tr><td>log($\beta_{1,3}^{Er,L}$)</td><td>15.89(4)</td><td>18.16(50)</td></tr><tr><td>log($\beta_{2,1}^{Er,L}$)</td><td>9.80(3)</td><td>13.63(16)</td></tr><tr><td>log($f_{N_{i,L}}^{Er}$)/$\Delta G_{N_{i,L}}^{Er}$ in kJ mol<sup>-1</sup> <sup>a</sup></td><td>5.5(4)/-32(2)</td><td>6.9(4)/-40(2)</td></tr><tr><td>log<sup>L</sup><sub>Er</sub>/(L)/$\Delta E_{Er}^{L,L}$ in kJ mol<sup>-1</sup> <sup>b</sup></td><td>-0.9(5)/5(3)</td><td>-1.6(5)/9(2)</td></tr><tr><td>log($u_{L}^{Er,Er}$)/$\Delta E_{L}^{Er,Er}$ in kJ mol<sup>-1</sup> <sup>c</sup></td><td>-3.1(9)/18(5)</td><td>-2.1(9)/12(5)</td></tr><tr><td>AF<sup>d</sup></td><td>1.23 &times; 10<sup>-2</sup></td><td>9.46 &times; 10<sup>-3</sup></td></tr></tbody></table><p><sup>a</sup> $\Delta G_{N_{i,L}}^{Er} = -2.303RT \log(f_{N_{i,L}}^{Er})$. <sup>b</sup> $\Delta E_{Er}^{L,L} = -2.303RT \log(u_{Er}^{L,L})$. <sup>c</sup> $\Delta E_{L}^{Er,Er} = -2.303RT \log(u_{L}^{Er,Er})$. <sup>d</sup> Agreement factor</p><p>AF = $\sqrt{\frac{\sum_{m,n}(\log(\beta_{m,n}^{Er,L}) - \log(\beta_{m,n,calcd}))^2}{\sum_{m,n}(\log(\beta_{m,n}^{Er,L}) - \log(\beta_{m,n,exp}))^2}}$.</p>

## Conclusion

The synthetic method developed by Housecroft and Constable⁴⁶ for the preparation of a semi-labile [(tpy)Cr(O₃SCF₃)₃] precursor can be successfully applied for [(tppz)Cr(O₃SCF₃)₃], but failed for the slightly more basic bis-benzimidazole derivative ebzpy, which is decomplexed from CrIII in trifluoromethanesulfonic acid. A subsequent reaction of [(L)Cr(O₃SCF₃)₃] (L = tpy, tppz) with a second tridentate binding unit L' leads to the targeted heteroleptic mononuclear [(L)Cr(L')]³⁺ complexes, a procedure which can be extended for the preparation of unprecedented dinuclear rod-like [(tpy)Cr(L')Cr(tpy)]⁶⁺ dyads when [(tpy)Cr(O₃SCF₃)₃] is reacted with the Janus-type bis-terdentate receptors L' = bbt or ebbt. In other words, [(tpy)Cr(O₃SCF₃)₃] can be considered as an analogue of [(tpy)Ru(DMSO)Cl₂]¹³⁸ for the introduction of [(tpy)M]²⁺ fragments into (supra)molecular architectures, thus opening large avenues for the selective introduction of trivalent [CrN₆]³⁺ chromophores in linear dyads and triads, and in di- and tridimensional networks similar to those designed with RuII.¹⁹⁻²⁴ While the assessment of the degree of communication between RuII centres requires partial reduction to get mixed-valence systems, the paramagnetic and spin-only character of CrIII centres offers a straightforward access to this parameter with the simple determination of the isotropic magnetic coupling constants. For the [Cl₃Cr(L)CrCl₃] and [(tpy)Cr(L)Cr(tpy)]⁶⁺ dyads investigated here as proof-of-concept, the distance dependence of the magnetic communication reveals subtle modulations due to ligand-field effects and orbital overlap, which are optimized when two CrN₆ chromophores are connected through an alkyne bridge in [(tpy)Cr(ebbt)Cr(tpy)]⁶⁺. Again, compared with RuII (strong-field low-spin d⁶ electronic configuration), the photophysical properties of CrIII (d³ electronic configuration) are better suited for unravelling intermetallic communication via the straightforward determination of ligand-field and Racah parameters, which are difficult to address in analogous ruthenium

complexes. Moreover, minor non-equivalence of the CrIII coordination sites is accompanied by efficient intramolecular intermetallic energy transfer processes, the rate constants of which can be exploited for estimating the efficiency of intermetallic interactions. Finally, our fear that the successive connection of two triply-charged CrIII-type cations (instead of two divalent RuII-type cations) to a Janus-type bridging ligand may be hindered by a strong (electrostatic) anti-cooperative contribution seems only justified for the smallest pyrazine bridge in tppz. For the longer distance found in bbt, the anti-cooperative factor estimated with Er³⁺ taken as a trivalent model cation is reduced to such an extent that successive metallic complexation processes become accessible as demonstrated by the isolation of [Cr₂(tpy)₂(bbt)](PF₆)₆ and [Cr₂(tpy)₂(ebbt)](PF₆)₆ in fair to good yields.

## Experimental section

### Solvents and starting materials

2,2':6',2''-Terpyridine (tpy) and the Janus-type bridging ligand tetra-2-pyridinylpyrazine (tppz) are commercially available. 2,6-Bis(1-ethyl-1H-benzo[d]imidazol-2-yl) pyridine (ebzpy),⁹⁰ N,N'-dimethyl-N,N''-dipyridin-2-ylpyridine-2,6-diamine (ddpd)¹²⁰ and 6',6''-di(pyridin-2-yl)-2,2':4',4":2",2'''-quaterpyridine (bbt)¹³⁹ were synthesized according to the published procedures. The synthesis of 4',4''''-(ethynyl)bis(2,2':6',2''-terpyridine) (ebbt) was adapted from the literature (Appendix 4†).¹⁰⁹ Reagent grade acetonitrile (ACN) and chloroform were distilled from CaH₂ when needed. All other chemicals were purchased from commercial suppliers and used without further purification. Silica-gel plates (Merck, 60 F₂₅₄) were used for thin-layer chromatography. Preparative column chromatography was performed using either neutral alumina gel from Fluka (Typ 507 C) 100–125 mesh or SiliaFlash® silica gel P60 (0.04–0.063 mm).

### Synthesis of gallium and chromium complexes

All complexes were characterized by IR spectroscopy (Tables S41–S44†) and gave satisfying elemental analyses (Table S1†).

[Ga(tpy)₂](PF₆)₃. A solution of Ga(CF₃SO₃)₃ (60.5 mg, 0.117 mmol, 1 eq.) in degassed acetonitrile was added into a solution of terpyridine (54.8 mg, 0.235 mmol, 2.01 eq.) in distilled acetonitrile (20 mL). The color of the mixture immediately turned yellow. After being stirred at 50 °C overnight, acetonitrile was evaporated and the resulting solid was re-solubilized in methanol (5–8 mL). A solution of saturated (n-Bu)₄NPF₆ (2.5 mL, C = 90–100 mg mL⁻¹) was added and the resulting pale yellow precipitate was filtered, washed with dichloromethane (2 × 5 mL) and diethyl ether (2 × 5 mL) and dried under vacuum to obtain [Ga(tpy)₂](PF₆)₃ as a yellow powder (98 mg, 0.101 mmol, yield 86%). Slow diffusion of diethyl ether into a solution of the complex in acetonitrile gave pale yellow single crystals of [Ga(tpy)₂](PF₆)₃·2CH₃CN (1) suitable for X-ray diffraction studies. ¹H NMR of [Ga(tpy)₂](PF₆)₃ (CD₃CN, 400 MHz, δ/ppm): 9.10 (6H, m), 8.80 (4H, d, ³J = 8 Hz), 8.43 (4H, td, ³J = 8 Hz, ⁴J = 0.8 Hz), 7.74 (4H, d, ³J = 8 Hz),

<figure><img src="image_17.png" /></figure>
7.63 (4H, t, $^3J$ = 8 Hz). ESI-MS (CH$_3$CN) m/z: 825.8
([Ga(tpy)$_2$(PF$_6$)$_2$] $^t$), 339.8 ([Ga(tpy)$_2$(PF$_6$)] $^{2+}$) and 178.7 ([Ga(tpy)$_2$] $^{3+}$).

[Cr(tpy)$_2$](PF$_6$)$_3$. In a glovebox, a solution of Cr(CF$_3$SO$_3$)$_2$·H$_2$O (166 mg, 0.450 mmol, 1 eq.)$^{48}$ in degassed acetonitrile was added into a solution of terpyridine (209 mg, 0.895 mmol, 1.99 eq.) in degassed acetonitrile (20 mL). The color of the mixture immediately turned deep dark green. After being stirred at 45 °C for 4 hours, a solution of (n-Bu)$_4$NCF$_3$SO$_3$ (177 mg, 0.450 mmol, 1 eq.) in degassed acetonitrile (2 mL) was added. The Schlenk tube was transferred into the lab and Cr(II) was oxidized by bubbling dioxygen. The colour changed to red-orange. After being stirred for 1 hour at RT, acetonitrile was evaporated and the resulting solid was solubilized in hot methanol (20 mL). A solution of saturated (n-Bu)$_4$NPF$_6$ in methanol (4 mL, C = 100 mg ml$^{-1}$) was added into the solution in order to precipitate a red-orange complex, which was filtered, washed with dichloromethane (3 × 15 mL) and diethyl ether (3 × 10 mL) and dried under vacuum to obtain a red-orange powder [Cr(tpy)$_2$](PF$_6$)$_3$ (326 mg, 0.342 mmol, yield 76%). Slow diffusion of diethyl ether into a solution of the complex in acetonitrile gave red-orange single crystals of [Cr(tpy)$_2$](PF$_6$)$_3$·2.5CH$_3$CN (2) suitable for X-ray diffraction studies.

[Cr(ebzpy)$_2$](PF$_6$)$_3$. In a glovebox, a sky blue solution of Cr(CF$_3$SO$_3$)$_2$·H$_2$O (155 mg, 0.420 mmol, 1 eq.)$^{48}$ in degassed acetonitrile was introduced into a 50 mL Schlenk tube containing a solution of 2,6-bis(1-ethyl-1H-benzo[d]imidazol-2-yl)pyridine (ebzpy, 307 mg, 0.835 mmol, 1.99 eq.) in degassed acetonitrile (20 mL). The blue color of the Cr(II) solution turned immediately dark green. After being stirred at 45 °C for 4 hours, a solution of (n-Bu)$_4$NCF$_3$SO$_3$ (165 mg, 0.420 mmol, 1 eq.) in degassed acetonitrile (2 mL) was added. The Schlenk tube was transferred into the lab and the Cr(II) was oxidized by bubbling dioxygen. The colour of the solution changed to red-orange to give [Cr(ebzpy)$_2$](CF$_3$SO$_3$)$_3$. The red-orange acetonitrile solution of [Cr(ebzpy)$_2$](CF$_3$SO$_3$)$_3$ was evaporated and the resulting solid was solubilized in hot methanol (20 mL). Anion metathesis was performed by adding 4 mL of a saturated solution of (n-Bu)$_4$NPF$_6$ in methanol (100 mg mL$^{-1}$). The red-orange precipitate was filtered, washed with dichloromethane (3 × 15 mL) and diethyl ether (3 × 10 mL) and dried under vacuum to give [Cr(ebzpy)$_2$](PF$_6$)$_3$ as a red-orange powder (385 mg, 0.315 mmol, yield 75%). Slow diffusion of diethyl ether into a solution of the complex in acetonitrile gave red-orange single crystals of [Cr(ebzpy)$_2$](PF$_6$)$_3$·5.5CH$_3$CN (3) suitable for X-ray diffraction studies. Slow diffusion of diethyl ether into a solution of the intermediate [Cr(ebzpy)$_2$](CF$_3$SO$_3$)$_3$ complex in acetonitrile gave red-orange single crystals of [Cr(ebzpy)$_2$](CF$_3$SO$_3$)$_3$·2CH$_3$CN (4) suitable for X-ray diffraction studies as well.

[Cr(ebzpy)Cl$_3$]. A solution of 2,6-bis(1-ethyl-1H-benzo[d]imidazol-2-yl)pyridine (182 mg, 0.495 mmol, 1.01 eq.) in dry dichloromethane (5 mL) was dropwise added into a solution of [CrCl$_3$(THF)$_3$] (184 mg, 0.490 mmol, 1 eq.) in dry dichloromethane (30 mL). The color of the mixture changed from purple to green. After being stirred at room temperature for 24 hours, the mixture was filtered and the solid was washed

with dichloromethane (3 × 15 mL) and diethyl ether (3 × 10 mL), and dried under vacuum to give [Cr(ebzpy)]Cl$_3$ (253 mg, 0.47 mmol, yield 98%). Slow diffusion of diethyl ether into a solution of a complex in DMF gave dark green single crystals of [Cr(ebzpy)Cl$_3$]·DMF (5) suitable for X-ray diffraction studies. The complex was characterized by elemental analysis (Table S1†).

[Cr(tppz)Cl$_3$]. Tetra-2-pyridinylpyrazine (tppz) (170 mg, 0.438 mmol, 2 eq.) was suspended in a distilled mixture of acetonitrile and ethanol (25 mL: 25 mL) and heated under reflux. A solution of [CrCl$_3$(THF)$_3$] in acetonitrile (82 mg, 0.219 mmol, 1 eq.) was added dropwise to the tppz solution mixture, the colour of which immediately turned from purple to green. After being stirred and refluxed for 24 hours under an inert N$_2$ atmosphere, the insoluble product was filtered (micro-filtering), then washed with a hot solution of acetonitrile and ethanol (1:1) for removing the excess ligand. The resulting solid was washed with diethyl ether (3 × 7 mL) and dried under vacuum to give Cr(tppz)Cl$_3$ (114 mg, 0.208 mmol, yield 95%). Slow diffusion of diethyl ether into a solution of the complex in DMF gave dark green single crystals of [Cr(tppz)Cl$_3$]·2DMF (6) suitable for X-ray diffraction studies.

[Cr(tppz)(SO$_3$CF$_3$)$_3$. Cr(tppz)Cl$_3$ (140 mg, 0.256 mmol, 1 eq.) and triflic acid (300 µL, 3.4 mmol, 13 eq.) were loaded into a 50 mL Schlenk tube under a N$_2$ atmosphere. The green colour of the complex turned to dark red immediately together with gas escape of HCl (confirmed by precipitation of AgCl when bubbling into an aqueous solution of AgNO$_3$). After being stirred at room temperature for 3 hours, the dark red complex of Cr(tppz)(CF$_3$SO$_3$)$_3$ was precipitated by the addition of 25 mL of diethyl ether. The complex was filtered, washed with diethyl ether (3 × 6 mL) and dried under vacuum to give Cr(tppz)(CF$_3$SO$_3$)$_3$ (204 mg, 0.230 mmol, yield 90%).

[Cr(ebzpy)(tpy)](PF$_6$)$_3$. A dark red solution of [Cr(tpy)(CF$_3$SO$_3$)$_3$] (168 mg, 0.230 mmol, 1 eq.) in distilled acetonitrile was loaded into a 50 mL Schlenk tube under an inert N$_2$ atmosphere. A solution of 2,6-bis(1-ethyl-1H-benzo[d]imidazol-2-yl) pyridine (85 mg, 0.230 mmol, 1 eq.) in acetonitrile (8–10 mL) was added to the Schlenk tube. The mixture was refluxed under N$_2$ for 3 hours, then the solution was evaporated to dryness and the residual solid solubilized in distilled acetonitrile (3 mL). Slow diffusion of diethyl ether into the concentrated solution of the complex in acetonitrile gave [Cr(tpy)(ebzpy)](CF$_3$SO$_3$)$_3$ as red crystals (126 mg, 0.115 mmol, yield 50%). [Cr(tpy)(ebzpy)](CF$_3$SO$_3$)$_3$ was solubilized in MeOH, then anion metathesis was initiated by adding 4 mL of a saturated solution of tetrabutylammonium hexafluorophosphate [(n-Bu)$_4$NPF$_6$] in methanol (100 mg mL$^{-1}$). The resulting red-orange precipitate was filtered, washed with diethyl ether and dried under vacuum to give [Cr(tpy)(ebzpy)](PF$_6$)$_3$. Slow diffusion of diethyl ether in a concentrated solution of the complex in acetonitrile (3 ml) produced red single crystals of [Cr(tpy)(ebzpy)](PF$_6$)$_3$·2CH$_3$CN (7) suitable for X-ray diffraction studies.

[Cr(tppz)(tpy)](PF$_6$)$_3$. A solution of Cr(tppz)(CF$_3$SO$_3$)$_3$ (177.5 mg, 0.2 mmol, 1 eq.) in distilled acetonitrile was drop
wise added into a concentrated solution of terpyridine in acetonitrile (58 mg, 0.25 mmol in 8 mL). The solution became warm during the addition and was then refluxed for 3 hours. The resulting mixture was cooled, filtered and the remaining dark-red solution was evaporated to dryness. Slow diffusion of diethyl ether into a concentrated solution of the complex in acetonitrile (3 ml) produced yellow single crystals of [Cr(tppz)(tpy)][CF₃SO₃]₃ suitable for X-ray diffraction studies in approximately 40–50% yields. [Cr(tppz)(tpy)][CF₃SO₃]₃ was solubilized in MeOH, then anion metathesis was initiated by adding 4 mL of a saturated solution of tetrabutylammonium hexafluorophosphate [(n-Bu)₄NPF₆] in methanol (100 mg mL⁻¹). The resulting red-orange precipitate was filtered, washed with diethyl ether and dried under vacuum to give [Cr(tppz)(tpy)][PF₆]₃ (104 mg, 0.094 mmol, yield 47%). Slow diffusion of diethyl ether in a concentrated solution of the complex in acetonitrile (3 ml) produced red single crystals of [Cr(tpy)(tppz)][PF₆]₃·3CH₃CN (8) suitable for X-ray diffraction studies.

[Cr₂Cl₆(tppz)]. Tetra-2-pyridinylpyrazine (220 mg, 0.566 mmol, 1 eq.), CrCl₃, 6H₂O (440 mg, 1.65 mmol, 2.9 eq.), and EtOH (12 mL) were introduced into a round bottom flask. After complete dissolution of CrCl₃, acetonitrile (24 mL) was added to the resulting green solution, and the mixture was refluxed for 24 hours. The brown greenish precipitate was filtered off, washed with boiling EtOH (4 times), and dried with diethylether to give [Cr₂Cl₆(tppz)] as a brown greenish solid (390 mg, 0.555 mmol, yield 98%). Slow diffusion of diethyl ether in a concentrated solution of the [Cr₂Cl₆(tppz)] complex in N-methyl-2-pyrrolidone (NMP) provided green crystals of [Cr₂Cl₆(tppz)]·3C₅H₉NO (11) suitable for X-ray diffraction studies.

[Cr₂Cl₆(bbt)]. 6',6"-Bis(2-pyridyl)-2,2':4',4:2",2"'-quaterpyridine (bbt, 50 mg, 0.108 mmol, 1 eq.), CrCl₃, 6H₂O (86 mg, 0.323 mmol, 3 eq.), and DMF (10 mL) were introduced into a round bottom flask. The mixture was stirred at 90 °C for 64 hours. The green precipitate was filtered on a PTFE membrane, washed with EtOH, and dried with diethylether to give Cr₂Cl₆(bbt)·H₂O (83 mg, 0.089 mmol, yield 96%) as a green solid. Slow diffusion of diethylether in a saturated solution of the [Cr₂Cl₆(bbt)] complex in N-methyl-2-pyrrolidone (NMP) provided green crystals of [Cr₂Cl₆(bbt)] (12) suitable for X-ray diffraction studies.

[Cr₂Cl₆(ebbt)]. 4',4""-(Ethynyl)bis(2,2':6',2"-terpyridine) (ebbt, 74 mg, 0.151 mmol, 1 eq.), CrCl₃, 6H₂O (121 mg, 0.454 mmol, 3 eq.), and DMF (20 mL) were introduced into a round bottom flask. The mixture was stirred at 90 °C for 64 hours. The green precipitate was filtered on a PTFE membrane, washed with EtOH, and dried with diethylether to give [Cr₂Cl₆(ebbt)]·2H₂O as a green solid (34 mg, 0.041 mmol, yield 27%). Due to the very low solubility of this complex in common organic solvents, we were not able to obtain crystals suitable for X-ray diffraction studies.

[Cr₂(tpy)₂(bbt)][PF₆]₆. 6',6"-Bis(2-pyridyl)-2,2':4',4:2",2"'-quaterpyridine (bbt) (30 mg, 0.065 mmol, 1 eq.), and distilled CHCl₃ (12 mL) were introduced into a Schlenk tube under argon. After complete ligand dissolution, a solution of [Cr(tpy)

(SO₃CF₃)₃] (109 mg, 0.148 mmol, 2.3 eq.)⁴⁶ dissolved in distilled acetonitrile (4 mL) was added. The mixture was stirred at 70 °C for 15 hours. The orange precipitate was filtered, washed with dichloromethane, and dried with diethylether. The orange solid so obtained was recrystallized from EtOH and dried with diethylether to give [Cr₂(tpy)₂(bbt)][SO₃CF₃]₃ (92 mg, 0.048 mmol, yield 74%) as an orange solid. [Cr₂(tpy)₂(bbt)](SO₃CF₃)₃ was dissolved in MeOH, and a saturated solution of TBAPF₆ in MeOH was slowly added until complete precipitation of the yellow compound. The precipitate was filtered, washed with a few drops of MeOH, and dried with diethylether, to provide [Cr₂(tpy)₂(bbt)][PF₆]₆ as a yellow solid. Slow diffusion of diethylether into a solution of [Cr₂(tpy)₂(bbt)][PF₆]₆ in acetonitrile provided orange crystals of [Cr₂(tpy)₂(bbt)][PF₆]₆·8CH₃CN·(CH₃CH₂)₂O (13) suitable for X-ray diffraction studies. ESI-MS *m/z*: [Cr₂(tpy)₂(bbt); 5SO₃CF₃]⁺ calc: 1779.0, found: 1780.3; [Cr₂(tpy)₂(bbt); 4SO₃CF₃]²⁺ calc: 815.0, found: 814.3; [Cr₂(tpy)₂(bbt); 3SO₃CF₃]³⁺ calc: 493.7, found: 493.6.

[Cr₂(tpy)₂(ebbt)][PF₆]₆. 4',4""-(Ethynyl)bis(2,2':6',2"-terpyridine) (ebbt, 40 mg, 0.082 mmol, 1 eq.), and distilled CHCl₃ (15 mL) were introduced into a Schlenk tube under argon. After complete ligand dissolution, a solution of [Cr(tpy)(SO₃CF₃)₃] (180 mg, 0.246 mmol, 3 eq.) dissolved in distilled acetonitrile (5 mL) was added. The mixture was stirred at 70 °C for 15 hours. The orange precipitate was filtered, washed with dichloromethane and dried with diethylether. The resulting orange solid was recrystallized from EtOH and dried with diethylether to give [Cr₂(tpy)₂(ebbt)][SO₃CF₃]₆ (130 mg, 0.066 mmol, yield 81%) as an orange solid. [Cr₂(tpy)₂(ebbt)](SO₃CF₃)₆ was dissolved in MeOH, and a saturated solution of TBAPF₆ in MeOH was slowly added until complete precipitation of the yellow compound. The precipitate was filtered, washed with a few drops of MeOH, and dried with diethylether to give [Cr₂(tpy)₂(ebbt)][PF₆]₆ as a yellow solid. Slow diffusion of diethylether into a solution of the [Cr₂(tpy)₂(ebbt)][PF₆]₆ complex in acetonitrile provided orange crystals of [Cr₂(tpy)₂(ebbt)][PF₆]₆·10CH₃CN (14) suitable for X-ray diffraction studies. ESI-MS *m/z*: [Cr₂(tpy)₂(ebbt); 5SO₃CF₃]⁺ calc: 1803.0, found: 1803.4; [Cr₂(tpy)₂(ebbt); 4SO₃CF₃]²⁺ calc: 827.0, found: 827.8; [Cr₂(tpy)₂(ebbt); 3SO₃CF₃]³⁺ calc: 501.7, found: 502.3; [Cr₂(tpy)₂(ebbt); 2SO₃CF₃]⁴⁺ calc: 339.0, found: 339.7; [Cr₂(tpy)₂(ebbt); 1SO₃CF₃]⁵⁺ calc: 241.4, found: 241.8; [Cr₂(tpy)₂(ebbt)]⁶⁺ calc: 176.4, found: 176.9.

[CrCl₃(ddpd)]. N,N'-Dimethyl-N,N'-dipyridin-2-ylpyridine-2,6-diamine (ddpd) (80 mg, 0.274 mmol, 1 eq.), CrCl₃, 6H₂O (95 mg, 0.357 mmol, 1.3 eq.), and EtOH (20 mL) were introduced into a round bottom flask. After refluxing for 15 hours, a green precipitate formed was filtered and dried with diethyl ether to give [CrCl₃(ddpd)] (75 mg, 0.167 mmol, yield 61%) as a green solid. Slow diffusion of diethylether into a concentrated solution of [CrCl₃(ddpd)] in DMF provided green crystals of [CrCl₃(ddpd)] (15) suitable for X-ray diffraction studies.

## Spectroscopic and analytical measurements

¹H and ¹³C NMR spectra were recorded on a Bruker Avance 400 MHz spectrometer equipped with a variable temperature
<figure><img src="image_18.png" /></figure>

unit. Chemical shifts are given in ppm with respect to tetra-
methylsilane Si(CH₃)₄. Pneumatically-assisted electrospray
(ESI) mass spectra were recorded from 10⁻⁴ M solutions on an
Applied Biosystems API 150EX LC/MS System equipped with a
Turbo Ionspray source®. Elemental analyses were performed
by K. L. Buchwalder from the Microchemical Laboratory of the
University of Geneva. Spectrophotometric titrations were per-
formed with a J&M diode array spectrometer (Tidas series) con-
nected to an external computer. In a typical experiment,
50 cm³ of ligand in acetonitrile : chloroform (65 : 35) (8 × 10⁻⁵
mol dm⁻³) were titrated at 298 K with a solution of
Er(CF₃SO₃)₃ (2 × 10⁻³ mol dm⁻³) in the same solvent under an
inert atmosphere. After each addition of 0.10 mL, the absor-
bance was recorded using a Hellma optrode (optical path
length 0.1 cm) immersed in the thermostated titration vessel
and connected to the spectrometer. Mathematical treatment of
the spectrophotometric titrations was performed with factor
analysis¹³⁰ and with the SPECFIT program.¹³¹ Absorption
spectra in solution were recorded using a Cary 5000 Varian
spectrometer (quartz cell path length 1 mm, 200–800 nm
domain). Absorption spectra in the solid state were recorded
on a Lambda 900 PerkinElmer spectrometer equipped with an
integration sphere (background recorded on MgO). Emission
spectra were recorded upon excitation at 400 nm from powder
samples at various temperatures from 3 K to 295 K with a
Fluorolog 3-22 (Horiba Jobin-Yvon), equipped with a peltier-
cooled photo multiplier tube (Hamamatsu R2658P), and cor-
rected for the spectral response of the system. Excitation at
355 nm was obtained with the third harmonic of a pulsed Nd:
YAG laser (Quantel Brilliant). The emitted light was collected
with a telescope and focused onto a light-guide with a fibre
bundle connected to a monochromator (Spex 270 M). Full
spectra were recorded with a CCD (Spex Spectrum One), decay
curves with a photomultiplier (Hamamatsu R928) and a digital
oscilloscope (Tektronix TDS540B) or a multichannel scaler
(Stanford Research SR430). For the latter the spectral band-
width of the monochromator was set to 20 nm, thus giving the
decay of the integral signal. Low temperatures were achieved
with a closed cycle cryosystem (Janis, SHI-950) with the sample
sitting in exchange gas for efficient cooling. Microcrystalline
samples were mounted on copper plates with rubber cement.
The copper plates were attached to the sample holder.
Magnetization was measured using a Quantum Design VSM
system (Department of Quantum Matter Physics, University of
Geneva) in the range of 2–300 K. Solid samples of Cr₂Cl₆(tppz)
(15.8 mg), Cr₂Cl₆(bbt) (16.0 mg), Cr₂Cl₆(ebbt) (4.7 mg),
[Cr₂(tpy)₂(bbt)][PF₆]₆ (8.1 mg) and [Cr₂(tpy)₂(ebbt)][PF₆]₆
(14.9 mg) were immobilized in capsules, which were locked in
a straw. The samples were introduced in the SQUID under an
inert atmosphere of helium.

X-Ray crystallography

A summary of crystal data, intensity measurements and struc-
ture refinements for compounds (1) to (15) is collected in
Tables S2, S3, S12, S17, S21, S26, S31 and S38 (ESI†). The crys-
tals were mounted on MiTeGen raptor cryoloops with protec-

tion oil. X-ray data collections were performed with an Agilent
SuperNova Dual diffractometer equipped with a CCD Atlas
detector (Cu[Kα] radiation). The structures were solved by
using direct methods.¹⁴⁰ Full-matrix least-square refinements
on *R*² were performed with SHELX97.¹⁴¹

Specific refinement details. [Cr(ebzpy)₂][CF₃SO₃]₃·2CH₃CN (4): One triflate (of the 3 which are required for electroneutral-ity) and 0.5 CH₃CN molecules were extremely disordered. Because of the lack of well-defined features in the electron density map, several attempts to model this disorder didn't give satisfactory refinement. We thus performed SQUEEZE after exclusion of these disordered molecules (using Platon)¹⁴² and found 8 voids of 123 Å³ containing 75 electrons (corresponding to one CF₃SO₃) and 4 voids of 71 Å³ containing 20 electrons (leading to 0.5 CH₃CN per formula unit).

[Cr₂Cl₆(tppz)]·3C₅H₉NO (11): The crystal was twinned. The twinned operation was a two-fold rotation along the c axis producing apparent Laue symmetry 6/m. The twin law [−1 0 0; 0 −1 0; 0 0 1] was applied in SHELXL,¹⁴¹ including racemic twinning (four components). The twin fraction was 0.405(5) and the corresponding racemic twinning fractions were close to zero. Reflections *hk2l* were weak. There was almost translational symmetry with vector *c*/2. Indeed, the structure could be solved and refined in the smaller unit-cell with one complex and three solvent molecules, one of them disordered over two positions. The packing of this molecule produced the superstructure.

[Cr₂Cl₆(bbt)] (12): A very large hole (around 1700 Å³) was present in the structure. The squeeze/bypass procedure as implemented in Platon¹⁴² was used to take care of the disordered solvent present in this hole (which could not be modelled otherwise). Around 505 electrons were found in each hole, which corresponded to about 4 acetone molecules per formula unit (Z = 4). These molecules were not added to the formula so that the density and absorption coefficients were somehow underestimated. R factors before squeezing: R₁ 0.0788 and wR₂ 0.22756 (all data).

CCDC 1542315-1542329† contain the supplementary crystallographic data.

Acknowledgements

Financial support from the Swiss National Science Foundation
is gratefully acknowledged.

References

1 M. P. McDaniel, *Adv. Catal.*, 1985, **33**, 47–98.

2 S. E. Schaus, J. Brånalt and E. N. Jacobsen, *J. Org. Chem.*, 1998, **63**, 403–405.

3 A. G. Dossetter, T. F. Jamison and E. N. Jacobsen, *Angew. Chem., Int. Ed.*, 1999, **38**, 2398–2400.

4 A. M. McDaniel, H.-W. Tseng, N. H. Damrauer and M. P. Shores, *Inorg. Chem.*, 2010, **49**, 7981–7991.
<figure><img src="image_19.png" /></figure>

5 A. M. McDaniels, H.-W. Tseng, E. A. Hill, N. H. Damrauer, A. K. Rappé and M. P. Shores, *Inorg. Chem.*, **2013**, *52*, 1368-1378.

6 T. Mallah, S. Thiébaut, M. Verdaguer and P. Veillet, *Science*, **1993**, *262*, 1554-1557.

7 V. Gadet, T. Mallah, I. Castro, M. Verdaguer and P. Veillet, *J. Am. Chem. Soc.*, **1992**, *114*, 9213-9214.

8 R. L. Carlin and R. Burriel, *Phys. Rev. B: Condens. Matter*, **1983**, *27*, 3012-3017.

9 M. Verdaguer, A. Bleuzen, V. Marvaud, J. Vaissermann, M. Seuleiman, C. Desplanches, A. Scuiller, C. Train, R. Garde, G. Gelly, C. Lomenech, I. Rosenman, P. Veillet, C. Cartier and F. Villain, *Coord. Chem. Rev.*, **1999**, *190-192*, 1023-1047.

10 O. Kahn and B. Briat, *J. Chem. Soc., Faraday Trans. 2*, 1976, **72**, 268-281.

11 W. Liu, J. H. Christian, R. Al-Oweini, B. S. Bassil, J. van Tol, M. Atanasov, F. Neese, N. S. Dalal and U. Kortz, *Inorg. Chem.*, **2014**, *53*, 9274-9283.

12 N. Novosel, D. Žilić, D. Pajić, M. Jurić, B. Perić, K. Zadro, B. Rakvin and P. Planinić, *Solid State Sci.*, **2008**, *10*, 1387-1394.

13 L. S. Forster, *Chem. Rev.*, **1990**, *90*, 331-353.

14 M. A. Jamieson, N. Serpone and M. Z. Hoffman, *Coord. Chem. Rev.*, **1981**, *39*, 121-179.

15 A. D. Kirk, *Coord. Chem. Rev.*, **1981**, *39*, 225-263.

16 T. H. Maiman, *Nature*, **1960**, *187*, 493-494.

17 F.-F. Chen, Z.-Q. Chen, Z.-Q. Bian and C.-H. Huang, *Coord. Chem. Rev.*, **2010**, *254*, 991-1010.

18 L. Aboshyan-Sorgho, M. Cantuel, S. Petoud, A. Hauser and C. Piguet, *Coord. Chem. Rev.*, **2012**, *256*, 1644-1663.

19 T. J. Meyer, *Pure Appl. Chem.*, **1986**, *58*, 1193-1206.

20 V. Balzani, A. Juris, M. Venturi, S. Campagna and S. Serroni, *Chem. Rev.*, **1996**, *96*, 759-833.

21 V. Balzani, G. Bergamini, F. Marchioni and P. Ceroni, *Coord. Chem. Rev.*, **2006**, *250*, 1254-1266.

22 F. R. Keene, *Dalton Trans.*, **2011**, *40*, 2405-2418.

23 A. K. Pal and G. S. Hanan, *Chem. Soc. Rev.*, **2014**, *43*, 6184-6197.

24 A. Winter and U. S. Schubert, *Chem. Soc. Rev.*, **2016**, *45*, 5311-5357.

25 L. Helm and A. E. Merbach, *Chem. Rev.*, **2005**, *105*, 1923-1960.

26 R. G. Pearson, R. A. Munson and F. Basolo, *J. Am. Chem. Soc.*, **1958**, *80*, 504.

27 C.-A. Palma, M. Cecchini and P. Samori, *Chem. Soc. Rev.*, **2012**, *41*, 3713-3730.

28 M. Murrie, S. Parsons, R. E. P. Winpenny, I. M. Atkinson and C. Benelli, *Chem. Commun.*, **1999**, 285-286.

29 E. J. L. McInnes, S. Piligkos, G. A. Timco and R. E. P. Winpenny, *Coord. Chem. Rev.*, **2005**, *249*, 2577-2590.

30 G. A. Timco, E. J. L. McInnes and R. E. P. Winpenny, *Chem. Soc. Rev.*, **2013**, *42*, 1796-1806.

31 J. Springborg, *Adv. Inorg. Chem.*, **1988**, *32*, 55-169.

32 G. Marinescu, M. Andruh, F. Lloret and M. Julve, *Coord. Chem. Rev.*, **2011**, *255*, 161-185.

33 S. Decurtins, M. Gross, H. W. Schmalle and S. Ferlay, *Inorg. Chem.*, **1998**, *37*, 2443-2448.

34 R. Sieber, S. Decurtins, H. Stoeckli-Evans, C. Wilson, D. Yufit, J. A. K. Howard, S. C. Capelli and A. Hauser, *Chem. - Eur. J.*, **2000**, *6*, 361-368.

35 M. E. von Arx, E. Burattini, A. Hauser, L. van Pietserson, R. Pellaux and S. Decurtins, *J. Phys. Chem. A*, **2000**, *104*, 883-893.

36 M. A. Subhan, T. Suzuki and S. Kaizaki, *J. Chem. Soc., Dalton Trans.*, **2001**, 492-497.

37 H.-Z. Kou, B. C. Zhou, S. Gao and R.-J. Wang, *Angew. Chem., Int. Ed.*, **2003**, *42*, 3288-3291.

38 Y. Li, Z. Jiang, M. Wang, J. Yuan, D. Liu, X. Yang, M. Chen, J. Yan, X. Li and P. Wang, *J. Am. Chem. Soc.*, **2016**, *138*, 10041-10046.

39 D. Liu, Z. Jiang, M. Wang, X. Yang, H. Liu, M. Chen, C. N. Moorefield, G. R. Newkome, X. Li and P. Wang, *Chem. Commun.*, **2016**, *52*, 9773-9776.

40 H. Iranmanesh, K. S. A. Arachchige, M. Bhadhade, W. A. Donald, J. Y. Liew, K. T.-C. Liu, E. T. Luis, E. G. Moore, J. R. Price, H. G. Yan, J.-X. Yang and J. E. Beves, *Inorg. Chem.*, **2016**, *55*, 12737-12751.

41 B. Doistau, A. Tron, S. A. Denisov, G. Jonusauskas, N. D. McClenaghan, G. Gontard, V. Marvaud, B. Hasenknopf and G. Vives, *Chem. - Eur. J.*, **2014**, *20*, 15799-15807.

42 B. Doistau, J.-L. Cantin, L.-M. Chamoreau, V. Marvaud, B. Hasenknopf and G. Vives, *Chem. Commun.*, **2015**, *51*, 12916-12919.

43 R. Chakrabarty, P. S. Mukherjee and P. J. Stang, *Chem. Rev.*, **2011**, *111*, 6810-6918.

44 M. Wang, K. Wang, C. Wang, M. Huang, X.-Q. Hao, M.-Z. Shen, G.-Q. Shi, Z. Zhang, B. Song, A. Cisneros, M.-P. Song, B. Xu and X. Li, *J. Am. Chem. Soc.*, **2016**, *138*, 9258-9268.

45 E. C. Constable and A. M. W. Cargill-Thompson, *J. Chem. Soc., Dalton Trans.*, **1995**, 1615-1627.

46 E. C. Constable, C. E. Housecroft, M. Neuburger, J. Schönle and J. A. Zampese, *Dalton Trans.*, **2014**, *43*, 7227-7235.

47 M. Maestri, F. Bolletta, N. Serpone, L. Moggi and V. Balzani, *Inorg. Chem.*, **1976**, *15*, 2048-2051.

48 M. Cantuel, G. Bernardinelli, D. Imbert, J.-C. G. Bunzli, G. Hopfgartner and C. Piguet, *J. Chem. Soc., Dalton Trans.*, **2002**, 1929-1940.

49 M. Cantuel, F. Gumy, J.-C. G. Bunzli and C. Piguet, *Dalton Trans.*, **2006**, 2647-2660.

50 L. Aboshyan-Sorgho, C. Besnard, P. Pattison, K. R. Kittilstved, A. Aebischer, J.-C. G. Bünzli, A. Hauser and C. Piguet, *Angew. Chem., Int. Ed.*, **2011**, *50*, 4108-4112.

51 Y. Suffren, D. Zare, S. V. Eliseeva, L. Guénée, H. Nozary, T. Lathion, L. Aboshyan-Sorgho, S. Petoud, A. Hauser and C. Piguet, *J. Phys. Chem. C*, **2013**, *117*, 26957-26963.
<figure><img src="image_20.png" /></figure>

52 D. Zare, Y. Suffren, L. Guénée, S. V. Eliseeva, H. Nozary, L. Aboshyan-Sorgho, S. Petoud, A. Hauser and C. Piguet, *Dalton Trans.*, 2015, **44**, 2529–2540.

53 Y. Suffren, B. Golesorkhi, D. Zare, L. Guénée, H. Nozary, S. V. Eliseeva, S. Petoud, A. Hauser and C. Piguet, *Inorg. Chem.*, 2016, **55**, 9964–9972.

54 I. Bertini, P. Turano and A. J. Vila, *Chem. Rev.*, 1993, **93**, 2833–2932.

55 E. Rousset, D. Chartrand, I. Ciofini, V. Marvaud and G. S. Hanan, *Chem. Commun.*, 2015, **51**, 9261–9264.

56 V. Balzani, A. Credi and M. Venturi, *ChemSusChem*, 2008, **1**, 26–58.

57 M. Schulze, V. Kunz, P. D. Frischmann and F. Würthner, *Nat. Chem.*, 2016, **8**, 576–583.

58 J. P. Collin, S. Guillerez, J. P. Sauvage, F. Barigelletti, L. De Cola, L. Flamigni and V. Balzani, *Inorg. Chem.*, 1991, **30**, 4230–4238.

59 C. K. Jorgensen, *Adv. Chem. Phys.*, 1963, **5**, 33–146.

60 A. B. P. Lever, *Inorganic Electronic Spectroscopy*, Elsevier, Amsterdam, Oxford, New York, Tokyo, 2nd edn, 1984, p. 126.

61 S. K. Padhi, D. Saha, R. Sahu, J. Subramanian and V. Manivannan, *Polyhedron*, 2008, **27**, 1714–1720.

62 T. J. Morsing, S. P. A. Sauer, H. Weihe, J. Bendix and A. Døssing, *Inorg. Chim. Acta*, 2013, **396**, 72–77.

63 C. Creutz and H. Taube, *J. Am. Chem. Soc.*, 1969, **91**, 3988–3989.

64 R. A. Marcus, *J. Chem. Phys.*, 1956, **24**, 966–978.

65 R. A. Marcus, *Rev. Mod. Phys.*, 1993, **65**, 599–610.

66 A. Heckmann and C. Lambert, *Angew. Chem., Int. Ed.*, 2012, **51**, 326–392.

67 M. B. Robin and P. Day, in *Advances in Inorganic Chemistry and Radiochemistry*, ed. H. J. Emeléus and A. G. Sharpe, Academic Press, 1968, vol. 10, pp. 247–422.

68 P. Day, N. S. Hush and R. J. H. Clarck, *Philos. Trans. R. Soc.*, A, 2008, **366**, 5–14.

69 J. P. Sauvage, J. P. Collin, J. C. Chambron, S. Guillerez, C. Coudret, V. Balzani, F. Barigelletti, L. De Cola and L. Flamigni, *Chem. Rev.*, 1994, **94**, 993–1019.

70 H. Ozawa, M. Baghernejad, O. A. Al-Owaedi, V. Kaliginedi, T. Nagashima, J. Ferrer, T. Wandlowski, V. M. García-Suárez, P. Broekmann, C. J. Lambert and M.-A. Haga, *Chem. - Eur. J.*, 2016, **22**, 12732–12740.

71 J.-P. Collin, P. Laine, J.-P. Launay, J.-P. Sauvage and A. Sour, *J. Chem. Soc., Chem. Commun.*, 1993, 434–435.

72 H. Torieda, K. Nozaki, A. Yoshimura and T. Ohno, *J. Phys. Chem. A*, 2004, **108**, 4819–4829.

73 H. Torieda, A. Yoshimura, K. Nozaki, S. Sakai and T. Ohno, *J. Phys. Chem. A*, 2002, **106**, 11034–11044.

74 B. Schlicke, P. Belser, L. De Cola, E. Sabbioni and V. Balzani, *J. Am. Chem. Soc.*, 1999, **121**, 4207–4214.

75 F. Barigelletti, L. Flamigni, V. Balzani, J.-P. Collin, J.-P. Sauvage, A. Sour, E. C. Constable and A. M. W. Cargill-Thompson, *J. Am. Chem. Soc.*, 1994, **116**, 7692–7699.

76 M. Bar, D. Maity, S. Das and S. Baitalik, *Dalton Trans.*, 2016, **45**, 17241–17253.

77 D. L. Dexter, *J. Chem. Phys.*, 1953, **21**, 836–850.

78 S. S. Skourtis, C. Liu, P. Antoniou, A. M. Virshup and D. N. Beratan, *Proc. Natl. Acad. Sci. U. S. A.*, 2016, **113**, 8115–8120.

79 C. C. Scarborough, S. Sproules, T. Weyhermueller, S. DeBeer and K. Wieghardt, *Inorg. Chem.*, 2011, **50**, 12446–12462.

80 C. C. Scarborough, K. M. Lancaster, S. DeBeer, T. Weyhermüller, S. Sproules and K. Wieghardt, *Inorg. Chem.*, 2012, **51**, 3718–3732.

81 K. D. Barker, K. A. Barnett, S. M. Connell, J. W. Glaeser, A. J. Wallace, J. Wildsmith, B. J. Herbert, J. F. Wheeler and N. A. P. Kane-Maguire, *Inorg. Chim. Acta*, 2001, **316**, 41–49.

82 M. Isaacs, A. G. Sykes and S. Ronco, *Inorg. Chim. Acta*, 2006, **359**, 3847–3854.

83 J. Schönle, E. C. Constable, C. E. Housecroft and M. Neuburger, *Inorg. Chem. Commun.*, 2015, **53**, 80–83.

84 J. Schönle, E. C. Constable, C. E. Housecroft, A. Prescimone and J. A. Zampese, *Polyhedron*, 2015, **89**, 182–188.

85 L. Pazderski, T. Pawlak, J. Sitkowski, L. Kozerski and E. Szlyk, *Magn. Reson. Chem.*, 2011, **49**, 237–241.

86 E. C. Constable, *Adv. Inorg. Chem. Radiochem.*, 1986, **30**, 69–121.

87 M. L. Scudder, H. A. Goodwin and I. G. Dance, *New J. Chem.*, 1999, **23**, 695–705.

88 S. Grimme, *Angew. Chem., Int. Ed.*, 2008, **47**, 3430–3434.

89 R. Zhao and R.-Q. Zhang, *Phys. Chem. Chem. Phys.*, 2016, **18**, 15452–25457.

90 C. Piguet, J.-C. G. Bünzli, G. Bernardinelli and A. F. Williams, *Inorg. Chem.*, 1993, **32**, 4139–4149.

91 W. A. Wickramasinghe, P. H. Bird, M. A. Jamieson and N. Serpone, *J. Chem. Soc., Chem. Commun.*, 1979, **1979**, 798–800.

92 W. A. Wickramasinghe, P. H. Bird and N. Serpone, *Inorg. Chem.*, 1982, **21**, 2694–2698.

93 N. Cloete, H. G. Visser and A. Roodt, *Acta Crystallogr., Sect. E: Struct. Rep. Online*, 2007, **63**, m45–m47.

94 W. Zhang, W.-H. Sun, S. Zhang, J. Hou, K. Wedeking, S. Schultz, R. Fröhlich and H. Song, *Organometallics*, 2006, **25**, 1961–1969.

95 R. S. Bitzer, C. A. L. Filgueiras, J. G. S. Lopes, P. S. Santos and M. H. Herbst, *Transition Met. Chem.*, 2005, **30**, 636–642.

96 R. C. Rocha, F. N. Rein, H. Jude, A. P. Shreve, J. J. Concepcion and T. J. Meyer, *Angew. Chem., Int. Ed.*, 2008, **47**, 503–506.

97 B. A. Albani, B. Pena, S. Saha, J. K. White, A. M. Schaeffer, K. R. Dunbar and C. Turro, *Chem. Commun.*, 2015, **51**, 16522–16525.

98 R. Davidson, J.-H. Liang, D. Costa Milan, B.-W. Mao, R. J. Nichols, S. J. Higgins, D. S. Yufit, A. Beeby and P. J. Low, *Inorg. Chem.*, 2015, **54**, 5487–5494.

99 M. Graf, H. Stoeckli-Evans, A. Escuer and R. Vicente, *Inorg. Chim. Acta*, 1997, **257**, 89–97.

100 T. Nagashima, T. Nakabayashi, T. Suzuki, K. Kanaizuka, H. Ozawa, Y.-W. Zhong, S. Masaoka, K. Sakai and M.-A. Haga, *Organometallics*, 2014, **33**, 4893–4904.
101 C.-J. Yao, Y.-W. Zhong and J. Yao, *Inorg. Chem.*, 2013, **52**, 4040–4045.

102 N. Yoshikawa, S. Yamabe, N. Kanehisa, T. Inoue, H. Takashima and K. Tsukahara, *J. Phys. Org. Chem.*, 2011, **24**, 1110–1118.

103 Á. J. Pérez-Jiménez, J. C. Sancho-García and J. M. Pérez-Jordá, *J. Chem. Phys.*, 2005, **123**, 134309.

104 M. P. Johansson and J. Olsen, *J. Chem. Theor. Comput.*, 2008, **4**, 1460–1471.

105 W. Ouellette, B.-K. Koo, E. Burkholder, V. Golub, C. J. O'Connor and J. Zubieta, *Dalton Trans.*, 2004, 1527–1538.

106 S. Jones, J. M. Vargas, S. Pellizzeri, C. J. O'Connor and J. Zubieta, *Inorg. Chim. Acta*, 2013, **395**, 44–57.

107 S. Dev, S. Maheshwari and A. R. Choudhury, *RSC Adv.*, 2015, **5**, 26932–26940.

108 E. Kryachko and S. Scheiner, *J. Phys. Chem. A*, 2004, **108**, 2527–2535.

109 V. Grosshenny, F. M. Romero and R. Ziessel, *J. Org. Chem.*, 1997, **62**, 1491–1500.

110 G. A. Bain and J. F. Berry, *J. Chem. Educ.*, 2008, **85**, 532–536.

111 J.-P. Launay and M. Verdaguer, *Electrons in Molecules from Basic Principles to Molecular Electronics*, Oxford University Press, Oxford, 2014.

112 O. Kahn, *Molecular Magnetism*, VCH Publishers, Weinheim, 1993, pp. 150–164.

113 Q. Ren and Z. Chen, *J. Mol. Struct. (THEOCHEM)*, 2005, **719**, 159–168.

114 M. Atanasov, P. Comba and C. A. Daul, *Inorg. Chem.*, 2008, **47**, 2449–2463.

115 H. Witzke, *Theor. Chim. Acta*, 1971, **20**, 171–185.

116 D. L. Wood, J. Ferguson, K. Knox and J. F. Dillon, *J. Chem. Phys.*, 1963, **39**, 890–898.

117 J. Ferguson, *Prog. Inorg. Chem.*, 1970, **12**, 159–293.

118 C. K. Jorgensen, *Modern Aspects of Ligand Field Theory*, North Holland Publishing Company, Amsterdam, 1971, ch. 23 and 26.

119 A. Hauser, M. Maeder, W. T. Robinson, R. Murugesan and J. Ferguson, *Inorg. Chem.*, 1987, **26**, 1331–1338.

120 S. Otto, M. Grabolle, C. Förster, C. Kreitner, U. Resch-Genger and K. Heinze, *Angew. Chem., Int. Ed.*, 2015, **54**, 11572–11576.

121 A. Harriman, A. Khatyr, R. Ziessel and A. C. Benniston, *Angew. Chem., Int. Ed.*, 2000, **39**, 4287–4290.

122 A. C. Benniston, G. Chapman, A. Harriman, M. Mehrabi and C. A. Sams, *Inorg. Chem.*, 2004, **43**, 4227–4233.

123 T. V. Duncan, K. Song, S.-T. Hung, I. Miloradovic, A. Nayak, A. Persoons, T. Verbiest, M. J. Therien and K. Clays, *Angew. Chem., Int. Ed.*, 2008, **47**, 2978–2981.

124 F. Castelli and L. S. Forster, *J. Am. Chem. Soc.*, 1975, **97**, 6306–6309.

125 M. E. Starzak, in *Mathematical Methods in Chemistry and Physics*, Plenum Press, New York, 1989, pp. 289–357.

126 B. Henderson and G. F. Imbusch, *Optical Spectroscopy of Inorganic Solids*, Clarendon Press, Oxford, 1989.

127 Y. Shen, T. Riedener and K. L. Bray, *Phys. Rev. B: Condens. Matter*, 2000, **61**, 11460–11471.

128 A. Zaïm, S. V. Eliseeva, L. Guénée, H. Nozary, S. Petoud and C. Piguet, *Chem. – Eur. J.*, 2014, **20**, 12172–12182.

129 J. Yuasa and S. Fukuzumi, *J. Am. Chem. Soc.*, 2008, **130**, 566–575.

130 (a) E. R. Malinowski and D. G. Howery, *Factor Analysis in Chemistry*, Wiley, New York, Chichester, 1980; (b) H. Gampp, M. Maeder, C. J. Meyer and A. Zuberbühler, *Talanta*, 1986, **33**, 943–951; (c) B. R. Hall, L. E. Manck, I. S. Tidmarsh, A. Stephenson, B. F. Taylor, E. J. Blaikie, D. A. Vander Griend and M. D. Ward, *Dalton Trans.*, 2011, **40**, 12132–12145.

131 (a) H. Gampp, M. Maeder, C. J. Meyer and A. Zuberbühler, *Talanta*, 1985, **32**, 1133–1139; (b) M. Maeder and P. King, Analysis of Chemical Processes, Determination of the Reaction Mechanism and Fitting of Equilibrium and Rate Constants, in *Chemometrics in Practical Applications*, ed. K. Varmuza, InTech, 2012, ISBN: 978-953-51-0438-4, DOI: 10.5772/31896; (c) Specfit/32 from ReactLab Equilibria: http://jplusconsulting.com/products/reactlab-equilibria/.

132 A. Duerrbeck, S. Gorelik, J. Hobley, J. Wu, A. Hor and N. Long, *Chem. Commun.*, 2015, **51**, 8656–8659.

133 C. Piguet, *Chem. Commun.*, 2010, **46**, 6209–6231.

134 G. Ercolani, C. Piguet, M. Borkovec and J. Hamacek, *J. Phys. Chem. B*, 2007, **111**, 12195–12203.

135 A. Escande, L. Guénée, K.-L. Buchwalder and C. Piguet, *Inorg. Chem.*, 2009, **48**, 1132–1147.

136 A. Albert and J. N. Phillips, *J. Chem. Soc.*, 1956, 1294–1304.

137 A. W.-H. Mau, J. H. Overbeek, J. W. Loder and W. H. F. Sasse, *J. Chem. Soc., Faraday Trans. 2*, 1986, **82**, 869–876.

138 V. Grosshenny and R. Ziessel, *J. Organomet. Chem.*, 1993, **453**, C19–C22.

139 (a) E. C. Constable and M. D. Ward, *J. Chem. Soc., Dalton Trans.*, 1990, 1405–1409; (b) E. C. Constable and A. M. W. C. Thompson, *J. Chem. Soc., Dalton Trans.*, 1992, 3467–3475.

140 (a) SHELXS97 G. M. Sheldrick, *Acta Crystallogr., Sect. A: Fundam. Crystallogr.*, 2008, **64**, 112–122; (b) SIR97 A. Altomare, M. C. Burla, M. Camalli, G. L. Cascarano, C. Giacovazzo, A. Guagliardi, A. G. Moliterni, G. Polidori and R. Spagna, *J. Appl. Crystallogr.*, 1999, **32**, 115–119; (c) SIR92: A. Altomare, G. Cascarano, C. Giacovazzo and A. Guagliardi, *J. Appl. Crystallogr.*, 1993, **26**, 343–350.

141 G. M. Sheldrick, *Acta Crystallogr., Sect. C: Struct. Chem.*, 2015, **71**, 3–8.

142 P. van der Sluis and A. L. Spek, *Acta Crystallogr., Sect. A: Fundam. Crystallogr.*, 1990, **46**, 194–201.