Deviations from statistical binding, that is cooperativity, in self-assembled polynuclear complexes partly result from intermetallic interactions DeltaE(M,M), whose magnitudes in solution depend on a balance between electrostatic repulsion and solvation energies. These two factors have been reconciled in a simple point-charge model, which suggests severe and counter-intuitive deviations from predictions based solely on the Coulomb law when considering the variation of DeltaE(M,M) with metallic charge and intermetallic separation in linear polynuclear helicates. To demonstrate this intriguing behaviour, the ten microscopic interactions that define the thermodynamic formation constants of some twenty-nine homometallic and heterometallic polynuclear triple-stranded helicates obtained from the coordination of the segmental ligands L1-L11 with Zn(2+) (a spherical d-block cation) and Lu(3+) (a spherical 4f-block cation), have been extracted by using the site binding model. As predicted, but in contrast with the simplistic coulombic approach, the apparent intramolecular intermetallic interactions in solution are found to be i) more repulsive at long distance (DeltaE(1-4)(Lu,Lu)>DeltaE(1-2)(Lu,Lu)), ii) of larger magnitude when Zn2+ replaces Lu3+ (DeltaE(1-2)(Zn,Lu)>DeltaE(1-2)(Lu,Lu) and iii) attractive between two triply charged cations held at some specific distance (DeltaE(1-3)(Lu,Lu)<0). The consequences of these trends are discussed for the design of polynuclear complexes in solution.

This work demonstrates how minor structural and electronic changes between Ln(NO 3 ) 3 and Ln(hfac) 3 lanthanide carriers (Ln ¼ trivalent lanthanide, hfac ¼ hexafluoroacetylacetonate) lead to opposite thermodynamic protocols for the metal loading of luminescent polynuclear single-stranded oligomers. Whereas metal clustering is relevant for Ln(hfac) 3 , the successive fixation of Ln(NO 3 ) 3 provides stable microspecies with an alternated occupancy of the binding sites. Partial anion dissociation and anion/ ligand bi-exchange processes occur in polar aprotic solvents, which contribute to delay the unambiguous choice of a well-behaved neutral lanthanide carrier for the selective complexation of different trivalent lanthanides along a single ligand strand. Clues for further improvement along this stepwise strategy are discussed.

The connection of an additional bidentate chelating unit at the extremity of a segmental bis-tridentate ligand in L5 provides an unprecedented sequence of binding sites for the self-assembly of heterometallic 3d-4f triple-stranded helicates. Thorough thermodynamic and structural investigations in acetonitrile show the formation of intricate mixtures of complexes when a single type of metal (3d or 4f) is reacted with L5. However, the situation is greatly simplified when Zn(II) (3d-block) and Lu(III) (4f-block) are simultaneously coordinated to L5, thus leading to only two identified species: the target C 3 -symmetrical trinuclear triple-stranded d-f-f helicate HHH-[ZnLu 2 (L5) 3 ] 8+ and a tetranuclear doublestranded complex [Zn 2 Lu 2 (L5) 2 ] 10+ . Interestingly, the removal of Zn(II) from the former triple-helical complex has only a minor effect on the coordination of Lu(III), and translational autodiffusion coefficients show a simple reduction of the length of the molecular rigid cylinder from L = 2.7 nm in HHH-[ZnLu 2 (L5) 3 ] 8+ to L = 2.3 nm in HHH-[Lu 2 (L5) 3 ] 6+ . Finally, the complete thermodynamic picture provides five novel stability macroconstants containing information about shortrange (ca. 9 A ˚) and long-range (ca. 18 A ˚) intramolecular intermetallic d-f and f-f interactions.

The replacement of terminal 2-benzimidazol-6-carboxypyridine (two internal rotational degrees of freedom) with 2-benzimidazol-8-hydroxyquinoline (one internal rotational degree of freedom) into segmental bis-tridentate ligands in going from L2 and [L3-2 H](2-) to [L12 b-2 H](2-) does not significantly affect the structures of the resulting binuclear lanthanide triple-stranded helical complexes [Ln(2)(L2)(3)](6+), [Ln(2)(L3-2 H)(3)], and [Ln(2)(L12 b-2 H)(3)] (palindromic helices, intermetallic contact distance approximately 9 A, helical pitch approximately 1.4 nm per turn). However, their thermodynamic assemblies are completely different in solution, as evidenced by the spectacular decrease of the effective concentrations by two orders of magnitude for [L12 b-2 H](2-). This key parameter in the [Ln(2)(L12 b-2 H)(n)] (n=2, 3) complexes is further abruptly modulated along the lanthanide series (Ln=La to Lu), which provides an unprecedented tool for 1) tuning the number of ligand strands in the final helicates, 2) selectively coordinating lanthanides in the various complexes, and 3) controlling the ratio of lanthanide-containing polymers over discrete assemblies.

satisfying estimation of the pair intramolecular intermetallic repulsions DE M;M gas , which limit the stability of the final (supra)molecular architectures (z 1 and z 2 are the effective charges in electrostatic units borne by the two metals considered as point charges, e = 1.602 10 À19 C is the elemental electric charge, N Av = 6.023 10 À23 mol À1 is Avogadros number, e 0 = 8.859 10 À19 C V À1 m À1 is the permittivity of vacuum, e r = 1 is the relative permittivity in the gas phase and in the molecule, [1] and d is the separation between the interacting metals). A more refined energetic balance includes polarization and covalent effects, which eventually rationalizes the stability of charged complexes detected by electrospray mass spectrometry in the gas phase (ESI-MS).[2]The same argument is frequently invoked to address the stability of these supramolecular complexes in solution, which is where the majority of self-assembly processes occur. [3] However, this approach neglects the changes in solvation energies D solv G 0 x that result from the complexation of additional components in the final complexes x.[4] For the pair of cationic metals considered in Equation (1), the global solvation energy of the final complex can be roughly approximated by using the Born Equation [Eq. (2)], in which R x is thepseudo-spherical Born radius deduced from the van der Waals [5] or from the Connolly volumes [6] of the final complex, and e solv r is the relative permittivity of the solvent. The recent application of the site-binding model [Eq. (3)] [7] for modeling the two-component self-assemblyprocesses that lead to polynuclear lanthanide helicates [Eq. (4)] gave estimations for the three different intermetallic Moreover, the thermodynamic interpretation of intramolecular intermetallic interactions in these tetranuclear lanthanide helicates is partially obscured by the screening effects produced by the four aligned triply charged cations. A more convincing and unambiguous proof for a chemically sensitive interpretation of the apparent intermetallic interactions that operates within complexes in solution requires a system in which DE M;M sol can be simply correlated with increasing intermetallic separation, and all other parameters