Selective lanthanide distribution within a comprehensive series of heterometallic [LnPr] complexes

The preparation of heterometallic, lanthanide-only complexes is an extremely difficult synthetic challenge. By a ligand-based strategy, a complete isostructural series of dinuclear heterometallic [LnPr] complexes has been synthesized and structurally characterized. The two different coordination sites featured in this molecular entity allow study of the preferences of the praseodymium ion for a specific position depending on the ionic radii of the accompanying lanthanide partner. The purity of each heterometallic moiety has been evaluated in the solid state and in solution by means of crystallographic and spectrometric methods, respectively, revealing the limits of this strategy for ions with similar sizes. DFT calculations have been carried out to support the experimental results, confirming the nature of the site-selective lanthanide distribution. The predictable selectivity of this system has been exploited to assess the magnetic properties of the [DyPr] and [LuPr] derivatives, showing that the origin of the slow dynamics observed in the former arises from the dysprosium ion.


INTRODUCTION
The design of molecular systems featuring lanthanide (Ln) ions is a worldwide-pursued research subject due to the exceptional physical properties exhibited by these types of materials. [1][2][3][4] Since 4f orbitals are particularly screened form external perturbations by the filled 5s and 5p shells, their corresponding electrons virtually exhibit the magnetic and spectroscopic character of a free ion. This allows, for example, Ln ions to preserve their orbital momentum practically unquenched (only partially removed by the ligand field created in the coordination environment) or to produce a well-defined distribution of the electronic levels, deriving in sharp and easily identifiable 4f-4f transitions. These peculiarities permit to exploit Ln-based molecular systems in a wide range of applications such as devices for light-emitting diodes, 5 agents for optical and magnetic resonance imagining, 6 materials for magnetic refrigeration 7 or molecular-based systems 3 for information storage and processing. 8 In particular, the influence of Ln-based materials in molecular magnetism raised notably in the last years since Ishikawa and coworkers observed slow relaxation of the magnetization in a mononuclear (Bu4N)[Ln(phthalocyanine)2] complex (Ln = Dy, Tb). 9 In fact, this area has recently reached one of its most relevant achievements with the discovery of a mononuclear dysprosium compound featuring such molecular-magnet behavior at almost liquid nitrogen temperature. 10 Considering the potential behind these materials, several research groups started to exploit the possibility of encapsulating more than one type of Ln ion within a molecular system, with the aim of controlling the nature of their metallic sites. These types of heterometallic moieties are particularly interesting since materials featuring combinations of different lanthanide ions can enhance or modify their physical properties. For example, they allow driving higher upconversion efficiencies in luminescent systems, 11 or tuning the color and the brightness of its emission. 12 Another interest is that compounds featuring lanthanide ions that emit at different wavelengths may allow contrast agents to cover both Vis and NIR regions. 13 Recently, the proposal of using lanthanide ions as the units of information for quantum computation (quantum bits or qubits) 14 raised also the interest for molecular systems featuring different Ln ions, since it allows the production of logical operators requiring more than one qubit. 15 Despite the strong interest for accessing these type of 4f-4f' molecular systems, their production is not straightforward. Indeed, the shielding caused by the 5s and 5p electrons described above not only allows Ln ions to be protected from external perturbations but also leads them to behave chemically very similarly. Thus, coordination chemists have faced strong difficulties to develop synthetic methods to produce systems with predictably more than one type of Ln ion. One possibility stands on the sequential addition of the different lanthanide ions 4 through consecutive synthetic steps using a multidonor ligand 16 or by linking preformed building blocks. 17 On the other hand, the design of ligands featuring different encapsulating pockets allows the self-assembly and site-selective distribution of different type of Ln ions within molecules driven by their different ionic radii 18 through simple one-pot reactions. This strategy has allowed the production of triple-stranded heterometallic dinuclear 19 or trinuclear 20 helicates showing two different lanthanide ions selectively incorporated inside the cavities depending on their size with varying degrees of purity. Recently, the use of a rather simple quinolate ligand has produced also molecular systems featuring different metallic environments able to favor nonstatistical distributions of different Ln ions among the various molecular locations. 21 In the last years, we have developed a ligand-based strategy in order to achieve highly selective 4f-4f' dinuclear systems with a purity not observed in the previously reported heterometallic compounds. 15 By synthesizing the asymmetric H3L ligand (H3L = 6-(3-oxo-3-(2hydroxyphenyl)propionyl)pyridine-2-carboxylic acid), a complete quasi-isostructural series of homometallic [LnLn] dinuclear compounds featuring two distinct metallic environments were initially synthesized (Scheme 1). 22 The flexibility of the system allowed to introduce any Ln III ion in the two available coordination sites 1 and 2 of the molecule. However, the Ln-O bond distances of Ln in site 1 were found to be systematically smaller than the ones observed in site 2.
This feature prompted us to exploit the possibility of introducing two different lanthanide ions with different ionic radii in order to produce, predictably, [LnLn'] compounds. Following this strategy, pure heterometallic systems were obtained for Ln pairs of considerable different sizes, although the selectivity was found to be reduced in solution, in the absence of the terminal ligands of the molecular entity. 23 5 We have studied in detail this molecular system and tested the limits of its performance by making a comprehensive series where only one of the two lanthanide ions was varied. In particular, we have combined the praseodymium ion (Pr III )
Alternating current (ac) data were collected with an applied ac field of 4 Oe oscillating at different frequencies in the range 0.1 ≤ ν ≤ 10 000 Hz. Data at variable temperatures were obtained with the PPMS set-up that allows to reach 10 kHz in frequency. Small variations between measurements done on the two set-ups may be ascribed to a lower sensibility as well as to the presence of a small remnant dc field for the latter.

RESULTS AND DISCUSSION
Synthesis.  (Figures 1 and S1). This molecular architecture thus  Figure S1).     A semi-logarithmic plot shows that the data tend towards a plateau of, ca. 12.6 cm 3 mol -1 K at 2 K. For 14, the χT value of 1.71 cm 3 mol -1 K at 300 K is slightly higher than expected for one Pr(III) ion, and decreases below ca. 150 K, first gradually and then more rapidly, to reach 0.10 cm 3 mol -1 K at 1.8 K. A semi-logarithmic plot shows that the data tend towards zero.
Magnetization vs. field data at 2 K are in line with the susceptibility data. For 9, a fast increase up to ca. 6 NAµB at 2 T is observed, followed by a further slower and quasi-linear increase at higher fields, which most likely is primarily associated with the Pr(III) ion. Indeed, in the case of  To evaluate the potential single-molecule magnet behaviour of 9, its magnetization dynamics were investigated through isothermal ac susceptibility measurements at variable frequency. In zero dc field, an out-of-phase signal is detected, indicative of slow relaxation of magnetization ( Figure S6). This relaxation however has two distinct components, one dominant faster mode with a characteristic frequency above the highest accessible with our set-up (10 kHz), and a minor, slower mode clearly visible at lower temperatures, in form of a hump within the studied frequency window. To extract the characteristic time of this slow relaxation mode, a generalized Debye model was fit to the out-of-phase data considering the sum of two components and fixing the fast component τ to 3.18×10 -6 s (see Table S6). This was not possible at higher temperatures and then only one characteristic time was derived. Under applied dc fields, the relaxation becomes slower, and maxima of the out-of-phase signal are observed in our frequency window ( Figure 5, top). In these conditions, only one relaxation mode is detected, and all further data were analyzed with a single generalized Debye model to extract the corresponding characteristic times for the various dc fields (at 1.8 K, Table S7) and temperatures (at 500 and 1000 Oe, Figure   S7 and S8, Table S6). Compound 14 was also studied under the same conditions. The absence of any out-of-phase susceptibility ( Figure S9) supports the hypothesis that the slow magnetization dynamics observed for 9 must be ascribed to the Dy(III) ion. The fast relaxation mode of [PrPr] (9) present in zero field and its cancellation upon applying a dc field suggests the presence of fast quantum tunnelling of magnetization, with τQTM likely of the order of 10 -5 s. At 1.8 K, the field dependence of the spin relaxation time τ of 9 shows a non-monotonous variation ( Figure 5, bottom). The increase observed at low fields is likely due to the reduced effect of spin-spin and spin-nuclei processes upon increasing the dc field, while the decrease at fields above 0.2 T likely results from the then dominant spin phonon direct mechanism, which is ∝B 4 . At 500 and 1000 Oe, the temperature dependence of τ clearly exhibits a strong thermal activation above 5 K, and a steady decrease below ( Figure 5, inset). To gain further insights on the relaxation processes at work avoiding over-parameterization, the expression was first fit to the field dependence of the spin relaxation time τ at 1.8 K (Table S8), allowing for a separate estimation of the direct process with A = 1.0×10 -4 s. Then, the expression , that includes respectively the temperature dependent direct, Orbach and Raman relaxation mechanisms, was fit to the temperature dependence of τ for 9 at 500 and 1000 Oe, fixing n at the expected value of 9 for a Kramers ion (Table S9). The derived parameters τ0 = 2.15×10 -6 s, Ueff = 53 K and C = 1.7×10 -6 s -1 K -9 at 1000 Oe and τ0 = 2.52×10 -6 s, Ueff = 53 K and C = 1.28×10 -5 s -1 K -9 at 500 Oe suggest both Orbach and Raman mechanisms are involved in the thermal activation of the relaxation and are thus difficult to accurately estimate.
One of the great benefits of the controlled site composition in polynuclear lanthanide complexes is that it provides a means to study the exchange interaction between lanthanide ions.
As mentioned above, this interaction is rather weak, which makes it hard to trace using standard magnetic measurements. The vanishing spin density of Pr at low temperatures reduces the relevance of this problem in this series of compounds. However, this important issue has required to study analogues containing the lanthanide of interest next to a diamagnetic anion within isolated molecules, diluted inside a fully diamagnetic crystalline matrix. 38 It would be better to use pure heterodimetallic compounds with the desired composition, and therefore the current system holds great potential in this respect.
DFT studies. In order to rationalize the selectivity of the metallic distribution and the stability  Table 2 demonstrate that in the solid state, each expected configuration is the most stable one, and that this preference is bigger for larger differences of ionic radii (Δr). In fact, the small value of ΔE obtained for 1 agrees with the results obtained in the crystallographic study where no significant differences where observed between type A and type B configurations in the structural refinement (Table   S1). Consistent with the experiment, the energy differences obtained without the terminal ligands (solution) are smaller than in the solid state. This feature, which had been noticed previously for [SmPr], 23 confirms the reduced selectivity in solution, perhaps due to the absence of these ligands. This decrease of selectivity is particularly important in compound 1, for which the preference for type A is no longer observed (-0.97 kcal mol -1 ). As expected, the selectivity for compounds 7 and 14 increases with Δr.

29
The description of chemical systems with unpaired number of electrons (open-shell) is a source of contention within the computational chemistry community. 39,40 Our group studied similar dinuclear systems previously using the BP86 functional 23 obtaining results in agreement with the experimental trend. However, in order to confirm the accuracy of the employed DFTfunctional (BP86), we have used a different DFT-functional (B3LYP) from which we obtained the same trend in the selectivity ( Table 2). On the other hand, relativistic Spin-Orbit calculations were also used to corroborate that scalar relativistic effects describe the system correctly. The results depicted in row 3 of Table 2 present minor differences with respect to the scalar relativistic ZORA methodology.

CONCLUSIONS
The complete series of [LnPr] complexes reported here represents an ideal showcase of the potential and limits of the (Hpy)[LnLn'(HL)3(NO3)(py)(H2O)] system to promote heterometallic molecular entities. The results found from a comprehensive crystallographic study evidence that when the difference between the ionic radii of the two Ln ions is small (Δr < 0.03 Å), the system cannot fully discriminate them. In contrast, when the difference is larger than 0.06 Å, the lanthanides are selectively distributed in the two different cavities of the molecular entity. This The Supporting Information is available free of charge on the ACS Publications website at DOI: XXXX. Additional structural data for compounds 1, 2, 4, 6-14 and magnetic data for compounds 9 and 14 (PDF). CCDC XXXX-XXXX contain the supplementary crystallographic data of the compounds reported in this paper, which can be obtained free of charge upon request.

Author Contributions
The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes
The authors declare no competing financial interest.