Thermodynamic Stability of Heterodimetallic [LnLn’] Complexes: Synthesis and DFT Studies

: The solid state and solution configuration of the heterodimetallic complexes, (Hpy) are analysed experimentally and through DFT calculations. Complexes 3 , 4 and 5 are described here for the first time, by means of single crystal X-ray diffraction and mass spectrometry. The theoretical study is also extended to the [LaCe] and [LaLu] analogues. The results are consistent with a remarkable selectivity of the metal distribution within the molecule while in the solid state, enhanced by the size difference of both ions. This selectivity is reduced in solution, especially for ions with the closest radii. This unique entry into 4 f-4f’ heterometallic chemistry for the first time establishes a difference between the selectivity in solution and that in the solid state, as a result of changes to the coordination that follow the dissociation of terminal ligands upon dissolution of the complexes. The authors thank the Spanish MINECO for funding through CTQ2012-32247, CTQ2015-68370-P (GA, LAB, DA, VV), CTQ2014–52824-R (CB, JGF, NAGB), MAT2014-53961-R (OR), the Marie Curie Co-funding of Regional, National, and International Programmes (COFUND) for funding scheme 291787-ICIQ-IPMP and Fundação para a Ciência e Tecnologia Grant SFRH/BPD/110419/2015 (NAGB) and the Severo Ochoa Excellence Accreditation SEV-2013–0319 (CB). Also we thank Generalitat de Catalunya for financial support through the CERCA Programme and 2014SGR409 grant. The Advanced Light Source is supported by the Director, Office of Science, Office of Basic Energy Sciences of the U. S. Department of Energy under contract no. DE-AC02-05CH11231.


Introduction
The electronic structure of lanthanide elements is at the root of their very rich physico-chemical properties and their potential applications in a large variety of fields. [1][2][3] Some of the sophisticated uses of these elements rely on interactions with other metals within homo- [4][5][6] or heterometallic polynuclear molecular entities. [7][8][9] Of the latter category, the vast majority combine metal ions from different blocks of the periodic table (e.g., 3d-4f) within coordination clusters. [10][11] The reason is that these atoms are sufficiently different chemically, thus exhibiting disparate affinities for various ligand donor atoms or distinct preferred coordination geometries, which allows a selective distribution of different metals within segregated sites in a molecule. By contrast, the task of preparing heterometallic 4f-4f' molecular assemblies is much more challenging. Indeed, all the metals of the series are chemically very similar, since their valence electrons (4f) are shielded by the filled 5s and 5p electrons. A way to tackle this problem is through designed synthetic procedures carried out in several steps, where the different metals are sequentially incorporated, [12][13][14][15][16][17][18] or by linking preformed metal containing moieties. [19][20][21] Alternatively, one could during the course of one-pot reactions, exploit the size difference existing between any two different lanthanide ions as a result of the lanthanide contraction, [22] by using ligands with two types of coordination pockets, able to selectively discriminate different Ln(III) centers by their radius. This method has been employed with asymmetric ligands, L 1 , conducing to the self-assembly of triple stranded dinuclear helicates of the type [Ln2(L 1 )3] or [LnLn'(L 1 )3]. [23][24] Similarly, a tri-topic ligand L 2 , capable of forming trinuclear helicates of the type [Ln3(L 2 )3] 9+ was employed to obtain mixtures of heterometallic species [LnxLn'(3-x) (L 2 )] 9+ , with a central site exhibiting a higher affinity for larger metal ions than the distal positions. [25] A combination of H-NMR and spectrophotometry allowed to determine the formation constants of the various possible trinuclear species (x = 0,1,2,3) and assess the free energy favoring deviations from statistical distributions. These deviations are ascribed to differences in intramolecular electrostatic interactions and solvation effects (these latter, only relevant in solution). [26][27] On a different approach, the serendipitous self-assembly of Ln(III) ions with the bridging and chelating ligand quinolato, Q -, produces clusters with formula [Ln3Q9] exhibiting two slightly different coordination sites, favoring larger ions at the central position of the molecule and smaller ions at the sides. [28] In all these cases, the purity of heterometallic analogues has not been reported to exceed 90%. The goal of preparing pure heterometallic 4f-4f' molecular species remains a crucial challenge; it is bound to have a direct impact in relevant and diverse applications. Some of these are the optical upconversion, [29] multimodal magnetic resonance imaging (MRI), [30] exploitation of sophisticated luminescence properties [31][32] or the realization of 2-qubit quantum gates for quantum computing. [33] We previously reported an exhaustive, quasi-isostructural series of homometallic dinuclear lanthanide complexes with formulae (Hpy)[Ln2(HL)3(NO3)(py)(H2O)] from the asymmetric ligand H3L (H3L = 6-(3-oxo-3-(2hydroxyphenyl)propionyl)pyridine-2-carboxylic acid, Scheme 1). [34][35] Within these molecules, each metal exhibits a completely distinct coordination environment.
A comprehensive structural analysis clearly shows the expected contraction with the Ln atomic number throughout the series.  (5,[LaYb]). Of all possible [LnLn'] combinations, this study was performed with a sample of compounds involving small, medium size and large Ln(III) ions, in addition of featuring large or small variations in ionic radius. The structural analysis of 1 to 5, in comparison with all the related [Ln2] analogues (Ln = Ce, La, Pr, Sm, Gd, Er and Yb), confirms the selectivity for the heterometallic derivatives, which is superior in the solid state than in solution. This is corroborated with DFT calculations, performed on the structures observed in the solid state as well as the moieties detected through mass spectrometry (MS). From these results, it is inferred that in addition to differences in bond distances, the difference in terminal ligands at both sites (observed in the solid state and not in solution) constitutes another source of stabilization of the heterometallic fragment. This synergic effect had not been revealed previously and opens the door to synthetic strategies towards the production of purer and more diverse 4f-4f' assemblies.

Synthesis
The new complexes (Hpy)[CeGd(HL)3(NO3)(py)(H2O)] (3), (Hpy) [PrSm(HL)3(NO3)(py)(H2O)] (4) and (Hpy)2[LaYb(HL)3(NO3)(H2O)] (NO3) (5) were obtained as crystals in the same manner as the previously reported analogues. Thus, equimolar amounts of the corresponding Ln(NO3)3 salts were mixed in pyridine with the stoichiometric quantity of the ligand H3L under aerobic conditions, and crystals were collected following the diffusion of Et2O or toluene into the reaction mixture. The single-crystal X-ray diffraction structures are consistent with the proposed formulation (see below) and the elemental analyses, including these for the metals, are fully satisfactory. From these and previous reactions, it is observed that the yields vary from compound to compound (ranging from 10% for [PrSm] to the 70% of [CeY]), a reflection of the different tendencies for crystallization of each compound. The exact formulation of compound 5 reveals interesting differences with respect to the composition observed hitherto in this family of compounds as explained in detail below.  Table 1). The unit cell contains four asymmetric units, each composed of one metal complex, one pyridinium cation hydrogen bonded to the latter and five lattice pyridine molecules. The complex moiety ( Fig. 1) exhibits the structure observed consistently for this family of compounds; [34,36] it is anionic and it is composed of two Ln(III) metal ions (one of Ce and one of Gd) bridged by and chelated by three HL 2− ligands, the latter showing two opposite orientations with respect to the Ce···Gd vector. This causes two different coordination environments around each metal; Ce(III) is chelated by two (O,N,O) pockets and one (O,O) moiety, whereas Gd(III) is bound to two bidentate and one triatomic coordination unit (Scheme 1). The coordination number (CN) of ten around Ce is completed by a bidentate NO3 − ligand, whereas CN of nine around Gd is reached with the concurrent coordination of one pyridine and one water ligand. The average of the Ln−O distances (Table 2), <Ln-O>, (O from HL 2− ligands) are 2.524 Å (Ce) and 2.406 A (Gd), thus leading to ΔO = 0.12 Å (Fig. 2). In the previously reported homodimetallic [Ce2] analogue, the <Ce−O> values are 2.524 and 2.481 Å (ΔO = 0.043 Å), respectively, whereas the corresponding parameters for the [Gd2] derivative are 2.430 and 2.404 A (ΔO = 0.026 Å). [34] The intermetallic Ce···Gd distance is 3.878 Å, compared with 3.9286(5) and 3.8038 (11), respectively, for the [Ce2] and [Gd2] compounds. These figures clearly show that in compound 3, Ce and Gd have selectively taken their preferred position based on their size difference (ionic radii, rLn, [37] in Å of rCe = 1.220 and rGd = 1.105, Δr = 0.115). This is supported by the fact that any other distribution of Ce and/or Gd leads to data refinements with unreasonable displacement parameters and bad agreement factors. This assignment is consistent with the results from DFT calculations (see below). The phenol hydrogen atoms of HL 2were localized crystallographically. The short N3S-O2 distance is evidence of the presence of a hydrogen bond between these atoms, since it is smaller than the sum of their van der Waals radii ( Table 3). The existence of a pyridinium cation (Hpy + ; N3S in Fig. 1) coordinated to the -COOgroup of one of the HL 2ligands was also demonstrated by DFT as discussed below. Complex 3 is chiral and both enantiomers are present within the unit cell, which is then racemic.    (7) 1.95 (7) 2.808 (6) 177 (6) O19-H19C···N6S#1 0.84 (7) 1.99 (7 [37] Again, the refinement of the crystallographic data and DFT calculations (see below) using other metal distributions confirm the selective nature of this heterometallic species.
The unit cell contains two asymmetric units. The complex anion in 5 (Fig. 4) is formed by two metal ions (La and Yb) wrapped by three deprotonated H3L ligands (as HL 2-) in two opposite orientations with respect to the metal axis. Therefore, the complex is negatively charged (-1) as all the other related complexes studied hitherto. Similarly, the disposition of the ligands creates two coordination sites. Here, the large position contains the metal ion La (  In analogy with 1 to 4, the two pyridinium cations (Hpy + ; N3s and N1S in Fig. 2) in 5 are inferred by their proximity to two -COOgroups from two HL 2ligands and the presence electron density near N3s and N1S. The [LaYb] complex cation is chiral, both enantiomers being present within the unit cell as a racemic mixture.
The relative <Ln−O> values plotted in Fig. 2 '2] counterparts. In this respect, relevant observations are; i) for all compounds, the values of <Ln−O> are consistent with the lanthanide contraction, when comparing Ln ions on equivalent positions (ie., in terms of size, La>Ce>Pr>Sm>Gd>Er>Yb), ii) for all compounds, a ΔO gap is maintained between the large coordination site and the small one, iii) ΔO is wider as Δr becomes larger, iv) in heterometallic compounds, <Ln−O> for a given position is closest to the corresponding value of the predicted metal when occupying this position in the homometallic analogue (red and black colors for the large and small positions, respectively; Ln1 and Ln2 in Scheme1). This excellent agreement with the expected behavior, also in line with the predictions from the lanthanide contraction, supports the high selectivity of this architecture for specific heterometallic dispositions.

Mass Spectrometry
Electrospray ionization mass spectrometry (ESI-MS) was used as a powerful technique to assess the integrity of the solid state structure in solution, and ascertain whether the metal distribution observed by X-ray diffraction was maintained. Thus, for complex Here the relative presence of homometallic fragments is even more prominent than with 3. This shows that these compounds in solution, especially the latter, undergo a process of scrambling and exhibit metal distributions different from these seen in the solid state. Therefore, in the absence of the terminal ligands (NO3 -, H2O and py), ligands H2Land HL 2lose selectivity in distributing ions according to their size. Keeping in mind the limitations of MS for quantitative analyses, the selectivity in solution, seems to increase with the magnitude of Δr (thus, it is larger for [CeGd], with Δr = 0.115 Å, than for [PrSm], Δr = 0.06 Å). Interestingly, the high selectivity of the structure observed in the solid state, together with the diminished selectivity of the system when the terminal ligands are removed is also predicted by DFT calculations (see below). In contrast with 3 and 4, the ESI-MS spectrogram of complex (Hpy)2[LaYb(HL)3(NO3)(H2O)](NO3) (5) shows a dominating signal with m/z of 1162.99, with the right isotopic multiplicity for the fragment [LaYb(HL)2(H2L)] + , this time in the almost complete absence of any of the homometallic counterparts. These observations are consistent with the fact that the metals of 3 exhibit much larger size disparity (Δr = 0.24 Å) and thus, high selectivity for a specific heterometallic distribution, even in solution and for the species without terminal ligands. This is also predicted by DFT calculations, in addition to a much higher drive for the [LaYb] metal arrangement in the structure observed in the solid state.

DFT Studies
DFT based methods were used to rationalize the selectivity in the metal distribution of the [LnLn'] complexes. First, the energy of two structures analogous to those seen in Scheme 1 were compared for various Ln1/Ln2 pairs. One structure bears Ln1 and Ln2 as experimentally observed (structure A, Fig. 6), and the other had the identity of the Ln ions inverted (structure B, Fig. 6). The three ligands were computed in the HL 2form, as seen in the solid state, thus, the complexes always bearing an overall negative charge of -1 and formula [LnLn'(HL)3(NO3)(py) (H2O)] -, with the NO3ligand always bound in a chelating fashion. This structure is consistent with the O-C bond lengths of the carboxylate groups of the HL 2ligands determined by X-ray diffraction, which showed them to be quasi identical. In order to ascertain the position of the putative protons involved in hydrogen bonding, both possible arrangements, RCOOH···py and RCOO − ···Hpy + were analyzed. Indeed, an energy minimum was only identified for the latter.  (CShM's). [19] The results obtained are collected in Table S1. The polyhedron first depends on the CN, with Pr, Ce and La exhibiting CN=10 (10 vertex polyhedron), Sm and Er featuring CN=9 and Yb displaying CN=8. A good match was found between the X-Ray and the DFT coordination polyhedra for structures with CN of 8 and 9, Yb being described as a biaugmented trigonalprism, Er as a spherical tricapped trigonal prism and Sm as a capped square antiprism. Regarding CN=10, only slight differences were observed between the X-Ray and the DFT polyhedra (Table S1 and Figure S1). In all cases, the maximum possible spin multiplicity was considered. The geometry optimization was performed for all the structures. The energy differences between structures A and B for all the compounds (ΔEAB) are collected on Table 4. It can be seen that with no exception, structure A is favored over B. Thus, the calculations predict that the larger metal has a preference for the site engaging one (O,O) and two (O,N,O) pockets, featuring CN = 10, while the smaller metal accommodates at the position with two (O,O) and one (O,N,O) moieties, with CN = 9. Indeed, ΔEAB is correlated with the difference in ionic radii of both metals, Δr, which is at the root of this selectivity. Since the structure of 3 ([LaYb]) does not incorporate the ligand pyridine, the Yb(III) ion thus exhibiting CN = 8, ΔEAB was also calculated for its real geometry. The stabilization of structure A with no pyridine was found to be 36% higher. This is consistent with the experimental findings, which show that 3 does not incorporate pyridine, despite being the solvent of the reaction. In order to understand the experimental results from the solution studies, optimized structures C and D related to the species detected by ESI-MS were also computed for [LaYb], [CeEr] and [PrSm]; specifically, the moieties [LnLn'(HL)3] (Fig. 6, bottom), which incorporate no terminal ligands. The results show that now the relative stability, ΔE*CD, is much smaller in all cases, resulting in a significantly less pronounced selectivity. All studied ΔE*CD values are marginally positive except for [PrSm] for which the favored arrangement is even reversed, also by a likewise small amount (-1.1 kcal.mol -1 ). The quasi cancelation of the selectivity for this derivative in this configuration is fully consistent with the experimental observations in solution. This corroborates that the effect of metal size in directing the selective disposition of the lanthanide ions within the [LnLn'] species is much more marked for the structure observed in the solid state than that detected in solution, as observed experimentally.   Fig. 6 (kcal·mol -1 ).
[b] Energy difference using the structure seen for this compound by X-ray diffraction, ie. without one pyridine ligand.
[c] Energy difference using structures without terminal ligands as C and D in Fig. 6. [d] Energy of the reaction in Eq. 1 (kcal·mol -1 ).
The energy of formation of all compounds from the corresponding homodimetallic analogues, ΔHform, (Eq. 1) was also calculated.
[ In all cases, the formation of the heterometallic species is favored (Table 4, column 4), with energies that exceed approximately by a factor of five these determined for heterolanthanide coordination helicates. [25] Here, the correlation with Δr is not so clear, therefore, other aspects, relative to the stability of the corresponding homometallic assemblies must also play a role. In any case, the results from all the calculations support the experimental data, since they reflect a clear selectivity and preference for the formation of the heterodimetallic species in the solid state.

Conclusions
In  3 . Data reduction and absorption corrections were performed with SAINT and SADABS, respectively. [38] Both structures were solved by SHELXS [39] and refined by full-matrix least-squares on F 2 with SHELXL-2014. [40] The heterometallic nature of the asymmetric unit in compound 5 is clearly indicated by the worse agreement factors unrealistic relative displacement parameters of an homometallic composition, either La2 or Yb2. For compound 4, the heterometallic composition cannot be confirmed unambiguously on sole basis of the structural data, since replacing Sm by Pr and Pr by Sm does not result in significant modifications of the agreement factors, even though the best situation remains that of the present heterometallic structural model. In both compounds, the relative position of each lanthanide ion is confirmed by the much poorer final agreement factors and worse or even unreasonable relative displacement parameters resulting from inverted relative positions. The Ln−O bond distances, compared to these on the homometallic counterparts confirm also the assignement. All details can be found in CCDC 1520532 (5) and CCDC 1520533 (4) that contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Center via https://summary.ccdc.cam.ac.uk/structure-summary-form. Crystallographic and refinement parameters are summarized in Table S1. Selected bond lengths and angles and intermolecular distances are given in Tables S2 and S3.
Experimental Details. IR spectra were recorded on KBr pellets, in the range 4000-400 cm -1 , with a Thermo Nicolet Avatar 330 FT-IR spectrometer. Elemental analyses were performed with a Perkin-Elmer Series II CHNS/O Analyser 2400 at the Servei de Microanàlisi of the CSIC, Barcelona. Positive ion ESI mass spectrometry experiments were performed on a LC/MSD-TOF (Agilent Technologies) with a dual source equipped with a lock spray for internal reference introduction, at the Unitat d'Espectrometria de Masses (SSR) of the University of Barcelona. The experimental parameters were: capillary voltage 4 kV, gas temperature 325ºC, nebulizing gas pressure 15 psi, drying gas flow 7.0 L min -1 , and fragmentor voltage ranging from 175 to 250 V. internal reference masses were m/z 121.05087 (purine) or 922.00979 (HP-0921). Samples (microlitres) were introduced into the source by a HPLC system (Agilent 1100), using a mixture of H2O/CH3CN (1/1) as eluent (200 μL min -1 ).
Computational Details. Geometries for the calculations were fully optimized using a DFT method by employing the ADF program (Scientific Computing and Modelling ADF-2013.01, http://www.scm.com) The Becke [41] and Perdew [42][43] gradient-corrected exchange and correlation functionals (BP86), respectively, were used in the calculations. The ZORA [44][45] scalar relativistic Hamiltonian was employed with a TZP basis set [44] for the metal atoms, oxygen and nitrogen, and DZP basis set for carbon and hydrogen atoms). The geometry optimizations were performed with the default numerical integration scheme of Becke. [46] Molecular geometries were optimized without constraints. Some counter measures to induce SCF convergence were included, namely level shift (0.15) to induce a HOMO-LUMO gap and strong damping (density mixing step of 0.05). A data set collection of computational results is available in the ioChem-BD repository [47] and can be accessed via http://dx.doi.org/10.19061/iochem-bd-1-22.