Pavel A Dub

Dr Natalia V Belkova

Dr Oleg A Filippov

Prof Jean-Claude Rinaldo Daran

Lina M Epstein

Agustí Lledόs

Elena S Shubina

Rinaldo Poli
email: rinaldo.poli@lcc-toulouse.fr

Dr Mr Pavel Dub

Poli

Prof M Lina

Prof. E S Epstein

A N Shubina

Prof Agustí Lledόs

Solvent-Dependent Dihydrogen/Dihydride Stability for [Mo(CO)(Cp*)H 2 (PMe 3 ) 2 ] + [BF 4 ] -Determined by Multiple Solvent•••Anion•••Cation Non-Covalent Interactions

Keywords:

Low temperature (200K) protonation of compound [Cp*Mo-(PMe 3 ) 2 (CO)H], 1, by Et 2 OꞏHBF 4 yields a different result depending on a subtle solvent change: the dihydrogen complex [Cp*Mo(PMe 3 ) 2 (CO)( 2 -H 2 )] + , 2, is obtained in THF, whereas the tautomeric classical dihydride [Cp*Mo-(PMe 3 ) 2 (CO)(H) 2 ] + , 3, is the only observable product in dichloromethane. Both products were fully characterized (ν CO IR, 1 H, 31 P, 13 C NMR) at low temperature; they loose H 2 upon warming to 230 K at approximately the same rate of ca 10 -3 s -1 (with no detection of the non-classical form in CD 2 Cl 2 ), generating [Cp*Mo(PMe 3 ) 2 (CO)-(FBF 3 )], 4. The latter also slowly decomposes at ambient temperature. One of the decomposition products was crystallized and identified by X-ray crystallography as [Cp*Mo(PMe 3 ) 2 -(CO)(FH•••FBF 3 )], 5, featuring a neutral HF ligand coordinated to a transition metal through the F atom and to the BF 4 - anion through a hydrogen bond. The reason for the switch of relative stability between 2 and 3 was probed by DFT calculations based on the B3LYP and M05-2X functionals, with inclusion of anion and solvent effects through the conductor-like polarizable continuum model (CPCM) and by the explicit consideration of solvent molecules. Calculations at the MP4(SDQ) and CCSD(T) levels on the simplified [CpMo(PH 3 ) 2 (CO)H 2 ] + model were also carried out for calibration. The calculations reveal the key role of non covalent anion-solvent interactions, which modulate the anion-cation interaction ultimately altering the energetic balance between the two isomeric forms.

Introduction

After the discovery of the first isolable transition metal dihydrogen complex by Kubas and co-workers, [1] this important class of coordination compounds spread rapidly into an active field of study. [2] Together with mono-or polyhydride complexes, dihydrogen complexes play an important role in many homogeneous catalytic processes. [3] The most common methods to generate (η 2 -H2)complexes are (a) addition of H2 gas to an unsaturated precursor, (b) ligand displacement by H2 gas, and (c) protonation of a hydride complex, [4] the latter being the simplest and most convenient method. Protonation of neutral hydride compounds most often leads to the kinetically controlled proton addition to a metal hydride, forming either a dihydrogen complex M( 2 -H2), or a cis-dihydride, M(H)2, depending on the nature of the metal and ligands. [5] Recently, the low temperature protonation of [Cp*M(dppe)H] was shown to produce [Cp*M(dppe)( 2 -H2)] + for M = Fe [6] or Ru [7] and [cis-Cp*M(dppe)(H)2] + for M = Os. [8] When a dihydrogen complex M( 2 -H2) is initially formed, its ultimate fate depends on the metal electronic properties: it is stable when the metal has suitable Lewis acidity and  back-bonding ability; it isomerizes to a polyhydride structure if the metal has a strong back-donating power; and it will evolve H2 if there is insufficient back-donation.

When a neutral hydride complex is protonated, the nature of the solvent may be expected to have a profound effect on the outcome through the effects of polarity (defined herein by the dielectric permittivity) and/or the possible establishment of specific interactions (H-bonding) with the neutral solutes (hydride complex, proton donor) or with the proton transfer product. [9] Few previous contributions have specifically addressed solvent effects on the protonation process of neutral hydride complexes. For instance, the low-temperature protonation of [Cp*RuH3(PCy3)] by RFOH (hexafluoroisopropanol or perfluoro-tert-butanol), yielding [Cp*Ru(H)2(η 2 -H2)(PCy3)] + [ORF] -, is assisted by the Freon mixture relative to toluene, because of the dielectric constant increase upon cooling. [10] The protonation kinetics of complex [W3S4(dmpe)3H3] + is also affected by the solvent (MeCN vs. CH2Cl2). [11] The solvent polarity effect on the proton transfer thermodynamics and energy barrier has been shown for the protonation of [CpRuH(CO)(PCy3)] [12] and [Ru(PP3)H2] [13] [PP3 = P(CH2CH2PPh2)3]. For the latter system, the ability of the H-bond donating solvent to interfere with the formation of H-bonds in the [M-H•••H-A] and [M(H2) + •••A -] species was demonstrated. More recently, we have shown that the protonation of Cp*Mo(dppe)H3 by CF3COOH can be directed toward the formation of either [Cp*Mo(dppe)H4] + or [Cp*Mo(dppe)H2(O2CCF3)] depending on the solvent ability to separate the initially formed [Cp*Mo(dppe)H4] + (CF3COO -) contact ion pair. [14] From those studies it is clear that the proton transfer rate and equilibrium position are sensitive to a complex combination of interactions of various nature such as hydrogen bond, ion pair, electrostatic, weak forces etc… The same forces could influence the preference for the classical vs. non-classical isomers, but up to date there is no example of switching such preference depending on the conditions. In the present contribution, we report the first direct observation of a solvent influence on the classical vs non-classical nature of the protonation product and a computational study that rationalizes this phenomenon.

Results (a) Proton transfer to compound 1 at low temperatures

A previously reported room temperature protonation study of complex [Cp*Mo(CO)(PMe3)2H], 1, by RCO2H (R = H, Me, Et) was shown [15] to directly afford Cp*Mo(PMe3)2(CO)(η 1 -O2CR) and H2, presumably via an initial (unobserved) intermediate (η 2 -H2)-complex. We now report our studies of the protonation of 1 by Et2OꞏHBF4 at room and low (193 K) temperatures in solvents possessing close polarity and different coordinating ability (THF and CH2Cl2), using IR (νCO) and NMR ( 1 H, 31 P{ 1 H}, 13 C{ 1 H}) spectroscopic methods. Like many other hydride complexes, 1 is not stable in CH2Cl2 at ambient temperature, slowly undergoing H/Cl exchange (ca. 11% conversion in 26 hours), [16] but this reaction does not take place at any measurable rate at low temperatures, allowing us to carry out low temperature studies in this solvent.

Addition of a stoichiometric amount of Et2OꞏHBF4 to a pale orange solution of 1 in benzene or THF at ambient temperatures yields an immediate color change to deep-purple and gas evolution. The 1 H and 31 P{ 1 H} NMR spectra showed complete consumption of the starting material and formation of new nonhydridic products (no resonances upfield of TMS). When the Et2OꞏHBF4 addition was carried out at 200K in THF-d8, however, the selective formation of the dihydrogen complex [Cp*Mo(CO)(PMe3)2( 2 -H2)] + (2) was observed, see Figure 1. This is suggested by the broad shape of the hydride resonance at -5.14 ppm in the 1 H NMR spectrum and confirmed by the low T1min value of 24 ms at 190K (500 MHz).

Application of the method of Halpern and co-workers gives an H-H distance of 1.1 Å in the slow rotation regime [17] , or 0.88 Å in the fast rotation regime. [18] Other selected NMR and IR properties of this compound can be found in Table 1 together with those of the starting material, whereas the complete characterization is provided as Supporting Information.

A parallel experiment with IR monitoring (νCO-region) showed the growth, after the acid addition, of a new band CO at 1852 cm -1 , attributed to the dihydrogen complex 2 (see Figure 2). The highfrequency shift (Δν = +76 cm -1 ) is in accord with a significant lowering of the M d(π) → CO (pπ*) back-donation upon protonation. [19] Upon raising the temperature to 230 K the hydride resonance in the NMR spectrum gradually disappeared while H2 evolved, as shown by the characteristic 1 H NMR resonance at  4.58. Correspondingly the intensity of the CO(2) band in the IR spectrum decreased, while a new νCO band appeared at 1800 cm -1 . The new compound ( 4) is characterized by a 31 P{ 1 H} NMR resonance at  19.4 and by 1 H NMR resonances at  1.85 for Cp* and 1.48 for the two PMe3 ligands at 230 K in THF-d8. No resonance was observed for this compound in the hydride region. The nature of this product will be addressed in a later section. Quite surprisingly, protonation of 1 with HBF4•Et2O in CD2Cl2 at 200K yielded completely different spectroscopic changes relative to those described above in THF, consistent with formation of the dihydride complex [Cp*Mo(PMe3)2(CO)(H)2] + , 3, see Figure 1 and Table 1. The hydride ligands exhibit only one triplet resonance at  -3.92 with a T1min value of 300 ms at 190K (500 MHz). A parallel IR experiment revealed a νCO band for 3 at 1954 cm -1 , at a much higher frequency (ΔνCO = +203 cm -1 ) relative to 2, in agreement with the formally higher oxidation state in the classical structure. Similar trends in CO shifts upon formation of non-classical and classical -7.00 -6.00 -5.00 -4.00 -7.00 -6.00 -5.00 -4.00

δ/ppm (1) (2) (a) (a) (b) (b) -7
.00 -6.00 -5.00 -4.00 -7.00 -6.00 -5.00 -4.00 -7.00 -6.00 -5.00 -4.00 -7.00 -6.00 -5.00 -4.00 -7.00 -6.00 -5.00 -4.00 -7.00 -6.00 -5.00 -4.00

δ/ppm (1) (2) (a) (a) (b) (b) Compd Solv.  hydride a T1min/ms (T/K)  PMe3 b  CO c νCO/ cm -1
dihydride derivatives were observed for the protonation of Cp*Os(CO)2H. [20] The thermal behaviour of 3 is identical to that of 2: warming the sample to 230 K resulted in H2 evolution (H2 resonance at  4.64) to give 4. The dihydrogen complex -a possible intermediate of the H2 evolution process, was not observed in this solvent. Such a subtle solvent control of the classical/non-classical equilibrium is unprecedented, to the best of our knowledge. The observation of a single hydride resonance for 3 indicates that the compound either adopts a structure with two equivalent hydrides or that they undergo rapid mutual exchange on the NMR time scale. The related compounds [CpMo(PMe3)3H2] + and [Cp*Mo(PMe3)3H2] + display averaged resonances at ambient temperature, which decoalesce at low temperatures, in agreement with structure I (L = PMe3; R = H or Me). [21] Analogous structures were shown by X-ray crystallography for the isoelectronic compounds [CpMo(PMe3)3(MeCN)H] 2+ , [CpW(PMe3)2(CO)H2] + and [(C6H5Me)W(PMe3)3H2] 2+ , [20][21]22] and was also proposed for [CpMo(dppe)(CO)H2] + which, like our complex 3, shows only one hydride resonance at low temperatures. [START_REF]H:  1.81[END_REF] Therefore, we presume that structure I (L = CO; R = Me) is also adopted for compound 3. As will be shown in a later section, the computational work confirms the lower energy of this geometry.

Mo R R R R R L Me 3 P PMe 3 H H I
On the basis of the NMR results alone, one could not conclude that the reaction selectively yields a different product in each solvent, because rapid interconversion (see the theoretical section below for an estimation of the barrier) would result in a single resonance under all circumstances. However, the much faster IR experiment can distinguish isomers with much shorter lifetimes. No observable IR absorption for the nonclassical isomer 2 was observed in the CH2Cl2 experiment (see Supporting Information, Figure S1) and, likewise, no significant IR intensity for the classical isomer 3 was observed in the THF experiment (supplemental Figure S2). Given the signal-to-noise ratio of the IR experiment, we can conservatively estimate that < 5% of 2 is present in the CH2Cl2 solution of 3 (K = [2]/[3] < 0.053) and that < 5% of 3 is present in the THF solution of 2 (K > 24). This corresponds to a relative stability of the two isomers at 200K, on the free energy scale, of > 1.1 kcal mol -1 in favor of 3 in CH2Cl2 and > 1.1 kcal mol -1 in favor of 2 in THF.

Other interesting information was obtained from the 13 C{ 1 H} NMR spectra of the protonation products at 200 K. The CO resonance moves upfield by 8.5 ppm upon transforming 1 to 2, whereas it moves upfield by 23.5 ppm upon transforming 1 to 3. There is a good correlation between the 13 C shifts and CO frequencies for these complexes in both THF and CH2Cl2 (Equation 1, r 2 = 0.999). Such correlations are known for various carbonyl complexes, [24] the 13 C shifts and CO frequencies being function of the ligand substituent properties like e.g. for the complexes with a variety of 4-substituted pyridine ligands cis-Mo(CO)4(py-4-X) [25] and Fe(TPP)(CO)(py-4-X), [26] . The computational investigation was motivated by the desire to understand the origin of the different isomeric preference in closely related solvents. All geometry optimizations were carried out by means of DFT calculations using both the standard B3LYP functional and the recently introduced [27] M05-2X functional. The latter was shown to give better results in studies of noncovalent interactions. [28] The internal geometries of the Mo complexes are quite functionalindependent, the main difference being a systematic shortening of all distances on going from B3LYP to M05-2X [by ca. 0.05 Å for Mo-P, 0.02 Å for Mo-C(Cp), 0.01 Å for Mo-CO and C-O, 0.005 Å for C-C(ring) and C(ring)-CH3]. Comparative structural details for the geometries optimized by the two different functionals are available in the Supporting Information (Tables S1-S4). Additional calculations on selected systems were carried out by MP2 and B3PW91 on the fixed B3LYP geometries (Table S5). The structural parameters henceforth reported refer only to the M05-2X calculations.

( 13 C) = -0.116 CO + 458.34 (1)
Among the two possible isomers of 1 with a cis or trans arrangement of the H and CO ligands, the latter was found more stable (by E g = -6.6 kcal mol -1 ), in agreement with the experimentally suggested geometry. Only this isomer (Figure 3) was therefore considered in further calculations. Optimization of the non-classical complex 2 revealed two isomers having the H2 ligand either parallel (see Figure S3 in the Supporting Information) or perpendicular (Figure 3) to the Cp* ring. The latter is lower in energy by 0.2 kcal mol -1 , but higher by 0.3 kcal mol -1 after ZPVE correction and by 0.6 kcal mol -1 on the free energy scale. Since most of the non-classical complexes optimized in this work (see below) have the H2 ligand perpendicular to the Cp* ring, the perpendicular geometry was used as the reference. The energy minimum for the classical dihydride 3 corresponds to the expected pseudo-octahedral geometry (see I). Other local minima include a second pseudo-octahedral geometry with axial hydride and two cis PMe3 ligands in the equatorial plane (+2.6 kcal mol -1 from I) and pseudo-pentagonal pyramids with either adjacent or non-adjacent PMe3 ligands (+5.4 and +4.1 kcal mol -1 , respectively). [29] The most stable classical geometry of 3 has almost equal energy as the nonclassical isomer 2 in the gas phase (higher by only 1.4 kcal mol -1 ), with a low Mo( 2 -H2) → Mo(H)2

(c) (c) (c) (d) A /cm -1
interconversion barrier (4.3 kcal mol -1 , see the transition state geometry in Figure S4). This low barrier is entirely consistent with the minor rearrangement of the coordination sphere during the isomerization. The proton affinity of the hydride 1 calculated as -H298.15K for the reaction 1 + H + → 2 is 242.6 kcal mol -1 . This gasphase value gives a first indication of the high basicity of the hydride ligand of 1.

The effects of the BF4 counter-anion and solvent on the relative stability of 2 and 3 were evaluated by the explicit inclusion of the counterion as well as one or more solvent molecules, and by inclusion of the polarizability of the medium through the CPCM. The results on the relative energy are summarized in Table 2. The individual formation energies relative to the separate cation, anion and solvent, in gas phase (E g ) and in solution (E solv ) are available in the Supporting Information (Table S6). An analysis of Table 2 immediately reveals that all the chosen models and computational levels do not provide quantitative agreement with the experimental evidence: the DFT methods predict greater stability for the nonclassical isomer under all conditions, except for a slight preference for the classical isomer in the case of the gas phase free cation at the B3PW91 level. The addition of the BF4 -anion, or solvent molecule, or both, whether in the gas phase or in the presence of the appropriate CPCM, increase the relative stability of the nonclassical isomer, including in CH2Cl2 where a preference for the classical structure is shown experimentally. Conversely, the MP2 method overestimates the stability of the classical isomer. However, all calculations indicate a delicate energetic balance between the two isomers. Note that the addition of the solvent, both by the explicit inclusion of solvent molecules in the optimization and by consideration of the CPCM, increases the relative stability of the nonclassical isomer to a greater extent for THF than for CH2Cl2 (for instance the Ion-pairꞏ3CH2Cl2 system shows a 5.9 kcal mol -1 preference for the nonclassical structure, whereas this preference increases to 7.4 kcal mol -1 for the Ion-pairꞏ3THF system).

All CPCM calculations were carried out on the fixed geometries obtained from the gas-phase optimization. The possibility that the CPCM might significantly affect the geometry of the energy minimum was tested by fully reoptimizing the 2BF4 and 3BF4 geometries (only at the M05-2X level) in the presence of the CH2Cl2 and THF CPCM. The internal geometry of the cation was practically unaffected, whereas the cation-anion interactions became slightly looser (slightly longer H•••F and shorter B-F H-bond distances), see Table S4. However, the energy differences in solution were not greatly affected (from +4.9 to +4.9 kcal mol -1 in CH2Cl2; from +4.8 to +4.6 kcal mol -1 in THF). Thus, we wondered whether there may be an inherent bias in favor of the nonclassical structure by the DFT method and in favor of the classical one by MP2.

Geometry optimizations at higher level are prohibitive for this system. Thus, calibration tests were carried out at the MP4(SDQ) and CCSD(T) levels using the MP2 optimized geometries of the [Cp*Mo(CO)(PMe3)2H2] + systems only as free ions in the gas phase, as well as the MP2, B3LYP, B3PW91 and M05-2X levels with full geometry optimization. These calculations yielded the following values for E g (3)-E g (2): +0.1 (B3LYP), -1.0 (B3PW91), +1.3 (M05-2X), -8.4 (MP2), -4.1 (MP4(SDQ)), and -3.7 (CCSD(T)). For this system, the higher-level MP4(SDQ) and CCSD(T) calculations yield essentially identical results, suggesting greater stability for dihydride complex by ca. 3 kcal mol -1 relative to the dihydrogen isomer. This results are half-way between those of the DFT methods, which overestimate the stability of the dihydrogen complex by 4-5 kcal/mol, and that of MP2, which overestimates the stability of the dihydride by the same amount. If we apply this 4-5 kcal/mol correction to the values shown in Table 2, these become in good agreement with the experimental observation. Thus, this calibration test is in agreement with the bias of DFT in favour of the non classical structure and of MP2 in favour of the classical one.

The remainder of this section will focus on a more detailed analysis of the effects introduced by anion and solvent on the structure and energetics properties, giving a clue as to how the solvent operates for switching the cation isomeric preference. The effects of anion and solvent on selected IR spectral parameters (HH, MH and CO) are analyzed in the Supporting Information section (Tables S7 andS8).

Ion-pairing.

Calculations show that in the gas phase, as well as in solution, the ion-pair interaction dominates over the solvent-cation and solvent-anion interactions, in agreement with the presence of the ion-pair in low polarity solvents, rather than the separated solvated ions (formation energies for cation•solvent, anion•solvent and cation•anion are collected in Table S6). The calculations also Table 2. Relative stability of the dihydrogen and dihydride isomers, using different models.

Model

Gas phase a CPCM (CH2Cl2 demonstrate that the presence of the counter-anion modifies significantly the classical-nonclassical equilibrium in favour of the dihydrogen complex (by 4.5 kcal mol -1 at the M05-2X level and by 5.4 kcal mol -1 at the MP2 level in the gas-phase). This effect is probably related to a stronger cation-anion interaction for 2BF4, as suggested by the shorter F•••H contacts (see Figure 4). For both 2BF4 and 3BF4, many of these 4). Bulk solvent effects. Calculations prove that the solvent, described as a continuum, plays a minor role in discriminating the two isomers, as could have been anticipated from the very similar dielectric constant (THF: ε = 7.58; CH2Cl2: ε = 8.93). Both solvents stabilize 2 by 0.7 kcal/mol, while 2BF4 is disfavoured by 1.0 kcal/mol in CH2Cl2 and by 1.1 kcal/mol in THF (M05-2X values). Although the continuum decreases the preference for 2BF4, ion-pairing is still providing greater stabilization to 2. Of course, depending on the relative stability of the two isomers of the isolated cation, the ion-pair formation in solution will reverse or not the energy ordering. However, bulk solvent effects alone are not able to explain the different behaviour in THF and CH2Cl2.

) b CPCM (THF) b M05-2X B3LYP B3PW91 c MP2 c M05-2X B3LYP M05-2X B3LYP cation +1.3(+1.0) +0.1 -1.0 -9

Discrete solvent effects.

The explicit addition of solvent molecule(s) (either CH2Cl2 or THF) to the ion pair model engenders additional non covalent interactions with the anion, solvent•••anion•••cation, rather than with the cation, and involves the solvent C-H bonds as proton donors. Therefore, any effect on the cation stabilization must be indirect, through a modulation of the noncovalent cation-anion interaction through the noncovalent solvent-anion interaction(s). The relative cation-anion orientation is only slightly disturbed by the solvent addition, without significant lengthening the F•••H(C) interactions (see supplementary Tables S3 andS4), whereas the solvent-anion (C)H•••F interactions are significantly longer (by ca. 0.1 Å for CH2Cl2 and by ca. 0.2 for THF) than in the absence of cation (Table S4). No clear trend could be identified in the internal structure of the Mo complexes (classical or nonclassical). Both M05-2X and MP2 calculations show that the interaction of the ion-pair with THF stabilizes 2BF4 (by 1.0 and 2.4 kcal mol -1 at the M05-2X and MP2 levels, respectively). The interaction with CH2Cl2 has less influence in the relative stabilities and works in favour of 3BF4 (by 0.4 and 0.8 kcal mol -1 at the M05-2X levels and MP2 levels). These calculations qualitatively reproduce the experimental trends: dihydrogen complex favoured in THF and classical dihydride in CH2Cl2. The inclusion of three THF molecules provides a relative stabilization of 2.9 kcal mol -1 to 2BF4, whereas three CH2Cl2 molecules only stabilize it by 0.7 kcal/mol. If the cluster formed by the ion-pair and three discrete solvent molecules are solvated with the continuum, the results are only slightly modified.

Concluding this section, the calculations show that ion-paring with the BF4 -counter-anion energetically stabilizes the dihydrogen complex and the theoretical modelling of the specific solute-solvent interactions suggests that the solvent establishes specific F•••H(C) interaction with the anion. The interaction of dichloromethane with the non-classical ion pair, [Cp*Mo(CO)(PMe3)2( 2 -H2)] + BF4 -, destabilizes the cation-anion bonding favoring its isomerization to the dihydride form. On the other hand, the weaker interaction with THF is insufficient to perturb the anion-cation interaction and the nonclassical form remains favoured as in the gas phase. It is arguable that these effects are responsible for the predominance of a different isomer depending on the solvent.

(c) Protonation of compound 1 by CF3COOD.

The protonation of 1 was also investigated in THF-d8 with CF3COOD, the aim of this study being the generation of complex 2-d1 and measuring the 1 JHD value. However, the 1 H and 31 P{ 1 H} NMR spectroscopic monitoring revealed no evidence for the formation of the desired product when using 1 equiv of the acid. The only observable species was compound 1-d as evidenced by an isotopically shifted 31 P{ 1 H} resonance at  32.3 (1:1:1 triplet, 2 JPD = 10 Hz). When the amount of acid was increased to 10 equiv, the relative intensity of the 1-d 31 P{ 1 H} resonance increased, consistent with a greater extent of H/D exchange at the hydride position, but the resonances of 1 in the 1 H and 31 P{ 1 H} spectra did not disappear. In addition, a broad and weak resonance at  -4.5 became visible in the 1 H NMR spectrum (cf. -5.14 for 2BF4). This chemical shift difference can be explained either by a direct counter-ion effect, presumably through hydrogen bonding, Mo(H2)•••X, on the proton chemical shift, or by an effect of X on the classical/nonclassical equilibrium position. Unfortunately, the resonance intensity was not sufficient for an accurate T1 determination.

The lower degree of protonation of 1 by CF3COOD relative to HBF4 can be explained by the lower acid strength of the former acid. However, reversible protonation to 2-d1 occurs to a sufficient extent to allow the H/D exchange process. Other hydride compounds, for instance CpRuHL2 (L2 = dppm, dppe, 2PPh3), have been shown to be protonated by HBF4 and not by other relatively strong acids such as TFA, HCl or HBr in THF. [30] (d) Investigation of the dihydrogen elimination product.

As mentioned above, the dihydrogen elimination from 2 in THF-d8 or 3 in CD2Cl2 occurs above 230 K yielding solutions with very similar spectroscopic properties, see Table 3. When the reaction was carried out in C6D6 at room temperature, the 31 P NMR spectrum showed a major, broader (w1/2 = 10 Hz) peak at  17.5 and a minor sharper one at  15.5 (w1/2 = 4 Hz). When carried out in THF-d8, the broader resonance (w1/2 = 16 Hz) was observed at  18.1 while the sharper one was now split into two separate resonances at  16.8 and 16.7 in a ca. 2:1 ratio (w1/2 = 3 and 4 Hz correspondingly). A THF solution obtained in the same manner showed a visible absorption with a maximum at 510 nm (  2•10 2 M -1 cm -1 ). The decomposition rate estimated from the IR data at 230 K is essentially the same for 2 in THF and 3 in CH2Cl2 (ca. 2ꞏ10 -3 s -1 ), corresponding to an activation free energy G ≠ H2 of 16.2 kcal mol -1 . This value is much lower than that obtained for the H2 loss from [Cp*MoH4(dppe)] + OCOCF3 -, yielding [Cp*Mo(dppe)H2(O2CCF3)] (G ≠ H2 = 22.1 kcal mol -1 at 270 K). [14] ‡ Possibilities envisaged for the structure of the product are either [Cp*Mo(PMe3)2(CO)(L)] + [BF4] -, with L being the solvent (implying that the different donor properties of the two solvents affect the spectroscopic properties of the complex only in a minor way), or [Cp*Mo(PMe3)2(CO)FBF3] where the BF4 -anion has entered the metal coordination sphere. The first hypothesis seems reasonable for THF-d8, which has relatively good coordinating properties, less so for CD2Cl2. However, note that complexes where dichloromethane acts as a ligand have been described. [31] The second hypothesis finds precedent in work by Beck et al., describing the formation of the thermolabile complexes [CpMo(CO)2(PR3)FBF3] (R = Ph, OPh, Et) as the products of the reaction between [CpMoH(CO)2(PR3)] and Ph3C + BF4 -. [32] Note that the protonation of hydride complexes is one of many general methods to access metal complexes of weakly coordinating anions, which are precursors of cationic organometallic Lewis acids. [33] Table 3. Selected spectroscopic data for the product of H2 evolution from 2 in THF-d8 and 3 in CD2Cl2 at 230K. A most enlightening observation comes from the 31 P{ 1 H} resonance of the sample obtained in THF-d8 and especially its coupling pattern, featuring a perfect binomial quintet with J = 8 Hz) at 230 K, see Figure 5, and coalescing into a singlet at room temperature. The only possible way to rationalize this coupling pattern is to invoke P-F scalar coupling and therefore BF4 coordination. However, the observed identical coupling to all F atoms implies a rapid mutual (intramolecular) exchange between the four atoms in the coordination position. This may occur by either an associative or a dissociative mechanism, as shown in Scheme 1. This situation has been previously described for [CpW(CO)2-{P(OPh)3}(FBF3)] [34] and also for complexes containing other weakly coordinating anions, such as [W(CO)3(NO)(PMe3)(FSbF5)]. [35] The product of H2 evolution from either 2 or 3 can therefore be formulated as [Cp*Mo(CO)(PMe3)2(FBF3)] (4). There are numerous crystallographically characterized compounds displaying this coordination mode for the BF4 -ion, mostly with late transition metals. No X-ray structure has so far been reported for mononuclear complexes of Mo II , but related examples for W II include W(CO)3(NO)(PMe3)(FBF3) [36] and WH(CO)3(PCy3)2(FBF3). [37] Contrary to the behavior in THF-d8, the 31 P{ 1 H} resonance is a singlet at all temperatures in CD2Cl2, consistent with a greater extent of dissociation of the ion pair in this solvent, which is expected to better solvate the BF4 -ion through the establishment of F3B-F•••H-CHCl2 hydrogen bonding [13,[START_REF]After inclusion of the BF4counter-anion, these alternative geometries are even higher than the global minimum[END_REF] (see also the computational work on 2BF4•••solvent and 3BF4•••solvent described in section b above). This leads to faster intermolecular anion exchange and consequently loss of P-F coupling. However, the similarity of the CO frequencies of 4 in the two solvents (Table 3) suggests that the major species present in solution also adopts a molecular geometry in CH2Cl2. It is interesting to compare the rate of mutual F exchange of 4 with that of the previously investigated similar compounds, all of which have at least one additional CO ligand in the coordination sphere, [CpM(CO)2(L)(FBF3)]. [32,34,[START_REF] Basallote | [END_REF] They are most typically at the slow exchange limit at low temperatures, revealing the averaged spectrum only in certain cases at room temperature. In our case, no decoalescence nor any sign of line broadening was noticeable down to 190 K. This comparison shows that the BF4 -ligand is much more labile in compound 4, probably for both steric and electronic reasons. The collective behavior of the different compounds appears most consistent with a dissociative exchange mechanism. The shape of this resonance in THF-d8 changes upon warming, becoming a singlet and shifting upfield on going to ambient temperatures (Δ = 1.3 ppm between 230 and 298 K). This behavior evidences the onset of an exchange involving more than one ion pair, probably assisted by solvent coordination as shown in Scheme 1, whereby coupling information between a specific Mo atom and a specific BF4 -group is lost. Again, this is a typical phenomenon already observed for other FBF3 complexes. [33] Thus, the compound exists at low temperatures in THF-d8 as an uncharged molecular species, perhaps in equilibrium with a tight ion pair (the dissociative intermediate of the mutual exchange process), but equilibrates at higher temperatures with increasing amounts of the free ions, allowing the intermolecular exchange, see Scheme 1. Leaving solutions of complex 4, either in THF-d8 or in CD2Cl2, at ambient temperature for extended periods of time resulted in further decomposition: 31 P and 13 C NMR monitoring revealed the formation of several products. Upon attempting to crystallize compound 4 prepared in situ from 1 and 0.5 eq of Et2OHBF4 in toluene at ca. 250 K, violet crystals were obtained. An X-ray analysis shows that this corresponds to [Cp*Mo(PMe3)2(CO)(FH•••FBF3)], 5, namely the coordination position occupied by the BF4 -anion in compound 4 has been replaced by a neutral HF molecule, which then further binds the BF4 -anion through a hydrogen bond.

Selected bond distances and angles for the structure of compound 5 are listed in Table 4. In the structure, each anion makes two short F•••(HF) contacts with two different cations through atoms F(13) and F( 14), while each cation is in close proximity of two different anions, such that the anions and cations are packed in pairs, as shown in Figure 6. Therefore, the proton of the HF ligand must be disordered among two sites, the F1•••F13 and F1•••F14 vectors. The disordered H atom was in fact directly located in both positions, with the intensity data suggesting a 50:50 distribution (see details in the Experimental Section). The other two F atoms of the anion, F(11) and F (12), do not display any contact with neighboring ions shorter than the van der Waals distances. The four B-F bonds are not equivalent, those involved in the hydrogen bond with HF (B(1)-F( 13) and B(1)-F( 14)) being the longest. The structure also contains one molecule of interstitial toluene. The coordination geometry of the cation is a typical four-legged piano stool, with one CO, two PMe3 and an HF molecule as "leg" ligands. The CNT-Mo-L angles are in the narrow 115-122° range. The most interesting structural feature is the hydrogen bonding interaction between the ions. Hydrogen bonds connecting two fluorine atoms in coordination compounds are common when the proton acceptor is metal bound F -, making up the hydrogen bifluoride (FHF) -ligand, crystallographically characterized examples being [M(PMe3)4H2F(FHF)] (M = Mo, W), [40] [Ru(dppe)2F(FHF)], [41] [Ru(PMe3)4H(FHF)], [42] [(COD)Rh(PPh3)(FHF)], [43] and [Pd(Ph)(PPh3)2(FHF)], [44] but we find no precedent in the CSD of an HF ligand bonded to a transition metal with an additional H-bond to BF4 -. In the structures above where the H atom was located, this is placed closer to the dangling F atom than to the metal-coordinated F atom. The structure can therefore be better represented as an HF adduct of a fluorido complex, M-F•••H-F, rather than as a cationic HF complex, [M(F-H)] + •••F -, whereas the disordered H atom in 5 is located closer to the molybdenum bound F atom than to FBF3 (0.96 vs 1.78 Å), allowing this compound to be better described as a cationic HF complex, [Cp*(PMe3)2(CO)Mo(FH)] + •••FBF3 -. The Mo-F distance in 5 is much longer than the typical terminal Mo II -F bond to a fluorido ligand (average of 2.01(4) Å over 9 distances in 7 structures retrieved from the CDS). [45] The above mentioned [Mo(PMe3)4H2F(FHF)] complex also has a shorter Mo-(FHF) distance (2.124(3) Å) than in our compound, because the fluorine atom bonded to Mo has a greater electron density in (FHF) -relative to (FH•••FBF3) -. The closest relative to the arrangement of the HF ligand in the structure of 5 are La(HF)2(AsF5)3, where intermolecular La-(FH)•••(FAsF5)La is observed. [46] It should be mentioned that intramolecular examples of M-(FH)•••B moieties (B = proton acceptor such as the 2-NH2 group of metal-coordinated o-aminopyridine) have also been described, though without structural characterization. [47] Comparison of all these results shows that with a proton acceptor as strong as F -, there is a preference for M-F•••H-F, whereas weaker proton donors (neutral NH2 groups or anionic AsF6 -and BF4 -) lead to In the solid state complex 5 displays a νCO band at 1780 cm -1 , i.e. very close to that of compound 4. Two BF bands appear at 937 and 1018 cm -1 , accompanied by unresolved bands of lower intensity at ca 1106 and 1163 cm -1 , in agreement with the expected lowering of the BF4 -symmetry. A broad band at 3477 cm -1 is assigned to the HF stretching vibration. This value is substantially higher than that of the hydrogen bifluoride ion in its various salts (νHF = 1250-1750 cm -1 ) [48] or in the above mentioned hydrogen bifluoride complexes of transition metals (νHF = 2310-2793 cm -1 ). [40b, 41] On the other hand, it is much lower than the HF stretching mode for free HF in the gas phase (3960 cm -1 ) [49] or weakly bonded HFꞏBF3 complex (3958 cm -1 ), [50] being in agreement with an HF bond elongation with respect to free HF (0.918 Å). [40b]

M-F-H•••B.

Discussion

Examples of tautomeric pairs of classical dihydride and dihydrogen complexes with very similar energy are rather common. [2] In some cases, the energetic preference was shown to switch by a subtle change in the donor/acceptor and steric properties of other ligands. For instance, complex [Mo(R2PCH2CH2PR2)2(CO)H2] is a classical dihydride when R = Et, iBu and a dihydrogen complex when R = Ph, Bz, [51] while complex W(CO)3(PR3)2H2 shows the two tautomeric forms in equilibrium when R = iPr but is present exclusively as the classical dihydride when R = Me. [52] It has been previously shown that the H-H distance in dihydrogen complexes may be very sensitive to intra-and intermolecular interactions, including ion pairing. [53] In one case, a switch was highlighted for the same cationic complex, [Co(PP3)H2] + [PP3 = P(CH2CH2PPh2)3], by a mere change of counter-anion in the solid state: the classical dihydride structure is adopted in the presence of the BPh4 anion, whereas the corresponding PF6 salt reveals a nonclassical dihydrogen structure (though the position of the two H atoms was not located). [54] An NMR study, on the other hand, only reveals the classical structure in solution. [55] The example herein described, with both cation and anion being invariant and a complete switch in solution being caused by a subtle solvent change, appears to be unprecedented.

The overall reaction of 1 with HBF4 may be described as shown in Scheme 2. The first question to address is whether the predominant formation of 2 in THF and 3 in CH2Cl2 has a kinetic or thermodynamic origin. High activation barriers for the interconversion of classical dihydrides and dihydrogen complexes are sometimes observed when the isomerization involves extensive ligand rearrangement. Examples are cis-[Cp*M(dppe)( 2 -H2)] + /trans-[Cp*M(dppe)H2] + (H ‡ = 20.4(8), 20.9(8), and 21.5 (10) kcal mol -1 for M = Fe, [6d] Ru, [7] and Os [56] respectively) and [W(CO)3(PR3)2( 2 -H2)]/[W(CO)3(PR3)2H2] with R = cyclopentyl (G ‡ = 11(2) kcal mol -1 ). [57] Theoretical investigations have shown that the M( 2 -H2)/cis-M(H)2 isomerization has a very small barrier when the rest of the coordination sphere does not undergo significant change. [58] The two hydride ligands in complex 3 occupy cis coordination sites as shown in I, thus the rearrangement to the nonclassical form must involve a very minor rearrangement of the coordination sphere. This proposition is confirmed by DFT calculations. Thus, the nature of the product is determined by thermodynamic factors. This conclusion is also consistent with the lack of observation of 2 during the thermal decomposition of 3 and with the essentially identical decomposition rate for the two isomers at the same temperature. From that rate (ca. 10 -3 s -1 at 230 K), we can derive an activation free energy of 16.5 kcal mol -1 at 230 K for the H2 release process, much larger than the energy barrier for the isomerization process. Thus, the rate limiting step must be the H2 dissociation from 2. If the solvent effect is on the thermodynamics and not on the kinetics, the next question to address is what is the origin of this effect, especially considering that THF and CH2Cl2 possess similar polarity (dielectric permittivity). [59] The relative stability may be quite small, as little as 1.1 kcal mol -1 in favour of 2 in THF and the same amount in favour of 3 in CH2Cl2 (vide supra). A possibility could be based on the ability of THF to establish H-bonding interactions as a proton acceptor with the H2 ligand in 2 (supposedly a stronger acid than 3), whereas dichloromethane rather displays weak proton donating properties and prefers to interact with the BF4 -anion. [13,[START_REF]After inclusion of the BF4counter-anion, these alternative geometries are even higher than the global minimum[END_REF]60] However, the computational work suggests that the cations establish much stronger non covalent interactions with the BF4 counter-anion than with the solvent molecules. Indeed, neither CH2Cl2 nor THF break the [Cp*(PMe3)2(CO)MoH2]BF4 ion pair but merely alter the cation-anion interaction in a rather minor way. Thus, the effect of the solvent on the classical/nonclassical equilibrium energetics can be described as operating through a second-order non covalent interaction: solvent•••anion•••cation. The computational study, especially with the aid of calibrations by high level MP4(SDQ) and CCSD(T) on a simplified model, suggest that the dihydride isomer is inherently more stable than the dihydrogen complex, though by a very small margin, and that the explicit inclusion of anion and solvent molecules tilts the balance in favour of the dihydrogen complex, to a greater extent in THF than in CH2Cl2.

Mo OC Me3P PMe3 H + CH2Cl2 200K Mo OC Me3P PMe3 (H2) Mo OC Me3P PMe3 H H 230K Mo OC Me3P PMe3 F B F F F BF3 Mo OC Me3P PMe3 F Mo OC Me3P PMe3 F H F B F F
The experimental observations reported in this contribution may be compared with previously published protonation reactions of similar compounds, in order to trace the influence of the ligand environment on the nature and stability of the protonation product. Treatment of [CpMo(CO)2(PMe3)H] with Et2O•HBF4 leads to immediate H2 evolution, even at -78°C in poorly coordinating or non coordinating solvents such as ether, toluene, and heptane. [61] In the presence of sufficiently coordinating solvents (for instance, L = MeCN), stable solvent adducts [CpMo(CO)2(PMe3)(L)] + were obtained. The protonation of [CpMo(PMe3)3H] [21a] or [Cp*Mo(PMe3)3H] [21b] with HBF4, on the other hand, leads to stable dihydride products, [(Ring)Mo(PMe3)3H2] + (Ring = Cp or Cp*), showing that the metal center in this compound is sufficiently electron-rich to prevent formation of a ( 2 -H2) complex and H2 evolution. The present results show that an intermediate electronic environment (only one CO ligand and two PMe3 ligands, Cp* in place of Cp) is sufficient to stabilize the primary protonation product -nonclassical hydride 2 at low temperatures in THF, but not sufficient to prevent H2 elimination at higher temperatures.

Bullock has reported a low-temperature NMR study of the protonation of complex [CpMo(dppe)(CO)H], which is electronically very similar to compound 1, with TfOH. The reaction, conducted in CD2Cl2, led to the direct formation of the dihydride product, [CpMo(dppe)(CO)H2] + , without observation of a dihydrogen complex intermediate. [START_REF]H:  1.81[END_REF] This product decomposes with loss of H2 upon warming with formation of [CpMo(dppe)(CO)(OTf)]. Like the latter system, compound 3 also loses H2 upon warming with incorporation of the counter-anion and yields 4 (Scheme 2). It is remarkable, in our opinion, that the metal in this compound prefers to accept the weakly coordinating BF4 -anion rather than a molecule of the THF solvent. Previously described [CpMo(CO)2(PR3)(FBF3)] analogues were apparently always handled in cold CH2Cl2 and the BF4 -ligand was readily substituted by phosphines and olefins, [32] but their behavior in more coordinating solvents does not appear to have been tested. Other compounds containing this and other weakly coordinating anions (PF6, SbF6, CF3SO3, etc.) have been generated in hydrocarbon solvents and the weakly coordinating anions were readily displaced under very mild conditions by a number of neutral donors, including weak ones such as R2O. [33] In the review by Beck and Sünkel, the affinity of [CpM(CO)2(L)] + systems (M = Mo, W; L = tertiary phosphine) for Lewis bases is described as CH2Cl2 < BF4 - < THF. [33] The different trend observed in our case for system [Cp*Mo(CO)(PMe3)2] + may be rationalized on steric grounds, since the metal coordination sphere is more crowded in the present system and THF requires more space in the coordination sphere than FBF3. The formation of complex 5 may be rationalized on the basis of the rupture of the B-F bond with loss of BF3 from compound 4, which is promoted by the Lewis acidity of the Mo atom, followed by trapping of the fluoride intermediate by an additional HBF4 molecule.

Conclusions

The present investigation has shown a striking example of how delicately the ligand environment and the solvent nature control the relative stability of a classical dihydride vs. its isomer dihydrogen complex for the protonation product of (Cp')MoL3H-type molecules. With an electron-rich ligand environment, e.g. Cp' = Cp or Cp* and L3 = (PMe3)3, stable compounds with a classical dihydride structure are obtained. With an electron poor environment, e.g. Cp' = Cp and L3 = (CO)2(PMe3), immediate decomposition occurs at 195 K, probably via a fleeting dihydrogen complex. For compound 1 with intermediate electronic properties, we have shown here for the first time how the reaction can be steered toward the classical or the non classical product by a small change of solvent properties. High level DFT calculations with the inclusion of counter-anion and solvent effects (through the CPCM and also through the explicit introduction of solvent molecules) have revealed intimate details on the organization of the 2BF4 and 3BF4 ion pairs in solution. A solvent regulation of a classical/nonclassical equilibrium with complete switch in solution, where both cation and anion are invariant, appears to be unprecedented. The analysis reported here also unveils that a network of solvent•••anion•••cation non covalent interactions is responsible for a dramatic change in the cation nature, showing the steering role of specific solute-solvent interactions.

Experimental Section

General. All manipulations were carried out under an argon atmosphere. All solvents were dried over appropriate drying agent (Na/benzophenone for toluene and THF; CaH2 for dichloromethane) and freshly distilled under an argon atmosphere prior to use. C6D6 and toluene-d8 (Euriso-Top) were kept over molecular sieves and deoxygenated with an argon flow before use. CD2Cl2 and THF-d8 (Euriso-Top) were degassed by three freezepump-thaw cycles, then purified by vacuum transfer at room temperature. Compound [Cp*Mo(CO)(PMe3)2H] was synthesized according to the literature procedure. [15] Et2OHBF4 (56%, Sigma Aldrich) was used as received.

Instrumentation. Room temperature NMR investigations were carried out on Bruker DPX300 and AV300LiQ spectrometers operating at 300.1 MHz ( 1 H), 121.49 MHz ( 31 P { 1 H}) and 75.47 MHz ( 13 C{ 1 H}). Low-temperature 1 H, 31 P{ 1 H} and 13 C{ 1 H} data were collected with a Bruker AV500 spectrometer, operating at 500.3, 202.5 and 125.8 MHz, respectively. The temperature was calibrated using a methanol chemical shift thermometer; the accuracy and stability was ±1 K. All samples were allowed to equilibrate at every temperature for at least 3 min. The spectra were calibrated with the residual solvent resonance relative to TMS ( 1 H, 13 C), and with external 85% H3PO4 ( 31 P). The conventional inversion-recovery-pulse method (180-τ-90) was used to determine the variable-temperature longitudinal relaxation time T1, the calculations being done with standard Bruker software. The IR spectra were recorded on PerkinElmer Spectrum 100 FT-IR (2.0 cm -1 resolution), Specord M-82 (4.0 cm -1 resolution) and FT Infralum-801 (2.0 cm -1 resolution) spectrometers; 0.12 or 0.04 cm cells were used for solutions.

In situ generation of compound 2 and subsequent thermal decomposition. In a 5 mm NMR tube was added compound 1 (10 mg, 0.024 mmol) followed by THF-d8 (0.6 mL). After cooling to 200 K, a 56% ether solution of HBF4 (3 L, 0.70 equiv from NMR integration) was added by microsyringe and the reaction was monitored directly by NMR probe.

In a separate experiment, the same reaction [5 mg (0.012 mmol) of 1 and ca. 1.5 L (ca. 0.012 mmol) of the HBF4 ether solution] was carried out in regular THF (1 mL) in a Schenk tube and the resulting solution was transferred by cannula into the IR cell inside a precooled cryostat, and monitored by IR spectroscopy in the CO region.

In situ generation of compound 3 and subsequent thermal decomposition. This experiment was run by an identical protocol as the previous one, using 10 mg (0.024 mmol) of 1 in 0.6 mL of CD2Cl2 and 3 L (0.78 equiv from integration) of the HBF4 ether solution.

In a separate experiment, the same reaction [5 mg (0.012 mmol) of 1 and ca. 1.5 L (ca. 0.012 mmol) of the HBF4 ether solution] was carried out in CH2Cl2 (1 mL) in a Schenk tube and the resulting solution was transferred by cannula into the IR cell inside a precooled cryostat, and monitored by IR spectroscopy in the CO region.

Generation of compound 5. To a solution of compound 1 (30 mg, 0.07 mmol) in toluene (1 mL) was added a 56% ether solution of HBF4 (ca. 4.5 L, ca. 0.035 mmol) by microsyringe at room temperature. A pentane layer (ca. 0.5 mL) was subsequently placed on top of the solution, which was set at -20°C. A few crystals of compound 5 formed in two days. The amount was only sufficient to record an IR spectrum and for an X-ray structural analysis. IR (neat/cm -1 ): 1780 s (CO), 1091 m, 1030 m, 1004 m, 936 s (BF4 -).

X-Ray Analysis of Compound 5.

A single crystal was mounted under inert perfluoropolyether at the tip of a glass fibre and cooled in the cryostream of an Oxford-Diffraction XCALIBUR CCD diffractometer. Data were collected using the monochromatic MoK radiation (= 0.71073). The structure was solved by direct methods (SIR97) [62] and refined by least-squares procedures on F 2 using SHELXL-97. [63] All H atoms attached to carbon were introduced in calculation in idealised positions and treated as riding on their parent atoms. The two positions of the disordered H atom attached to F1 were located in the difference Fourier map and refined first using restraints (F-H= 0.94(1) Å), then treated as riding on the F atom during the last stages of refinement with Uiso= 1.2Ueq (F). There is one well behaved toluene solvate molecule per asymmetric unit. The drawing of the molecule was realised with the help of ORTEP32. [64] Crystal data and refinement parameters are shown in Table 5. Crystallographic data (excluding structure factors) have been deposited with the Cambridge Crystallographic Data Centre as supplementary publication no. CCDC 714915. Copies of the data can be obtained free of charge on application to the Director, CCDC, 12 Union Road, Cambridge CB2 1EZ, UK (fax: (+44) 1223-336-033; e-mail: deposit@ccdc.cam.ac.uk).

Computational details. All calculations were performed at the DFT level, by means of the M05-2X functional [27] as well as the hybrid B3LYP functional, [65] as implemented in Gaussian03. [66] The optimizations of the dihydrogen/dihydride cations, the ion pairs with the BF4 -counter-anion, and the adducts containing one solvent molecule were also performed at the DFT/B3PW91 and MP2 levels. The MP4(SDQ) and CCSD(T) methods were used for single-point calculations at the MP2-optimized geometry of the model [CpMo(CO)(PH3)2H2] + complexes. The basis set for the Mo and P atoms was that associated with the pseudopotential [67] with a standard double-ζ LANL2DZ contraction, [66] supplemented in the case of P with a set of d-polarization functions. [68] The 6-31G(d) basis set was used for C atoms of Cp* ring and CH2Cl2 as well as for B and F atoms of BF4. The 6-31++G(d,p) basis set was used for the CO group, the hydride ligands, the O atom of THF, the CH2Cl2 chlorine atoms and the acidic H atoms of HBF4 and CH2Cl2. The 6-31G basis set was used for all other atoms. The structures of the reactants, intermediates, transition states, and products were fully optimized without any symmetry restriction. Transition states were identified by having one imaginary frequency in the Hessian matrix. No scaling factor was applied to the calculated frequencies since the optimization was run in the gas phase and the IR spectra were measured in solution. The average ratio between experimental and calculated CO values is ca 0.95. Non-specific solvent effects were introduced through CPCM (conductor-like polarizable continuum model) representation of the solvent by single-point calculations [69] on gas phase optimized geometries for dichloromethane (ε = 8.93) and THF (ε = 7.58). The ΔE solv and ΔG solv values have been obtained adding the contribution of the free energy of solvation to the gas-phase potential energy and gas phase free energy, respectively. [70] Specific solvent effects in the ion pairs were considered by introducing discrete solvent molecules (either CH2Cl2 or THF) to solvate the BF4 anion of the ion pair. To generate good starting points for the optimization of the solvated ion-pairs the most stable conformation of the solvated free BF4 anion was initially investigated. Then the arrangement of the solvent molecules found was introduced in the most stable conformations of the ion-pairs and the system was fully optimised. reference [71] .

Figure 1 . 1 H

 11 Figure 1. 1 H NMR (500 MHz) spectra in THF-d8 (1) or CD2Cl2 (2) of: (a) compound 1 alone; (b) compound 1 in the presence of slightly less than 1 equiv of Et2OꞏHBF4. [1] = 0.04 M; T = 200 K.

a 1 H

 1 NMR, multiplicity and JHP/Hz in parentheses. b 31 P{ 1 H} NMR, multiplicity in parentheses. c 13 C{ 1 H} NMR, multiplicity and JCP/Hz in parentheses. d In toluene-d8. e No information on the multiplicity could be obtained.

Figure 2 .

 2 Figure 2. IR spectra in the CO region of compound 1 in THF (C = 1.2ꞏ10 -2 M, l = 0.4 mm, 4 cm -1 resolution): (a) alone, at 200K; (b) in the presence of ca. 1 eq HBF4•Et2O, at 200K; (c) after warming to 230K (ca. 10 min after spectrum b); (d) 3 min after (c).

( b )

 b Theoretical study of the factors affecting the dihydrogendihydride equilibrium in the [Cp*Mo(CO)(PMe3)2H2] + system.

Figure 3 .

 3 Figure 3. View of the M05-2X optimized geometries for complexes 1, 2 and 3.

Figure 4 .

 4 Figure 4. View of the M05-2X optimized geometries for the ion pairs 2BF4 and 3BF4.

Figure 5 .

 5 Figure 5. Enlargement of the 31 P{ 1 H} NMR resonance for the compound obtained from the decomposition of 2 in THF-d8 at 230K.

  Scheme 1.

  and characterization of an HF complex.

Figure 6 .

 6 Figure 6. An ORTEP view of the molecular geometry of compound [Cp*Mo(PMe3)2-(CO)(FH•••FBF3)], 5, with the atom-labelling scheme showing the formation of a pseudodimer through F-H•••F hydrogen bonds. Displacement ellipsoids are drawn at the 30% probability level and the disordered H atoms are represented as small spheres of arbitrary radius. Symmetry code: ( i ) 1-x, 1-y, 1-z.

Table 4 .

 4 Selected bond distances (Å) and angles (deg) for compound [Cp*Mo(PMe3)2(CO)(FH•••FBF3)], 5. a

  Scheme 2

Table 1 .

 1 Selected NMR and IR data for compounds 1

, 2 and 3 at 200K.

Table 5

 5 Only the average values are given for chemically equivalent parameters. [b] From

	. Crystal [Cp*Mo(PMe3)2(CO)(FH•••FBF3)]•C6H5CH3, 5. a data and structure	refinement	for
	Empirical formula	C24 H42 B F5 Mo O P2
	Formula weight	610.27
	Crystal colour, habit	dark violet, box
	Crystal size (mm)	0.54 x 0.32 x 0.16

Acknowledgements

Support of this work through two bilateral programs (France-Russia: PICS grant 2004-07, continuing within the framework of a GDRE (groupe de recherche européen) 2008-11; France-Spain: LEA-CTPMM) is gratefully acknowledged. Additional national support was obtained in France from the CNRS, the IUF, and the CICT (project CALMIP), in Russia from the RFBR (08-03-00464), the Division of Chemistry and Material Sciences of RAS and the Russian Federation President grant (МК-380.2008.3) and in Spain from MICINN (projects CTQ2008-06669-C02-01 and Consolider Ingenio 2010 CSD2007-00006). OAF thanks INTAS for an individual YSF grant (№06-1000014-5809). Thanks are also expressed to Dr. Y. Coppel (LCC CNRS) for assistance with the low temperature NMR measurements.

Supporting Information available

Complete spectroscopic data for compounds 2, 3, 4. Low-T IR spectra in CH2Cl2 and THF. Tables and Figures of the DFT results. Cartesian coordinates of all optimized structures.


Pegdwendé Etienne Scholly
email: etienne.scholly@bial-x.com

Nicolas Sawadogo

Pengfei Liu
email: pengfei.liu@eric.univ-lyon2.fr

Javier Alfonso Espinosa-Oviedo

Cécile Favre
email: cecile.favre@univ-lyon2.fr

Sabine Loudcher
email: sabine.loudcher@univ-lyon2.fr

Jérôme Darmont
email: jerome.darmont@univ-lyon2.fr

Camille Noûs
email: camille.nous@cogitamus.fr

Étienne Scholly

Pegdwendé N Sawadogo
email: pegdwende.sawadogo@univ-lyon2.fr

Coining goldMEDAL: A New Contribution to Data Lake Generic Metadata Modeling

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

While the big data revolution has shaken up the entire field of data management and analytics, new concepts have emerged to meet these new challenges. Data lakes belong to such new concepts. First introduced by James Dixon, a data lake is a vast repository of raw and heterogeneous data from which various analyses can be performed [START_REF] Dixon | Pentaho, Hadoop, and Data Lakes[END_REF]. Data lakes quickly gained popularity and several teams started to address research issues [START_REF] Madera | The next information architecture evolution: the data lake wave[END_REF][START_REF] Miloslavskaya | Big Data, Fast Data and Data Lake Concepts[END_REF]. A key one is efficient metadata management for avoiding data lakes to turn into unexploitable data swamps [START_REF] Inmon | Data Lake Architecture: Designing the Data Lake and avoiding the garbage dump[END_REF][START_REF] Phyu | Data Lake: A New Ideology in Big Data Era[END_REF][START_REF] Quix | Data Lake. Encyclopedia of Big Data Technologies[END_REF][START_REF] Sawadogo | On data lake architectures and metadata management[END_REF][START_REF] Suriarachchi | Crossing Analytics Systems: A Case for Integrated Provenance in Data Lakes[END_REF].

However, most metadata management proposals in the literature [START_REF] Beheshti | CoreKG: A Knowledge Lake Service[END_REF][START_REF] Hai | Constance: An Intelligent Data Lake System[END_REF][START_REF] Mehmood | Implementing Big Data Lake for Heterogeneous Data Sources[END_REF], and their associated implementations, give few details on the way data are conceptually organized and are thence hardly reusable. Thus, other researchers proposed more theoretical approaches named metadata models. Such approaches aim to provide detailed guidelines to metadata system design, while being generic, i.e., flexible and adaptable to many use cases. Yet, data lake generic metadata modeling is still an open research issue. A feature-based assessment indeed shows that none of the existing metadata models is generic enough, including our own MEtadata model for DAta Lakes (MEDAL) [START_REF] Pegdwendé N Sawadogo | Metadata systems for data lakes: models and features[END_REF].

To address this genericity issue, we introduce goldMEDAL, a revision of our MEDAL model. We define goldMEDAL through a classical three-level modeling process (i.e., conceptual, logical and physical). We choose a formal representation to avoid ambiguity but also provide a UML representation for readability. The logical level is a translation of the concepts using graph theory. Eventually, we describe three different physical models as proofs of concept. Furthermore, to highlight goldMEDAL's genericity, we show that the concepts of our metadata model help model state-of-the-art metadata models from the literature.

The remainder of this paper is organised as follows. Section 2 reviews and discusses existing data lake metadata models. Section 3 presents goldMEDAL's conceptual and logical models. Section 4 illustrates how goldMEDAL generalises other data lake metadata models and how it can be used to implement different data lakes. Finally, Section 5 concludes this paper and hints at future research.

Metadata Models for Data Lakes

GEMMS (Generic and Extensible Metadata Management System) is a pioneer generic metadata model for data lakes [START_REF] Quix | Metadata Extraction and Management in Data Lakes With GEMMS[END_REF]. GEMMS features two abstract entities: data file and data unit. A data file represents a generic data source. A data unit represents an identifiable data element inside a data source. Each data file is composed of a set of data units (e.g., a spreadsheet file is composed of a set of sheets). Data files and data units can be enriched with atomic or complex metadata values. However, GEMMS requires information on data structure to operate. Thus, making it unsuitable for working with unstructured data.

Ground is another generic metadata model [START_REF] Hellerstein | Ground: A Data Context Service[END_REF] that can be used for modeling metadata in data lakes (although not specifically designed for that). Ground tracks data context (metadata) at three levels: 1) metadata properties, 2) data usage history and 3) data versioning. Although more extensive than GEMMS, Ground (as well as GEMMS) does not take in charge data linkage even though this type of metadata has been identified as relevant in data lakes [START_REF] Farrugia | Towards Social Network Analytics for Understanding and Managing Enterprise Data Lakes[END_REF][START_REF] Pegdwendé N Sawadogo | Metadata systems for data lakes: models and features[END_REF].

Based on GEMMS' data file and data units concepts, The model of Diamantini et al. adds similarity links between data units to indirectly link data files [START_REF] Diamantini | A New Metadata Model to Uniformly Handle Heterogeneous Data Lake Sources[END_REF]. However, their model does not include important metadata such as data versioning and usage tracking as compared to Ground.

Similar to Diamantini et al., Ravat and Zhao propose a model where each data file can be associated with atomic and complex metadata [START_REF] Ravat | Metadata management for data lakes[END_REF], including metadata properties, data history and links with other data files. The main contribution of this model is the notion of zone metadata. Many data lake architectures consider the existence of zones (e.g., raw data zone, processed data zone) [START_REF] Giebler | Leveraging the Data Lake -Current State and Challenges[END_REF][START_REF] Ravat | Metadata management for data lakes[END_REF]. Zone metadata specifies the zones where data is located. However, Ravat and Zhao's model cannot simultaneously represent different data granularity levels as previous models do [START_REF] Diamantini | A New Metadata Model to Uniformly Handle Heterogeneous Data Lake Sources[END_REF][START_REF] Quix | Metadata Extraction and Management in Data Lakes With GEMMS[END_REF].

MEDAL represents data through three main concepts: data objects, representations and versions [START_REF] Pegdwendé N Sawadogo | Metadata systems for data lakes: models and features[END_REF]. Data objects correspond to GEMMS' data files. Representations correspond to the result of transformed objects. Versions represent objects updates. Both, representations and versions, are materialized in the data lake. Thus, MEDAL gives alternative ways to track data linkage and zone metadata through the concepts of versions and representations, respectively. MEDAL also supports linkage metadata through categorizations and similarity links. However, MEDAL does not support multiple data granularity levels either.

Finally, HANDLE (Handling metAdata maNagement in Data LakEs), uses the generic concept of data entity to represent both, data files and parts of data files, which helps HANDLE support any granularity level [START_REF] Eichler | HANDLE-A Generic Metadata Model for Data Lakes[END_REF]. In HANDLE, each data entity is associated with tags that represent zones, granularity levels or categorizations. HANDLE can also connect data entities together through containment links (e.g., between a table and a tuple). HANDLE provides concepts that subsume most of the concepts of the previous metadata models.

Genericity of Metadata Models

A generic metadata model should adapt to any data lake use case. As each use case requires specific metadata management features, we consider that the most abundant features a metadata model supports, the most generic it is. Therefore, features are a suitable way to compare metadata models.

To the best of our knowledge, there exist two feature-based comparisons of data lake metadata models in the literature. We introduced six relevant features: semantic enrichment, data indexing, data polymorphism, data versioning, link generation and usage tracking [START_REF] Pegdwendé N Sawadogo | Metadata systems for data lakes: models and features[END_REF]; while Eichler et al. identified three other features: metadata properties, zone metadata and the support of multiple granularity levels [START_REF] Eichler | HANDLE-A Generic Metadata Model for Data Lakes[END_REF].

Considering that both the above sets of features are relevant, we propose to combine them for comparing the genericity of metadata models. Beyond simply unioning features, we merge data polymorphism with zone metadata, as these features both refer to the same concept. We also split link generation in two new features, namely similarity links and categorization, because some metadata models support only one of them. Eventually, we omit data indexing in this comparison, considering that indexing does not actually induce metadata modeling issues. Although indexing is definitely relevant to assess metadata systems [START_REF] Pegdwendé N Sawadogo | Metadata systems for data lakes: models and features[END_REF], this feature seems less suited to metadata models.

All in all, we obtain a list of eight features that can serve to compare data lake metadata models and evaluate their genericity.

(1) Semantic enrichment (2) Data polymorphism/multiple zones (3) Data versioning (4) Usage tracking (5) Categorization (6) Similarity links [START_REF] Giebler | Leveraging the Data Lake -Current State and Challenges[END_REF] Metadata properties (8) Multiple granularity levels Table 1 highlights the features supported by all the models reviewed in Section 2.1. It shows that none of them support all the features we identify.

GOLDMEDAL METADATA MODEL

Section 2.1 establishes that, of the eight criteria used to compare data lake metadata models, none ticked all the boxes. In this section, we thoroughly describe goldMEDAL, a substantial evolution of MEDAL that generalizes its concepts while addressing all the features identified in Section 2.2.

A metadata model can be expressed "in the form of an explicit schema, a formal definition, or a textual description" [START_REF] Eichler | HANDLE-A Generic Metadata Model for Data Lakes[END_REF]. In this paper, we choose a formal approach for the sake of precision. Yet, for the sake of readability and communication with possibly non-computer scientists, we also provide a semi-formal UML model. Moreover, we use a conventional data modeling approach that leverages a conceptual, a logical and a physical model, to demonstrate the actual implementation process of our metadata model.

Section 3.1 presents goldMEDAL's formal and semi-formal conceptual models. Section 3.2 details the translation of goldMEDAL's concepts into a logical, graph-based model. For the sake of clarity, the examples we use are the same examples in both sections, i.e., examples at the conceptual level are translated at the logical level. Eventually, example physical models, i.e., metadata models actually implemented in data lakes with goldMEDAL, are presented in Section 4.2.

Conceptual Model

In MEDAL, data items were considered either as raw data, or as versions or representations derived from raw data. The concepts of version and representation were used to express updated and transformed data, respectively. While modeling metadata for Accordingly, we also generalized in goldMEDAL:

• update and transformation operations that served to track the lineage of representations and versions, respectively, as well as parenthood relationships that express fusion operations, into the concept of process; • similarity links into the global concept of link. Eventually, we retained in goldMEDAL the MEDAL concept of grouping, which notably allows multiple data granularity levels.

All the main goldMEDAL concepts (data entity, grouping, link and process) are characterized by attributes or properties that constitute their internal metadata.

3.1.1 Data Entity. Data entities are the basic units of our metadata model. They are flexible in terms of data granularity. For example, a data entity can represent a spreadsheet file, a textual or semi-structured document, an image, a database table, a tuple or an entire database. The introduction of any new element in the data lake leads to the creation of a new data entity. Definition 3.1. The set of data entities is denoted E = {𝑒 𝑖 } 𝑖 ∈N * .

Grouping.

A grouping is a set of groups; a group brings together data entities based on common properties. For example, the raw and preprocessed data zones common in data lake architectures are the groups of a zone grouping. Another example is a grouping of textual documents according to the language of writing.

Definition 3.2. The set of groupings is denoted G = {𝐺 𝑗 } 𝑗 ∈N * , with 𝐺 𝑗 = {Γ 𝑗𝑘 } 𝑘 ∈N * and Γ 𝑗𝑘 ⊆ E is a group. Example 3.3. To get back to our previous examples, G = {𝐺 1 , 𝐺 2 }. 𝐺 1 = {Γ 11 , Γ 12 }
is the zone grouping, with Γ 11 and Γ 12 being the raw data and processed data zones, respectively. 𝐺 2 = {Γ 21 , Γ 22 } is the language grouping, with Γ 21 and Γ 22 the groups corresponding to French and English languages, respectively. Note that the groupings 𝐺 𝑗 are deliberately not partitions of E. Thus, a bilingual French-English document can belong to both groups Γ 21 and Γ 22 .

3.1.3 Link. Links are used to associate either data entities with each other or groups of data entities with each other. They can be oriented or not. They allow the expression of, e.g., simple similarity links between data entities or hierarchies between groups. For example, a temporal hierarchy month → quarter would have the months of January, February and March linked to the first quarter of a given year.

Definition 3.4. The set of links is denoted L = {𝑙 𝑚 } 𝑚 ∈N * , with either:

• 𝑙 𝑚 : E → E, • 𝑙 𝑚 : 𝐺 𝑗 → 𝐺 𝑗 ′ and 𝑗 ≠ 𝑗 ′ .
Example 3.5. Let us elaborate the sample hierarchy month → quarter. Let 𝐺 3 = {𝐽𝑎𝑛, 𝐹𝑒𝑏, ..., 𝐷𝑒𝑐} a grouping of data entities per month and 𝐺 4 = {𝑄1, 𝑄2, 𝑄3, 𝑄4} be a grouping of quarters in a year. Now, let us make explicit some data entities and their groups:

𝐽𝑎𝑛 = {𝑒 1 , 𝑒 2 }, 𝐹𝑒𝑣 = {𝑒 3 }, 𝑀𝑎𝑟 = {𝑒 4 }; 𝑄1 = {𝑒 1 , 𝑒 2 , 𝑒 3 , 𝑒 4 }.
Link 𝑙 1 materializes the hierarchical link between groups 𝐺 3 and 𝐺 4 :

𝐽𝑎𝑛 -→ 𝑙 1 𝑄1, 𝐹𝑒𝑏 -→ 𝑙 1 𝑄1, 𝑀𝑎𝑟 -→ 𝑙 1 𝑄1. Inversely, 𝑄1 --→ 𝑙 -1 1 {𝐽𝑎𝑛, 𝐹𝑒𝑏, 𝑀𝑎𝑟 }.
A functional notation may also be used:

𝑙 1 (𝐽𝑎𝑛) = 𝑄1, 𝑙 1 (𝐹𝑒𝑏) = 𝑄1, 𝑙 1 (𝑀𝑎𝑟 ) = 𝑄1, 𝑙 -1 1 (𝑄1) = {𝐽𝑎𝑛, 𝐹𝑒𝑏, 𝑀𝑎𝑟 }. Also note that 𝑄1 = 𝐽𝑎𝑛 ∪ 𝐹𝑒𝑏 ∪ 𝑀𝑎𝑟 .
3.1.4 Process. A process refers to any transformation applied to a set of data entities that produces a new set of data entities. Definition 3.6. The set of processes is denoted P = {𝑃 𝑛 } 𝑛 ∈N * , with 𝑃 𝑛 = {𝐼 𝑛 , 𝑂 𝑛 }, 𝐼 𝑛 ⊆ E the set of input data entities of 𝑃 𝑛 and 𝑂 𝑛 the set of output data entities that is integrated into E (E ← E ∪ 𝑂 𝑛 ). Eventually, although they are not depicted in Figure 1, all classes and association classes bear attributes that model metadata properties. These attributes may be of any type, including lists, and of course vary with respect to use cases.

Logical Model

As MEDAL and HANDLE did, though at the physical level, we choose to design goldMEDAL's logical model as a graph, which is Thus, in this section, we translate the concepts defined in Section 3.1 into graph nodes, edges and hyperedges, using the same indices, e.g., 𝑖, 𝑗, 𝑘... Moreover, we illustrate the translation with the examples used at the conceptual level. Finally, we also propose a graphic illustration of goldMEDAL's logical model. Example 3.9. A PDF file stored in the data lake can be represented by a node 𝑛 1 . • an edge, oriented or not, connecting two nodes. Then, 𝑎 𝑚 = (𝑛 𝑖 , 𝑛 𝑖 ′ ) ∈ N 2 ; • an oriented edge connecting two hyperedges. Then, 𝑎 𝑚 = (𝜃 𝑗𝑘 , 𝜃 𝑗 ′ 𝑘 ′ ) ∈ 𝐻 𝑗 × 𝐻 𝑗 ′ . In both cases, the edge carries attributes. Example 3.12 is depicted on the left-hand side of Figure 2. Groups of 𝐻 1 are colored in purple, while 𝐻 2 's are blue. We can see that 𝑛 1 and 𝑛 3 belong to the raw data group 𝜃 11 , while 𝑛 2 and 𝑛 4 are in the processed data group 𝜃 12 . Moreover, 𝑛 1 , 𝑛 2 and 𝑛 3 are in the French language group 𝜃 21 , and 𝑛 4 is in the English language group 𝜃 22 .

Translation of

Example 3.14 is represented at the center of Figure 2. Groups of 𝐻 3 , namely 𝜃 𝐽 𝑎𝑛 , ..., 𝜃 𝐷𝑒𝑐 are colored in green and groups of 𝐻 4 (𝜃 𝑄1 , ..., 𝜃 𝑄4 ) are colored in grey. Hyperedge 𝑎 1 connects groups of 𝐻 3 to 𝐻 4 's.

Finally, Example 3.16 is depicted on the right-hand side of Figure 2. 𝑛 5 is a textual document split in fragments 𝑛 6 , 𝑛 7 and 𝑛 8 . Π 1 's input and output Υ 1 and Ω 1 , respectively, are colored in yellow.

GOLDMEDAL ASSESSMENT

In this section, we discuss goldMEDAL's genericity. To this end, we show in Section 4.1 that all three most complete metadata models can be modeled with goldMEDAL. In Section 4.2, we present our ongoing implementation work of goldMEDAL on distinct use cases.

Comparison of State-of-the-Art Metadata Models with goldMEDAL

To evaluate goldMEDAL's genericity, we compare it with the three metadata models that are both the most recent and the most complete among metadata models, i.e., MEDAL, Ravat and Zhao's and HANDLE (Section 2.2).

For each comparison, we use a two-column table. The first column lists goldMEDAL's concepts, and the second column the corresponding concepts of the compared model. When any concept does not have an equivalent, it is marked with "-". Note that we do not mention in this comparison global metadata existing in MEDAL. We indeed consider that elements such as logs or indexes mostly induce implementation rather than metadata modeling issues.

MEDAL vs. goldMEDAL. goldMEDAL's four main concepts help generalize all of MEDAL's concepts (Table 2). Data entity generalizes the concepts of version and representation. Grouping generalizes the concepts of object and grouping (in

Yet, other forms of global metadata, namely semantic resources such as thesauruses and ontologies, can definitely be modeled with goldMEDAL using the node, grouping and link concepts.

4.1.2 Ravat and Zhao's Metadata Model vs. goldMEDAL. gold-MEDAL can handle nearly all concepts of Ravat and Zhao's metadata model [START_REF] Ravat | Metadata management for data lakes[END_REF] (Table 3). Data entity generalizes the concept of dataset and all its subclasses, such as Datalake_Datasets or Source _Datasets. Grouping generalizes the concepts of keyword. Finally, link and process directly correspond to relationship and process, respectively. 4). Data entity generalizes both data and metadata, since a data entity is a representation of data that also contains metadata properties. Grouping generalizes three concepts: Categorization, ZoneIndicator, and Granulari-tyIndicator. Finally, process has no direct match in HANDLE, although its authors show processes can be modeled through Action metadata instances of HANDLE's categorization extension [START_REF] Eichler | HANDLE-A Generic Metadata Model for Data Lakes[END_REF]. Handling multiple granularity levels as in HANDLE was not supported by MEDAL, so it was a design objective for goldMEDAL. Although there is no explicit granularity indicator in goldMEDAL, any data entity could have a granularity property. However, there is more efficient way by defining data entities on the finest possible granularity level. Then, coarser granularity levels are obtained with groupings. For example, if each data entity corresponds to a tuple in a relational database, then a grouping represent a set of tables.

goldMEDAL Physical Models

To show that goldMEDAL can model different business issues and manage various functionalities while remaining as simple as possible, we apply our metadata model to three different use cases. We also exemplify how goldMEDAL's logical model (Section 3.2) can be translated into different physical models.

Public

Housing Data Lake. For social landlords (agents or agencies providing social housing), the use of data is nothing new, whether through business intelligence for patrimony management or with data science methods for non-payment forecasting. However, landlords are facing two main problems. On the one hand, their analyses are conducted separately: in different environments, by different individuals and with different tools. This implies that collaborative work on the same data is impossible. On the other hand, landlords know how to use their data, but have much more difficulty capturing and exploiting "external" data. Yet their dwellings are located in environments with their own characteristics (transportation, climate, employment rate, education, etc.), which affect the attractiveness of the dwellings. Being able to combine this external information with landlords' data would be a real asset for understanding their patrimony.

A data lake can store both "internal" data from social landlords as well as "external" data gathered on the Internet. In addition, all types of analyses can be carried out from the data lake.

HOUDAL (public HOUsing DAta Lake). The data lake implemented for social landlords [START_REF] Scholly | Business Intelligence & Analytics Applied to Public Housing[END_REF] is based on a Web application, and thus is composed of two major parts: the front-end (or client part) is the user interface for depositing new data, for creating new metadata and for consulting existing metadata; the backend (or server part) features various services such as an API, the metadata system, data storage, and a user management service. HOUDAL Metadata System. goldMEDAL's metadata model has been implemented into the Neo4J graph database management system 1 . Since Neo4J does not allow to have hyperedges, we create a node for each concept. Thus, entities, groups, groupings, links and processes translate as nodes, each bearing a label and attributes.

Data entities. The different data files that populate the data lake are data entities. They can be either raw data files sent by landlords (often in comma separated value files) or reworked data, sometimes stored in various formats such as .pkl or .RData, for Python and R analyses, respectively. Each data entity has its node labeled :ENTITY and the entity's properties, such as file name or description, are stored in the node's attributes.

Groupings for Categorizing Data Entities. With HOUDAL, users can create as many groupings as necessary, and several groups for each grouping. Data entities can be linked to zero, one or several groups for each grouping. In Neo4J, groupings are modeled by nodes carrying a :GROUPING label. Groups are also nodes, carrying both a :GROUP label and the grouping's name as a second label, in order to facilitate querying. A data entity node (resp. group node) is linked to a group node (resp. grouping node) with an edge labeled with the grouping's name (resp. :GROUPING). With groups and groupings, users can, for example, determine whether it is internal or external data, or the data refinement level (zones), and so on.

Processes for Tracking Data Lineage. Like other goldMEDAL concepts, a process is also modeled by a node in Neo4J, bearing the :PROCESS label. A process can be a script for transforming or cleaning a data file, i.e., a data entity. If a data entity is the input of a process, there is an edge labeled :PROCESS_IN from the entity node to the process node. Inversely, an edge labeled :PROCESS_OUT from the process node to the entity node is created if a new data entity is generated by the process.

Example. Figure 3 presents a sample of metadata stored in Neo4J. Data entity nodes are colored in red. On both sides of the 1 https://neo4j.com figure, a data entity node is highlighted: some of its attributes are depicted at the bottom in grey.

The left-hand side of Figure 3 gives an example of groupings. There are three groupings: a zone grouping, a format grouping and a granularity grouping. Each grouping has its group nodes, colored in green, purple and blue, respectively. Data entity nodes are connected to group nodes with an edge. For example, we can see that the highlighted data entity node (on the left) is a raw .csv file, and the granularity level is "Tenant", meaning that each line corresponds to a tenant. Note that in Neo4J, groupings are also modeled as nodes, but are not represented in this Figure .  An example of process is depicted on the right-hand side of Figure 3. The process node is colored in yellow. We can see that three data entity nodes are the process' input, and three data entity nodes are the process' output, meaning that they are generated by the process.

HOUDAL is operational and is currently being tested by social landlords. Nevertheless, we have many areas for improvement to work on, to make the application more robust and more userfriendly. In addition, we continue to discuss with social landlords to identify new needs, which could be the subject of future work to add a new feature to our data lake.

4.2.2

Textual and Tabular Data Lake. The AUDAL data lake is motivated by researchers in management science who want to analyze the effect of servicization (i.e., the transition from supplying products to supplying services) and digitization on small and medium sized companies' economic performance [START_REF] Darmont | Data Lakes for Digital Humanities[END_REF]. Source data are various textual documents (annual reports, press releases, websites, social media posts) and spreadsheet files featuring qualitative (e.g., stocks) and qualitative (e.g., degree of servicization) characteristics.

Metadata Management in AUDAL. AUDAL's metadata system is architectured in three levels. The first level manages data entities. Data entities, i.e., textual documents and spreadsheet tables, are categorized as raw and refined. Raw tables or documents are actually pointers to the corresponding files in their original format. Raw data entities store metadata properties, in the form of Neo4J node attributes, e.g., file author(s), date of creation, etc. Refined data entities are automatically generated from raw data entities. They are transformed so as to be exploited in analyses. More concretely, raw textual documents are refined into bag-of-word vectors or document embedding vectors stored in the MongoDB document-oriented database management system 2 , and referenced from Neo4J nodes (Figure 4). Similarly, raw spreadsheet tables are refined in relational tables to benefit from SQL querying.

The second level in AUDAL's metadata system handles relationships between data items. We use two kinds of relationships in accordance with goldMEDAL concepts: groupings and (similarity) links. Some of the groupings relate to both tabular and textual data, e.g., groupings on the MIME type or data source. Conversely, others are relevant for only one type of data, e.g., the grouping on the language of documents. We materialize groupings in Neo4J through a set of nodes. Each grouping is a simple node with which all associated groups are linked. Then, groups are in turn linked to the corresponding data entities.

We define two types of links with respect to the type of data they relate to. Document similarity links express how much 4) actually represent some automatically detected functional dependencies between columns from different tables. In Neo4J, table joinability edges are oriented.

Eventually, our model's third level is constituted of metadata used to speed up or enhance analyses. It includes indexes that allow and speed up keyword-based search on textual documents as well as spreadsheet files. These indexes are managed by Elas-ticSearch 3 . Moreover, AUDAL's metadata system also includes semantic resources, i.e., dictionaries and thesaurus. Such resources, stored in MongoDB, allow amongst other automatic query extension.

Analyses with AUDAL. AUDAL allows both data retrieval and content analyses. Data retrieval works in three different ways. The first way exploits indexes to allow term-based queries. It is effective for both textual documents and tabular data. AUDAL also provides navigation as a solution to discover data of interest. This is done by intersecting groups from different groupings. For example, such queries allow finding data from a specific source and created on a specified year. Finally, data can be retrieved using relatedness, starting from a specified data object and then finding the most related data, namely similar documents or joinable tables.

Content analyses are actually a way to aggregate data. In the case of textual documents, such analyses include document clustering or scoring with respect to a set of keywords and text concordance. Tabular data are exploited through SQL queries, the clustering of table rows and correlation analyses between columns.

4.2.3

Archaeological Data Lake. This data lake was designed during the course of the multidisciplinary project "Hyper thesaurus and data lakes: Mine the city and its archaeological archives" (HyperThesau) [START_REF] Darmont | Data Lakes for Digital Humanities[END_REF][START_REF] Liu | Metadata model for an archeological data lake[END_REF]. Let us name it ArchaeoDAL, in echo to HOUDAL and AUDAL, though it was actually never called so.

Archaeological data may bear many different types, e.g., textual documents (excavation reports), images (photographs, drawings, plans...), sensor data, chemical analysis results, etc. Even structured data are often produced by various devices that are not compatible with each other. Moreover, the description of an archaeological object also differs with respect to users, usages and time. Thus, archaeologists use semantic resources such as thesauruses to interoperate data from various origins.

Physical Model of Data Entities. The implementation of Ar-chaeoDAL heavily relies on the Apache ecosystem. In particular, its metadata system rests on the Atlas4 data governance and metadata framework. Atlas' objects match with goldMEDAL's data entities. In addition to metadata properties (in the form of keyvalue pairs), objects may also relate to terms from thesauruses, i.e., goldMEDAL links, and classifications, i.e., goldMEDAL groupings (Figure 5).

Moreover, we exploit Atlas' object types to fulfill domainspecific requirements regarding metadata properties. For example, in the HyperThesau project, users need not only semantic metadata to understand data contents, but also geographical metadata to know where archaeological objects were discovered. The benefits of having an object type system include:

• consistency: a universal definition of metadata can avoid terminological variations that may cause data retrieval problems; • flexibility: a domain-specific type system helps define specific metadata for requirements in each use case; • efficiency: with a given metadata type system, it is easy to write and implement search queries. Because names and types of all metadata properties are known in advance, we can filter data with metadata predicates such as 𝑢𝑝𝑙𝑜𝑎𝑑_𝑑𝑎𝑡𝑒 > '10/02/2016'.

Physical Model of Processes. Atlas also includes a nice lineage feature that helps visualize chains of processes. For instance, Figure 6 represents a simple ingestion process of raw data stored in HDFS into a Hive table, where objects are symbolized by blue hexagons and the process by a green hexagon. category but no subcategory. A term may have relationships (i.e., goldMEDAL links) with other terms, e.g., related words, synonyms, antonyms, etc. Note that it would be easy to represent ontologies or taxonomies, too.

Eventually, we add specific links between data nodes associated with term nodes from the thesaurus. The left-hand side of Figure 7 displays an excerpt of the thesaurus. Figure 7 also shows how a term (arme défensive, i.e., defensive weapon) points to the corresponding metadata (short and long descriptions) and related terms.

CONCLUSION

In this paper, we introduced goldMEDAL, a generic data lake metadata model. goldMEDAL is based on four main concepts: data entity, grouping, link and process, which are defined at the conceptual and logical levels. These concepts interact altogether to support data lake metadata management requirements and they generalize almost all the concepts proposed in stateof-the-art metadata models : the concept of grouping supports the organization of data lakes in zones [START_REF] Ravat | Metadata management for data lakes[END_REF]; groupings allow managing multiple data granularity levels as in HANDLE [START_REF] Eichler | HANDLE-A Generic Metadata Model for Data Lakes[END_REF].

Moreover, goldMEDAL supports all the features identified to compare data lake metadata models (Section 2.2), making it the most generic metadata model to the best of our knowledge.

Another particularity of goldMEDAL is the explicit possibility of data lineage tracing with the concept of process. goldMEDAL thus manages the dynamics of data, while the most recent metadata model from the literature, HANDLE [START_REF] Eichler | HANDLE-A Generic Metadata Model for Data Lakes[END_REF], does not natively support it.

Eventually, we show as a proof of concept how goldMEDAL can be translated from conceptual and logical models to actual physical models with three different implementations of metadata models from distinct data lakes that feature both structured and unstructured data.

Future research and open issues include the "industrialization" of data lakes, i.e., providing a software layer, connected to the metadata system, which allows non-data or non-computer scientists to transform and analyze their own data in autonomy, just as dynamic reports are prepared on top of data warehouses for the use of business (i.e, non technical) users. However, such a software layer must not become yet another black box. In consequence, we must take great care of accompanying users in their appropriation of our analysis tools, not only by training, but also by interweaving research methodologies from computer science with business practices by design, in close collaboration with the partners.

Moreover, exploiting a data lake and its metadata system may contribute to open data and open science. A well-designed data lake should indeed readily enforce the four FAIR principles 5 , i.e., findability, accessibility, interoperability and reusability. By adding an industrialization layer that allows non-data or noncomputer scientist exploit the data lake, we can further improve accessibility in a non-technical way, i.e., not only through suitable communication protocols. FAIR principles are very appealing to researchers in humanities and social sciences, as illustrated by AUDAL (management sciences; Section 4.2.2) and ArchaeoDAL (archaeology; Section 4.2.3).

Finally, to the best of our knowledge, the maintenance of data lake metadata is a completely open issue. For instance, how to manage a new categorization of metadata? How to change or transform the metadata system when it hits some limits, whether technical or functional? What if metadata become big in the sense of voluminous big data? Should obsolete data be deleted, which is contrary to the principle of data lakes, and how to ensure that the metadata accessibility FAIR principle remains enforced when source data are no longer available?

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  2021 Copyright held by the owner/author(s). Published in Proceedings of the 24th International Conference on Extending Database Technology (EDBT), March 23-26, 2021, ISBN 978-3-89318-084-4 on OpenProceedings.org. Distribution of this paper is permitted under the terms of the Creative Commons license CC-by-nc-nd 4.0.

Example 3 . 7 .

 37 Process 𝑃 1 splits a set of textual documents 𝐷 ⊆ E into a set of text fragments 𝐹 ⊆ E. Here, 𝐼 1 = 𝐷 and 𝑂 1 = 𝐹 .

3. 1

 1 .5 UML model.

  Figure 1 features goldMEDAL's conceptual model as a UML class diagram. All the concepts of goldMEDAL, including group, are modeled as classes (data entity, grouping, group and process) or association classes (entity link and group link, which are labeled E-Link and G-Link in Figure 1, respectively).

Figure 1 :

 1 Figure 1: UML class diagram of goldMEDAL

3. 2 . 1

 21 Translation of Data Entity. Data entities are modeled by nodes that carry attributes. Definition 3.8. The set of nodes is denoted N = {𝑛 𝑖 } 𝑖 ∈N * . Each node 𝑛 𝑖 ∈ N carries attributes.

Example 3 . 14 . 1 𝜃 1 𝜃 1 𝜃 1 1{𝜃

 3141111 To get back to the sample hierarchy month → quarters from Example 3.5, 𝐻 3 = {𝜃 𝐽 𝑎𝑛 , 𝜃 𝐹𝑒𝑏 , ..., 𝜃 𝐷𝑒𝑐 } is a set of hyperedges representing a grouping of data entities per month. 𝐻 4 = {𝜃 𝑄1 , 𝜃 𝑄2 , 𝜃 𝑄3 , 𝜃 𝑄4 } is a set of hyperedges representing the grouping of quarters in a year. Let us make this explicit with instances. 𝜃 𝐽 𝑎𝑛 = {𝑛 1 , 𝑛 2 }, 𝜃 𝐹𝑒𝑣 = {𝑛 3 }, 𝜃 𝑀𝑎𝑟 = {𝑛 4 }; 𝜃 𝑇 1 = {𝑛 1 , 𝑛 2 , 𝑛 3 , 𝑛 4 }. Edge 𝑎 1 materializes the hierarchical link between 𝐻 3 and 𝐻 4 : 𝜃 𝐽 𝑎𝑛 --→ 𝑎 𝑄1 , 𝜃 𝐹𝑒𝑏 --→ 𝑎 𝑄1 , 𝜃 𝑀𝑎𝑟 --→ 𝑎 𝑄1 . Inversely, 𝜃 𝑄1 ---→ 𝑎 -𝐽 𝑎𝑛 , 𝜃 𝐹𝑒𝑏 , 𝜃 𝑀𝑎𝑟 }.

3. 2 . 4

 24 Translation of Process. A process is modeled by an oriented hyperedge. Definition 3.15. The set of oriented hyperedges modeling processes is denoted Q = {Π 𝑛 } 𝑛 ∈N * , with Π 𝑛 = {Υ 𝑛 , Ω 𝑛 }, Υ 𝑛 ⊆ N being the set of input nodes of Π 𝑛 and Ω 𝑛 the a set of output nodes integrated to N (N ← N ∪ Ω 𝑛 ). Any Π 𝑛 carries attributes. Example 3.16. Π 1 = {Υ 1 , Ω 1 } is an oriented hyperedge representing the process of splitting a set of textual documents (Example 3.7) represented by the set of nodes 𝑁 𝐷 ⊆ N , into a set of text fragments represented by the set of nodes 𝑁 𝐹 ⊆ N . Then, Υ 1 = 𝑁 𝐷 and Ω 1 = 𝑁 𝐹 . 3.2.5 Sample Graph Representation.

  Figure 2 provides a schematic representation of the examples above. Let us introduce eight data entity nodes {𝑛 𝑖 } 𝑖 ∈ [1,8] colored in orange.

Figure 2 :

 2 Figure 2: Sample goldMEDAL graph logical model

Figure 3 :

 3 Figure 3: HOUDAL sample Neo4J metadata

Figure 4 :

 4 Figure 4: AUDAL sample Neo4J metadata

Figure 5 :

 5 Figure 5: Sample Atlas object

Figure 6 :

 6 Figure 6: Sample Atlas lineage

Figure 7 :

 7 Figure 7: Sample Atlas thesaurus

Table 1 :

 1 Features supported by data lake metadata models Features ↓ \ Models → GEMMS Ground Diamantini et al. Ravat & Zhao MEDAL HANDLE goldMEDAL

	Semantic enrichment	✓	✓	✓	✓	✓	✓	✓
	Polymorphism/multiple zones			✓	✓	✓	✓	✓
	Data versioning		✓		✓	✓		✓
	Usage tracking		✓		✓	✓	✓	✓
	Categorization	✓	✓		✓	✓	✓	✓
	Similarity links			✓	✓	✓	✓	✓
	Metadata properties	✓	✓		✓	✓	✓	✓
	Multiple granularity levels	✓		✓			✓	✓
	Total	4/8	5/8	4/8	7/8	7/8	7/8	8/8
	various data lakes, we found that more data items were possible,
	e.g.

, temporal representations. Thus, we decided to generalize any such concepts into a global concept named data entity in goldMEDAL.

  Grouping. A group is represented by a non-oriented hyperedge, i.e., an edge that can link more than two nodes. A grouping is modeled by a set of hyperedges. Definition 3.10. A hyperedge (a group) is denoted 𝜃 𝑗𝑘 ⊆ N , with 𝑗, 𝑘 ∈ N * . Any 𝜃 𝑗𝑘 carries attributes. Definition 3.11. The set of hyperedges of grouping 𝑗 is denoted 𝐻 𝑗 = {𝜃 𝑗𝑘 } and carries attributes. The set of hyperedge sets (set of groupings) is denoted H . Example 3.12. Let us translate Example 3.3. H = {𝐻 1 , 𝐻 2 }. 𝐻 1 = {𝜃 11 , 𝜃 12 } is the set of hyperedges representing the zone grouping, with 𝜃 11 and 𝜃 12 the hyperedges representing the raw data and processed data zones, respectively. 𝐻 2 = {𝜃 21 , 𝜃 22 } is the set of hyperedges representing the language grouping, with 𝜃 21 and 𝜃 22 the hyperedges representing the groups corresponding to French and English languages, respectively. Definition 3.13. The set of edges is denoted A = {𝑎 𝑚 } 𝑚 ∈N * , with any 𝑎 𝑚 being either:

	3.2.3 Translation of Link. Links may model relationships be-
	tween either data entities (nodes) or groups (hyperedges). They
	are modeled by edges.

Table 2 :

 2 goldMEDAL and MEDAL concepts

	goldMEDAL MEDAL
	Data entity	Version, Representation
	Grouping	Object, Grouping
	Link	Similarity link
	Process	Update, Transformation,
		Parenthood relationship

Table 3 :

 3 Ravat and Zhao's metadata model, namely user and access, have no explicit equivalent in goldMEDAL, though they could be classified as global metadata. Users and accesses can indeed be modeled as data entities and processes, respectively.

	goldMEDAL and Ravat & Zhao concepts
	goldMEDAL Ravat & Zhao
	Data entity	Dataset, Subclass
	Grouping	Keyword
	Link	Relationship
	Process	Process
	-	User, Access
	However, two concepts of

4.1.3 HANDLE vs. goldMEDAL. goldMEDAL can also generalize HANDLE's concepts (Table

Table 4 :

 4

	goldMEDAL and HANDLE concepts
	goldMEDAL HANDLE
	Data entity	Data, Metadata
	Grouping	Categorization, ZoneIndicator
		GranularityIndicator
	Link	Link
	Process	-

  Table joinability links. Such links (labeled PK_FK_LINK in Figure

https://www.mongodb.com

https://www.elastic.co

https://atlas.apache.org

https://www.go-fair.org/fair-principles/

https://www.bial-x.com/

ACKNOWLEDGEMENTS

E. Scholly's PhD is funded by BIAL-X 6 . P.N. Sawadogo's PhD is funded by the Auvergne-Rhône-Alpes Region through the