Rationalizing the Reactivity of Mixed Allyl Rare-Earth Borohydride Complexes with DFT Studies

: The reactivity of rare-earth complexes RE(BH 4 ) 2 (C 3 H 5 )(THF) x (RE = La, Nd, Sm, Y, Sc) toward the Ring-Opening Polymerization (ROP) of ε -caprolactone ( ε -CL) was rationalized by Density Functional Theory (DFT) calculations. Even if the polymerization reaction can be initiated by both RE-(BH 4 ) and RE-allyl bonds, experimental investigations have shown that the initiation via the borohydride ligand was favored, as no allyl group could be detected at the chain-end of the resulting polymers. DFT studies could conﬁrm these observations, as it was highlighted that even if the activation barriers are both accessible, the allyl group is not active for the ROP of ε -CL due to the formation of a highly stable intermediate that disfavors the subsequent ring-opening.

On the other hand, several studies have dealt with the ROP of cyclic esters initiated by rare-earth allyl complexes [16][17][18][19], where the polymer chain end-group is expected to be of the allyl type.
By using the mixed allyl-borohydride RE(BH 4 ) 2 (C 3 H 5 )(THF) x complexes as initiators of lactone or lactide ROP, the polymerization may proceed either via allyl or borohydride initiation, as shown in Scheme 1.
Such a behavior of dual initiation ability is rather scarce in the literature. To our knowledge, one unique example to mention regarding the ROP of cyclic esters is the work of Okuda et al., who recently [20] showed that when the mixed alkyl-borohydride complex [Y(Me)(BH4)(thf)5][BPh4] (synthesized in [21]) is used as the initiator, the ROP of ε-CL can be promoted by either the borohydride or the methyl ligand, with comparable occurrences, based on DFT calculations. By replacing in silico the BH4 by a dimethylamido ligand (thus considering the [Y(Me)(NMe2)(thf)5] + cation), the initiation is computed to take place preferentially through the methyl group and in a more facile way. This was attributed to a trans effect.
In our case, we could establish that the borohydride ligand initiates the polymerization at the expense of the allyl ligand, thanks to the 1 H NMR analysis of intentionally prepared low Mn polylactides that display signals relative to dihydroxytelechelic-or aldehyde-terminated macromolecules. Moreover, no allyl signals could be detected as the end-groups on these polymers, which excludes the occurrence of the initiation of the polymerization reaction via the Ln-allyl bond.
These results could be confirmed by Maldi-ToF analysis of low molecular weight polylactides, displaying a major population of aldehyde-terminated polylactide for the polymer synthesized with the neodymium complex and a major population of dihydroxytelechelic polylactide for the one synthesized with the yttrium analog, while no allyl-terminated polylactide could be observed in either case (see Figures S1 and S2). Another minor population of methoxy-terminated polylactide could be observed in both cases, which was attributed to the opening of cyclic polylactide by methanol when the reaction was quenched with the alcohol.
In order to tentatively rationalize this peculiar reactivity due to the presence of two possibly reactive groups on the same metal, we conducted a study in the form of a two-pronged approach. First, we explored the reactivity of such mixed allyl-borohydride complexes toward small molecules by 1 H NMR monitoring in order to observe, or not, a preference for the reactivity of one or the other ligand, and tentatively confirm, or not, the features observed in our experimental results of the ROP of cyclic esters. Second, a theoretical study was undertaken by means of Density Functional Theory (DFT) methods in order to weigh up each of the possibilities of reactivity and to deduce, or not, an understanding of the facts observed on an experimental scale.
Such a behavior of dual initiation ability is rather scarce in the literature. To our knowledge, one unique example to mention regarding the ROP of cyclic esters is the work of Okuda et al., who recently [20] showed that when the mixed alkyl-borohydride complex [Y(Me)(BH 4 )(thf) 5 ][BPh 4 ] (synthesized in [21]) is used as the initiator, the ROP of ε-CL can be promoted by either the borohydride or the methyl ligand, with comparable occurrences, based on DFT calculations. By replacing in silico the BH 4 by a dimethylamido ligand (thus considering the [Y(Me)(NMe 2 )(thf) 5 ] + cation), the initiation is computed to take place preferentially through the methyl group and in a more facile way. This was attributed to a trans effect.
In our case, we could establish that the borohydride ligand initiates the polymerization at the expense of the allyl ligand, thanks to the 1 H NMR analysis of intentionally prepared low M n polylactides that display signals relative to dihydroxytelechelic-or aldehyde-terminated macromolecules. Moreover, no allyl signals could be detected as the end-groups on these polymers, which excludes the occurrence of the initiation of the polymerization reaction via the Ln-allyl bond.
These results could be confirmed by Maldi-ToF analysis of low molecular weight polylactides, displaying a major population of aldehyde-terminated polylactide for the polymer synthesized with the neodymium complex and a major population of dihydroxytelechelic polylactide for the one synthesized with the yttrium analog, while no allyl-terminated polylactide could be observed in either case (see Figures S1 and S2). Another minor population of methoxy-terminated polylactide could be observed in both cases, which was attributed to the opening of cyclic polylactide by methanol when the reaction was quenched with the alcohol.
In order to tentatively rationalize this peculiar reactivity due to the presence of two possibly reactive groups on the same metal, we conducted a study in the form of a two-pronged approach. First, we explored the reactivity of such mixed allyl-borohydride complexes toward small molecules by 1 H NMR monitoring in order to observe, or not, a preference for the reactivity of one or the other ligand, and tentatively confirm, or not, the features observed in our experimental results of the ROP of cyclic esters. Second, a theoretical study was undertaken by means of Density Functional Theory (DFT) methods in order to weigh up each of the possibilities of reactivity and to deduce, or not, an understanding of the facts observed on an experimental scale.

1 H NMR Monitoring Experiments
The reactions of the mixed allyl-borohydride complexes with benzophenone, tetramethyl-and tetramethylethylcyclopentadiene, dimethylanilinium tetraphenylborate and phenylsilane (Scheme 2) were monitored by 1 H NMR. The idea was to see which of the two reactivities, allyl or borohydride, if any, was taking place. To this end, we selected this set of small substrates for which the reactivity was already known for each of these functionalities.
Catalysts 2020, 10, x FOR PEER REVIEW 3 of 10 were monitored by 1 H NMR. The idea was to see which of the two reactivities, allyl or borohydride, if any, was taking place. To this end, we selected this set of small substrates for which the reactivity was already known for each of these functionalities. It is known that benzophenone can insert into an RE-allyl bond, as previously shown by Okuda et al. [22]. On the other hand, a ketone is also able to insert into an RE-borohydride bond to give the corresponding alkoxide [23]. By adding one equiv. of Ph2CO to a THF-D8 solution of RE(BH4)2(C3H5)(THF)x (RE = La, Y, Sc), we found by 1 H NMR that benzophenone reacts exclusively with the RE-(allyl) moiety, leading to the corresponding allyldiphenylalkoxide compound (Scheme 2, path a). Furthermore, the addition of one equivalent of substituted cyclopentadiene (C5Me4RH, R = H or Et) to Nd(BH4)2(C3H5)(THF)x afforded the immediate formation of the corresponding halfsandwich of the formula (C5Me4R)Nd(BH4)2 (Scheme 2, path b) [24], as unambiguously observed by 1 [25,26]. These two latter examples show that the allyl group is also more reactive than the borohydride one toward protic reagents. Finally, we checked that upon the addition of one equiv. of phenylsilane (d), the allyl signal of Nd(BH4)2(C3H5)(THF)x disappears while the borohydride resonances are maintained, even though the residual compound is not identified.
Clearly, this set of experiments allows the conclusion that, toward small-molecule insertion or acid/base reactions, the allyl group in the mixed Nd(BH4)2(C3H5)(THF)x compounds is more reactive than the borohydride, in sharp contrast to the reactivity observed in ring-opening polymerization. This prompted us to perform Density Functional Theory (DFT) calculations of the reaction mechanisms in order to shed light onto the reactivity difference between the borohydride and the allyl as active ligands for the ROP of ε-CL.

DFT Studies
For the sake of clarity, the study of the ROP of ε-CL mediated by the active ligands is separately analyzed in the following sections. The initiation step involving the allyl group is first discussed, followed by the initiation mediated by the borohydride ligands. Finally, the first propagation step is also investigated. The enthalpy profiles computed for the initiation step of the ROP of ε-CL with both It is known that benzophenone can insert into an RE-allyl bond, as previously shown by Okuda et al. [22]. On the other hand, a ketone is also able to insert into an RE-borohydride bond to give the corresponding alkoxide [23]. By adding one equiv. of Ph 2 CO to a THF-D 8 solution of RE(BH 4 ) 2 (C 3 H 5 )(THF) x (RE = La, Y, Sc), we found by 1 H NMR that benzophenone reacts exclusively with the RE-(allyl) moiety, leading to the corresponding allyldiphenylalkoxide compound (Scheme 2, path a). Furthermore, the addition of one equivalent of substituted cyclopentadiene (C 5 Me 4 RH, R = H or Et) to Nd(BH 4 ) 2 (C 3 H 5 )(THF) x afforded the immediate formation of the corresponding half-sandwich of the formula (C 5 Me 4 R)Nd(BH 4 ) 2 (Scheme 2, path b) [24], as unambiguously observed by 1 H NMR monitoring in C 6 D 6 . The reaction of Nd(BH 4 ) 2 (C 3 H 5 )(THF) x with one equiv. of [HNMe 2 Ph][B(C 6 F 5 ) 4 ] in THF-D 8 gave the already reported [Nd(BH 4 ) 2 ][B(C 6 F 5 ) 4 ] cationic species (Scheme 2, path c) [25,26]. These two latter examples show that the allyl group is also more reactive than the borohydride one toward protic reagents. Finally, we checked that upon the addition of one equiv. of phenylsilane (d), the allyl signal of Nd(BH 4 ) 2 (C 3 H 5 )(THF) x disappears while the borohydride resonances are maintained, even though the residual compound is not identified.
Clearly, this set of experiments allows the conclusion that, toward small-molecule insertion or acid/base reactions, the allyl group in the mixed Nd(BH 4 ) 2 (C 3 H 5 )(THF) x compounds is more reactive than the borohydride, in sharp contrast to the reactivity observed in ring-opening polymerization. This prompted us to perform Density Functional Theory (DFT) calculations of the reaction mechanisms in order to shed light onto the reactivity difference between the borohydride and the allyl as active ligands for the ROP of ε-CL.

DFT Studies
For the sake of clarity, the study of the ROP of ε-CL mediated by the active ligands is separately analyzed in the following sections. The initiation step involving the allyl group is first discussed, followed by the initiation mediated by the borohydride ligands. Finally, the first propagation step is also investigated. The enthalpy profiles computed for the initiation step of the ROP of ε-CL with both initiator ligands are presented in Figure 1.

Allyl Initiation
On the allyl side, the ROP reaction proceeds via a coordination/insertion mechanism. Thus, the reaction begins by the formation of an endothermic ε-CL adduct, A al (6.4 kcal·mol −1 with respect to the entrance channel). In this adduct, one of the THF molecules in the cis position, with respect to the allyl group, is replaced by ε-CL. The endothermicity of this adduct can be explained by the fact that ε-CL interacts with the metal center through its two oxygen atoms (exocyclic and endocyclic), forcing an η 3 to η 1 hapticity change of the allyl group. This adduct leads to a kinetically accessible transition state, which corresponds to the nucleophilic attack of the allyl group onto the carbonyl carbon of ε-CL, lying only 8.2 kcal·mol −1 above the separated reactants (1.8 kcal·mol −1 above the adduct). This transition state leads to a very stable intermediate, B al , located at −25.3 kcal mol −1 with respect to the separated reactants. It is interesting to note that, in this intermediate, the ε-CL ring remains closed (C-O distance of 1.495 Å ), and the lanthanum atom is still interacting with two THF molecules and the two η 3 -borohydride ligands. This system evolves to the acyl-oxygen bond cleavage transition state, i.e., the ring-opening, with a barrier of 9.7 kcal·mol −1 with respect to the previous intermediate (− 15.6 kcal·mol −1 with respect to the separated reactants). This step corresponds to the rate-limiting step of the ROP initiation reaction of ε-CL mediated by the allyl ligand. This transition state leads to a final endothermic product (+5.1 kcal·mol −1 ) with respect to the intermediate obtained after the nucleophilic attack of the allyl group but an exothermic one with respect to the entrance channel (−20.2 kcal·mol −1 ), called C al . This makes this step loosely productive since the ring closure is kinetically more favorable than the ring-opening. It is interesting to note that in the final product, the endocyclic oxygen atom ensures not only the coordination to the metal center (La-O distance = 2.189

Allyl Initiation
On the allyl side, the ROP reaction proceeds via a coordination/insertion mechanism. Thus, the reaction begins by the formation of an endothermic ε-CL adduct, A al (6.4 kcal·mol −1 with respect to the entrance channel). In this adduct, one of the THF molecules in the cis position, with respect to the allyl group, is replaced by ε-CL. The endothermicity of this adduct can be explained by the fact that ε-CL interacts with the metal center through its two oxygen atoms (exocyclic and endocyclic), forcing an η 3 to η 1 hapticity change of the allyl group. This adduct leads to a kinetically accessible transition state, which corresponds to the nucleophilic attack of the allyl group onto the carbonyl carbon of ε-CL, lying only 8.2 kcal·mol −1 above the separated reactants (1.8 kcal·mol −1 above the adduct). This transition state leads to a very stable intermediate, B al , located at −25.3 kcal mol −1 with respect to the separated reactants. It is interesting to note that, in this intermediate, the ε-CL ring remains closed (C-O distance of 1.495 Å), and the lanthanum atom is still interacting with two THF molecules and the two η 3 -borohydride ligands. This system evolves to the acyl-oxygen bond cleavage transition state, i.e., the ring-opening, with a barrier of 9.7 kcal·mol −1 with respect to the previous intermediate (− 15.6 kcal·mol −1 with respect to the separated reactants). This step corresponds to the rate-limiting step of the ROP initiation reaction of ε-CL mediated by the allyl ligand. This transition state leads to a final endothermic product (+5.1 kcal·mol −1 ) with respect to the intermediate obtained after the nucleophilic attack of the allyl group but an exothermic one with respect to the entrance channel (−20.2 kcal·mol −1 ), called C al . This makes this step loosely productive since the ring closure is kinetically more favorable than the ring-opening. It is interesting to note that in the final product, the endocyclic oxygen atom ensures not only the coordination to the metal center (La-O distance = 2.189 Å) but also the presence of an interaction between the metal center and the exocyclic oxygen (La-O distance = 2.640 Å). The relaxation of the growing polymer chain leading to the break of this interaction is endothermic by ca. 2.5 kcal·mol −1 . Thus, the initiation step involving the allyl group is kinetically accessible and thermodynamically favorable even if one of the intermediates is more stable than the final product.

Borohydride Initiation
On the borohydride side, the ROP reaction also proceeds via a coordination/insertion mechanism. In this case, the coordination of ε-CL to La(BH 4 ) 2 (C 3 H 5 )(THF) 3 is followed by a hydride transfer to the ε-CL carbonyl carbon and the trapping of the borane molecule by the exocyclic carbonyl oxygen of the ε-CL. A second hydrogen transfer of the O-C(H)(R)-O···BH 3 group to the carbonyl carbon of the ε-CL leads to the cleavage of the acyl-oxygen bond and to the formation of an R-CH 2 -O-BH 2 group, thus generating an alkoxyborane derivative (BH 4 )(C 3 H 5 )(THF) 2 La-O(CH 2 ) 5 CH 2 OBH 2 . In this case, the reaction also starts with the formation of a first adduct in which one of the THF molecules is replaced by ε-CL. For the sake of clarity, only the most favorable possibility (represented as solid lines over dotted lines, Figure 1), i.e., involving the replacement of the THF molecule in the trans position to the allyl group by ε-CL, will be discussed. Subsequently, from this adduct, A BH4 trans , the nucleophilic attack takes place via an accessible transition state, located at 11.5 kcal·mol −1 with respect to the separated reactants, yielding the first endothermic intermediate trans . Finally, the formation of the R-CH 2 -O-BH 2 terminal group can occur through a concerted pathway (hydrogen transfer + ring-opening) or through a multistep pathway (ring-opening followed by a second hydrogen transfer). In our case, as generally observed, the multistep pathway is higher in energy than the concerted one, 17.6 kcalmol −1 (ring-opening) and 24.1 kcalmol −1 (reduction process) vs. 22.1 kcal·mol −1 , with respect to the entrance channel. These transition states lead to the exothermic formation of the final alkoxyborane derivative, E BH4 trans , which lies 22.9 kcal·mol −1 below the entrance channel. This step is thermodynamically favorable, making the overall ring-opening reaction thermodynamically possible. In this case, and contrary to the allyl product, the alkoxyborane chain is fully linear, with the decoordination of the exocyclic oxygen atom from the metal center.
In summary, both initiation reactions are possible. However, the overall formation of an alkoxyborane growing chain is slightly more favorable than the alkoxide chain with an allyl as the end-group, −20.2 (allyl) vs. −22.9 kcal·mol −1 (borohydride). From a kinetic point of view: (i) when the nucleophilic attack involves the allyl group, the rate-determining step corresponds to the ring-opening step with an activation barrier of 9.7 kcal·mol −1 ; (ii) in the case of the borohydride group, the rate-determining step corresponds to the concerted pathway with an activation barrier of 37.4 kcal·mol −1 . Thus, the formation of the alkoxide chain with an allyl as the end-group is kinetically preferred over the formation of an alkoxyborane growing chain. Therefore, the allyl would afford the kinetic product, whereas the borohydride leads to the thermodynamic one. The next insertion was therefore investigated to corroborate our findings.

Propagation Step
In order to get a better insight into the reactivity difference between the borohydride and the allyl groups as active ligands for the ROP of ε-CL, the first propagation step, namely, the second ε-CL insertion, was investigated. For this second step, we have only considered the possible reactions after the formation of a growing chain with an allyl as the end-group. The enthalpy profiles computed for this step are presented in Figure 2. Starting from the complex La(BH 4 ) 2 (OC 5 H 10 COC 3 H 5 )(THF) 2 , the calculated reaction profile supports the idea that the alkoxide undergoes a nucleophilic attack onto the carbonyl carbon of the second ε-CL monomer, and a subsequent ring-opening generates the final La(BH 4 ) 2 (OC 5 H 10 COOC 5 H 10 COC 3 H 5 )(THF) 2 complex, F al . With respect to La(BH 4 ) 2 (OC 5 H 10 COC 3 H 5 )(THF) 2 , this second insertion is thermodynamically favorable (by 2.4 kcal·mol −1 ). The activation barriers for the nucleophilic attack and the ring-opening are low and similar (ca. 5 kcal·mol −1 ). At this second insertion stage, a nucleophilic attack can also be done by one of the two borohydrides onto the ε-CL carbonyl carbon. This mechanism is very similar to that of the initiation step, as discussed in the previous section. It is interesting to note that no significant difference (less than 3 kcal·mol −1 ) is observed concerning the stability of the intermediates and the activation barriers between the initiation and this propagation step. From a geometric point of view, the structures of the different intermediates and transition states are also similar.
Catalysts 2020, 10, x FOR PEER REVIEW 6 of 10 La(BH4)2(OC5H10COC3H5)(THF)2, this second insertion is thermodynamically favorable (by 2.4 kcal·mol −1 ). The activation barriers for the nucleophilic attack and the ring-opening are low and similar (ca. 5 kcal·mol −1 ). At this second insertion stage, a nucleophilic attack can also be done by one of the two borohydrides onto the ε-CL carbonyl carbon. This mechanism is very similar to that of the initiation step, as discussed in the previous section. It is interesting to note that no significant difference (less than 3 kcal·mol −1 ) is observed concerning the stability of the intermediates and the activation barriers between the initiation and this propagation step. From a geometric point of view, the structures of the different intermediates and transition states are also similar. In conclusion, from a kinetic point of view, there is a clear preference for the alkoxide nucleophilic attack. However, whereas this second step is kinetically favorable, from a thermodynamic point of view, the formed product remains, as for the initiation reaction, less stable than the intermediate obtained after the first nucleophilic attack of the allyl group, −25.3 vs. −22.6 kcal·mol −1 . Thus, even if the activation barriers are accessible, the allyl group is not active for the ROP of ε-CL due to the formation of this highly stable intermediate that disfavors the subsequent ringopening. On the other hand, the ROP of ε-CL mediated by the borohydride ligands is less favorable from a kinetic point of view, but the insertion of the monomers is thermodynamically favorable. This confirms and rationalizes the results previously obtained at the laboratory scale.
In contrast to the ROP reactivity, the higher nucleophilicity of the allyl group over the borohydride one in the simple cases of insertion and acid/base reactions with small molecular substrates is highlighted thanks to 1 H NMR experiments. In conclusion, from a kinetic point of view, there is a clear preference for the alkoxide nucleophilic attack. However, whereas this second step is kinetically favorable, from a thermodynamic point of view, the formed product remains, as for the initiation reaction, less stable than the intermediate obtained after the first nucleophilic attack of the allyl group, −25.3 vs. −22.6 kcal·mol −1 . Thus, even if the activation barriers are accessible, the allyl group is not active for the ROP of ε-CL due to the formation of this highly stable intermediate that disfavors the subsequent ring-opening. On the other hand, the ROP of ε-CL mediated by the borohydride ligands is less favorable from a kinetic point of view, but the insertion of the monomers is thermodynamically favorable. This confirms and rationalizes the results previously obtained at the laboratory scale.

Materials and Methods
In contrast to the ROP reactivity, the higher nucleophilicity of the allyl group over the borohydride one in the simple cases of insertion and acid/base reactions with small molecular substrates is highlighted thanks to 1 H NMR experiments.

Experimental
All manipulations were performed under an inert atmosphere using Schlenk techniques, or in a dry solvent-free glovebox (Jacomex O 2 < 1 ppm, H 2 O < 4 ppm). The solvents for synthesis (THF and toluene) were dried over sodium/benzophenone ketyl, degassed and stored in solvent pots under static vacuum. C 6 D 6 and d 8 -THF were dried over NaK. RE(BH 4 ) 3 (THF) 2-3 (La, Nd, Sm, Y and Sc) compounds were prepared as reported [1,2]. Benzophenone (Aldrich, 99%) was purified by crystallization. Tetramethylcyclopentadiene, tetramethylethylcyclopentadiene and phenylsilane (Aldrich) were dried over molecular sieves. Dimethylanilinium tetraphenylborate (Aldrich) was used as received. Technical grade L-LA (Aldrich) was purified by two subsequent recrystallizations in hot toluene followed by sublimation. ε-Caprolactone (Aldrich) was dried over calcium hydride, distilled twice and stored over molecular sieves (3 Å) in a glovebox. 1 H NMR spectra were recorded on a Bruker Avance 300 instrument at 300 K. All 1 H chemical shifts (reported in ppm) were determined using residual signals of the deuterated solvents.

Methodological Details
All the DFT calculations were performed with Gaussian 09 [27]. Calculations were carried out at the DFT level of theory using the hybrid functional B3PW91 [28][29][30][31][32]. Geometry optimizations were achieved without any symmetry restriction. Vibrational frequencies were systematically computed in order to characterize the nature of the stationary points. The Stuttgart effective core potentials [33,34] and their associated basis sets were used for lanthanum. For the La atom, the basis sets were augmented by a set of polarization functions (ζf = 1.0 for La). The H, B, C and O atoms were treated with 6-31G(d,p) double ζ basis sets [35]. The electron density and partial charge distribution were examined in terms of localized electron-pair bonding units using the NBO program [36,37].

Conclusions
In this paper, the activity of the nucleophilic ligand, allyl vs. borohydride, in the two first steps (initiation and first propagation) of the ROP of ε-caprolactone mediated by La(BH 4 ) 2 (C 3 H 5 )(THF) 3 is investigated. This study highlights that even if, from the kinetic point of view, there is a preference for the ROP of ε-CL mediated by the allyl ligand, this ligand is not active due to the low stability of the inserted products. On the other hand, the ε-caprolactone ROP with the borohydride ligand is more energetically costly but thermodynamically favorable. Thus, on La(BH 4 ) 2 (C 3 H 5 )(THF) 3 , only the borohydride ligands are active for the ROP of ε-CL.