Radical-like reactivity for dihydrogen activation by coinage metal–aluminyl complexes: computational evidence inspired by experimental main group chemistry

The computational study of an unprecedented reactivity of coinage metal–aluminyl complexes with dihydrogen is reported. In close resemblance to group 14 dimetallenes and dimetallynes, the complexes are predicted to activate H2 under mild conditions. Two different reaction pathways are found disclosing a common driving force, i.e., the nucleophilic behavior of the electron-sharing M–Al (M = Cu, Ag, Au) bond, which enables a cooperative and diradical-like mechanism. This mode of chemical reactivity emerges as a new paradigm for dihydrogen activation and calls for experimental feedback.


Introduction
The recent synthesis of the gold-aluminyl complex 1 (Scheme 1) and its outstanding reactivity in capturing CO 2 under mild experimental conditions represent a unique case in the framework of gold chemistry. 1 We have thoroughly discussed that the driving force of this reactivity is the presence of an electron-sharing, weakly polarized Au-Al bond acting as a nucleophilic site inducing a cooperative diradical-like reactivity. [2][3][4][5] Shortly aer this, analogous reactivity was reported to occur for copper-and silveraluminyl complexes, for which, however, the reaction proceeds towards the formation of carbonate complexes with CO extrusion. 6 A surprising feature concerning the reaction of 1 with carbon dioxide is that it bears strict analogies with amido-digermyne compound 3 (Scheme 1), which, in reducing CO 2 to CO, proceeds through an intermediate 4 that is structurally very similar to insertion product 2. 7 Particularly intriguing, aryl-and amido-digermynes RGeGeR (R = [C 6 H 3 -2,6(C 6 H 3 -2,6 i Pr 2 ) 2 ], 8 [N(SiMe 3 )(C 6 H 2 Me{C(H)Ph 2 } 2 )], 9 and [N(Si i Pr 3 )(2,6-[C(H)Ph 2 ]2-4-i PrC 6 H 2 )] 10 ) 5 (Scheme 1) are reported to easily activate H 2 under mild experimental conditions both in solution 8,10 and the solid state at temperatures as low as −10°C. 9 In all cases, experiments and theoretical investigations outline a reaction mechanism that proceeds via a singly bridged intermediate [RGe(m-H)GeHR] species 6, which subsequently, upon isomerization, yields different hydrogenation products, which are experimentally revealed depending on the steric hindrance of the substituents. 11,12 Notably, the facile reactivity with H 2 has also been reported for other group 14 dimetallenes and dimetallynes. 13 The digermyne is suggested to possess substantial diradical character and therefore to react through H atom abstraction from H 2 , followed by recombination of the resultant radical pair. 8 As bare ligands, aluminyls resemble singlet carbenes in possessing an electron lone pair and an accessible vacant p orbital, thus potentially showing a similar reactivity. Interestingly, it has been reported that acyclic and cyclic (alkyl)(amino) carbenes 7 and 8a, b can activate H 2 under mild conditions, by behaving as nucleophiles (Scheme 2). 14 In analogy, the ability of [M{Al(NON)}] 2 (M = Li, Na, K) species to react with H 2 has been also reported (Scheme 2, complex 9) [15][16][17] together with detailed mechanistic studies. 18 Despite these similarities, when used as coordination ligands, aluminyls and carbenes have a strikingly different chemical behaviour. In a recent work, we have shown that gold-aluminyl complexes, unlike gold carbene analogues featuring a dative Au-C bond, are able to react with CO 2 . 4 In this scenario the interest in exploring the reactivity of gold-aluminyl complexes towards H 2 naturally arises. The electron-sharing nature of the Au-Al bond in complex 1 allowed the rationalization of its reactivity with CO 2 , 2 in close resemblance with that of digermyne complex 3, and thus, we reasoned that the same bonding model may also favor the reaction of complex 1 with H 2 analogous to that of complexes 5. The possibility for H 2 activation to occur with aluminyl complexes is very attractive, especially in light of potential applications in hydrogen storage and catalysis, beside H 2 being vital in several industrial processes, organic synthesis and also in biological functions. 19,20 In addition, given the similar reactivity of gold-copper-and silver-aluminyl complexes with CO 2 , a possible H 2 activation by copper-and silver-aluminyl complexes is certainly worth exploring.
Herein we report that [ t Bu 3 PMAl(NON)] (M = Cu, Ag, Au) complexes should indeed react with dihydrogen, with the Cu-Al complex featuring the most kinetically favored and exergonic reaction with H 2 . The calculations predict the experimentally accessible formation of a singly bridged [ t Bu 3 PM(m-H)Al(H) (NON)] species for all the metal-aluminyl complexes and an additional doubly bridged [ t Bu 3 PM(m-H) 2 Al(NON)] product for copper and silver. Detailed electronic structure calculations highlight the central role of the electron-sharing M-Al bond in inducing a diradical-like reactivity towards H 2 , in close resemblance to digermynes, as surmised.

Results and discussion
The free energy proles for the reaction of [ t Bu 3 PMAl(NON)] complexes with H 2 have been calculated using the same computational protocol employed in ref. 2 for the reaction of [ t Bu 3 PAuAl(NON)] with CO 2 (see Computational details). For [ t Bu 3 PAuAl(NON)], the free energy prole is depicted in Fig. 1 together with the schematic structure of all stationary points. The optimized structures of all the stationary points in Fig. 1  Au which is in equilibrium with the more stable PC Au (via TS III Au , DG = 8.3 kcal mol −1 ). Interestingly, the overall RC Au -to-PC Au conversion is practically thermoneutral, suggesting a possibly reversible reaction and a virtually ideal condition for the use of complex 1 as a hydrogen-transfer catalyst. The free energy activation barriers for the two paths roughly t in the 25-30 kcal mol −1 range, Scheme 2 Similar reactivity of (alkyl)(amino)carbenes 7 and 8a, b and aluminyl 9 with H 2 .  The structural analogy between the gold-aluminyl PC Au and digermyne 6 (Scheme 1) singly bridged species is striking.
Notably, at variance with digermyne 6, PC Au is not expected to easily undergo isomerization (see Scheme S1 and Discussion in the ESI †) and, in particular, dissociation into two separate hydride complexes (i.e. Given the thermoneutrality of this reaction, experimental evidence for H 2 cleavage could not be straightforward. In light of the reported more efficient reaction of copper-and silveraluminyl complexes with carbon dioxide, it is interesting at this point to investigate the reactivity of [ t Bu 3 PMAl(NON)] (M = Cu, Ag) complexes with H 2. The reaction proles are depicted in Fig. 2. The structures of all stationary points for both copper-and silveraluminyl complexes are shown in Fig. S2-S4 in the ESI. † For the silver-and copper-aluminyls, H 2 activation can occur symmetrically at the Ag (blue line prole, DG = 33.2 kcal mol −1 ) and the Al (red line prole, DG = 33.6 kcal mol −1 ) sites, and remarkably unsymmetrically at the Cu (blue line prole, DG = 18.7 kcal mol −1 ) and the Al (red line prole, DG = 32.0 kcal mol −1 ) sites. From the Al site, the reaction leads directly to the formation of the singly bridged aluminyl species PC Cu /PC Ag for both copper and silver complexes via the concerted transition state TS IV Cu /TS IV Ag . Although both are found to have similar energy to that of TS IV Au , the respective products are found to be more stable. In particular, the formation of PC Ag is slightly exergonic (−1.1 kcal mol −1 ) and the formation of PC Cu is even more exergonic (−5.0 kcal mol −1 ).
The alternative path, where H 2 approaches the complexes closer to the metal site (blue paths in Fig. 2), highlights appreciable differences between lighter coinage metals and gold, instead. Qualitatively, the rst step is analogous in all cases: H 2 approaches the metal site, yielding intermediates INT Cu /INT Ag . In the second step, however, copper and silver complexes remarkably differ from gold, since the intermediate is converted unequivocally to a stable doubly bridged product From a quantitative perspective, differences between the three metals are even more pronounced. Indeed, the silver-aluminyl complex displays a higher activation barrier for TS I Ag (33.2 kcal mol −1 ) and a slightly exergonic formation of PC 0 Ag (DG = −1.9 kcal mol −1 ) via isomerization from the unstable INT Ag . On the other hand, the path for the copper-aluminyl complex shows much more favorable energetics overall with respect to silver and gold complexes. In the rst step, a more stable intermediate (INT Cu ) is formed via a much lower activation barrier at TSI Cu (DG = 18.7 kcal mol −1 ). Subsequently, the INT Cu isomerization leads to the highly stable doubly bridged product PC Ag and TS III Au structures are similar, even though for gold the doubly bridged species is not a minimum energy point. Thus, preferential formation of singly bridged aluminyl species with the second hydrogen bound to Al is found for gold.
The reaction proles described above clearly indicate that coinage metal-aluminyl complexes can activate H 2 , and a particularly facile H 2 cleavage is predicted with the copper-aluminyl complex. Based on the RC Cu À TS I Cu À INT Cu À TS II Cu À PC 0 Cu path, due to the relatively low activation barrier and high exergonicity, dihydrogen activation could be experimentally demonstrated more easily. Under suitable conditions, isolation and characterization of the doubly bridged copper species should be achievable. Furthermore, as reported extensively in the literature, [25][26][27][28][29][30] this type of reaction may be affected by the presence of tunnel effects that contribute to the lowering of the activation barriers. With the aim of assessing if such effects may be important in this context, we used transition state theory (TST) 31 and the Eckart tunneling correction 32 (see Computational details) to estimate the tunnel effect on the Eyring tted activation barrier associated with TS I M . The results show that, indeed, a moderate tunnel-related lowering of the activation barriers associated with TS I M may be expected (in the range of 1.3-3.7 kcal mol −1 , see Table S1 †). A proper assessment of this effect is beyond the scope of this work, but this estimate suggests that the tunnel effects may impact, to some extent, the reactivity reported here.
A common feature of the reaction proles in Fig. 1 and 2 is the possible H 2 activation at two different sites (M and Al),  Table S2 and Fig. S5-S16 in the ESI †).
As shown in Fig. 3, the NOCV analysis at TS IV Au for the goldaluminyl complex reveals a main component ðDr (NON)] interaction, which can be depicted, upon decomposition of the corresponding donor and acceptor NOCVs (see Fig. S5 and S6 in the ESI †), as mainly dominated by a charge transfer from the HOMO of the complex (a s MO representing the electron-sharing Au-Al bond) towards the LUMO of H 2 (Fig. 2a and  S5 †). A second non-negligible component can be envisaged (Dr Notably, analogous results arise upon NOCV analysis of the H 2 -complex interaction at TS IV M and TS I M for copper-and silveraluminyl complexes. As can be inferred from the results reported in Fig. S9-S16 in the ESI, † at both TS I Cu /TS I Ag and TS IV Cu /TS IV Ag the main component of the H 2complex interaction is represented by a charge transfer from the s bonding M-Al molecular orbital towards the H 2 antibonding LUMO. This nding is fully consistent with the nature of the M-Al bond. As previously reported for the Cu-Al bond 2 and based on Fig. S17, S18 and Table S3 in the ESI and Discussion therein, † despite small changes in the bond polarization, in these complexes the M-Al (M = Cu, Al, Au) is an electronsharing bond, acting as a nucleophilic site for the activation of H 2 .
Furthermore, similar to the gold complex, both copper-and silver-aluminyl complexes feature a second driving force in the interaction with H 2 at the two TSs, that is a charge transfer from the H 2 HOMO towards the LUMO of the complex. So apparently, for all the metals and at both TSs, the nature of the H 2 -complex interaction is qualitatively analogous.
Differences between TS IV M and TS I M and between copper and its heavier homologues silver and gold become evident on a quantitative ground. In particular, the ETS-NOCV and CD analyses reveal that Dr   The extent of the P-M-Al bending also rationalizes the more energetically favourable pathway for the copper complex with respect to its silver and gold analogues. While the P-M-Al angle is below 130°for both TS I Ag and TS I Au (129.1°and 126.0°, respectively), the Cu-Al complex features a larger P-Cu-Al angle at TS I Cu (133.0°). This apparently marginal difference has a signicant effect on the activation barrier, as shown by the activation strain model analysis [41][42][43] (ASM, see Tables S5-S7 in the ESI and Discussion therein †) of the reaction pathways. The less bent copper structure actually reduces the distortion penalty associated with the complex rearrangement from 18.7 kcal mol −1 at TS I Au to 5.2 kcal mol −1 at TS I Cu , thus lowering the activation barrier. The analysis of the variation of the metal AO contributions to the LUMO of the complex at different P-M-Al angles (see Fig. S19 and Table S8 in the ESI †) shows that the bending required to efficiently enhance the metal contribution to the LUMO is signicantly lower for copper with respect to that of silver and gold, thus rationalizing the reduced bending deviation and therefore the lower distortion penalty for the copper-aluminyl system.
The coinage metal-aluminyl complex reactivity described here is very different from that of general transition metal-Lewis acid (TM-LA) compounds. For TM-LA, the presence of dative polarized TM(d−)-LA(d+) bonds usually favours the polarization of H 2 and, thus, its dissociation and oxidative addition to the metal center. 44 A quantitative assessment of the different reactivities of M-Al (M = Cu, Ag, Au) vs. TM-LA is given in the ESI (see Fig. S20, Table S9 and Discussion therein), † where a platinum-aluminium complex featuring a dative Pt/Al bond, reported by Bourissou and coworkers 21 to experimentally activate H 2 , has been selected by us as a test case.
On the other hand, further analogies between gold-aluminyl (and copper-and silver-aluminyl) and digermyne compounds can be inferred by investigating the radical pair recombination mechanism for the formation of product PC Au in comparison with that of 6. As mentioned earlier, this mechanism (radical Hc abstraction followed by radical pair recombination) has been proposed for digermynes. 8 As shown in Fig. S21 in the ESI † and in Fig. 4, we modelled homolytic and heterolytic breaking of the two substrate -H bonds in PC Au for probing which of these two mechanisms is the most favourable in this case.
The most suitable fragmentation (i.e. the one featuring the lowest associated energy for the dissociation of the substrate -H bonds) is the radical one (see Fig. 4 and S21 in the ESI †), meaning that the most favorable mechanism would be Hc abstraction followed by a radical pair recombination (the associated DE values are 83.6 and 84.6 kcal mol −1 , while DE values of 362.4/179.9 kcal mol −1 and 195.2/388.8 kcal mol −1 are calculated for hydride/proton abstraction and recombination). Interestingly, the dissociation of the remaining hydrogen from the radicals to yield the gold-aluminyl complex still features positive dissociation energies (Fig. 4a), suggesting that the complex is able to stabilize the radical pair. Such an ability is preserved even when accounting for the geometrical relaxation of the gold-aluminyl complex, which is, in absolute value, smaller than the dissociation energies.
Even more interestingly, this model indirectly reveals the diradical-like nature of this mechanism. By inspection of the spin densities on the radical [ t Bu 3 PAu(m-H)Al(NON)]c and [ t Bu 3 PAuAlH(NON)]c fragments (Fig. 4b), no spin polarization is observed on the bound hydrogen, with the spin density being mostly localized either on Al (spin polarization of 0.89 e) or in the region between Au and Al atoms, (spin polarization values of 0.43 and 0.22 e for Au and Al, respectively). This nding demonstrates that the radical-like reactivity of these fragments has a fundamental role in favoring the activation of H 2 via homolytic H-H dissociation and the consequent formation of the thermodynamically accessible PC Au . This picture is strongly supported by the analogous dissociation paths and spin densities (Fig. S22 in the ESI †) observed for the model digermyne reported in ref. 12. Analogously, the same model applied for studying the formation of PC Cu /PC Ag and PC 0 Cu =PC 0 Ag supports a similar radical-pair stabilization mechanism for both copper-and silveraluminyl complexes. As displayed in Fig. S23-S26 in the ESI, † Hc abstraction followed by radical pair recombination is favored for both PC Cu and PC Ag (the associated DE values are 88.7/85.9 and 83.3/85.0 kcal mol −1 respectively, see Fig. S24 †), while the DE values associated with the hydride/proton abstraction and recombination mechanism are much higher (see Fig. S23 †). Analogous values have also been calculated for the same mechanisms in the case of PC 0 Cu and PC 0 Ag (see Fig. S25 and S26 †). Notably, monitoring the charge migration along the reaction paths with the evolution of Voronoi deformation density (VDD) 45 atomic charges on the metal (q M ) and aluminium (q Al ) atoms, as well as on the two hydrogen atoms of H 2 (q H 1 and q H 2 ), indirectly conrms this mechanistic picture. As shown in Table  S10 in the ESI, † both q M and q Al become increasingly positive along the reaction paths (indicating charge depletion), while q H 1 and q H 2 become increasingly negative (indicating charge accumulation on H 2 ). Remarkably, both increases of q M /q Al and q H 1 /q H 2 are almost symmetrical for all the stationary points, indicating the absence of H 2 polarization and further conrming the bimetallic cooperative radical pair stabilization mechanism. Furthermore, the VDD atomic charge evolution along the reaction proles suggests that, starting from what we Starting from PC Au , hydrogenation of ethylene occurs in a single, exergonic step (−25.6 kcal mol −1 ), via a concerted transition state (TS cat Au , see Fig. S28 in the ESI †), where both hydrogens are simultaneously transferred to the substrate, forming ethane and regenerating the gold-aluminyl catalyst, with a kinetically accessible barrier (21.7 kcal mol −1 ). Given the enhanced stability of PC Cu and PC Ag (thus representing larger thermodynamic sinks), this catalytic mechanism is predicted to be less efficient for copper-and silver-aluminyl complexes. Indeed, as shown in Fig. S27, † while the ethane formation is found to be exergonic for both species (DG = −15.7 and −20.3 kcal mol −1 for Cu and Ag, respectively), the activation barrier is higher for both metals (29.4 and 26.8 kcal mol −1 for Cu and Ag, respectively), thus reducing the possible catalytic performance of the copper-and silver-aluminyl complexes.

Conclusions
In conclusion, computational evidence for the activation of H 2 by coinage metal-aluminyl complexes via a radical pair stabilization mechanism is provided, in close resemblance with experimentally observed dihydrogen activation with group 14 dimetallenes and dimetallynes, and at a variance with the reactivity of general TM-LA complexes. This offers an alternative paradigm for small molecule activation by electronrich and highly covalent metal-metal bonds which are able to induce a radical-like reactivity. The kinetically accessible and almost thermoneutral formation of product species appears certainly as an ideal condition for the use of the [ t Bu 3 PAuAl(NON)] complex as a catalyst for hydrogenation of, for instance, unsaturated C-C bonds. 47 This work falls within the sustainable "catalysis by design" as a green key technology in continuing the search for innovative strategies for small molecule activation, and strongly calls for systematic experimental feedback. 48

Computational details
Complexes [ t Bu 3 PMAl(NON)] (M = Cu, Ag, Au) have been slightly simplied at the NON site by replacing the two tert-butyl groups at the peripheral positions of the dimethylxanthene moiety with hydrogen atoms and the two Dipp substituents on the nitrogen atoms with phenyl groups. The effect of modelling on this class of complexes has been extensively evaluated in ref. 2 and 4 where the same computational set up as that used in the present work was applied. Good agreement with experimental data was found for geometries, and in general, both the reaction mechanism and the electronic structure calculations show negligible deviations due to the structural simplications used.
All geometry optimizations and frequency calculations on optimized structures (minima with zero imaginary frequencies and transition states with one imaginary frequency) for the H 2 reaction with the [ t Bu 3 PMAl(NON)] (M = Cu, Ag, Au) complexes have been carried out using the Amsterdam density functional (ADF) code 49,50 in combination with the related Quantumregions Interconnected by Local Description (QUILD) program. 51 The PBE 52 GGA exchange-correlation (XC) functional, the TZ2P basis set with a small frozen core approximation for all atoms, the ZORA Hamiltonian 53-55 for treating scalar relativistic effects and the Grimme's D3-BJ dispersion correction were used. 56,57 Solvent effects were modelled employing the conductor-like screening model (COSMO) with the default parameters for toluene as implemented in the QUILD code. 58 Effects of the exchangecorrelation functional and solvation in this framework have been recently evaluated and are found, overall, to negligibly affect the results. 4 The effect of different exchange-correlation functionals on the reaction energetics has been also investigated in this work, highlighting an overall marginal impact on both the kinetics and thermodynamics of the reported reactions (see Table S11 and Fig. S29 in the ESI †).
The same computational setup has also been used for the AMS, EDA, CD-NOCV and ETS-NOCV analyses, as well as for the calculation of Voronoi deformation density (VDD) 45 charges along the reaction paths. This computational protocol has been used in ref. 1 and 2 to study the [ t Bu 3 PAuAl(NON)] and [ t Bu 3 PAuCO 2 Al(NON)] complexes and to investigate the mechanisms of the CO 2 insertion reaction in similar compounds featuring gold and group 13 elements. [3][4][5] The analysis of the transition state TS2 for the reaction of the aluminium-platinum complex with H 2 has been carried out with the same computational protocol on the geometry optimized in the original work. 21 Similarly, the radical recombination pathways for the model digermyne compounds have been investigated at the same computational level using the geometries provided in ref. 12.
The transition state theory (TST) 31 calculations for the evaluation of tunnel effects have been carried out with the kinetic and statistical thermodynamic package (KiSThelP) 59 computer code. Activation energies have been computed from the rate constant with the three-parameter tted Arrhenius equation. The non-corrected activation energy (E TST a ) has been obtained from tting of the conventional TST-calculated rate constant, while the tunneling-corrected activation energy (E TST-Eckart a ) has been obtained via tting of the TST rate constant corrected with the Eckart tunneling correction. 32

Data availability
All the relevant data (including methodology description, and mechanistic, CD-NOCV, ASM, EDA, VDD and TST data discussed in the manuscript) are provided within the ESI. †

Conflicts of interest
There are no conicts to declare.