Unraveling differences in aluminyl and carbene coordination chemistry: bonding in gold complexes and reactivity with carbon dioxide

The electronic properties of aluminyl anions have been reported to be strictly related to those of carbenes, which are well-known to be easily tunable via selected structural modifications imposed on their backbone. Since peculiar reactivity of gold-aluminyl complexes towards carbon dioxide has been reported, leading to insertion of CO2 into the Au–Al bond, in this work the electronic structure and reactivity of Au–Al complexes with different aluminyl scaffolds have been systematically studied and compared to carbene analogues. The analyses reveal that, instead, aluminyls and carbenes display a very different behavior when bound to gold, with the aluminyls forming an electron-sharing and weakly polarized Au–Al bond, which turns out to be poorly modulated by structural modifications of the ligand. The reactivity of gold–aluminyl complexes towards CO2 shows, both qualitatively and quantitatively, similar reaction mechanisms, reflecting the scarce tunability of their electronic structure and bond nature. This work provides further insights and perspectives on the properties of the aluminyl anions and their behavior as coordination ligands.


 Natural Orbitals for Chemical Valence and Charge Displacement analysis
Natural Orbitals for Chemical Valence (NOCV) 1,2 represents a suitable approach for describing the chemical bond. This approach is based on the rearrangement of the electron density occurring when a chemical bond is formed and such rearrangement can be expressed as electron density difference between the formed adduct (AB) and sum of the densities of the two non-interacting fragments (A and B) frozen in their adduct geometry.
This deformation density can be brought into diagonal contributions in terms of NOCVs. In the NOCV scheme, the charge rearrangement taking place upon bond formation is obtained from the occupied orbitals of the two fragments suitably orthogonalized to each other and renormalized (promolecule). The resulting electron density rearrangement (Δρ') can be expressed in terms of NOCV pairs which are defined as the eigenfunctions of the so-called ''valence operator'' 3-5 as follows: where ϕ+k and ϕ-k are the NOCV pairs orbitals and ν±k are the corresponding eigenvalues. Upon formation of the adduct from the promolecule, a fraction νk of electrons is transferred from the ϕ-k to the ϕ-k orbital (donor and acceptor orbitals, respectively).
The NOCV scheme can be coupled with the framework of the Charge Displacement (CD) 6 analysis.
The CD analysis allows to quantify the amount of electronic charge that is transferred between the two fragments upon the formation of the A-B bond. The Charge Displacement function (Δq) can be defined as the partial progressive integration on a suitable z-axis of the deformation density Δρ': 7 The CD function, Δq(z), quantifies at each point of the chosen z-axis (which usually corresponds to the bond axis) the exact amount of electron charge that, upon formation of the bond, is transferred from the right to the left across a plane perpendicular to the bond axis through z.
When coupled with the NOCV scheme, the density rearrangement due to the bond formation between two fragments, (Δρ′), is partitioned in different NOCV deformation densities (Δρ′k) and therefore one is able to quantify the charge transfer (CT) associated to the components. Note that only few of the S3 NOCV pairs contributes to the chemical bond. Therefore, when the CD-NOCV analysis is carried out, usually only the first Δρk' components are investigated in order to understand which significant chemical contribution to the bond they represent.
Usually we choose to evaluate the charge transfer between A and B by taking the CD value at the "isodensity boundary", i.e. the z-point where equally valued isodensity surfaces of the isolated fragments become tangent. 7,8 When we apply this scheme to both TSI and INT, with [ t Bu3PAuX] (X=I, II, III, IV, V, VI) and [CO2] as fragments, such approach becomes complicated, since the two fragments display multiple interactions with multiple atomic centres and thus it is clearly impossible to define a unique bond axis and it is very hard to rely on the isodensity boundary for the estimation of the charge transfer. In order to avoid any ambiguity in the definition of the z-axis, we recall an approach that may be useful for evaluating the charge transferred between the [ t Bu3PAuX] and [CO2] fragments at TSI and INT. 9 Within this approach, the electron density rearrangement (Δρ'), which typically shows charge By defining two arbitrary regions that are associated with the interacting fragments, we can evaluate the charge transfer as follows: By combining Eqs.
[S4] and [S5], CT can also be expressed as: Ultimately, this approach can also be expressed in the CD-NOCV framework. By combining Equations [S1] and [S5], we can use to this approach for calculating the charge transfer associated to each NOCV deformation density as follows: Despite the spatial regions associated to the two interacting fragments being defined arbitrarily, this approach is particularly suitable for the analysis of the interaction between the [ t Bu3PAuX] and [CO2] fragments at INT, being the two fragments well-separated in space.

 Energy Decomposition Analysis and ETS-NOCV approach
The Energy Decomposition Analysis (EDA) 10 where ΔE Pauli corresponds the Pauli repulsion interaction between occupied orbitals on the two fragments, ΔVelst represents the quasiclassical electrostatic interaction between the unperturbed charge distribution of the fragments at their final positions, ΔEdisp takes into account the dispersion contribution and ΔEoi is the orbital interaction, which arises from the orbital relaxation and the orbital mixing between the fragments, and accounts for electron pair bonding, charge transfer, and polarization.
The orbital interaction term ΔEoi can be further decomposed within the ETS-NOCV 12 scheme into NOCV pairwise orbital contributions ( = ∑ ) which associates an energy contribution ( ) to each NOCV deformation density (Δρk).

 Activation Strain Model
The Activation Strain Model (ASM) 13-15 allows to get insights into the factors controlling the activation barrier of a process. Within this framework, the activation barrier (ΔE # ) can be decomposed as follows: where the "ΔEdist TSI " and "ΔEdist RC " terms represent the energy penalty due to the distortion of the fragments (i.e. [ t Bu3PAuX] and CO2) constrained in the structures of the transition state (TSI) and the reactant complex (RC) respectively, whereas "ΔEint TSI " and "ΔEint RC " represent the interaction energies between the fragments (with the geometries constrained at the ones assumed in the TSI and RC, respectively) in the two structures. These terms can be grouped in the "ΔΔEdist" and "ΔΔEint" terms, that represent the overall distortion and interaction contributions to the activation barrier, respectively.
Additionally, we can rearrange Equation [S9] in order to express the distortion contributions relatively to the two fragments as follows: where "ΔEdist CO2 " represent the distortion penalty (or stabilization) due to CO2 rearranging from its structure in the RC going into TSI and the "ΔEdist comp " term represents the same distortion contribution concerning the rearrangement of the [ t Bu3PAuX] complexes.
Since, for the sake of comparison, we analysed in the detail the electronic structure of intermediates INT, in order to exploit the factors controlling the different degrees of stabilization, we extended the ASM scheme as follows: where the "ΔEdist INT " term represents the energy penalty due to the distortion of the fragments (i.e. [LAuX] and CO2) constrained in the structures of the intermediate (INT), whereas "ΔEint INT " represents the interaction energy between the fragments (with the geometries constrained at the ones assumed in the INT).  Table S9. Contributions from Al/C ns and npz (n=2,3) atomic orbitals to the HOMOs of isolated aluminyls I-VI and carbenes I C -VI C , respectively. The proton affinity (ΔE PA ) for each species is also reported.

Modelling of the ligand
The choice of using slightly simplified structures for anions I-VI was made for achieving the best compromise between computational cost and accuracy. Surely we do expect an influence of the modified steric hindrance of the ligand on the actual reactivity (as we also mention in the text). However, we also expect much smaller deviations in terms of the electronic effects (which are the focus of our work) induced by such modifications. On this matter, we mention that in our previous work on gold complex with I, 16 we showed that the simplified geometry optimized at the PBE/TZ2P level is comparable to the non-simplified (real) one optimized at the same level of theory and also in good agreement with the experimentally determined one via X-Ray diffraction. 17 Nonetheless, we recognize that the effect of such structural simplifications on the calculations we carried out (particularly their influence on the electronic properties under study) has not been assessed quantitatively. For this reason, we have selected compound with VI as a test case study, since the anion in this compound features the most simplified structure along the series (thus one may expect for complex with VI the largest deviations due to structural simplifications, i.e. i.e. 12 methyl groups replaced by 12 hydrogen atoms). We optimized the real structure of complex with VI, together with the following stationary points along the reaction path: RC, TSI, INT, PC. This allows us to evaluate not only the properties of the complex but also the first activation barrier (which is key for understanding the interaction between the complex and carbon dioxide), the stabilization of the intermediate and the thermodynamics of the overall process. A first insight on the influence of such modifications can be obtained by analysing the optimized geometries of the real complex with VI (VI real) as well as the corresponding stationary points (see Figures S18-S19). It is immediately clear that the applied simplifications slightly affect the optimized structures, with the main geometrical parameters involved in the interaction with carbon dioxide only marginally differing from those of the simplified complex. The most remarkable difference can be found for RC, where, due to the steric hindrance of the 12 Me groups, the incoming CO2 is oriented at about 90º with respect to the Au-Al bond (compare Figure S15 and S18). As for the reaction mechanism, a comparison between the two reaction profiles (for complexes with VI and VI real) shows that the TSI, INT and PC are destabilized with respect to those of complex with VI, whereas RC is stabilized (see Figure S19), consistently with the ASM results on complex with VI real, which indicate a larger distortion of the complex mainly due to the larger steric hindrance of the real aluminyl ligand (see below). Indeed, we also assessed the effects of such simplifications on the ASM, EDA and CD-NOCV calculations by comparing the findings for complexes with VI and VI real (and the corresponding stationary points). Concerning the ASM analysis, the results (see Tables S14-S15 and Figure S20), highlight only marginal differences between the simplified and the real system. In detail, we observe an increase of the electronic energy activation barrier for the real complex (1.4 vs. 4.9 kcal/mol) and a destabilization of INT (-16.6 vs. -10.4 kcal/mol). Upon inspection of the ASM terms, we find that the distortion component is increased for complex with VI real mainly due to an increased distortion associated to the complex (0.6 vs 4.0 kcal/mol at TS1 and 11.4 vs 17.5 kcal/mol at INT), which could be expected in the case of complex with VI real due to the increased steric hindrance of the aluminyl. Importantly, the interaction stabilization terms remain practically unaltered upon ligand simplification, which indicate that this component (which is the essential one for the purpose of the electronic structure analysis) should not be affected by the structural modelling introduced. We also quantitatively assessed this finding by carrying out EDA and CD-NOCV calculations for the complex with VI real and the corresponding TSI and INT structures. In all the cases, the results confirm quantitatively that the electronic properties of complex with VI real are negligibly affected by such simplifications. In particular, results of the EDA and ETS-NOCV analysis at TS1 (Table S16) reveal that dispersion is the only term that differs (as could be expected) for more than 1 kcal/mol upon simplification (-4.6 vs. -6.5 kcal/mol). All the other EDA and ETS-NOCV terms are practically left unchanged. The electronic structure analysis of complex with VI real leads to analogous conclusions, as it can be inferred by the EDA results (Table S17), CD-NOCV calculated stabilization energies and charge transfer values (Table S18) and clearly by the CD-NOCV curves, which practically overlap for the simplified and real complexes with VI ( Figure S21). Figure S18. ΔEoi 1 -15.9 -14.9

S40 PBE vs. PBE0 functional results
The choice of using the PBE functional for all calculations is based on the combined experimental/theoretical work where complex with I was originally reported. 17 In that framework, DFT calculations using PBE and PBE0 were benchmarked against the reference DLPNO-CCSD(T) approach and the authors concluded that both PBE and PBE0 were accurate in reproducing the magnitude and the trends in bond energies and thus they could be considered reliable. We also mention that we already discussed in a previous work how the PBE-D3(BJ)/TZ2P optimized geometry for compound with I is in good agreement with the experimental one. 16 However, it is clear that a proper assessment/benchmark of the actual performance of various XC functionals in this context would be highly desirable. Despite an extensive benchmark would be far from the scope of this work, we have tested the effect of using a hybrid functional for the energy reaction profile and electronic structure calculations we present. We selected the PBE0 functional since it belongs to a different familiy of density functionals (hybrid) from the one we used (GGA) and because of its good performance in this context when benchmarked against DLPNO-CCSD(T). In particular, we used the PBE0 functional for calculating the energies of compounds with I-VI and of the corresponding most significant stationary points along the reaction paths (RC, TSI, PC), which should give an idea of the effect on the functional on both the kinetics and thermodynamics of the reaction. Furthermore, we tested the effect of the functional on the EDA, ETS-NOCV and CD-NOCV analyses using compound with VI as a test case.
Our comparative analysis reveals that, overall, the effect of the functional is not remarkable for the discussion we present here: the results are unbiased with respect to the use of PBE/PBE0 functionals. Concerning the reaction mechanism, the electronic energy profiles (see Table S21 and Figure S23) obtained with PBE0 are in agreement with the PBE ones: in most cases, the energy of RC, TSI and the relative electronic activation barrier differ by 1 kcal/mol ca. In the worst case scenario, represented by compound with VI, we observe larger deviations for RC and TS1 (deviation of -5.4 kcal/mol on both RC and TSI) but overall the electronic barrier is unchanged upon using PBE0, thus highlighting that the relative stationary points are only shifted at lower energies. Concerning the stability of PC, we find that, PBE0 yields more stable PC in all cases (on average there is a deviation of 7 kcal/mol ca); however, the shift is found to be practically systematic, as it can be clearly inferred from the profiles reported in Figure S23. Overall, we can conclude that both the kinetics and thermodynamics trends of the reactions under study are unbiased upon choice of a different density functional.
Concerning the impact of the functional on the electronic structure calculations, the effect of using PBE0 functional is even less remarkable. The analysis of the Au-Al bond in complex VI leads to practically identical results for PBE and PBE0, as demonstrated by the small variations reported for the EDA terms (Table S22), CD-NOCV terms (Table S23) as well as the CD-NOCV curves (which practically overlap, see Figure S24) and related deformation densities.