Reactivity of a Gold-Aluminyl Complex with Carbon Dioxide: A Nucleophilic Gold?

A gold-aluminyl complex has been recently reported to feature an unconventional gold nucleophilic center, which was revealed through reactivity with carbon dioxide leading to the Au-CO2 coordination mode. In this work, we computationally investigate the reaction mechanism, which is found to be cooperative, with the gold–aluminum bond being the actual nucleophile and Al also behaving as electrophile. The Au–Al bond is shown to be mainly of an electron-sharing nature, with the two metal fragments displaying a diradical-like reactivity with CO2.

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: ' = ∑ (| + k | 2 − | -k | 2 ) = ∑ ' [1] where ϕ+k and ϕ-k are the NOCV pairs orbitals and ν±k are the corresponding eigenvalues. When the adduct is formed from the promolecule, a fraction νk of electrons is transferred from the ϕ-k to the ϕ-k orbital, which are envisaged as donor and acceptor orbitals, respectively. For the sake of interpretation, a population analysis can also be performed in order to single out, for ϕ-k and ϕ+k orbitals, which molecular orbitals (MOs) of the two constituting fragments contribute to the interaction (with a resulting associated coefficient accounting for the magnitude of the contribution).
The NOCV scheme can be coupled with the framework of the Charge Displacement (CD) analysis.
The CD analysis allows to quantify the amount of electronic charge that is transferred between the The CD function, Δq(z), quantifies at each point of 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.
The CD and NOCV frameworks can be coupled in the CD-NOCV scheme. 7 In the latter, the density rearrangement due to the bond formation between two fragments, (Δρ′), can be partitioned in different NOCV deformation densities (Δρ′k) and therefore one is able to quantify the charge transfer (CT) associated to each different component. It must be noted that only few of the 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.
In equation [2], the integration axis is usually conveniently chosen as the bond axis between the two fragments constituting the adduct and 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. 6,8 In this case, since we also apply this scheme to the transition state TSI, with [ t Bu3PAuAl(NON')] and [CO2] as fragments, such approach is complicated, since the two fragments display multiple interactions with multiple atomic centers 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 Bu3PAuAl(NON')] and [CO2] fragments at TSI. 9 Within this approach, the electron density rearrangement (Δρ'), which typically shows charge so that ( )′ = + ( ) − -( ) [4] By defining two arbitrary regions that are associated with the interacting fragments, we can evaluate the charge transfer as follows: = ∫ ( )′ = − ∫ ( )′ [5] By combining Eqs. [4] and [5], CT can also be expressed as: = ∫ + ( ) − ∫ -( ) = − ∫ + ( ) + ∫ -( ) [6] Ultimately, this approach can also be expressed in the CD-NOCV framework. By combining Equations [1] and [5], 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 Bu3PAuAl(NON')] and [CO2] fragments in TSI, being the two fragments well-separated in space.

 Energy Decomposition Analysis and ETS-NOCV approach
In this work the Energy Decomposition Analysis (EDA) 10  where ΔE Pauli represents the Pauli repulsion interaction between occupied orbitals on the two fragments, ΔVelst is the quasiclassical electrostatic interaction between the unperturbed charge S5 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 11 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, which is also referred to as "distortion/interaction analysis") [12][13][14] is a popular approach often used in order 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: [9] where the "ΔEdist TSI " and "ΔEdist RC " terms represent the energy penalty due to the distortion of the fragments (i.e. [ t Bu3PAuAl(NON')] and CO2 in the case of the barrier involving the transition state TSI) 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 also rearrange Equation [9] in order to express the distortion contributions relatively to the two fragments as follows: observed along the reaction energy path (see Table S5 and discussion) is nearly cost-less. The interaction stabilization (ΔΔEint= -12.88 kcal/mol) is able to efficiently counterbalance the distortion penalty. The orbital interaction energy at TSI (-53.30 kcal/mol) is the key contribution to it (see Table S6).  Figure S3. Breakdown of the donor (Ψ1) and acceptor (Ψ-1) orbitals that are associated with the deformation density Δρ'1 in the transition state TSI into the most important MOs of the fragments frozen at their TSI geometry. The orbital mixing coefficients are given in parentheses. S14 Figure S4. Breakdown of the donor (Ψ2) and acceptor (Ψ-2) orbitals that are associated with the deformation density Δρ'2 in the transition state TSI into the most important MOs of the fragments frozen at their TSI geometry. The orbital mixing coefficients are given in parentheses.

S15
In Figure S4 Such evidence is confirmed by the electron density rearrangement occurring upon formation of the Au-Al bond starting from open-shell radical fragments ( Figure 3 in the text), where electron density is transferred in the region between the two metals, thus matching well with the previously depicted picture of the Au-Al bond behaving as a nucleophile.
In Figure S5 and S6 a direct comparison between TSI, INT, TSII and PC structures (singlet ground state) and separated corresponding neutral radical fragments optimized structures (doublet ground state) is presented. The similarity between each stationary state and its separated neutral radical fragments is indeed remarkable.

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Notably, this geometrical analogy holds true also for the inserted CO2 in PC and in [CO2Al(NON)]• fragment, which closely resembles the geometry of the free radical anion CO2 -. We should mention that the electron attachment to CO2 is energetically unfavorable, 36 although the radical anion CO2has been experimentally characterized 37 and its controlled production for radical chain reactions has been very recently reported. 38 Surprisingly, this simple model accounts for a possible radical-like mechanism for the CO2 insertion into the Au-Al bond in the [ t Bu3PAuAl(NON')] complex. The stationary points in Figure   1 in the text have been also optimized at open-shell (unrestricted) singlet level, attaining the same geometries and energies as those calculated at closed-shell (restricted) level. This finding is consistent with the experimental evidence that the aluminyl anion K2[Al(NON)]2 reacts rapidly with 1 atm of CO2 at room temperature to generate the carbonate and CO species. 39

Selection of the fragments for the Au-Al bonding analysis in [ t Bu3PAuAl(NON')]
The choice of how to fragment a bond may be critical and in some cases subject to a certain arbitrariness. Our choice here is based on the results of the Energy Decomposition Analysis (EDA) 10