How reduced are nucleophilic gold complexes?

Nucleophilic formal gold(-i) and gold(i) complexes are investigated via Intrinsic Bond Orbital analysis and Energy Decomposition Analysis, based on density functional theory calculations. The results indicate gold(0) centres engaging in electron-sharing bonding with Al- and B- based ligands. Multiconfigurational (CASSCF) calculations corroborate the findings, highlighting the gap between the electonic structures and the oxidation state formalism.


Computational Details
All geometries were optimized in ORCA 5.0.2, 1, 2 using with the low-cost composite DFT method B97-3c from Grimme and co-workers 3 based on Becke's 1997 local exchange correlation functional 4 and uses the triple-zeta mTZVP basis set (based on the Ahlrichs basis set def2-TZVP) 5 and the corresponding effective core potential, 6,7 to model relativistic effects by replacing the inner 60 electrons of gold. Dispersion effects are accounted for via the D3 model. 8,9 Analytical frequencies were computed, and all structures were found to be well defined minima i.e. all calculated frequencies were positive. An energetic convergence criterion of 10 -8 au was request via the TightSCF keyword. The default integration grid (DefGrid2) was used. Solvent effects were included via the conductor-like polarization continuum model (CPCM), 10 with toluene specified as the solvent.
Intrinsic bonding orbital analysis (IBO) was performed in IboView, [11][12][13] via additional single point calculations which were performed at the (B97-3c) optimized geometries with the PBE0 14 /def2-TZVPP 5 level of theory. The RIJCOSX approximation 15 was employed to speed up the integral evaluation, using Weigend's universal fitting basis set (def2/J). An energetic Electronic Supplementary Material (ESI) for Dalton Transactions. This journal is © The Royal Society of Chemistry 2022 S2 convergence criterion of 10 -8 au was requested via the TightSCF keyword. The default integration grid (DefGrid2) was used. Solvent effects were included via the conductor-like polarisation continuum model (CPCM), 10 with toluene specified as the solvent.
CASSCF (4,4) calculations were performed by starting with a RHF/def2-SVP calculation at the optimized B97-3c geometries, with separate Pipek-Mezey (PM) orbital localization of the occupied and virtual spaces in ORCA 5.0.2. The CASSCF active space was chosen by identifying σ-bonding and σ-antibonding orbitals with large coefficients on the Al, Au and P centres (see Figure S1 for an example). Once the CASSCF(4,4) calculation was converged, further PM localization of the active space only was performed in ORCA, followed by a final CAS-CI calculation. The PM localized active spaces of 1a, 1b, 2a and 2b and shown in Figure  3 and Table S1, respectively.

Examples inputs
Geometry  Figure S1: Localized PM orbitals of 1a calculated with RHF, used as the initial active space in the subsequent CASSCF (4,4) calculation. Shown is the Al-Au-P(Me3) moiety with hydrogens and all other atoms hidden. Rendered in IboView. Table S1: PM localized active spaces of 1b, 2a and 2b, calculated with CASSCF (4,4). The X-Au-L moieties are rendered in IboView with orbitals of arbitrary colours, all other atoms are hidden for clarity.

Species
Active space (

Energy Decomposition Analysis
To further probe the electronic structure, and in particular the Au configuration, Morokuma-Ziegler Energy Decomposition Analysis (EDA) [16][17][18] was performed in the Amsterdam Density Functional (ADF) suite of the AMS2020 package. 19 These calculations were performed at the B97-3c optimized geometry from ORCA, and employed the PBE0 functional 14 in combination with the triple-ζ TZ2P basis set. 20 No frozen core approximation was made. Scalar relativistic effects were modelled via a ZORA Hamiltonian. [21][22][23][24][25] Numerical quality was defined with the Good keyword. For each EDA calculation only two fragments were defined: i) the metal centre, Au n+ and ii) the entire remaining ligand framework L n-. The optimised coordinates were reoriented such that the Au-L bonds lay along the xy axes. The data in Table 2 are a summary of the results in Table S2.

Au partial atomic charges
Partial atomic charges were calculated at the PBE0/def2-TZVPP level of theory, using various computational schemes. The Hirshfeld, Voronoi, Mulliken, Löwdin and Fuzzy partial atomic charges were calculated in MultiWFN 3.8. 26,27 The IAO charges were calculated in IboView. 12 Note: these calculations used pseudopotentials to replace the inner 60 electrons of gold, 6 and account for relativistic effects. When integrating electron density within an atomic basin (as in the fuzzy topological scheme), this causes a mismatch e.g. the integrated electron density is ~18 but the Au nuclear charge is set to 79, so the calculated net charge is ~61. To remedy this, the charge of Au in the ORCA molden file was manually changed to 19, as described in the MultiWFN manual. To verify the reliability of this procedure, an all-electron calculation was run for 1a, using a ZORA Hamiltonian, the ZORA-def2-TZVPP basis set for all atoms expect gold (for which the SARC-ZORA-TZVPP basis set was used). A comparison of entries 1a and 1a* in Table S3 shows that Hirshfeld, Voronoi and Fuzzy atomic partial charges are less sensitive to a change in the level of theory, as compared to Muulliken and Löwdin charges.

IBOs of all species
In addition to the IBO analysis of complex 1a ( Figure 2) and the IAO partial charge distributions of all species (Table 1), the following plots of the key IBOs of 1a, 1b, 2a and 2b are included here for completeness.  2 of the X-Au and Au-L bonds in complexes 1 and 2, calculated with PBE0/def2-TZVPP//B97-3c. Orbital isosurfaces rendered in IboView 11, 12 using arbitrary colours to enclose 80% of their electron density.

Method dependency of IBOs
Given the large method dependencies exhibited by partial atomic charges calculated with various schemes (Table S3), we sought to test the method dependence of the IAO partial charge distributions. To this end, we reoptimized the geometry of 1a (starting from the B97-3c optimized geometry, vide supra) with a dispersion-corrected hybrid-GGA exchangecorrelation functional paired with a spilt-valence basis set (B3LYP 33-36 -D3 8 (BJ) 37 /def2-SVP) 5 ; a composite DFT method featuring geometrical counterpoise corrections, 38 dispersion corrections 8,37 and an increased percentage of HF exchange (PBEh-3c); 39 and a dispersion corrected 40 tight-binding DFT method (GFN2-xTB). 41 These methods performed well for gold complexes in our recent benchmark study. 42 As for the other calculations, these optimizations were also performed in ORCA 5.0.2. Increased convergence thresholds we requested with the TightOpt keyword. The minima were verified via frequency analysis. An analytical Hessian was calculated for B3LYP-D3(BJ)/def2-SVP using the Freq keyword. Numerical Hessians were the requested for PBEh-3c and GFN2-xTB using the NumFreq keyword. For B3LYP-D3(BJ)/def2-SVP and PBEh-3c, the cPCM solvation model was used, with toluene as the solvent. For the GFN2-xTB calculation, the xtb executable (v6.4.1) was placed in the ORCA directory and was called using the xTB2 keyword. The ALPB solvation modelled was used, with toluene specified as the solvent. All of these calculations used effective core potentials to replace the inner 60 electrons of gold. 6 Additional single point calculations with PBE0/def2-TZVPP were performed at the optimized geometries to tease apart geometric and electronic effects in the method dependences. These calculations used the same settings as those performed at the optimized B97-3c geometry (vide supra). The doubly occupied σ-IBOs of the Al-Au and Au-P bonds calculated with these methods, and with the PBE0 single point calculations, are shown in Table S5. The crucial Al-Au bond polarity varies by just 0.11e. The largest variation (0.22e) is seen for the Au-P bond, calculated with GFN2-xTB vs. PBE0-def2-TZVPP//GFN2-xTB. With all tested methods, the IAO partial charge distributions of the Al-Au and Au-P bonds leave their respective characterization as electron-sharing and dative covalent, and therefore all conclusions regarding oxidation states, unchanged.

Comparison to alkyl gold complexes
To compare highly electron-sharing covalent nature of the Au-Al bond in 1 and 2, we applied the same PBE0/def2-TZVPP//B97-3c level of theory (vide supra) to calculate the IAO partial charges in the X-Au-L alkyl gold complexes, where X = Me and L= (P t Bu3, Me-Au-IPr) i.e. the same L ligands as in 1 and 2. The gold-alkyl bonds are significantly less polarized than their gold-aluminyl and gold-boryl analogues (Table S6). If we choose some arbitrary threshold for 'ownership' of the bonding pair, say 70%, we might say that the Au-Me bonds lie close to the boundary between the electron-sharing and dative bonding regimes. Similar IAO partial charge distributions are found in other coinage metal carbon bonds e.g., [Cu(CF3)4] 1-. 43 Table S6: (σ-IBO) 2 of the Me-Au and Au-L bonds in the X-Au-L alkyl gold complexes, where X = Me and L= (P t Bu3, IPr).

Me-Au
Au-L

Valence bond calculations
Valence bond SCF calculations 44,45 were performed with TURTLE, 46, 47 as implemented in GAMESS-UK. 48 For the Valence Bond calculations, the def2-SVP basis set 5 was used. The model molecules (1a-VB and 2a-VB) were divided in two fragments, viz. the (PH3)Au fragment and the Al(C4N2H6O)/BH2 fragment. Startup orbitals for the VB calculation were taken from a prior RHF calculation followed by a Pipek-Mezey 49 localization. The Au-M localized bond was used to form the two orbitals, that are used to form the spin coupled Au-M bond. Three structures were included in the calculation: A Au-M, B Au + M -, and C Au -M + . The Gallup and Norbeck (GN) 50 and Chirgwin and Coulson (CC) 51 schemes are used to calculate the weights of the individual, non-orthogonal, VB structures. During the orbital optimization, the orbitals were kept localized on each fragment.
The final orbitals and their composition are depicted in Figure S2, and the weights of the individual structures are listed in Table S5.

Compound Abbreviation
The gold orbital in both compounds have a similar composition, and it has mainly s-character, with some p and d character. The orbital localized on Al is a sp hybrid, while the B orbital is more sp 2 -like hybridized. For both models, the covalent structure has the highest weight. For Au-Al, the bond is polarized towards the Au atom, indicating a nucleophilic Au species. For Al-B, the polarity is reversed, with the Au + Bstructure more important than the Au -B + structure.