Selective Gold Precipitation by a Tertiary Diamide Driven by Thermodynamic Control

The simple diamide ligand L was previously shown to selectively precipitate gold from acidic solutions typical of e-waste leach streams, with precipitation of gallium, iron, tin, and platinum possible under more forcing conditions. Herein, we report direct competition experiments to afford the order of selectivity. Thermal analysis indicates that the gold-, gallium-, and iron-containing precipitates present as the most thermodynamically stable structures at room temperature, while the tin-containing structure does not. Computational modeling established that the precipitation process is thermodynamically driven, with ion exchange calculations matching the observed experimental selectivity ordering. Calculations also show that the stretched ligand conformation seen in the X-ray crystal structure of the gold-containing precipitate is more strained than in the structures of the other metal precipitates, indicating that intermolecular interactions likely dictate the selectivity ordering. This was confirmed through a combination of Hirshfeld, noncovalent interaction (NCI), and quantum theory of atoms in molecules (QTAIM) analyses, which highlight favorable halogen···halogen contacts between metalates and pseudo-anagostic C–H···metal interactions in the crystal structure of the gold-containing precipitate.

Although the fit was poor, the refined unit cell parameters from analysis of the PXRD data and the unit cell parameters from the single crystal XRD data refinement are similar (see table above).Furthermore, the fit suggests the single crystal phase is the major phase present in the precipitate, with the unmatched peaks likely corresponding to another phase, such as a polymorph of the single crystal phase.Table S1.Calculation of ∆U ex -The energy required to exchange each metalate with [AuCl 4 ]  in the precipitate was calculated according to equations 2 and 3 in the main text using the ground state electronic energies given below, with the exchange energy given in the final column.] -∆U ex was used in conjunction with the zero-point energy (ZPE) and entropy (S) corrections given below to calculate ∆G ex for the gallium complex, given the smallest exchange energy was observed for this structure.∆G ex was calculated as follows:

M Ground State Electronic Energy / kJ mol
(1) ∆  = ∆ + ∆  -∆ Where T=293 K and ∆ZPE and ∆S are the change in ZPE and S respectively.With very small variation between complexes the ZPE had a negligible effect on the final energy, with the major contribution to the final Gibbs free energy due to the entropic contribution.

Species
Zero Point Energy / kJ mol -1 Entropy / kJ mol  Analysing these colour patches reveals that the ligand in the gold structures uses 3.8% of its surface area to bind to the gold metalate, 3.4% for gallium, iron and tin and 3.2% for platinum.This consolidates the conclusions drawn in this study that the gold metalate is the most efficiently packed in the crystal lattice and therefore maximises intermolecular interactions with the ligand.

Figure S4 .
Figure S4.PXRD Pawley Refinement of [HL][FeCl 4 ] -The observed pattern of the bulk [HL][FeCl 4 ] precipitate, recorded on the high-resolution powder diffraction beamline (I11) at the Diamond Light Source, is shown in grey with the fit calculated using a multiphase Pawley refinement shown in purple.The difference profile is shown in dark blue and tick marks associated with the [HL][FeCl 4 ] refined single crystal data are shown in light blue and those associated with the ligand (taken from the CCDC structure of L under collection code 1150349) are shown in green.Although the fit was poor, the refined unit cell parameters from analysis of the PXRD data and the unit cell parameters from the single crystal XRD data refinement are similar (see table above).Furthermore, the fit suggests the single crystal phase is the major phase present in the precipitate, with the unmatched peaks likely corresponding to another phase, such as a polymorph of the single crystal phase.

Figure S5 .
Figure S5.PXRD Pawley Refinement of [HL] 2 [SnCl 6 ](H 2 O) 2 -The observed pattern of the bulk [HL] 2 [SnCl 6 ](H 2 O) 2 precipitate is shown in grey with the fit calculated using a Pawley refinement shown in purple.The difference profile is shown in dark blue and tick marks in light blue.An excellent match between the refined unit cell parameters from analysis of the PXRD data with the unit cell parameters from the single crystal XRD data refinement confirms the two phases are the same, with only slight variations in the unit cell parameters (see table above).

Figure S6 .
Figure S6.PXRD Pawley Refinement of [HL] 2 [SnCl 6 ] -The observed pattern of the bulk [HL] 2 [SnCl 6 ] precipitate, recorded on the high-resolution powder diffraction beamline (I11) at the Diamond Light Source, is shown in grey with the fit calculated using a Pawley refinement shown in purple.The difference profile is shown in dark blue.An excellent match between the refined unit cell parameters from analysis of the PXRD data with the unit cell parameters from the single crystal XRD data refinement confirms the two phases are the same, with only slight variations in the unit cell parameters (see table above).The remaining unmatched peaks correspond to residual ligand in the starting material.

Figure S8 .
Figure S8.In situ DSC -PXRD measurements of [HL][AuCl 4 ] -a) Selected PXRD patterns from the 20 -200 C heat cycle, showing the slight peak shift of observed diffraction peaks to lower scattering angles (orange selection, right of figure (a)) and eventual loss of crystallinity at ca. 180 C for the [HL][AuCl 4 ] precipitate.Pawley refinement of the unit cell parameters for the selected patterns above

Figure S9 .
Figure S9.In situ DSC -PXRD measurements of [HL][GaCl 4 ] -a) Selected PXRD patterns from the 20 -200 C heat cycle, showing thermal expansion of the crystallites as diffraction peaks shift to lower scattering angles with an eventual loss of crystallinity at ca. 142 C.Pawley refinement of the unit cell parameters to further confirm thermal expansion was not possible with this data set due to the high signal to noise ratio which results from the short collection time implemented in these measurements.b) DSC curve over the 20 -200 C heat cycle, showing a diffuse peak at an onset temperature of ca.130 C and ending at ca. 150 C, which corresponds to a loss of crystallinity in the PXRD pattern.

Figure S10 .
Figure S10.In situ DSC -PXRD measurements of [HL][FeCl 4 ] -a) Selected PXRD patterns from the 20 -200 C heat cycle, showing the slight peak shift of observed diffraction peaks to lower scattering angles with an eventual loss of crystallinity at ca. 139 C.Again, refinement of the unit cell parameters was not possible with this data set due to very high signal to noise, arising from the presence of iron in the sample and the short collection time of each pattern.b) DSC curve over the 20 -200 C heat cycle, showing a diffuse peak at an onset temperature of ca.120 C and ending at ca. 160 C, which corresponds to a loss of crystallinity in the PXRD pattern.

Figure S12 .
Figure S12.In situ DSC -PXRD measurements of [HL] 2 [PtCl 6 ](H 2 O) 2 -a) Selected PXRD patterns from the 20 -200 C heat cycle for the [HL] 2 [PtCl 6 ](H 2 O) 2 precipitate, showing two transitions.The first transition corresponds to a loss of lattice water and occurs at an onset temperature of ca.62 C with a gradual loss of crystallinity observed from this temperature, confirming that water of crystallisation is important in crystal formation for this precipitate.The second transition occurs at ca. 150 C, whereby the sample melts, losing all crystallinity, with an amorphous solid formed upon cooling.b) DSC curve over the 20 -200 C heat cycle, showing a small bowing endotherm peak at ca. 60 C which correlates with the loss of lattice water in the PXRD pattern.A further transition occurs at ca. 150 C and corresponds to the melting endotherm.

Figure S13 .
Figure S13.Determination of Optimum Simulation Box size for the Extracted Ligand Coils -The optimum width of the vacuum layer in the simulation boxes was determined through a series of single point energy calculations, whereby the box size was incrementally increased by changing the d sep values.At a d sep value of 35 Å, the predicted change in energy when the vacuum layer width was increased by 1 Å was 2.5 kJ mol -1 Å -1 .With the maximum difference in the extension of the coil from its central axis 0.29 Å across all structures, a d sep value of 35 Å was deemed appropriate to sufficiently capture energy differences greater than approximately 1 kJ mol -1 .

Figure S14 .
Figure S14.Hirshfeld surface fragment patches -Fragment patches on Hirshfeld surfaces for one [HL] + unit for three representative structures, namely a) gold b) gallium andc) tin.Different colours on the plots represent areas of close contacts with neighbouring molecules.Analysing these colour patches reveals that the ligand in the gold structures uses 3.8% of its surface area to bind to the gold metalate, 3.4% for gallium, iron and tin and 3.2% for platinum.This consolidates the conclusions drawn in this study that the gold metalate is the most efficiently packed in the crystal lattice and therefore maximises intermolecular interactions with the ligand.

Figure S15 .
Figure S15.2D NCI plot analysis -2D Reduced gradient, s vs sign(λ)ρ plots for the a) [HL][AuCl 4 ] b) [HL][GaCl 4 ], c) [HL][FeCl 4 ] and d) [HL] 2 [SnCl 6 ](H 2 O) 2 crystal structures, coloured to highlight the nature of the interactions according to the legend, with the full reduced density plot shown on the left and an excerpt of the plot shown on the right to highlight the dispersive interactions.Unassigned interactions (shown in black) correspond to the remaining [HL] + •••[HL] + interactions.Features approaching zero on the Y-axis indicate a stationary point on the reduced density surface (i.e., a noncovalent interaction), and the value of the intercept on the X-axis indicates whether the interaction is attractive (sign(λ 2 )ρ < 0), repulsive (sign(λ 2 )ρ > 0) or dispersive (sign(λ 2 )ρ ≈ 0) in nature.
table above).Furthermore, the fit suggests the single crystal phase is the major phase present in the precipitate, with the unmatched peaks likely corresponding to another phase, such as a polymorph of the single crystal phase.

UC Parameter 24 C - 29 C 52 C - 59 C 88 C - 95 C 125 C - 132 C
table above).The remaining unmatched peaks correspond to residual ligand in the starting material.b 11.0954(14) 11.1667(6) c 12.0668(15) 12.0992(9) α 113.978(5) 114.058(4) β 103.941(5) 103.711(7) γ 96.913(5) 97.211(7) Figure S7.PXRD Pawley Refinement of [HL] 2 [PtCl 6 ](H 2 O) 2 -The observed pattern of the bulk [HL] 2 [PtCl 6 ](H 2 O) 2 precipitate is shown in grey with the fit calculated using a Pawley refinement shown in purple.The difference profile is shown in dark blue and tick marks in light blue.An excellent match between the refined unit cell parameters from analysis of the PXRD data with the unit cell parameters from the single crystal XRD data refinement confirms the two phases are the same, with only slight variations in the unit cell parameters (see table above).

Figure S11. In situ DSC -PXRD measurements of [HL] 2 [SnCl 6 ](H 2 O) 2 -a) Selected
PXRD patterns from the 20 -200 C heat cycle for the[HL]2[SnCl 6](H 2 O) 2 precipitate, detailing three transitions.The first transition corresponds to a loss of channel water and occurs at an onset temperature of ca.42 C with complete water loss observed at 57 C, shown by a shift in the peaks to higher scattering angles without an overall change in the powder pattern.Although Pawley refinement of this data was not possible due to poor signal to noise, the data were indexed, with refined unit cell parameters similar to those determined by analysis of single crystal data for both phases (see table above).The unit cell parameters of the dehydrated phase show a decrease in all cell lengths and the α and β angles, resulting in a reduction in unit cell volume from the loss of water at 57 C -62 C.The second transition occurs at ca. 127 C, which appears to be a second order transition such as a glass transition, with a change in the PXRD pattern observed.The final transition occurs at 175 C and corresponds to the endotherm melting point of the ligand, which has a literature melting point of 177 C.1The remaining crystalline phase must therefore correspond to a SnCl x species, which explains the good scattering and apparent high crystallinity of this phase.b) DSC curve over the 20 -200 C heat cycle, showing a small bowing endotherm peak at ca. 45 C which correlates with the loss of channel water noted in the PXRD pattern (see orange insert).A further monotropic phase transition is observed at ca. 125 C with the final transition at 175 C corresponding to the melting point endotherm of the ligand.

Optimised atomic coordinates and energies
•••H 2 O interaction only present in the [SnCl 6 ] 2 plot (green troughs (d)).Therefore, in order to identify variations in the intermolecular interactions between structures, detailed analysis of the plots must focus on the dispersion interactions close to sign(λ 2 )ρ = 0 which characterise the [HL] + •••[MCl x ] y and [MCl x ] y •••[MCl x ] y interactions (Figure S15, right).The most notable difference in this area of the plots is that the host•••guest interactions seem to increase in strength in the reverse order of selectivity, with the weakest interactions (closest to sign(λ 2 )ρ = 0) observed in the [HL][AuCl 4 ] plot, followed by [HL][GaCl 4 ] and [HL][FeCl 4 ], while the strongest interactions are observed in the [HL] 2 [SnCl 6 ](H 2 O) 2 plot.However, this analysis does not take the multiplicity of the individual interactions into account, and therefore this observation is not indicative of overall host•••guest interaction strengths.The 2D plot for [HL][AuCl 4 ] depicts the CH Space group, space group number, unit cell parameters (not optimised) and optimised symmetry inequivalent coordinates for the geometry optimised complexes presented in this work are given below.
2 •••Au and Cl•••Cl interactions as stabilising, consolidating their importance in precipitate stability, and although CH 2 •••metalate interactions appear more stabilising in the [HL][GaCl 4 ], [HL][FeCl 4 ] and [HL] 2 [SnCl 6 ](H 2 O) 2 plots, this is due to a change in the type of interaction.The CH 2 moiety interacts directly with the metal centre in the gold structure providing complete encapsulation of the metalate, whereas in the other structures the group interacts with the metalate through non-classical hydrogen bonds, which we would expect to be a stronger interaction but less significant in encapsulating the metalate.[HL]+ •••metalate interactions appear at similar negative sign(λ 2 )ρ values in the [HL][GaCl 4 ] and [HL][FeCl 4 ] plots however are more delocalised and shifted to a higher sign(λ 2 )ρ in the iron structure, indicating a more destabilising character.Furthermore, a trace signature of the favourable [MCl x ] y •••[MCl x ] y interactions is observed in the [HL][GaCl 4 ] plot, while only present as a destabilising interaction in the [HL][FeCl 4 ] plot.Finally, fewer [HL] + •••[MCl x ] y interactions are present in the 2D [HL] 2 [SnCl 6 ](H 2 O) 2 plot, with the [MCl x ] y •••[MCl x ] y interaction being completely absent.Section 5:

Python script for preparing model unit cells
Cu at home/near, Atlas Absorption correction For a sphere CrysAlis PRO 1.171.42.81a (Rigaku Oxford Diffraction, 2023) Spherical absorption correction using equivalent radius and absorption coefficient.Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.