Argentophilic Interactions, Flexibility, and Dynamics of Pyrrole Cages Encapsulating Silver(I) Clusters

Recently, pyrrole cages have been synthesized that encapsulate ion pairs and silver(I) clusters to form intricate supramolecular capsules. We report here a computational analysis of these structures using density functional theory combined with a semiempirical tight-binding approach. We find that for neutral pyrrole cages, the Gibbs free energies of formation provide reliable predictions for the ratio of bound ions. For charged pyrrole cages, we find strong argentophilic interactions between Ag ions on the basis of the calculated bond indices and molecular orbitals. For the cage with the Ag4 cluster, we find two minimum-geometry conformations that differ by only 6.5 kcal/mol, with an energy barrier <1 kcal/mol, suggesting a very flexible structure as indicated by molecular dynamics. The predicted energies of formation of [Agn⊂1]n-3+ (n = 1–5) cryptands provide low energy barriers of formation of 5–20 kcal/mol for all cases, which is consistent with the experimental data. Furthermore, we also examined the structural variability of mixed-valence silver clusters to test whether additional geometrical conformations inside the organic cage are thermodynamically accessible. In this context, we show that the time-dependent density functional theory UV–vis spectra may potentially serve as a diagnostic probe to characterize mixed-valence and geometrical configurations of silver clusters encapsulated into cryptands.


Pyrrolide cages incorporating mixed-valence silver clusters
We investigated structural variations for a series of caged silver clusters, denoted as m [Agn⊂1] q with n = 3 to 5. Multiplicity m was varied from singlet to triplet or from doublet to quartet as appropriate, and charge q ranges from (n-3)+ to 3-.Geometries were optimized in CH3CN, 1propanol (1-Pr(OH)), CH2Cl2 (DCM) or in the gas phase.Table S8 summarizes the results for m [Ag5⊂1] q .Each row corresponds to a geometry optimization at (PCM) UwB97X-d/6-31G** ~ LANL2DZ confirmed by no imaginary frequencies.The initial geometry in all cases was 1 [Agn⊂1] (n-3)+ in the gas phase (e.g., 1 [Ag5⊂1] 2+ for the n = 5 case), unless indicated otherwise.
Relative energies ∆Erel and ∆Grel in kcal/mol were calculated considering only species with the same charge q (separated by double-line borders in the table).Expected square values of S are reported along with <S 2 >annih to inspect spin contamination.Spin densities (SAg) and Mulliken charges (qAg) in each Ag atom were added to account for total values for the metal clusters.Even though SAg and qAg may be inaccurate due to spin contamination and methodological aspects, respectively, these are only considered as a reference point.The root-mean-square deviation (RMSD) indicates a change in the cluster configuration: no change, RMSD < 0.5 Å; distorted bipyramid, 0.0 < RMSD < 0.5 Å; and square pyramid, RMSD > 1.0 Å.In these cases, geometry optimizations failed, and re-optimizations proceeded from the optimized geometry of 2 [Ag5⊂1] 1+ in CH3CN.Henceforth, re-optimizations correspond to this adjustment so that m [Ag5⊂1] q in solvent was used as the initial geometry.
-High spin configurations are highly destabilized.

S22
The results for q = 0, 1-and 2-suggest that structural variations in the Ag5 cluster are related to changes in q rather than changes in the phase.
-1 [Ag5⊂1] 0 exhibits a square pyramidal Ag5 cluster, RMSD = 1.1 Å, and the triplet state is highly destabilized.In this square pyramidal cluster, the 3Ag + plus 2Ag 0 configuration confirms a closed-shell singlet state (ΣSAg = 0.0 e), but each Ag atom transferred to the cage a small amount of charge (< 0.3 e) as indicated by ΣqAg = 0.6 e.
-The Ag5 cluster in 2 [Ag5⊂1] 1-displays a structure between the initial trigonal bipyramid and square pyramid, RMSD = 0.6 Å, and the quartet state is highly destabilized.In this case, ΣSAg = 0.0 e suggests that the doublet electron is localized in the cage, where a partial charge was transferred from the Ag5 cluster to the cage (ΣqAg = 0.3 to 0.5 e).Only 2 [Ag5⊂1] 1-in gas phase could be optimized in trigonal bipyramidal geometry, yet it is spincontaminated and destabilized.
-The Ag5 cluster in 1 [Ag5⊂1] 2-also exhibits a distorted bipyramid, RMSD = 0.6 to 0.8 Å, but the triplet state resulted more stabilized than the closed-shell state, probably because of the stabilizing exchange of the two unpaired electrons related to the 2-charge.These two unpaired electrons are located in the cage for both the triplet and singlet states due to ΣSAg and ΣqAg < |0.2| e, indicating an Ag + plus 4Ag 0 configuration counteracting 1 3-.Table S10.Energy, electronic and structural parameters for m [Ag5⊂1] q with q = 3-.Structures in the case of 2 [Ag5⊂1] 3-show spin contamination, and the square pyramidal configuration seems to be preferred (although this optimization failed for the gas phase).The quartet state is not spin contaminated, but it is destabilized compared with the attempts for the doublet state (except for results in DCM that seem identical).Overall, due to the spin contamination, the description of this case in terms of structural variability is inconclusive.
Table S11.Energy, electronic and structural parameters for m [Ag4⊂1] q with q = 1+ and 0. The results for q = 1+ and 0 in the case of four Ag atoms are summarized as follows: -RMSD for [Ag4A⊂1] and [Ag4B⊂1] was calculated comparing the initial rhomboidal and trigonal pyramidal geometries in the gas phase, respectively.In general, there are no structural variations, RMSD < 0.4 Å, but in some cases the rhomboidal [Ag4A⊂1] turned into trigonal pyramid as indicated by RMSD = 0.5 to 0.7 Å.Indeed, the trigonal pyramidal configuration is energetically more stable than the rhomboidal counterpart.
-High spin configurations are highly destabilized.
Table S12.Energy, electronic and structural parameters for m [Ag4⊂1] q with q = 1-.The results for q = 1-are summarized as follows: -High spin configurations are highly destabilized.

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-In the case of the trigonal pyramidal (1) optimized from 1 [Ag4A⊂1] 1-, the charge 1-is in the cage, as expected due to the two 2Ag + counteracting 1 3-.In fact, together with the other 2Ag 0 it corresponds to a closed-shell system with a small amount of charge transferred to the cage, as indicated by ΣSAg =0.0 e and ΣqAg < 0.4 e.In contrast, we observe that the rhomboidal structure (first entry) is a doublet that may contain spin contamination.Table S13.Energy, electronic and structural parameters for m [Ag4⊂1] q with q = 2-.The results for q = 2-are summarized as follows: -The rhomboidal 2 [Ag4A⊂1] 2-could not be optimized, so that the trigonal pyramid 2 [Ag4B⊂1] 2-remains the equilibrium geometry.
-Structures 2 [Ag4B⊂1] 2-in solution exhibit spin contamination and, unexpectedly, the other parameters are nearly identical to those calculated for the quartet state.This suggests that the doublet state will not be formed, except for the gas-phase 2 [Ag4B⊂1] 2-.
Table S14.Energy, electronic and structural parameters for m [Ag4⊂1] q with q = 3-.Finally, rhomboidal 1 [Ag4A⊂1] 3-could not be optimized, except for a destabilized planar rhomboid in the gas phase.The trigonal pyramid 1 [Ag4B⊂1] 3-also exhibited optimization issues, and the structure in 1-propanol was the only case with an optimized geometry, but with spin contamination.The geometry in the triplet state did optimize in the trigonal pyramidal (4) structure, and 3 [Ag4A⊂1] 3-was highly rearranged (RMSD = 1.2 Å).The trigonal pyramidal (5) in 3 [Ag4B⊂1] 3-also rearranged (RMSD = 0.7 Å), but it became more destabilized and with spin contamination.In general, due to the spin contamination and geometry-optimization issues, the description of this case in terms of structural variability is inconclusive.
-High spin configurations are highly destabilized.
-In the case of 2 [Ag3⊂1] 1-, the assumed 2Ag + plus Ag 0 configuration may be represented as 3Ag + ; that is, the doublet electron due to Ag 0 was partially transferred to the cage, as indicated by ΣSAg =0.0 e and ΣqAg = 0.6 e.Therefore, the charge 1-in 2 [Ag3⊂1] 1-is originated by 3Ag + counteracting the cage 1 4-with a doublet electron.
-High spin configurations in solution are highly destabilized.
-In the case of trigonal (1) 1 [Ag3⊂1] 2-in solution, the assumed Ag + plus 2Ag 0 configuration does correspond to a closed-shell system (ΣSAg =0.0 e), but the cage transferred ca.0.25 e to each Ag 0 , as indicated by ΣqAg = -0.5 e.We observed a similar trend for trigonal (1) 2 [Ag3⊂1] 3-in CH3CN.→ The spectra exhibit variations in the shortwave UV region.On the other hand, it may be more illustrative to examine the main excitation, which occurs in the longwave UV region (300-325 nm).Considering that the solvent slightly shifts and alters intensity of a band, differences in the spectra are attributed to structural variations.

Figure S13.
Comparisons of electronic excitations due to silver(I) and mixed-valence silver clusters in 1 [Ag5⊂1] q in the gas phase and in solution.
→ The introduction of metallic Ag to form mixed-valence clusters slightly alters the main excitation, but a more interesting effect is observed: excitations in the visible region!Such an effect is even more pronounced when the number of Ag 0 > number of Ag + , for example in 1 [Ag5⊂1] 2-(four Ag 0 and one Ag + ).These colored compounds can be attributed to the presence of mixed-valence Ag clusters.→ The triplet spin state 3 [Ag5⊂1] 2-is more stable than the singlet state 1 [Ag5⊂1] 2-.Therefore, we also calculated triplet-triplet transitions, but only for this case.However, the same observation persisted: These colored compounds may be attributed to the presence of mixed-valence Ag clusters.→ Results reported for the mixed-valence Ag cluster in 1 [Ag4⊂1] 1-suggest that absorptions in the visible region is driven by the condition of Ag 0 > Ag + , which is not met in 1 [Ag4⊂1] 1- (2Ag 0 and 2Ag + ), unlike the previous case 1 [Ag5⊂1] 2-(4Ag 0 and Ag + ).→ Despite differences in the shortwave UV region that may indicate mixed Ag valence, weak absorptions in the visible region appeared in the gas phase for 1 [Ag3⊂1] 2-.In this case, the condition Ag 0 > Ag + is met, so that colored compounds may be attributed to the presence of mixed-valence clusters.→ We compared the TDDFT spectra with those obtained with a larger basis set: (phase) TD-wB97XD/6-311+G** ~ LANL2TZ // (phase) wB97XD/6-31G** ~ LANL2DZ While the electronic transitions remain the same, the results suggest that excitation energies are red shifted, although within a small variation of less than 10 nm.Therefore, results using the double-zeta basis sets are similar to those with the triple zeta basis sets.→ Results obtained with the PCM method are virtually identical to those calculated with the SMD approach.

Figure S1 .
Figure S1.DFT-optimized structures of reduced complex containing three pyrrole and two

Figure S4 .
Figure S4.Ag-N bond distances during the 5 ns molecular dynamics run of the [Ag4-B⊂1] + system

Figure S6 .
Figure S6.Ag-N bond distances during the 5 ns molecular dynamics run of the [Ag3⊂1] system

Figure S7 .
Figure S7.Potential energy surface (PES) of a single Ag + ion exiting the cavity of 1 for [Agn⊂1] n-

Figure S12 .
Figure S12.Effect of the Agn cluster size inside the cage 1 in the gas phase and in solution.

Figure S14 .
Figure S14.Comparisons of electronic excitations due to singlet-to-single transitions in

Figure S15 .
Figure S15.Comparisons of electronic excitations due to silver(I) and mixed-valence silver

Figure S16 .
Figure S16.Comparisons of electronic excitations due to silver(I) and mixed-valence silver

Figure S17 .
Figure S17.Effect of the Agn cluster size inside the cage 1 in the triplet-to-triplet spectra in

Figure S18 .
Figure S18.Comparisons of singlet-to-singlet and triplet-to-triple electronic transitions for

Table S8 .
Energy comparisons (kcal/mol), electronic properties, and structural characterization of m [Ag5⊂1] q structures.In bold the most stabilized structure for a given charge q.