Nature of hydride and halide encapsulation in Ag₈ cages: insights from the structure and interaction energy of [Ag₈(X){S₂P(OⁱPr)₂}₆]⁺ (X = H⁻, F⁻, Cl⁻, Br⁻, I⁻) from relativistic DFT calculations

Abstract

Unraveling the different contributing terms to an efficient anion encapsulation is a relevant issue for further understanding of the underlying factors governing the formation of endohedral species. Herein, we explore the favorable encapsulation of hydride and halide anions in the [Ag₈(X){S₂P(OPr)₂}₆]⁺ (X⁻ = H, 1, F, 2, Cl, 3, Br, 4, and, I, 5) series on the basis of relativistic DFT-D level of theory. The resulting Ag₈–X interaction is sizable, which decreases along the series: −232.2 (1) > −192.1 (2) > −165.5 (3) > −158.0 (4) > −144.2 kcal mol⁻¹ (5), denoting a more favorable inclusion of hydride and fluoride anions within the silver cage. Such interaction is mainly stabilized by the high contribution from electrostatic type interactions (80.9 av%), with a lesser contribution from charge-transfer (17.4 av%) and London type interactions (1.7 av%). Moreover, the ionic character of the electrostatic contributions decreases from 90.7% for hydride to 68.6% for the iodide counterpart, in line with the decrease in hardness according to the Pearson's acid–base concept (HSAB) owing to the major role of higher electrostatic interaction terms related to the softer (Lewis) bases. Lastly, the [Ag₈{S₂P(OPr)₂}₆]²⁺ cluster is able to adapt its geometry in order to maximize the interaction towards respective monoatomic anion, exhibiting structural flexibility. Such insights shed light on the physical reasoning necessary for a better understanding of the different stabilizing and destabilizing contributions related to metal-based cavities towards favorable incorporation of different monoatomic anions.

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Introduction

Chemical bonding in confined spaces¹ is of great interest towards the understanding of fundamental characteristics underlying anion recognition, receiving, and sensing, which are crucial to the rational design of supramolecular systems.^2,3 Such understanding is of further interest owing to the relevant role of anions in fields ranging from biology, environmental science, drug delivery, catalysis, among others subjects^4–10 to pursuing improved host cavities.^3,11–14

To achieve an effective incorporation of halides and hydrides into confined cavities, different stabilizing features are involved ranging from metal bonding,¹⁵ hydrogen bonding¹⁶ among other weak interactions,¹⁷ resulting in favorable aggregates.¹⁸ In this sense, prototypical templates provide reliable scenarios to further rationalize the stabilizing terms accounting for the nature of anion encapsulation when going from harder to a softer guest, with variable sizes.^19–21 Stabilization of anion encapsulation involves different contributions to the electrostatic stabilization of the interaction such as ion–ion, ion–dipole, and dipole–dipole, among others terms,^22–26 where analysis of their variation and characteristics of the suitable host species is crucial for the understanding and design of further anion receptors.

The reported [Ag₈(X){S₂P(OⁱPr)₂}₆]⁺ (X = H⁻, F⁻, Cl⁻, Br⁻, I⁻) series, hydride, and halogens are introduced in a confined cage provided by eight Ag atoms leading to an almost symmetrical cubic environment for anion encapsulation, denoting sizable structural distortions for H⁻ case.^27–30 Such features denote the flexibility of the Ag₈ cage towards maximization of the host–guest interaction.³¹ Such species are prototypical examples to evaluate the characteristics of metal based cavities^32–36 or metallocages as extension of the well-developed molecular recognition of anions traditionally performed on organic cavities.^37–41

According to the HSAB concept,^21,42 Ag⁺ ions involved in such clusters are considered as a soft acid, which interacts with soft and hard bases, providing recognition of relevant anion-binding characteristics for suitable confined cavities. In addition, theoretical studies on the bonding nature of coinage metals and different ligands denote silver as the least covalent counterpart, which decrease as follows: Au > Cu > Ag,^43–45 offering the [Ag₈{S₂P(OⁱPr)₂}₆]²⁺ cage as a prototypical example of a weakly covalent environment to further explore non-covalent halide encapsulation.

In this report, we account for the main features related to the incorporation of hydride and halide anions into the confined Ag₈ cavity provided by [Ag₈{S₂P(OⁱPr)₂}₆]²⁺ clusters, in the [Ag₈(X){S₂P(OⁱPr)₂}₆]⁺ cluster (X⁻ = H, 1, F, 2, Cl, 3, Br, 4, and, I, 5). From density functional theory calculations, the anion-cavity interaction is rationalized under different energetic terms underlying the stabilization of the aggregate. The obtained interaction energy is further decomposed into the relative contribution towards the stabilization of the overall complex via a quantitative energy decomposition analysis (EDA).^46–50 This approach provides quantities accounting for Pauli repulsion, electrostatics, charge transfer, and dispersion, which are informative for the understanding of the anion–cavity interaction nature, informative towards a rational design of efficient host cavities.

Computational details

Calculations were performed via relativistic density functional theory with Slater-type orbitals (STOs) of triple-zeta quality basis set plus two polarization functions (TZ2P),⁵¹ by using the ADF2019 suite.⁵² Relativistic effects were accounted through the scalar ZORA Hamiltonian.^53,54 Becke exchange and the Perdew correlation functional (BP86),^55,56 in conjunction with the Grimme's empirical dispersion correction with the Becke–Johnson damping functions, D3(BJ), were employed for all the calculations.^57,58 Calculated geometries were optimized without any symmetry constraints. All the obtained structures correspond to a minimum on the potential energy surface by the absence of imaginary eigen values in the hessian matrix.

Results and discussions

The representative structures for [Ag₈(X){S₂P(OPr)₂}₆]⁺ (X⁻ = H, 1, F, 2, Cl, 3, Br, 4, and, I, 5) series are given in Fig. 1, denoting that the Ag₈ cluster is able to offer tetrahedral Ag₄ and hexahedral Ag₈ cages in order to incorporate different monoatomic anions. For 1, the central tetrahedron is further capped by four Ag atoms, with the hydride located at the center. For the halide series (2–5), a hexahedral (cube) cage is depicted where the calculated shorter and longer Ag–Ag edge distances (Table 1), namely Ag–Ag^Short and Ag–Ag^Long, respectively, vary towards increased separations according to: Ag–Ag^Short: 3.088 (2) < 3.256 (3) < 3.308 (4) < 3.369 Å (5), and, Ag–Ag^Long: 3.291 (2) < 3.500 (3) < 3.443 (4) < 3.614 Å (5). In turn, the Ag–X average increases as 2.602 (2) < 2.882 (3) < 2.961 (4) < 3.068 Å (5). For 1, the Ag–H is 1.890 Å with an Ag₄ cage of 3.024 Å edges. These values agree well with the available experimental data for 1–4, where differences from the experimental data may be originated from packing effects in the crystal.

Fig. 1 Calculated structures for 1 (a) and 2 (b), denoting the Ag₄ encapsulating cage for 1, and the Ag₈ cube for 2 as representative for 2–5.

Table 1 Relevant geometrical parameters for the [Ag₈(X){S₂P(OPr)₂}₆]⁺ (X⁻ = H, 1, F, 2, Cl, 3, Br, 4, and, I, 5) series, in comparison to the experimentally available data from X-ray diffraction. Values in Å

	1	2	3	4	5
	H^−	F^−	Cl^−	Br^−	I^−
Experimental values for 1–3 from ref. 27, and for 4 from ref. 28. Data not available for 5.
Ag–X	1.890	2.602	2.882	2.961	3.068
Exp.^a	1.921	2.735	2.892	2.927
Ag–Ag^Short	3.024	3.088	3.256	3.308	3.369
Exp.^a	3.028	3.043	3.196	3.269
Ag–Ag^Long	3.450	3.291	3.500	3.443	3.614
Exp.^a	3.312	3.260	3.469	3.328
CShM-Cube	6.60	0.35	0.17	0.17	0.15

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The different structural deviations from ideal tetrahedral and hexahedral cages of the Ag₈ core are depicted by employing the continuous-shape-measure (CShM) approach developed by Alvarez and coworkers,^59–61 which correlate each structure in relation to the respective ideal polyhedron (Table 1). For a fully coincident structure, the root mean square deviation values of CShM analysis tend to zero and increases according to the distortion degree of the structure. For 1, the structure largely deviates from a perfect hexagonal structure (CShM = 6.60), where the central tetrahedron is distorted in relation to a tetrahedron (CShM = 1.49) owing to the main elongation of one vertex, where the outer capping of 4 Ag atoms lead to a more symmetrical tetrahedron (CShM = 0.059). In the 2–5 series, the hexahedral or cubic cage shows several distortion degrees, which decrease as the anion radius increases (CShM = 0.35 (2) > 0.17 (3) ≃ 0.17 (4) > 0.15 (5)).

Such different distortion degrees suggest amenable structural flexibility of the [Ag₈{S₂P(OPr)₂}₆]²⁺ cluster or cage, which is able to undergo geometrical distortions in order to maximize the interaction towards the endohedral anion involving small energy changes. In this sense, the preparation energy (ΔE_prep) is related to the required energy to promote a geometry from an isolated state to its final geometry in each [Ag₈(X){S₂P(OPr)₂}₆]⁺ species and allows for the quantification of the related energy cost. For 2, ΔE_prep amounts to 4.2 kcal mol⁻¹, varying as 3.7 (3) < 4.9 (4) < 8.8 kcal mol⁻¹ (5) along with the different halides, denoting that for the Cl⁻ encapsulated counterpart (3) the geometry of the supporting cluster varies in a lesser amount, and for I⁻ (5), in a larger degree. In contrast, for [Ag₈(H){S₂P(OPr)₂}₆]⁺ (1), the required geometrical arrangements favoring the observed encapsulation of the hydride are to a larger extent leading to a ΔE_prep of 15.8 kcal mol⁻¹. Hence, for the smaller hydride atom and the larger iodine (1 and 5), the cage–X interaction required a larger distortion in comparison to Cl⁻ (3). Similar to previous calculations, the charge distribution in the overall cluster retains most of the negative charge at the endohedral atom.²⁸

The favorable Ag₈–X interaction is further evaluated by the interaction energy (ΔE_int, Table 2). As a result, the interaction is decreasing considerably along the series amounting to: −232.2 (1) > −192.1 (2) > −165.5 (3) > −158.0 (4) > −144.2 kcal mol⁻¹ (5), denoting a more favorable inclusion of hydride and fluoride atoms within the silver cage. Further analysis accounting for the nature of interaction is achieved by using the energy decomposition analysis (EDA) within the Morokuma–Ziegler scheme,^46,62,63 which dissects the ΔE_int quantity in different chemically meaningful terms, according to eqn (1):^49,63–66

ΔE_int = ΔE_Pauli + ΔE_elstat + ΔE_orb + ΔE_disp (1)

ΔE_elstat and ΔE_orb stand for the stabilizing contributions from both electrostatic and covalent character of the interaction, whereas the ΔE_Pauli term is related to the repulsive four-electron two-orbital interactions between the occupied orbitals giving rise to steric hindrance between the interacting fragments.⁶⁷ In addition, the London dispersion interactions (ΔE_disp) are accounted for by the pairwise correction of Grimme⁶⁸ (DFT-D3), of stabilizing character. Moreover, the basis set superposition error (BSSE) in the fragment interaction analysis to ΔE_orb was corrected via the counterpoise method.

Table 2 Energy decomposition analysis for the [Ag₈{S₂P(OPr)₂}₆]²⁺–X⁻ interaction, values in kcal mol⁻¹, for 1–5 clusters, and the hypothetical centered case for H⁻ (1^cent) involving a Ag₈ cage related to the clusters 2–5. i–d% denotes the contribution from the ionic character of the endohedral anion (see text below)

	1		1 ^cent		2		3		4		5
	H		H^cent		F		Cl		Br		I
a Percentual values denote the contribution from each stabilizing term to the overall favorable interaction.
ΔEprep	15.8		4.2		4.2		3.7		4.9		8.8
ΔEPauli	427.2		149.6		75.2		157.2		213.9		276.0
ΔEelstat	−556.7	84.4%^a	−282.6	82.0%^a	−190.6	71.3%^a	−257.5	79.8%^a	−308.9	83.1%^a	−357.5	85.1%^a
ΔEorb	−100.7	15.3%^a	−58.8	17.1%^a	−73.2	27.4%^a	−57.3	17.8%^a	−53.4	14.4%^a	−51.5	12.3%^a
ΔEdisp	−2.0	0.3%^a	−3.1	0.9%^a	−3.5	1.3%^a	−7.8	2.4%^a	−9.6	2.6%^a	−11.3	2.7%^a
ΔEint	−232.2		−195.0		−192.1		−165.5		−158.0		−144.2
i–d%	90.7%		97.1%		84.2%		76.6%		72.2%		68.6%

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From the relative contributions given by the stabilizing terms, ΔE_orb, ΔE_elstat, and ΔE_disp, the nature of the interaction (ΔE_int) can be evaluated. For the [Ag₈{S₂P(OPr)₂}₆]²⁺–X⁻ interaction, the contribution from ΔE_elstat is to a large extent leading to an electrostatic character of the encapsulation of 71.3% to 85.1% along with the halide series (2–5), and of 84.4% for the hydride case (1). In addition, the ΔE_orb related to charge transfer contributes 27.4 to 12.3% from 2 to 5, and 15.3% for 1, where London dispersion interactions (ΔE_disp) contribute to a lesser extent.

Moreover, ΔE_elstat tends to be more favorable from 2 to 5, with values of −190.6 to −357.5 kcal mol⁻¹, which is higher for 1 (−556.7 kcal mol⁻¹). This shows the relevance of the electrostatic character in the halide and hydride encapsulation and how it increases towards the softer halides in terms of the Pearson's HSAB concept.²¹ Lastly, the repulsive term (ΔE_Pauli) increases from 2 to 5, according to the halide size within the Ag₈ cage (75.2 to 276.0 kcal mol⁻¹). ΔE_Pauli is higher for 1 owing to the rearrangement of the core into an Ag₄H cage (427.2 kcal mol⁻¹), which in turn is overcome by the sizable stabilizing terms of the interaction, mainly given by ΔE_elstat increase, denoting the ability of the cage to modify its structure according to the incoming encapsulated species in order to favor stabilization. The ΔE_orb remains similar from Cl⁻ to I⁻ (3–5), denoting the small variation in charge transfer between the endohedral atom and the silver cage, which is larger for 2 and 1. Moreover, the role of relativistic effects is evaluated by non-relativistic calculations (Table S1, ESI†), which denote small deviations from the obtained values at the relativistic level (Table 2) suggesting a decrease in the values of ΔE_int for the clusters 2–5, given mainly by a small decrease of the ΔE_orb term upon inclusion of the relativistic effects, which decreases the radial distribution of 5s-Ag orbitals, and hence affect the anion → Ag₈ bonding. For the hydride case (1), the relativistic effect increases the ΔE_orb term favoring the ΔE_int value owing to a shorter Ag–X distance (Table 1).

For comparison, a hypothetical case with the hydride atom encapsulated in a hexagonal Ag₈ cage, related to halide species is calculated in order to discuss the two different cage environments given by Ag₄ in 1 and Ag₈ in 2–5 clusters (Fig. 1), leading to the enhanced interaction energy in the former. For Ag₈H (1^cent), the ΔE_int decreases to −195.0 kcal mol⁻¹, in the range of halide cases particularly similar to 2 (Ag₈F), owing to a large decrease of both stabilizing ΔE_elstat and ΔE_orb contributions. In addition, the steric hindrance accounted by ΔE_Pauli is also decreased when going from an Ag₄ to an Ag₈ encapsulating cage for the hydride case. Thus, the Ag₄ cage offers a relevant increase in the stabilizing terms of interaction, leading in turn to a sizable increase in the steric hindrance for the encapsulation, which is only avoided for the hydride case. This comparison between 1 and 1^cent supports the preference of Ag₄H encapsulation.

Further evaluation of the nature of the electrostatic term involving ion–ion, ion–dipole, and other higher-order interactions, such as dipole–dipole, quadrupole–dipole, and quadrupole–quadrupole, is achieved by analysis of hypothetically related noble-gas (Ng) counter parts. Noble gases are isoelectronic to the corresponding hydride and halides, in a neutral case, effectively allowing to remove the contribution from the ionic character ascribed to the endohedral atom, unraveling the stabilizing contribution from higher-order interactions.^69–72 As the electrostatic interactions accounted by ΔE_elstat can be expressed as a multipole–multipole power series, the contribution from ion–ion and ion–dipole contribution (i–d) to ΔE_elstat was estimated according to eqn (2), in which ΔE_elstat,N is the electrostatic energy term for the isoelectronic neutral analogs of each anion (H⁻/He, F⁻/Ne, Cl⁻/Ar, Br⁻/Kr, and I⁻/Xe), as given in Table 2.

As a result, the contribution from the ionic character (i–d) of the endohedral Lewis base to ΔE_elstat accounts to 90.7% for the hydride case (1) and 84.2% for fluoride (2), which decreases along the halide series as 76.6% (3) > 72.2% (4) > 68.6% (5). Interestingly, the character of the ionic contribution decreases from 1 to 5, owing to the contribution from higher-order interactions, when going from harder to softer anions.^19,20 Hence, the increase observed from 2 to 5 in relation to the electrostatic character of the interaction is given by the contribution of increasing softer character of halides. Similar results with related trend and magnitude are obtained by using dispersion corrected hybrid (B3LYP-D3 and PBE0-D3) and meta-hybrid levels of theory (M06-2X), as given in Tables S3–S5 (ESI†).

Moreover, the computed thermodynamic parameters denote an enthalpy change (ΔH) for [Ag₈{S₂P(OPr)₂}₆]²⁺ + X⁻ → [Ag₈(X){S₂P(OPr)₂}₆]⁺, given by −397.6 kJ mol (1) > −295.9 (2) > −128.5 (3) > −103.0 (4) > −29.2 (5). These values denote a decrease in the favorable enthalpy change along the series, which is lowest for 5.

Lastly, the ligand–core interaction is calculated in order to evaluate the role of the endohedral atom (Table 3) and its related interaction energy in the bonding characteristics of the protecting ligands. The energy decomposition analysis (EDA) applied to the [Ag₈(X){S₂P(OPr)₂}₅]²⁺–{S₂P(OPr)₂}⁻ interaction, showing ΔE_int values in the range between −207.8 and −203.0 kcal mol⁻¹, suggests similar features along the series with slight variation according to the respective endohedral atoms. The ligand–core interaction is mainly electrostatic (73.2 av%), with contributions from the orbital interaction character of 23.2 (av%) and lesser from London dispersion interactions (3.6 av%).

Table 3 Energy decomposition analysis for the [Ag₈(X){S₂P(OPr)₂}₅]²⁺–{S₂P(OPr)₂}⁻ interaction, values in kcal mol⁻¹

	1		2		2		3		4
	H		F		Cl		Br		I
a Percentual values denote the contribution from each stabilizing term to the overall favorable interaction. b Percentual values denote the contribution from each density deformation channel to the ΔEorb term (Fig. 2).
ΔEPauli	215.4		215.8		210.1		208.0		201.0
ΔEelstat	−304.8	72.5%^a	−308.5	72.8%^a	−305.6	73.5%^a	−304.0	73.6%^a	−297.4	73.6%^a
ΔEorb	−98.5	23.4%^a	−101.2	23.9%^a	−96.2	23.1%^a	−94.7	22.9%^a	−92.2	22.8%^a
ΔEdisp	−17.0	4.0%^a	−13.9	3.3%^a	−14.3	3.4%^a	−14.3	3.5%^a	−14.4	3.6%^a
ΔEint	−204.9		−207.8		−206.0		−205.0		−203.0
Δρ1	−24.1	24.5%^b	−27.2	26.8%^b	−22.5	23.3%^b	−21.6	22.8%^b	−19.9	21.6%^b
Δρ2	−17.8	18.0%^b	−17.9	17.6%^b	−16.2	16.8%^b	−15.6	16.5%^b	−14.8	16.1%^b
Δρ3	−11.4	11.6%^b	−10.7	10.6%^b	−11.7	12.1%^b	−12.0	12.7%^b	−12.6	13.7%^b
Δρ4	−8.2	8.3%^b	−8.8	8.7%^b	−9.9	10.3%^b	−10.2	10.8%^b	−10.9	11.9%^b

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Moreover, the orbital contribution (ΔE_orb) to the ligand–core interaction can be decomposed through the Natural Orbitals for Chemical Valence^48,73,74 extension of EDA (EDA-NOCV),⁴⁸ leading to the identification of individual deformation density channels accounting for contributions from each set of interacting orbitals (Fig. 2).^75,76 From the inspection of resulting deformation densities (Δρ_N), four relevant ligand→core charge-transfer channels are found associated with each ligand (Table 3). Particularly, Δρ₁ and Δρ₂ besides the ligand→core charge transfer involve a subsequent core→X charge transfer, which is not observed for the remaining Δρ₃ and Δρ₄. Hence, the ligands contribute towards retaining the ionic character of the endohedral atom, suggesting the plausible possibility to tune the ionic character by further modification of the ligand shell, which can be interesting for a series of ligands with variable donor/acceptor characteristics.⁷⁷

Fig. 2 Schematic representation of the deformation densities related to the bonding scheme related to the ligand–core interaction, denoting the charge flow from red to blue showing a ligand to core charge donation as a result of the cluster ligand interaction.

Conclusion

The stabilizing factors ascribed to the hydride and halide encapsulation in a confined hard (Lewis) acid Ag₈ cavity is evaluated by the relativistic DFT-D level of theory for the [Ag₈(X){S₂P(OPr)₂}₆]⁺ (X⁻ = H, 1, F, 2, Cl, 3, Br, 4, and, I, 5) series. Our results indicated that the confined Ag₈–X aggregate is mainly stabilized by high contribution from the electrostatic type interactions (80.9 av%), with additional stabilization in lesser extent from charge-transfer (17.4 av%) and London type interactions (1.7 av%). The resulting interaction considerably decreases along the series amounting to: −232.2 (1) > −192.1 (2) > −165.5 (3) > −158.0 (4) > −144.2 kcal mol⁻¹ (5), denoting a more favorable inclusion of hydride and fluoride atoms within the silver cage.

Further analysis of the electrostatic contribution in terms of the negatively charged nature of the encapsulated atoms reveals that ionic-based electrostatic contributions decrease from 90.7% for the hydride to 68.6% for the iodide counterpart, following the decrease in hardness according to the Pearson's HSAB concept. This observation is explained by the increasing major role of higher electrostatic interaction terms related to softer (Lewis) bases. Moreover, the ligand-core interaction remains almost independent along the series, denoting a ligand→core charge transfer.

The preparation energy (ΔE_prep), accounting for the required energy to accommodate the cluster geometry to incorporate the respective monoatomic anion, ranges from 4.2 (2) to 15.8 (1) kcal mol⁻¹, denoting the flexibility of [Ag₈{S₂P(OPr)₂}₆]²⁺ in order to maximize the Ag₈–X interaction.

Such insights may contribute to the understanding of different stabilizing and destabilizing terms related to the formation of confined aggregates, where the use of metal-based cavities offers flexibility and versatility towards favorable incorporation of different monoatomic anions.

Author contributions

The manuscript was written through the contributions of all authors.

Conflicts of interest

The authors have no conflicts to disclose.

Acknowledgements

RLTP thanks Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) (313648/2018-2) for a research fellowship. GFC thanks CNPq (311132/2020) for a research fellowship. P. L. R.-K. thanks the financial support from FONDECYT under the postdoctoral grant number 3190329. A. M.-C. thanks Fondecyt 1180683.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1cp04249a

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