Counterintuitive noncovalent interactions of ammonia with the all metal ring of cyclic trinuclear Ag(I) clusters: a DFT study

Abstract

Density functional theory electronic structure calculations were employed to study a proposed novel type of interaction between NH₃ and the metallic ring of cyclic trinuclear Ag(I) clusters of the general formula cyclo-Ag₃(μ₂-L)₃ bearing 15 different bridging organic ligands L. Scan single point energy calculations revealed that the most stable orientation of NH₃ is that with a N atom facing the center of the silver metallic ring and bridging the three metal centers. Starting with this orientation we performed geometry optimizations of the cyclo-Ag₃(μ₂-L)₃(μ₃-NH₃) complexes. The optimized geometries retain the initial orientation of NH₃. The zero point energy corrected interaction energies, D₀, of NH₃ with the metallic ring are found in the range 4.2–12.4 kcal mol⁻¹ while the distance of NH₃ from the center of the ring is in the range 2.317–2.519 Å, both indicative of a relatively strong interaction. A multitude of theoretical methods employed revealed that the interaction of NH₃ with the silver metallic ring is mainly of ionic nature with a contribution of van der Waals forces. Molecular structure–property relationships indicate that the magnitude of D₀ increases upon increasing the charge of the silver metal centers and decreasing the LUMO energy of the cyclo-Ag₃(μ₂-L)₃ clusters.

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1. Introduction

Weak noncovalent interactions are of paramount importance in many research areas such as in molecular biology,^1–3 chemical and biological recognition,^4,5 crystal engineering^6,7 and supramolecular chemistry.^8,9 There are numerous types of noncovalent interactions including H-bonding,^10,11 π⋯π stacking,¹² cation⋯π,¹³ anion⋯π,¹⁴ CH⋯π,^15,16 NH⋯π,^17,18 and even OH⋯π, FH⋯π, and BH⋯π.¹⁹ XH⋯π (X = C, N, O, etc.) interactions refer to the interaction of the X–H bond facing a perpendicular aromatic ring.¹⁹ Among the XH⋯π interactions, the most widely studied^20,21 are the CH⋯π and OH⋯π interactions while the NH⋯π interactions are less well studied. Hobza et al.²² studied theoretically the interaction of benzene with NH₃, H₂O and CH₄ and found that the strength of the NH⋯π interaction lies between those found for CH⋯π and OH⋯π interactions. Tsuzuki et al.,¹⁷ upon employing ab initio calculations, demonstrated the importance of the electrostatic and dispersion interactions in the adducts formed between benzene molecules and water, ammonia or methane. In this study, various different orientations of ammonia relative to the benzene molecule were taken into account and among them the most stable is found to be that where one N–H bond is perpendicular to the benzene ring facing its center. The dispersion forces are the main component of the interaction energy while electrostatic forces govern the orientation of ammonia relative to benzene.¹⁷

Another less studied noncovalent interaction is the so called lone pair⋯π (lp⋯π), which is a bonding interaction between a lone pair and a π system.²³ The lp⋯π interaction was introduced by Egli et al.²⁴ to explain the contradicting stability of the Z-DNA conformation where O₄′ of cytidine ‘sits’ above the six membered ring of guanine at the d(CpG) steps. The lone pair of the O₄′ faces the π system of guanine thus giving rise to an n → π* interaction. The nature of the latter is counterintuitive and cannot be explained based only on simple electrostatic interactions. The elusive nature of the lp⋯π interaction may involve molecular orbital interactions along with electrostatic ones. Fomine et al.,²⁵ employing LMP2 ab initio calculations, demonstrated that, depending upon the electronegativity of the aromatic system, a water molecule should form either an OH⋯π or an lp⋯π interaction. The latter involves the interaction of the HOMO of the water molecule with the π* orbitals of the aromatic system. The magnitude of the lp⋯π interaction can be as high as that of a strong H-bond, especially in the case where the aromatic system is positively charged. Accordingly, the interaction energy between a water molecule and a positively charged imidazole ring was calculated to be as high as −8.1 kcal mol⁻¹ at the MP2/6-31+G** level of theory.²³

To date, the largest body of the work on the lp⋯π interaction was devoted to biomolecules such as DNA, RNA, and proteins as well as materials and small molecules.²⁶ The most common lp⋯π interactions studied so far were those related to the interactions of an aromatic system with O and N lone pairs.²⁷

To the best of our knowledge, all the studies of the lp⋯π interaction have been limited to systems where the lone pair faces a π organic ring. In contrast, there are no such studies focusing on the interaction between a lone pair and an all-metal ring. It is noticed that various ligand stabilized all metal rings have been proposed to exhibit the so-called metallaromaticity phenomenon.²⁸ In these systems, there exist molecular orbitals (MOs) delocalized over the entire metallic ring similar to the delocalized MOs found for aromatic organic rings. Cundari et al.²⁹ employed DFT calculations at the B3LYP/CEP-31G(d) level of theory to study the π-acid/base – properties of cyclic trinuclear complexes of monovalent coinage metals of the formula cyclo-M₃(μ-L)₃. Depending upon the interplay of the ligand, metal and substituents, cyclo-M₃(μ-L)₃ exhibits either π-basicity or π-acidity which in some cases is superior to those estimated for various organic π-systems, e.g. benzene, pyridine, pyrazol, etc. It should also be noticed that the cyclic trinuclear complexes can participate in π stacking interactions with π organic molecules. Accordingly, Balch et al.³⁰ demonstrated that the cyclic trinuclear Au(I) complex, Au₃(MeN=COMe)₃, forms stacking compounds with nitro-9-fluorenones. In these compounds, the trinuclear Au(I) metallic ring faces, in a parallel fashion, the organic rings of nitro-9-fluorenones forming charge transfer adducts. The ability of cyclic trinuclear coinage metal complexes to form π stacking supramolecular systems with organic π molecules was revealed in a number of studies by Dias et al.³¹ More specifically, the cyclic trinuclear {[3,5-(CF₃)₂Pz]Au}₃ complex forms π stacks with toluene while the cyclic trinuclear {[3,5-(CF₃)₂Pz]Ag}₃ cluster forms π-acid–base adducts with benzene and substituted benzenes. In other studies,³² it was shown that the cyclic trinuclear Au(I) compounds could form π stacking supramolecular assemblies with the cyclic trinuclear Hg(I), cyclo-Hg₃(μ-C₆F₅) complex. The latter is considered to be a strong π-acid that could form 1 : 1 π-acid–base stacking compounds with various arenes.³³ In addition, the cyclic trinuclear Au(I) complexes could interact with Tl(I) or Ag(I) cations as well as organic π-acids, e.g. C₆F₆ and the TCNQ molecule forming π stacks.³²

Also, the importance of the interactions of ammonia with various species is exemplified in MOFs used as ammonia storage materials. In the latter, ammonia interacts with either the organic linkers or the open metal sites.^34–39

Taking into account all the above mentioned ammonia interactions, as well as their implications in ammonia storage in MOFs, we thought it would be advisable to study theoretically the interaction of ammonia with various cyclic trinuclear Ag(I) clusters of the general formula cyclo-Ag₃(μ₂-L)₃ by means of DFT electronic structure calculations. Our aims were (i) to reveal if NH₃ could interact with metallic rings, (ii) what would be the orientation of ammonia relative to the metallic rings, (iii) what is the strength of this interaction and how is this affected by the bridging ligands L, and finally (iv) to delineate the nature of this interaction.

2. Computational details

All calculations were performed using the Gaussian09 version D.01 program suite.⁴⁰ Geometry optimizations were performed without symmetry constrains, employing the 1997 hybrid functional of Perdew, Burke, and Ernzerhof (PBE0)⁴¹ along with the Def2-TZVP basis set.⁴² Dispersion interactions were accounted by using the D3 version of Grimme dispersion with Becke–Johnson damping.⁴³ The computational protocol will be hereafter denoted as PBE0-GD3BJ/Def2-TZVP. All stationary points have been identified as minima (the number of imaginary frequencies, NImag = 0). Natural bond orbital (NBO) population analysis was done employing the methodology by Weinhold.⁴⁴ The atoms in molecules (AIM) of Bader⁴⁵ and the reduced gradient density (RDG) method⁴⁶ were used as implemented in the Multiwfn software.⁴⁷

3. Results and discussion

3.1 Structural data

3.1.1 Orientation of the NH₃ molecule. The six possible orientations of the NH₃ molecule relative to the cyclic trinuclear metallic ring of the cyclo-[Ag₃(μ₂-L)₃] clusters are depicted in Scheme 1. Initially, we performed a rigid scan of the potential energy hypersurface, PES, for all six conformations, A–F, by only changing the distance of the ammonia molecule from the center of the metallic ring (A–D) or from the middle of a Ag–Ag bond (E) or from a Ag metal center (F), while keeping all the rest of the structural parameters frozen.

Scheme 1 Possible orientations of NH₃ relative to the silver(I) metallic clusters.

Fig. 1 depicts the scan curves for two representative complexes with NH₃, namely the cyclo-{Ag₃[μ₂-(1H-tetrazole)]₃}, 1, and the cyclo-{Ag₃[μ₂-(3,5-bis-trifluoromethyl-1H-1,2,4-triazole)]₃}, 2. Perusal of Fig. 1 reveals that in both 1 and 2 the most stable is conformation A. Table 1 shows the relative stabilities of all conformations calculated for 1 and 2. Similar scan curves are obtained for the rest of NH₃ complexes under study.

Fig. 1 Rigid scan curves of the distance R between NH₃ and the cyclo-{Ag₃[μ₂-(1H-tetrazole)]₃} (a) and the cyclo-{Ag₃[μ₂-(3,5-bis-trifluoromethyl-1H-1,2,4-triazole)]₃} (b) calculated at the PBE0-GD3BJ/Def2-TZVP level of theory.

Table 1 Relative stabilities (in kcal mol⁻¹) of the conformations A–F calculated for 1 and 2 at the PBE0-GD3BJ/Def2-TZVP level of theory

Conformation	1	2
A	0.0	0.0
B	6.6	6.4
C	6.4	6.3
D	6.1	5.7
E	2.7	0.8
F	2.8	1.7

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Inspection of Table 1 reveals that conformations B–F are less stable by about 0.8–6.6 kcal mol⁻¹ with respect to the most stable conformation A.

3.1.2 Structural and energetic parameters. Taking into account the above mentioned results, we proceed with the full geometry optimizations of a series of Ag(I) cyclic trinuclear complexes with the general formula cyclo-[Ag₃(μ₂-L)₃(μ₃-NH₃]. Taking into account that conformation A of these clusters is the most stable (vide supra), we started our calculations with NH₃ located exactly above the centre of the metallic ring as in conformation A (Scheme 1). The bridging ligands, L, of the clusters under study are depicted in Scheme 2.

Scheme 2 Bridging ligands, L considered in this study. Donor atoms are indicated with arrows.

Fig. 2 also depicts the optimized geometries of a few representative complexes (1 and 2). The optimized structures of the rest of the complexes under study are given in Fig. S1–S3 of the ESI.†

Fig. 2 Optimized geometries of 1 and 2 at the PBE0-GD3BJ/Def2-TZVP level of theory.

The most important structural parameters of the optimized geometries of complexes 1–15 are given in Table 2. These are, the distance between the N atom of ammonia and a centroid, cd pseudoatom located at the centre of the metallic ring, R_e(N-cd), and the intermetallic Ag–Ag distance, R_e(Ag–Ag) (Scheme 2). It should be noticed that in all cases <N-cd-Ag is 90° while the metallic rings form equilateral triangles. The optimization procedure yielded local minima which correspond to conformation A. The R_e(N-cd) distance, depending upon L, is found in the range of 2.317–2.519 Å while the R_e(Ag–Ag) distance is in the range of 3.329–3.500 Å. In addition, in Table 2, the interaction energies of the ammonia molecule with the metallic clusters are shown. These correspond to the bond dissociation energies, D₀, of ammonia from the metallic cluster (zero point energies included). The D₀ is found in the range of 4.2–12.4 kcal mol⁻¹. Both the R_e(N-cd) distance and the D₀ indicate that the interaction of ammonia with the silver metallic ring is relatively strong.

Table 2 Structural and energetic parameters of complexes 1–15 calculated at the PBE0-GD3BJ/Def2-TZVP level of theory

Complex	R e(N-cd) (Å)	R e(Ag–Ag) (Å)	D 0 (kcal mol^−1)
1	2.399	3.493	8.7
2	2.358	3.500	9.7
3	2.445	3.432	4.6
4	2.519	3.329	4.2
5	2.385	3.454	7.4
6	2.362	3.438	7.0
7	2.346	3.415	9.7
8	2.328	3.422	7.9
9	2.328	3.452	12.2
10	2.317	3.451	12.4
11	2.356	3.419	7.3
12	2.394	3.512	9.0
13	2.352	3.422	7.2
14	2.391	3.543	5.2
15	2.350	3.466	7.7

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3.2 Bonding analysis

3.2.1 Atoms in molecules and reduced density gradient analysis. Taking into account the strength of the ammonia–the metallic ring interaction we instigated to perform bonding analysis by means of the atoms in molecules (AIM) method and the reduced density gradient (RDG) function. The bond critical points (BCPs) found are depicted schematically in Fig. 3 for the representative complexes 1 and 2. Inspection of Fig. 3(a) reveals that there are three BCPs (denoted as a, b and c) between ammonia and the metallic ring. Actually, these BCPs are located in the midpoints between the N atom and each Ag(I) metallic centre, forming an equilateral triangle. Similar BCPs are also found for the rest of the complexes under study namely 3–15. The existence of these BCPs is indicative of bonding interactions between ammonia and the metallic Ag(I) clusters. Also, in Fig. 3(b), the 3D surface of the RDG function is depicted. The green colour of the RDG indicates that the ammonia–metallic cluster interaction is of van der Waals type.⁴⁷

Fig. 3 BCPs (a) and 3D plot of the RDG function (b) for 1 and 2.

This is further corroborated upon the inspection of the scatter graph plots of 1 and 2, as depicted in Fig. 4, of RDG vs. sign(λ₂)ρ, where λ₂ is a function obtained as the second largest eigenvalue of the averaged electron density Hessian matrix computed throughout the dynamical trajectory and ρ is the electron density. Similar scatter RDG vs. sign(λ₂)ρ graphs are obtained for the rest of the complexes under study.

Fig. 4 Scatter graph plots of RDG vs. sign(λ₂)ρ for complexes 1 (a) and 2 (b).

According to the noncovalent interaction method⁴⁸ (NCI), the existence of ‘spikes’ in the region of −0.01 to 0.01 of sign(λ₂)ρ indicates a van der Waals interaction. In order to further delineate the bonding between ammonia and the metallic cluster we have calculated, a number of parameters at the BCPs a, b and c namely the electron density, ρ_BCP, the Laplacian of the electron density, ∇²ρ_BCP, the potential energy density, V_BCP, the kinetic energy density, G_BCP, and the energy density, H_BCP. Espinoza⁴⁹ classified the bonding interactions into three categories based on the values of these parameters at the relevant BCPs. Accordingly, if |V_BCP|/G_BCP < 1, ∇²ρ_BCP > 0 and H_BCP > 0, the interaction is characterized as pure-closed shell (e.g. ionic bonds, hydrogen bonds, and van der Waals interactions). If |V_BCP|/G_BCP > 2, ∇²ρ_BCP < 0 and H_BCP < 0 then, the interaction is characterized as pure open-shell (covalent) and finally if 1 < |V_BCP|/G_BCP < 2, ∇²ρ_BCP > 0 and H_BCP < 0 is of the intermediate nature. The values of all the above mentioned parameters at BCPs a, b and c are given in Table S1 of the ESI.† Perusal of Table S1 (ESI†) confirms that the ammonia–metallic cluster interaction is of closed shell ionic type since in all cases, it is found that at the bonding BCPs, the conditions |V_BCP|/G_BCP < 1, ∇²ρ_BCP > 0 and H_BCP > 0 are met.

3.2.2 Molecular electrostatic potentials. Fig. 5 depicts schematically the 3D surfaces of the molecular electrostatic potentials (MEPs) of representative silver metallic clusters included in the respected complexes with ammonia along with the MEP of the ammonia molecule. The MEPs of the silver metallic clusters included in complexes with ammonia, 1, 3, 5 and 7, exhibit a positive surface (red colour, Fig. 5). The same also holds true for the rest of the complexes under study. On the other hand, the MEP of ammonia exhibits a negative surface (blue colour, Fig. 5) protruding the N atom as a result of its lone pair. Accordingly, based on MEPs, ammonia is expected to favourably interact with the silver metallic ring bearing positive MEP.

Fig. 5 MEP surfaces of NH₃ and representative silver metallic clusters included in complexes 1, 3, 5 and 7.

3.3 Electronic structures

3.3.1 Natural bond orbital analysis. Next, we employed natural bond orbital (NBO) analysis to find the electron density partitioning of the systems under study. Table 3 presents the natural charges on the ammonia N atom, q_N, and on the Ag metal center, q_Ag, and the natural electron configuration (nec) of these atoms, nec(N) and nec(Ag), as obtained from the NBO analysis of 1–15.

Table 3 NBO analysis of complexes 1–15 at the PBE0-GD3BJ/Def2-TZVP level of theory

Species	q N	q Ag	nec(N)	nec(Ag)
1	−1.072	0.622	2s^1.492p^4.563p^0.013d^0.01	5s^0.454d^9.815p^0.11
2	−1.066	0.626	2s^1.492p^4.563p^0.013d^0.01	5s^0.414d^9.835p^0.14
3	−1.061	0.400	2s^1.482p^4.563p^0.013d^0.01	5s^0.664d^9.785p^0.16
4	−1.048	0.400	2s^1.482p^4.553p^0.013d^0.01	5s^0.634d^9.795p^0.18
5	−1.068	0.608	2s^1.492p^4.563p^0.013d^0.01	5s^0.474d^9.815p^0.12
6	−1.061	0.575	2s^1.482p^4.563p^0.013d^0.01	5s^0.494d^9.805p^0.13
7	−1.063	0.626	2s^1.482p^4.563p^0.013d^0.01	5s^0.394d^9.835p^0.15
8	−1.068	0.608	2s^1.492p^4.563p^0.013d^0.01	5s^0.474d^9.805p^0.11
9	−1.094	0.575	2s^1.492p^4.583p^0.013d^0.01	5s^0.574d^9.705p^0.16
10	−1.079	0.638	2s^1.492p^4.573p^0.013d^0.01	5s^0.434d^9.825p^0.11
11	−1.067	0.598	2s^1.492p^4.563p^0.013d^0.01	5s^0.484d^9.805p^0.12
12	−1.073	0.628	2s^1.492p^4.563p^0.013d^0.01	5s^0.444d^9.825p^0.11
13	−1.066	0.597	2s^1.482p^4.563p^0.013d^0.01	5s^0.494d^9.805p^0.12
14	−1.057	0.469	2s^1.482p^4.553p^0.013d^0.01	5s^0.604d^9.795p^0.15
15	−1.066	0.605	2s^1.492p^4.563p^0.013d^0.01	5s^0.464d^9.815p^0.13

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It can be seen from Table 3 that the N atom of ammonia acquires negative charges from −1.048 to −1.094 while the Ag metal centres acquire positive charges from 0.400 to 0.638. Clearly, there is an electrostatic/ionic interaction since the negatively charged N atom of ammonia faces three positively charged Ag cations. From the necs given in Table 3, it can be seen that there is no charge transfer between the ammonia N atom and the metallic cluster.

3.3.2 Molecular orbitals. Fig. 6 depicts the most important MOs for a few representative complexes namely 3 and 10 exhibiting the lowest and the highest D₀, respectively (Table 2).

Fig. 6 3D surfaces of bonding MOs relevant to ammonia–silver cluster interactions in complexes 3 and 10.

In Fig. 6 we observe three bonding MOs for 3 and two bonding MOs for 10 indicating a covalent interaction between the sp³ hybrid bearing the lone pair with d AOs located on the silver metal centers. However, it should be emphasized that despite the existence of these MOs, the covalent interaction between ammonia and the silver metallic ring is expected to be negligible. The latter is further corroborated by the fact that the Wiberg bond indices between the N atom of ammonia and the three silver metals of the ring amount to only 0.090 for 3 and 0.126 for 10. The same also holds true for the rest of the complexes under investigation, i.e. the respective Wiberg bond indices are quite small.

3.4 Molecular structure–property correlations

From Table 2 it is obvious that the strength of the interaction between ammonia and the silver metallic ring depends upon the nature of the bridging ligand. In other words, D₀ depends upon the molecular structure of the silver clusters. Since D₀ is of central importance, we set out to extract molecular structure–property correlations in order to find which factors modulate D₀. Tables S2 and S3 (ESI†) present the values of a series of parameters related to the molecular structure of the systems under study. These parameters are the quadrupole moments, Q_xx and Q_zz, the energies of the frontier MOs, E_HOMO and E_LUMO, the chemical potential, μ, the hardness, η, the electrophilicity, ω, the electronegativity, χ, and the polarizability, α. Parameters μ, η, ω and χ were calculated according to the following eqn (1)–(4):⁵⁰

μ = −(E_HOMO + E_LUMO)/2 (1)

μ = −χ (2)

η = (E_LUMO − E_HOMO)/2 (3)

ω = μ²/2η (4)

In addition, other parameters include the Mulliken and NBO charges on the Ag metal centres of clusters (Table S2, ESI†) and complexes (Table S3, ESI†) as well as on the N atom, q_N, of ammonia in complexes. For the latter, the dipole moment, p, of the complexes is also included in Table S3 (ESI†). Fig. 7 depicts the two best correlations found namely D₀versus q_Ag of the complexes with NH₃ and versus E_LUMO of the ‘free’ clusters.

Fig. 7 Linear correlations of D₀versus (a) the Mulliken charge, q_Ag, of complexes and (b) E_LUMO of the metallic clusters.

The linear correlations depicted in Fig. 7 indicate that the strength of the interaction of NH₃ with the metal ring increases as the positive charge on silver metal centres increases. This reflects the electrostatic nature of the interaction. On the other hand, the lower the LUMO energy of the cluster the stronger its interaction with NH₃. This implies the favourable HOMO–LUMO interaction between the HOMO of NH₃ and the LUMO of the ‘free’ clusters (see Fig. S4, ESI†).

4. Conclusions

In the present study, we introduce for the first time, a novel type of intermolecular interaction between NH₃ and the metallic ring of Ag(I) cyclic trinuclear clusters, cyclo-Ag₃(μ₂-L)₃. The most favourable orientation is that with the N atom of NH₃ facing the trinuclear metallic ring and bridging the three Ag(I) metal centres. A multitude of methods have been employed in order to delineate the nature of the novel interaction namely AIM, RDG, NBO and MEP. It is found that the interaction of NH₃ with the Ag(I) clusters in the cyclo-[Ag₃(μ₂-L)₃(μ₃-NH₃] complexes is mainly of the ionic/electrostatic nature also with a small contribution from van der Waals forces. The covalent interactions are expected to be negligible while there is no charge transfer. Taking into account that the strength of the proposed novel type of interaction is in the range of 4–13 kcal mol⁻¹, it could be possibly utilized for ammonia storage in solid state materials such as MOFs. Finally, taken the significance of the noncovalent interactions of the [NH₄]⁺ cation in biological systems⁵¹ we indent to expand our studies on its interactions with all metal rings.

Conflicts of interest

There are no conflicts to declare.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3nj03420h

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