[2.2.2]Paracyclophane, preference for η⁶ or η¹⁸ coordination mode including Ag(I) and Sn(II): a survey into the cation–π interaction nature through relativistic DFT calculations

Abstract

[2.2.2]Paracyclophane is a versatile π-cryptating structure, which can exhibit η²:η²:η² and η⁶:η⁶:η⁶ coordination with metal ions, involving two or six carbon atoms in each aromatic ring. According to the nature of the metallic cation, the interaction can occur at the centre of the cage or upper face of the structure, which is determined mainly by the ligand-to-metal charge transfer ruled by symmetry and energetic considerations, and thus by the nature of the cation–π interaction. For Ag(I), the 5s-Ag shell is close in energy to the frontier orbitals of paracyclophane, resulting in the formation of a bonding combination with the symmetric combination of the π₂-type levels, which leads to a non-centered conformation. In contrast, the Sn(II) case exhibits a largely favourable bonding interaction with the π₂ and π₃ type levels, which involve the 5p-Sn shell and result in a centered conformation. The interaction between the metal and paracyclophane was studied via molecular orbitals diagram, energy decomposition analyses (EDA) and non-covalent indexes (NCI).

---

Introduction

Cyclophanes constitute an interesting class of compounds in which benzene rings are held together generally by aliphatic chains.^1,2 Usually, the aromatic rings are disposed in such a way that their π-orbitals face each other in a parallel or slightly distorted fashion. The close proximity of such aromatic rings leads to unique properties^3–5 in cyclophanes, which have been employed in several disciplines, including polymer chemistry and material science^6,7 and have promising applications in catalysis⁸ and as probes for biological recognition processes^9,10 among other application.

The fixed transannular π–π interactions between the six-membered rings influence the distinctive features in comparison with common arenes.^11–14 This leads to enhanced reactivity towards some addition reactions, such as Diels–Alder cycloaddition,¹⁵ especially for the formation of organometallic derivatives such as ruthenophanes¹⁶ and the arene–chromium tricarbonyl complexes from the reaction with chromium hexacarbonyl.^17,18

One of the simplest member of the cyclophane family is [2.2]paracyclophane, in which two benzene rings are held at short distances in a cofacial disposition and connected by –(CH₂)₂– bridges.^1,2 Because of the large strain induced by the short ethylenic bridges, the aromatic rings exhibit a boat-type deformation; however, despite such deviation from planarity, the aromatic character is retained as has been characterized via the magnetic criteria of aromaticity, among other approaches.^19–21 Interestingly, the magnetic response at the center of the [2.2]paracyclophane increases due to the additive interaction between the induced magnetic fields from the two stacked aromatic rings.^19–21

The next higher cyclophane, namely, [2.2.2]paracyclophane ([2.2.2]pCp), exhibits three aromatic rings that have a π–π interaction between their inner faces.^11,22,23 Such structure forms a suitable polyaromatic receptor for metal cations,^24–29 which continue to attract attention owing to their potential importance in the areas of metal-ion sensing, electrical conductors, and photoresponsive devices, which has been also observed for other polyaromatic compounds.^29–31

For [2.2.2]paracyclophane, the inclusion of several metal cations, such as Ag(I), Ga(I) and Sn(II), has been characterized,^24–29 which have a favourable interaction with the inner faces of the aromatic rings involving a η²:η²:η² (or, an overall η⁶) and η⁶:η⁶:η⁶ (or, an overall η¹⁸) coordination mode. Interestingly, both modes have been characterized for the metallic cations of the fifth period, e.g. a 5s⁰ and 5s²5p⁰ electronic configuration is observed in Ag(I) and Sn(II), respectively. For the former, Ag(I) is located above the center of the structure, resulting in the [Ag(η²:η²:η²-[2.2.2]pCp)]⁺ compound,²³ whereas for Sn(II), a centered structure is obtained, leading to a highly symmetric [Sn(η⁶:η⁶:η⁶-[2.2.2]pCp)]²⁺ conformation,²⁸ which can be roughly considered as a D₃ structure.

As part of our current interest in the chemistry of paracyclophane derivatives,^2,13–16,20 we focus on the differences of the coordination modes, involving both Ag(I) and Sn(II) cations, which have the rich coordination chemistry of systems such as several aromatic rings in the same molecular entity. In this contribution, we study via relativistic DFT methods the differences that determine a η²:η²:η² or η⁶:η⁶:η⁶ coordination mode in order to gain more insight into the versatility of [2.2.2]paracyclophane, leading to a particularly strong π–cation interaction.^32,33 In addition, the inclusion of externally coordinating electron-withdrawing groups, such as Cr(CO)₃,¹¹ was studied with the aim to characterize the bonding situation in Ag(I) and Sn(II) systems according to the decrease of the inner π density. The interaction between the metal and paracyclophane was studied using energy decomposition analyses (EDA)^34,35 and non-covalent indexes (NCI).^36–38

Results and discussion

The structure of [2.2.2]paracyclophane (1) features three arene moieties held together by p-ethyl bridges having a rigid structure with a cavity diameter of about 2.5 Å.²³ Such a structure has been recognized as a relevant metal-ion receptor structure, leading to a variety of host–guest systems that involve several metal cations such as Ag⁺, Ga⁺ and Sn²⁺.^24–28 The optimized structures for 1–Ag⁺ and 1–Sn²⁺ are shown in Fig. 1, where the calculated structural parameters are in good agreement with the experimentally available data^23,28 (Table 1). The inclusion of Ag⁺ modifies the structure of the isolated paracyclophane host, slightly increasing the diameter formed by the three aromatic rings; however, in the case of Sn²⁺, the structure remains similar. Moreover, the characterized solid state structure for 1–Sn²⁺ shows a displacement of Sn²⁺ from the centre, due to the proximity of a [AlCl₄]⁻ counteranion. The latter point is accounted by the [1–Sn]²⁺[AlCl₄]⁻ model (ESI†), showing a centre-Sn distance of 0.412 Å.

Fig. 1 Optimized structure for Ag⁺–1 (left) and Sn²⁺–1 (right).

Table 1 Selected distances of Ag⁺–1 and Sn²⁺–1 in Å, and the respective Cr(CO)₃ derivatives. Experimental results are given in parentheses

	Ag–1	Ag–1(Cr(CO)3)	Ag–1(Cr(CO)3)2	Ag–1(Cr(CO)3)3
a Experimental data from ref. 23 and 28.b Average of the carbon–cation distances involving the arene rings.c Distance from the centroid of paracyclophane to the cation.d Averaged C=C cation distance involving the upper and lower CC aromatic bonds.e Average of the carbon–Cr(CO)3 distances involving the arene rings.f Displacement due to the proximity of the counter-anion, see the text and ref. 28.
Av. C–Ag^b	2.599 (2.588)^a	2.701	2.686	2.681
Cent-Ag^c	1.383 (1.433)^a	1.313	1.262	1.231
C=C–Ag^d	2.502 (2.502)^a	2.606	2.591	2.585
C6–Cr^e		1.731	1.724	1.721

---

	Sn–1	Sn–1(Cr(CO)3)	Sn–1(Cr(CO)3)2	Sn–1(Cr(CO)3)3
Av. C–Sn^b	2.975 (2.958)^a	2.993	3.041	2.986
Cent-Sn^c	0.000 (0.382)^a^,^f	0.338	0.596	0.193
C=C–Sn^d	2.897 (2.877)^a	2.912	2.961	2.900
C6–Cr^e		1.675	1.671	1.670

---

The binding mode of Ag⁺ reflects the interaction with two carbon atoms in each aromatic ring, depicting a cation–π interaction via a η²:η²:η² coordination mode (Fig. 1). The Ag⁺ atom is located at 1.383 Å above the center of the [2.2.2]pCp structure with a carbon–Ag⁺ distance of 2.599 Å av. (exp. 2.588 Å (ref. 23) av.), involving carbon forming the upper face of 1. In contrast, the Sn²⁺ ion is located at the center of the [2.2.2]paracyclophane. Thus, the resulting interaction exhibits a η⁶:η⁶:η⁶ coordination mode with a carbon–Sn²⁺ bond length of 2.981 Å av. (exp. 2.958 Å (ref. 28) av.) and three aromatic rings.

In order to gain more insight into the nature of the overall interaction and the differences between the characterized Ag⁺ and Sn²⁺ coordination modes, their electronic structures were studied in terms of constituent fragments, namely, M^q+ and [2.2.2]pCp (M = Ag¹⁺ and Sn²⁺). In Fig. 2, the electronic structure of 1 is described qualitatively, depicting the combination of the π orbitals from the aromatic rings (Fig. S1†) according to π₁, π_2, π_3, labels, for simplicity. Thus, each combination can be directly related to the π orbitals of benzene. The formation of Ag⁺–1 involves the bonding combination between the totally symmetric π₂ combination (77%) (Fig. 3) and the initially unfilled 5s-Ag shell (9%) and part of the 4d-Ag shell (14%), denoting both ligand- and 4d-Ag charge transfer towards the 5s-Ag shell. The antibonding counterpart (π₂–5s, in Fig. 3) of such combination gives rise to the LUMO, which exhibits a larger 5s-Ag character (52%) (see Fig. 3).

Fig. 2 Molecular orbital diagram denoting the interaction between the respective metallic cation and [2.2.2]paracyclophane (pCp), showing the π-type levels.

Fig. 3 Isosurface representation of relevant molecular orbitals.

The small participation of the 5s-Ag shell in the occupied levels is supported by the natural population analysis,⁴⁷ which describes a Ag^0.67+[2.2.2]pCp^0.33+ charge distribution in the overall structure (Table 2). The natural valence population of the Ag⁺ center exhibits a 4d^9.895s^0.22 configuration. This is in agreement with the inner charge transfer between the 4d → 5s shells as described above, which occurs mainly in the bonding orbital described in Fig. 3. Thus, the bonding scheme in Ag–1 can be ascribed to the π₂–5s–Ag interaction, involving contribution from the 4d shell.

Table 2 Natural population analyses of the studied systems

	Ag–1	Ag–1(Cr(CO)3)	Ag–1(Cr(CO)3)2	Ag–1(Cr(CO)3)3
a Natural electronic configuration.b Ligand to metal charge donation.
Ag	0.67	0.77	0.78	0.79
NEC^a	4d^9.895s^0.22	4d^9.925s^0.15	4d^9.925s^0.14	4d^9.915s^0.12
LMCT^b	0.33	0.23	0.22	0.21

---

	Sn–1	Sn–1(Cr(CO)3)	Sn–1(Cr(CO)3)2	Sn–1(Cr(CO)3)3
Sn	1.18	1.29	1.38	1.42
NEC^a	5s^1.995p^0.81	5s^1.985p^0.69	5s^1.975p^0.59	5s^1.975p^0.55
LMCT^b	0.82	0.71	0.62	0.58

---

The Sn²⁺ case exhibits a different bonding scheme, involving contribution from both 5s- and 5p-Sn shells (Fig. 2). The bonding and antibonding combinations generated between the π₁ and 5s-Sn levels (Fig. 3) are populated, and hence such interaction does not contribute to the overall Sn–1 bonding. Because of the central position of the tin cation, the 5p shell is able to interact with both π₂ and π₃ combinations of [2.2.2]paracyclophane (Fig. S1†), in which by symmetry considerations, the 5p_z orbital interacts with the former combination, whereas the 5p_x,y shells interact with the latter. For simplicity, only the π₂–5p_z interaction is denoted in Fig. 3. Such bonding scheme leads to the ligand to metal charge transfer, resulting in a Sn^1.18+[2.2.2]pCp^0.82+ charge distribution according to the natural population analyses (Table 2). The natural valence population suggests a 5s^1.995p^0.81 configuration, which is in agreement with the bonding combination between the 5p and π₂ and π₃ ligand orbitals.

Hence, the η²:η²:η² coordination mode of the Ag⁺–1 system is a consequence of the 5s–π₂ interaction, given by symmetry consideration. Moreover, the hypothetical η⁶:η⁶:η⁶ coordination mode for such a system, in which the Ag⁺ ion is located at the center of the structure, is less favorable by 12.3 kcal mol⁻¹ mainly due to the smaller ligand to metal charge transfer that results in Ag^0.87+ in contrast to the abovementioned case (Ag^0.67+).

Thus, our results suggest that a η² coordination mode in the cation–arene interaction can be obtained if the metallic center is able to interact via a s-type shell. However, for a η⁶ coordination mode, an available p-type shell is required to form a symmetric bonding interaction with both π₂ and π₃ arene levels.

The overall charge transfer from the paracyclophane structure towards the cationic centers varies according to the coordination mode, resulting in 0.33 (au) for the silver case, and 0.82 (au) for the tin center (LMCT, on Table 2). This fact denotes the versatility of the multiarene system, which can act as an electronic donor charge ligand in different amounts, according to the nature of the metallic center that is involved. Moreover, the charge transfer per each carbon remains similar in both cases, amounting to 0.055 (au) (0.33/6 = 0.055) in the η²:η²:η² case and 0.045 (0.82/18 = 0.045) for the η⁶:η⁶:η⁶ coordination mode. This fact denotes that the charge-transfer capabilities of the organic ligand remain almost independent from the nature of the metallic cation and are mostly dependent on the coordination mode.

The inclusion of the respective cation into the [2.2.2]paracyclophane (1) leads to the formation of energetically favourable complexes (Tables 3 and 4). The total interaction energy, ΔE^int, between Ag⁺ and 1 exhibits a value of −100.1 kcal mol⁻¹ (Table 3), which accounts for the stabilizing bonding scheme discussed above. In contrast, the centered Sn²⁺ atom denoting a η⁶:η⁶:η⁶ coordination mode, exhibits a larger ΔE^int of −217.1 kcal mol⁻¹, which is in agreement with the stronger bonding scheme involving the 5p-Sn shell discussed above.

Table 3 EDA–NOCV of complexes Ag⁺–1–Ag⁺–1(Cr(CO)₃)_n (n = 1–3) (kcal mol⁻¹), at BP86-D3/TZ2P+, in which Ag⁺ and the remaining [2.2.2]paracyclophane moieties, 1(Cr(CO)₃)_n (n = 0–3) are employed as interacting fragments. The ΔE^orb is later decomposed into ΔE^ab_n contributions

	Ag–1	Ag–1(Cr(CO)3)	Ag–1(Cr(CO)3)2	Ag–1(Cr(CO)3)3
a Hirshfeld charges for each fragment.b Percentage of attractive interactions (ΔE^elstat and ΔE^orb).
ΔE^prep	3.9	1.1	2.7	3.3
ΔE^int	−100.1	−86.6	−79.0	−72.3
ΔE^Pauli	74.1	55.8	58.8	59.1
ΔE^elstat	−72.2 (44.2%)^b	−45.1 (34.8%)^b	−34.6 (27.9%)^b	−23.4 (20.1%)^b
ΔE^orb	−91.0 (55.8%)^b	−84.5 (65.2%)^b	−89.3 (72.1%)^b	−93.1 (79.9%)^b
ΔE^ab1	−27.1	−24.2	−25.1	−25.7
ΔE^ab2	−8.9	−8.1	−8.7	−9.0
ΔE^ab3	−8.9	−7.4	−7.0	−6.8
ΔE^ab4	−6.6	−5.5	−5.6	−5.9
ΔE^ab5	−6.5	−4.5	−5.5	−5.8
ΔE^ab6	−2.6	−2.8	−3.3	−3.8
ΔE^ab7	−2.3	−2.2	−2.5	−2.6
ΔE^ab8	−2.4	−2.1	−2.3	−2.3
ΔE^ab9	−2.0	−1.7	−2.2	−2.2
ΔE^ab10	−2.0	−2.2	−1.8	−1.9
ΔE^abres	−21.6	−23.7	−25.4	−27.1
ΔEDisp	−11.1	−12.8	−13.9	−15.0
^aAg^+	0.757	0.754	0.754	0.755
^aLigand	0.243	0.246	0.246	0.245

---

Table 4 EDA–NOCV of complexes Sn²⁺–1–Sn²⁺–1(Cr(CO)₃)_n (n = 1–3) (kcal mol⁻¹), at BP86-D3/TZ2P+, in which Sn²⁺ and the remaining π-prismand moieties, 1(Cr(CO)₃)_n (n = 0–3) are employed as interacting fragments. The ΔE^orb is later decomposed into ΔE^ab_n contributions

	Sn–1	Sn–1(Cr(CO)3)	Sn–1(Cr(CO)3)2	Sn–1(Cr(CO)3)3
a Hirshfeld charges for each fragment.b Percentage of attractive interactions (ΔE^elstat and ΔE^orb).
ΔE^prep	2.1	4.2	7.9	9.7
ΔE^int	−217.1	−204.5	−193.2	−183.2
ΔE^Pauli	86.0	83.7	73.6	90.0
ΔE^elstat	−66.5 (22.4%)^b	−41.6 (14.9%)^b	−16.4 (6.4%)^b	−2.3 (0.9%)^b
ΔE^orb	229.9 (77.6%)^b	238.1 (85.1%)^b	239.8 (93.6%)^b	259.2 (99.1%)^b
ΔE^ab1	−38.9	−39.5	−39.9	−39.4
ΔE^ab2	−38.9	−37.3	−35.7	−39.3
ΔE^ab3	−38.9	−36.6	−33.9	−33.0
ΔE^ab4	−8.3	−8.3	−7.6	−9.1
ΔE^ab5	−8.2	−7.9	−7.3	−9.0
ΔE^ab6	−7.9	−7.8	−7.1	−7.2
ΔE^ab7	−7.9	−7.2	−7.0	−6.9
ΔE^ab8	−5.5	−6.7	−6.1	−6.9
ΔE^ab9	−3.0	−6.3	−6.1	−6.6
ΔE^ab10	−2.8	−5.3	−5.8	−5.9
ΔE^ab11	−2.0	−3.2	−5.4	−5.9
ΔE^ab12	−2.0	−2.5	−4.4	−5.3
ΔE^ab13	−1.6	−2.5	−4.0	−5.0
ΔE^ab14	−1.5	−2.2	−2.7	−5.0
ΔE^ab15	−1.4	−1.8	−2.1	−4.6
ΔE^abres	−61.2	−63.1	−64.6	−70.2
ΔEDisp	−6.7	−8.5	−10.6	−11.7
^aSn^2+	1.394	1.403	1.402	1.422
Ligand	0.606	0.597	0.598	0.578

---

The formation of Ag⁺–1 involves structural changes of 3.9 kcal mol⁻¹ mainly due to the rearrangement of the structure to maximize the η²:η²:η² coordination mode, which shows deviation from the equilibrium geometry (i.e. relaxation of the fragments leading the in-complex conformation, namely, preparation energy). Moreover, the high symmetric coordination of Sn²⁺ involves a smaller structural deformation leading to a preparation energy of about 2.1 kcal mol⁻¹.

The interaction energy, ΔE^int, accounts for the favourable inclusion of M into the paracyclophane moiety, which is evaluated by obtaining the interaction energy between the metallic cation and the organic ligand (namely, fragment a and b, respectively). The relation between the stabilizing terms, ΔE^orb, ΔE^elstat, and ΔE^disp allows the evaluation of the nature of the given interaction (Tables 3 and 4). In both cases, ΔE^int depicts a covalent character, given by the major contribution from ΔE^orb. For Ag⁺–1, ΔE^orb amounts to −91.0 kcal mol⁻¹, which accounts for 55.8% of the overall stabilizing terms. Note that the Sn²⁺–1 case involves a sizeable increase in the ΔE^orb term, which amounts to −229.9 kcal mol⁻¹, thus has a larger role (77.6%) in the stabilizing interaction, i.e. a larger covalent character. Thus, the large difference between the silver and tin compounds is given mainly by the stronger centered conformation of Sn²⁺–1, denoting the difference between the η²:η²:η² and η⁶:η⁶:η⁶ coordination modes, as given by the ΔE^orb term. This point agrees with the more effective [2.2.2]pCp → 5p-Sn charge transfer depicted from the molecular orbital analysis (vide infra).

The inclusion of external coordinating organometallic groups (i.e. the external faces of paracyclophane) has been recognized¹¹ to decrease the non-covalent π–π interactions between the aromatic rings. Here, we evaluate the influence of the acceptor Cr(CO)₃ group into the formation of Ag⁺–1 and Sn²⁺–1 based on the characterized structures of [2.2.2]paracyclophane(η⁶-Cr(CO)₃) and [2.2.2]paracyclophane(η⁶-Cr(CO)₃)₂.¹¹ The hypothetical structures involving both Cr(CO)₃ and M^q+ (M = Ag⁺, Sn²⁺) are depicted in the ESI.† The distances remain similar with a longer carbon–Ag⁺ distance ranging from 2.599 to 2.701 Å. As a consequence of the inclusion of the Cr(CO)₃ coordinating groups, the Ag⁺–paracyclophane total interaction energy, ΔE^int, becomes less stabilizing from −100.1 kcal mol⁻¹ for Ag⁺–1 to −86.6 > −79.0 > −72.3 kcal mol⁻¹, according to the increasing number of Cr(CO)₃ (Table 3). Thus, the hypothetical Ag⁺–1(CrCO₃)₃ system exhibits a less favourable situation.

From the analysis of the different terms related to ΔE^int, it can be seen that the ΔE^disp term becomes more relevant along the series, in comparison to Ag⁺–1 (−11.1 kcal mol⁻¹) > −12.8 > −13.9 > −15.0 kcal mol⁻¹. The ΔE^orb term decreases from −91.0 to −84.5 kcal mol⁻¹ with the inclusion of one Cr(CO)₃ group, which increase slightly according to the inclusion of Cr(CO)₃ groups (−84.5 > −89.3 > −93.1 kcal mol⁻¹), suggesting that such a term is not influenced to a large extent; thus, it is not mainly responsible for the decrease in the overall interaction energy for the Ag⁺ complexes. Interestingly, the ΔE^elstat term is the more influenced quantity of ΔE^int, which decreases from −72.2 kcal mol⁻¹ for Ag⁺–1 to −45.1 > −34.6 > −23.4 kcal mol⁻¹ with increase in the number of Cr(CO)₃ groups (Table 3). Hence, the electrostatic character of the interaction exhibits smaller contribution to the formation of the hypothetical compounds involving the Cr(CO)₃ groups, which suggests lesser role of related interactions such as ion–dipole and ion–quadrupole interactions.⁴⁸ The latter point leads to the relative increase of the covalent character, due larger decrease of the interaction electrostatic term. The EDA analysis for the Sn²⁺–1 system, reveals results similar to the Ag⁺–1 case, which becomes less stabilizing from −217.1 kcal mol⁻¹ to −204.5 > −193.2 > −183.2 kcal mol⁻¹, according to the inclusion of Cr(CO)₃ groups. The obtained total binding energies suggest that the resulting cation–π interactions can be described as strong non-covalent bonds, which involves several binding sites. The analysis from the EDA scheme reveals that such a strong interaction involves a slightly covalent character, accounting for the charge transfer between the paracyclophane structure and the metallic cation.

The EDA–NOCV scheme was employed to study in detail the metal–ligand bonding situation in complexes Ag⁺–1(Cr(CO)₃)_n (n = 0–3) (Table 3) and Sn²⁺–1(Cr(CO)₃)_n (n = 0–3) (Table 4) by focusing on the ΔE^orb term, which is later decomposed into several contributions given by ΔE^ab_n (Fig. 4 and 5). The covalent character of the cation–π interaction can be understood in terms of the bonding situation depicted above, in which the dominant density deformation, namely, ΔP₁, arises particularly from the ligand–metal donation, which is related to the donation from π orbitals (HOMO-5) of [2.2.2]paracyclophane to 5s-Ag⁺ (Fig. 4, S4, and S6, ESI†) as described in Fig. 2. ΔP₁ provides the highest energy stabilization, ΔE^orb₁ = −27.1 kcal mol⁻¹, with a charge transfer Δq₁ = 0.528e. Two other significant density deformation channels, ΔP₂ and ΔP₃, provide energetic stabilizations, ΔE^orb₂ and ΔE^orb₃, of −8.9 kcal mol⁻¹. These density deformations include the ligand–metal donation from π orbitals (HOMO-3) of [2.2.2]paracyclophane to 5p-Ag⁺ and the polarization of 4d-Ag⁺ orbitals, providing a charge accumulation inside the cavity (Fig. 4, S4, and S6†). Density deformation channels such as ΔP₄ and ΔP₅ also characterize the metal–ligand donations by providing stabilization of −6.6 kcal mol⁻¹. Less significant density deformations, ΔP₆–ΔP₈, comprise the density polarization from the cyclophane structure towards the cage. Metal–ligand back-donations are less significant and provide only −2.0 kcal mol⁻¹ of stabilization. EDA–NOCV reveals that the most significant density deformation channels, ΔP_i, involve density outflows and inflows that tend to push the density from the aromatic rings of [2.2.2]paracyclophane towards the Ag⁺ ion, which is also confirmed by the Hirshfeld charges of the interacting fragments.

Fig. 4 Selected contours of deformation densities, ΔP_i(r), describing the interaction between Ag⁺ and 1(Cr(CO)₃)_n (n = 0–3), with their corresponding energy, ΔE^orb_i (kcal mol⁻¹), and charge estimation, Δq_i = ν_i (a.u.). Red and blue surfaces indicate density outflow and density inflow, respectively (contour value 0.0003).

Fig. 5 Contours of deformation densities, ΔP_i(r), describing the interaction between Sn²⁺ and the remaining [2.2.2]paracyclophane moieties, 1(Cr(CO)₃)_n (n = 0–3) and their corresponding energy, ΔE^orb_i (kcal mol⁻¹), and charge estimation, Δq_i = ν_i (a.u.). Red and blue surfaces indicate density outflow and density inflow, respectively (contour value 0.0003).

In contrast, the richer bonding situation for the Sn²⁺–1(Cr(CO)₃)_n (n = 0–3) complexes provides a larger ΔE^int that ranges from −217.1 to −183.2 kcal mol⁻¹ (Table 4) as discussed above. As a consequence, the covalent character of metal–ligand bonding in the Sn²⁺ counterparts is much more significant (77.6–99.1%) when compared with Ag⁺ analogues. The EDA–NOCV analysis confirms the stronger bonding scheme, involving the 5p-Sn shell as discussed above (Fig. 2). Similarly, the number of external coordinating groups (Cr(CO)₃)_n on the metal bonding situation reveals that the Cr(CO)₃ groups reduce and increase the electrostatic and orbital contributions, respectively. The dominant density deformation channels, ΔP₁–ΔP₃ reveals that the high covalent character is related with the 5p-Sn shell, in which the ligand–metal donation provide stabilizations, ΔE^orb₁–ΔE^orb₃ of −38.9 kcal mol⁻¹ (Table 4, Fig. 5, S5, and S7†). Other significant density deformation channels such as ΔP₄–ΔP₄ arrive from the ligand–metal donation from π orbitals of [2.2.2]paracyclophane to 5d-Sn²⁺, providing stabilizations of −8.0 kcal mol⁻¹ (Fig. 5, S5, and S7†). A large number of density deformation channels with a small magnitude showing the polarization of the [2.2.2]paracyclophane moiety towards the centre of the cage are also observed. Despite the small magnitude, they occur in a large number. EDA–NOCV does not show any density deformation channel that indicates a significant metal–ligand back-donation.

Lastly, the different size of the involved metallic cation (respective ionic radius, Ag⁺ = 1.13 Å and Sn²⁺ = 0.93 Å), suggests a more effective centered conformation for the tin counterpart. Moreover, the Pauli repulsion term, which allows to account for the steric hindrance, for the silver case in η²:η²:η², amount to 74.1 kcal mol⁻¹, and for its η⁶:η⁶:η⁶ coordination case, 45.4 kcal mol⁻¹. Such values suggest that the [2.2.2]pCp cavity is able to include the silver cation in a centered conformation; however, the bonding scheme discussed above seems to be the more relevant argument to determine the coordination mode of the cation–π interaction in the studied systems.

In order to gain understanding of the spatial distribution of the discussed cation–π interaction in different coordination modes, we calculate the noncovalent interactions (NCI) index^44–46 for Ag⁺–1 and Sn²⁺–1. The NCI index offers a suitable description of noncovalent interactions based on the reduced density gradient (s(ρ)) at low-density regions (ρ(r) < 0.06 a.u). The s(ρ) quantity is employed to denote an inhomogeneous electron distribution, as given by the form:

where s(ρ) exhibits small values in regions where both covalent bonding and noncovalent interactions are located. To distinguish the nature of the interaction, each point in this region is correlated with the second eigenvalue of the electron density Hessian (λ₂), which accounts for the accumulation (attractive) or depletion (repulsive) of density in the plane perpendicular to the interaction. The product between ρ(r) and the sign of λ₂ has been proposed as a useful descriptor to reveal stabilizing or attractive interactions (λ₂ < 0), weak interactions (λ₂ ≈ 0) or repulsive characters of the interaction (λ₂ > 0);^44–46 thus, ρ*sign(λ₂) ranges from negative to positive values according to the nature of the non-covalent interaction.

Fig. 6, which is the NCI analysis for Ag⁺–1 and Sn²⁺–1, shows the characteristic internal ring repulsion of the aromatic moieties (positive values of ρ*sign(λ₂)). Note that the analysis clearly reveals the spatial distribution of the favourable η²:η²:η² and η⁶:η⁶:η⁶ coordination modes involving two or six coordinating sites per ring, respectively, in agreement with the discussion given above. The region between Ag⁺ and the upper face of 1, depicts three independent stabilizing sections (ρ*sign(λ₂) < 0), which involves two carbons atoms and the silver cation and accounts for the η² coordination mode towards each ring. Thus, the calculated strength of about −100.1 kcal mol⁻¹ is obtained by the contribution from the three cation–π stabilizing interaction denoted in Fig. 6. In addition, the analysis also reveals the weak van der Waals interaction between the p-carbons of the aromatic rings. In contrast, the η⁶:η⁶:η⁶ coordination for Sn²⁺ is denoted by three independent regions involving the six carbons atoms of each aromatic ring. The ρ*sign(λ₂) values are similar to those obtained for the silver case. Consequently, the obtained interaction energy of about −217.1 kcal mol⁻¹ is given by the sum of several cation–π stabilizing interactions involving the three aromatic rings.

Fig. 6 NCI analysis for Ag⁺–1 (left) and Sn²⁺–1 (right).

Conclusions

[2.2.2]Paracyclophane is a versatile structure, which can exhibit η²:η²:η² and η⁶:η⁶:η⁶ coordination, involving two or six carbon atoms in each aromatic ring. According to the nature of the metallic cation, the interaction is based on the interaction with the upper face or allowing the inclusion to the center of the structure, which is determined mainly by the ligand-to-metal charge transfer ruled by symmetry and energetic considerations. For Ag(I), the 5s-Ag shell is close in energy to the frontier orbitals of paracyclophane, resulting in the formation of a bonding combination with the symmetric combination of the π₂-type levels, leading to a non-centered conformation. In contrast, the Sn(II) case exhibits a largely favourable interaction, involving the bonding interaction with the π₂ and π₃ type levels, which involve the 5p-Sn shell.

The analysis of the total interaction energy shows a value of −100.1 kcal mol⁻¹ for the silver case and −217.1 kcal mol⁻¹ for the tin system. Both values suggest a strong cation–π interaction with a covalent character of 55.8% and 77.6%, respectively. The charge distribution analysis on the basis of the NBO scheme reveals a net ligand to metal charge donation of 0.33 (au) on formation of the η²:η²:η²-silver compound, which is given by the Ag^0.67+[2.2.2]pCp^0.33+ form. For the η⁶:η⁶:η⁶-compound, an increase in the charge donation is observed, which increases to 0.82 (au), as a result of the centered coordination and suitable p-shell of the tin cation, leading to the Sn^1.18+[2.2.2]pCp^0.82+ natural charge distribution.

The graphical representation of the non-covalent interactions given by the NCI indexes allows for characterization and determination of the nature of the regions bearing the cation–π interactions. As a result, three individual regions are observed between the metallic cation, and each aromatic ring shows characteristic shapes for the η² and η⁶ coordination modes, which are of stabilizing nature.

Thus, the combination of several non-covalent cation–π interaction results in a sizeable ligand to metal charge donation, leading a favourable affinity of the paracyclophane towards the Ag(I) and Sn(II) cations with a covalent character.

In addition, the role of the internal through-space non-covalent π–π interactions between the aromatic rings in [2.2.2]paracyclophane into the affinity of the studied cations was evaluated by the inclusion of the hypothetical series involving the Cr(CO)₃ acceptor groups. The obtained results denotes that the electrostatic character of the interaction is decreased, a more relevant role of the covalent character into the stabilization of the Ag(I) or Sn(II) complex. According to the number of Cr(CO)₃ groups, the interaction becomes less stabilizing for the former, from −100.1 kcal mol⁻¹ to −86.6 > −79.0 > −72.3 kcal mol⁻¹, and from −217.1 kcal mol⁻¹ to −204.5 > −193.2 > −183.2 kcal mol⁻¹ for the latter.

Experimental section

Relativistic density functional theory calculations were performed using the ADF2013 code,^4,39 via the scalar ZORA Hamiltonian.⁴¹ Triple-ξ Slater basis set plus two polarization functions, and one diffuse function were employed within the generalized gradient approximation (GGA) according to the Becke–Perdew (BP86) exchange–correlation functional.^42,43 The molecular structures have been optimized via the analytical energy gradient method implemented by Verluis and Ziegler.⁴⁴ The pair-wise correction of Grimme was employed to take into account long-range interactions⁴⁵ (BP86-D3). The non-covalent interaction (NCI) analysis was carried out by using the NCIPLOT program developed by Weitao Yang and coworkers³⁶ and the NCI Milano program developed by Saleh and coworkers,^37,38 which are both based on the analysis of electron density descriptors. The NCI isosurfaces have been plotted using the Visual Molecular Dynamics (VMD) software.⁴⁶ To overcome the basis set superposition error (BSSE), the counterpoise method was employed.

The EDA–NOCV³⁵ calculations were performed using BP86-D3/TZ2P+ model,^42,43,45 along with the zero-order regular approximation, ZORA,⁴¹ as implemented in ADF2013 package.^39,40 The EDA–NOCV scheme decomposes the interaction energy, ΔE^int, into different components (1): ΔE^elstat corresponds to the classical electrostatic interactions between the interacting fragments; ΔE^Pauli accounts for the repulsive Pauli interaction between the occupied orbitals of the fragments; and ΔE^orb describes both the interactions between occupied molecular orbitals of one fragment with the unoccupied orbitals of the other fragments and the inner-fragment polarization. The NOCV pairs (Ψ_−i, Ψ_i) decomposes the differential density, ΔP(r), into contributions ΔP_i(r) (2), where ν_i and N stand for the NOCV eigenvalues and the number of basis functions, respectively. The deformation density, ΔP_i(r), provides information about symmetry and the direction of the flow of charge. In the EDA–NOCV scheme, the orbital component, ΔE^orb, is stated in terms of the eigenvalues ν_i (3), where F^TS_i,i are the diagonal transition-state Kohn–Sham matrix elements. The component ΔE^orb_i provides the energetics estimation of the ΔP_i(r) related with a particular electron flow channel for the bonding between two interacting fragments. Since BP86-D3 functional is employed, the dispersion correction, ΔE^disp, is added to the ΔE^int values to describe the total bond energy (1).

ΔE^int = ΔE^elstat + ΔE^Pauli + ΔE^orb + ΔE^disp (1)

Acknowledgements

A.M.-C. acknowledges the financial support of FONDECYT Grant 1140359 and PROJECT MILLENNIUM No. RC120001. C.O.U acknowledges DI-402-13/I UNAB. M.P.-V. acknowledges CONICYT 63130036 Doctoral fellowship. G.F.C. thanks the Coordination for the Improvement of Higher Level Education Personnel (Capes) for a post-doctoral research scholarship (grant 3181-13-8) and the excellent service provided by the Hochschulrechenzentrum of Philipps-Universität-Marburg. We thank the reviewers for their useful comments and suggestions.

References

1. Modern Cyclophane Chemistry, ed. R. Gleiter and H. Hopf, Wiley-VCH, Weinheim, Germany, 2004.
2. G. F. Caramori, S. E. Galembeck and K. K. Laali, J. Org. Chem., 2005, 70, 3242–3250.
3. S. Amthor and C. Lambert, J. Phys. Chem. A, 2006, 110, 3495–3503.
4. Y. Morisaki and Y. Chujo, Angew. Chem., Int. Ed., 2006, 45, 6430–6437.
5. L. Valentini, F. Mengoni, A. Taticchi, A. Marrocchi, S. Landi, L. Minuti and J. M. Kenny, New J. Chem., 2006, 30, 939–943.
6. H. Henning, Angew. Chem., Int. Ed., 2008, 47, 9808–9812.
7. L. Bondarenko, I. Dix, H. Hinrichs and H. Hopf, Synthesis, 2004, 16, 2751–2759.
8. V. Rozenberg, E. Sergeeva and H. Hopf, in Modern Cyclophane Chemistry, ed. R. Gleiter and H. Hopf, Wiley-VCH, Weinheim, Germany, 2004, pp. 435–462.
9. K. Schlotter, F. Boeckler, H. Hübner and P. Gmeiner, J. Med. Chem., 2006, 49, 3628–3635.
10. B. Ortner, R. Waibel and P. Gmeiner, Angew. Chem., Int. Ed., 2001, 40, 1283–1285.
11. P. J. Dyson, D. G. Humphrey, J. E. McGrady, P. Suman and D. Tocher, J. Chem. Soc., Dalton Trans., 1997, 1601–1606.
12. K. A. Lyssenko, M. Antipin and D. Antonov, ChemPhysChem, 2003, 4, 817–823.
13. G. F. Caramori and S. E. Galembeck, J. Phys. Chem. A, 2007, 111, 1705–1712.
14. G. F. Caramori and S. E. Galembeck, J. Phys. Chem. A, 2008, 112, 11784–11800.
15. J. Kleinschroth and H. Hopf, Angew. Chem., Int. Ed., 1982, 21, 469–480.
16. G. F. Caramori, L. C. Garcia, D. M. Andrada and G. Frenking, Organometallics, 2014, 33, 2301–2312.
17. P. J. Dyson, D. G. Humphrey, J. E. McGrady, D. M. P. Mingo and D. J. Wilson, J. Chem. Soc., Dalton Trans., 1995, 4039–4043.
18. C. Elschenbroich, J. Schneider, M. Wünsch, J.-L. Pierre, P. Baret and P. Chautemps, Chem. Ber., 1988, 121, 177–183.
19. J. Poater, J. M. Bofill, P. Alemany and M. Sola, J. Org. Chem., 2006, 71, 1700–1702.
20. A. Muñoz-Castro, Chem. Phys. Lett., 2011, 517, 113–115.
21. S. Pelloni, P. Lazzeretti and R. Zanasi, J. Phys. Chem. A, 2007, 111, 3110–3123.
22. F. Imashiro, Z. Yoshida and I. Tabushi, Tetrahedron, 1973, 29, 3521–3526.
23. C. Cohen-Addad, P. Baret, P. Chautemps and J.-L. Pierre, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1983, 39, 1346–1349.
24. J.-L. Pierre, P. Baret, P. Chautemps and M. Armand, J. Am. Chem. Soc., 1981, 103, 2986–2988.
25. G. Pierre, P. Baret, P. Chautemps and J.-L. Pierre, Electrochim. Acta, 1983, 28, 1269–1287.
26. H. C. Kang, A. W. Hanson, B. Eaton and V. Boelelheide, J. Am. Chem. Soc., 1985, 107, 1979–1985.
27. H. Schmidbaur, R. Hager, B. Huber and G. Muller, Angew. Chem., Int. Ed., 1987, 26, 338–340.
28. T. Probst, O. Steigelmann, J. Riede and H. Schmidbaur, Angew. Chem., Int. Ed., 1990, 29, 1397–1398.
29. P. Debroy, S. V. Lindeman and R. Rathore, J. Org. Chem., 2009, 74, 2080–2087.
30. V. J. Chebny, M. Banerjee and R. Rathore, Chem.–Eur. J., 2007, 13, 6508–6513.
31. A. S. Mahadevi and G. N. Sastry, Chem. Rev., 2013, 113, 2100–2138.
32. H. C. Kang, A. W. Hanson, B. Eaton and V. Boekelheide, J. Am. Chem. Soc., 1985, 107, 1979–1985.
33. J. Gross, G. Harder, F. Vögtle, H. Stephan and K. Gloe, Angew. Chem., Int. Ed., 1995, 34, 481–484.
34. (a) F. M. Bickelhaupt and E. J. Baerends, in Reviews in Computational Chemistry, ed. K. B. Lipkowitz and D. B. Boyd, Wiley-VCH, New York, 2000, vol. 15, p. 1; (b) K. Morokuma, J. Chem. Phys., 1971, 55, 1236–1244; (c) T. Ziegler and A. Rauk, Theor. Chim. Acta, 1977, 46, 1–10.
35. (a) M. P. Mitoraj, A. Michalak and T. Ziegler, J. Chem. Theory Comput., 2009, 5, 962–975; (b) M. von Hopffgarten and G. Frenking, WIREs Comput. Mol. Sci., 2012, 2, 43–62.
36. J. Contreras-García, E. R. Johnson, S. Keinan, R. Chaudret, J. Piquemal, D. N. Beratan and W. Yang, J. Chem. Theory Comput., 2011, 7, 625–632.
37. G. Saleh, C. Gatti and L. Lo Presti, Comput. Theor. Chem., 2012, 998, 148–163.
38. G. Saleh, C. Gatti, L. Lo Presti and J. Contreras-García, Chem.–Eur. J., 2012, 18, 15523–15529.
39. Amsterdam Density Functional (ADF) Code, Vrije Universiteit, Amsterdam.
40. (a) G. te Velde, F. M. Bickelhaupt, E. J. Baerends, C. F. Guerra, S. J. A. van Gisbergen, J. G. Snijders and T. Ziegler, J. Comput. Chem., 2001, 22, 931–967; (b) C. F. Guerra, J. G. Snijders, G. te Velde and E. J. Baerends, Theor. Chem. Acc., 1998, 99, 391–403.
41. (a) E. van Lenthe, E. J. Baerends and J. G. Snijders, J. Chem. Phys., 1993, 99, 4597–4610; (b) M. Filatov, ChemPhysChem, 2002, 365, 222–231; (c) C. van Wüllen, J. Chem. Phys., 1998, 109, 392–399.
42. A. D. Becke, Phys. Rev. A, 1988, 38, 3098–3100.
43. J. P. Perdew and Y. Wang, Phys. Rev. B: Condens. Matter Mater. Phys., 1986, 33, 8822–8824.
44. L. Verluis and T. Ziegler, J. Chem. Phys., 1988, 88, 322–328.
45. S. Grimme, WIREs Comput. Mol. Sci., 2011, 1, 211–228.
46. W. Humphrey, A. Dalke and K. Schulten, J. Mol. Graphics, 1996, 14, 33–38.
47. E. D. Glendening, J. K. Badenhoop, A. E. Reed, J. E. Carpenter, J. A. Bohmann, C. M. Morales and F. Weinhold, NBO 5.0, Theoretical Chemistry Institute, University of Wisconsin, Madison, 2001.
48. M. Ponce-Vargas and A. Muñoz-Castro, Phys. Chem. Chem. Phys., 2014, 16, 13103–13111.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra12859a

---