Elucidating the structures and binding of halide ions bound to cucurbit[6]uril, hemi-cucurbit[6]uril and bambus[6]uril using DFT calculations

Abstract

Understanding the binding and nature of the interactions present in host–guest complexes are central to supramolecular chemistry. In this paper, we tried to understand the nature of bonding between halides and three related host molecules using density functional theory. We have addressed a number of issues such as the role of solvation, the role of cations and the use of appropriate density functional calculations that are crucial for modeling host–guest complexes. Calculations show that the binding of halides in cucurbit-[6]-uril is assisted by a cation, whereas in hemi-cucurbit-[6]-uril, it is assisted by solvents. AIM calculations reveal the nature of non-bonded interactions present in these host–guest complexes and in particular brings out the two types of hydrogen bonding present in hm-CB-[6] and BU-[6] complexes.

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Introduction

The condensation of glycoluril units lead to the discovery of the supramolecules, cucurbit-urils [CBs] which have gained considerable attention in recent years (Fig. S1, ESI†).¹ CBs possess a hydrophilic moiety at the portals and a hydrophobic core. Depending on the number of monomer glycoluril units, the CBs are further classified into CB-[5], CB-[6], CB-[7], CB-[8] and CB-[10] and their cavity size increases with the increasing number of glycoluril units.^2,3

CBs have attracted a lot of interest due to their ability to bind a variety of species, including neutral^4,5 and cationic^6,7 molecules. However, anions binding to CBs are somewhat rare.^8,9,10 In fact it was suggested that CBs form complexes with toxic heavy metal oxides such as chromate and dichromate, although their corresponding crystal structures were not known.¹⁰ However the X-ray crystal structures of chloride and nitrate anions encapsulated inside CB-[5] are reported.^8,9

Recently two new macrocycles known as hemi-cucurbit-urils (hm-CBs),¹¹ which bind anions selectively over cations (Fig. S1, ESI†), have been reported. Although, hm-CB-[6] has six glycoluril units, its complex formation with cations has not been observed.¹²

Very recently, another family of macrocycles known as Bambus-[6]-uril (BU-[6]) have been reported which resemble part of the bamboo plant (bambusoideaes, Fig. S1, ESI†).¹³ Thus BU-[6] is the hybrid version of CB-[6] and hm-CB-[6]. Interestingly, BU-[6] binds anions much more efficiently than thought before.¹³

Due to the large size of the host molecule (108 atoms in CB-[6] and 138 atoms in BU-[6]), computational studies are somewhat restrained, even at the density functional theory (DFT) level. To our knowledge, the very first calculations at the Hartree–Fock (HF) level were performed by Kim and co-workers.^3,14 Later Pichierri used DFT to further pin-point the large stabilities of native and thio-derivatives of CBs based on the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).^15,16 Gejji and co-workers used DFT to understand the binding behaviour of ferrocene in CB-[6] by computing the NMR chemical shifts for different conformers of ferrocene and for other molecules.^17–21 The binding preferences of an anti-cancer metal complex (oxaliplatin) to CBs were studied recently.²² Through DFT calculations, Carlqvist and Masaras²³ confirmed the predictions of Mock et al²⁴ on the enhanced reaction rates of the polar cyclo-addition reaction inside CB-[6].

It should be noted that in chloride encapsulated CB-[5], a potassium ion is sealed at one portal of CB-[5]⁸ and in hm-CB-[6], only water molecules are hydrogen bonded to the chloride ion.¹¹ In BU-[6], experimental studies indicate that due to the rigidity of the cavity, iodide ions fit better than the more electronegative chloride ion.¹³ Due to similar monomer units present in three host molecules, we would like to address why the binding preference towards the anion is large for BU-[6] as compared to other two host molecules. We here report the structures, the nature of the bonding interactions between the three host molecules with three halide ions (Cl⁻, Br⁻ and I⁻) and the halide binding affinities of CB-[6], hm-CB-[6] and BU-[6] using DFT based calculations. We have investigated the nature of bonding that exists between the halide and the host by performing Atoms in Molecules (AIM) calculations.²⁵ The role of the cation and water molecules in assisting the stabilization of the structures, leading to higher binding energies, are also investigated.

Computational details

We have used the BP86 functional^26,27 in conjunction with def2-SV(P)²⁸ for geometry optimizations. For energetics, we used the B3LYP^29,30 functional with TZVP^31,32 (triple zeta quality) for all atoms. For iodide ions, a def2-TZVP basis set was used to describe the valance orbitals and the core orbitals were modeled via def-ECP pseudo potential. It has been known in the past that such an approach saves computational time as geometries are less sensitive to larger basis sets, but the corresponding energies will be significantly influenced by the large basis set.^33,34 To speed up the calculations, a resolution of identity (RI) approximation^35–39 is invoked as implemented in TURBOMOLE⁴⁰ by using def2-SV(P) auxiliary basis for the Coulomb exchange terms. No such approximations have been used for the energy evaluation with a TZVP basis set. It is worth pointing out that our largest system of BU-[6] complexed with iodide ions with six water molecules is the largest system and contains 159 atoms and 1432 and 2171 Cartesian basis functions at the level of def2-SV(P) and TZVP basis sets.

The binding energies of the three halide ions with the CB-[6] host molecule are computed as shown below.

CB-[6] + X⁻·(H₂O)₆ → CB-[6]-X⁻ + (H₂O)₆ (1)

CB-[6] + X⁻·(H₂O)₆ → CB-[6]-X⁻.(H₂O)₆ (2)

In eqn (1), the water molecules do not solvate the formation of adducts whereas in eqn (2) the solvent molecules were explicitly included, thus solvating the host–guest complex. Further, in eqn (1), six water molecules that form part of the product are not individual molecules, but rather form a cyclic planar hydrogen bonded complex. (Fig. 1 (a)). Our calculated formation of the cyclic hydrogen bonded network of six waters with a binding energy of 50.7 kcal mol⁻¹ is close to the value reported by Bryantsev et al. (48.8 kcal mol⁻¹).⁴¹ Further, due to the importance of non-covalent interaction present between the host and guest molecules, we have evaluated the binding energies using the M06 density functional⁴² in conjunction with the TZVP basis using G09 suite program.⁴³

Fig. 1 Optimized structures of (a) cyclic planar water cluster, (H₂O)₆ and (b) solvated halides, [X(H₂O)₆]¹⁻ (Color code: yellow = oxygen, brown = halide ion and white = hydrogen).

In order to gain further insights into the bonding that exists between the halide ions and the three host molecules, topological analysis has been performed using AIM2000 package⁴⁴ and the corresponding wave functions were generated at the B3LYP functional in conjunction with 6-31+G* basis sets were chosen for all the atoms. For iodide ions, a SDD pseudo potential is used.

Results and discussion

(i) Structures of bare hosts and solvated guest molecules

We first present results of the optimized structures of the three host molecules and the halide ion solvated species.

Due to the anionic nature of the halide species, it is expected that these ions exist in solution via strong hydrogen bonding. We considered solvation of the three halides with six water molecules whose hydrogen bonding pattern are previously known.⁴⁵ Unlike the fluoride ion, the three heavier anions (Cl⁻, Br⁻ and I⁻) are partially exposed to vacuum and hence the water molecules form pyramid like structure with the halide ions (Fig. 1 (b)). The optimized chloride structure was used for subsequent optimizations for the hydrated bromide and iodide species. In all three structures, it was observed that four water molecules are hydrogen bonded to the halide ion and two water molecules are involved in secondary hydrogen bonding with the first coordination hydrogen bonded waters (Fig. 1 (b)). In all cases, one hydrogen bonding with the halide is stronger in comparison to the other three. Due to the differing electronegativity of the three halides, hydrogen bonding interactions vary for the chloride, bromide and iodide (Fig. 1 (b)). We notice that this interaction is weaker for iodide (H⋯I⁻ = 2.8 Å) as compared to the bromide (H⋯Br⁻ = 2.5 Å) and chloride (H⋯Cl⁻ = 2.3 Å) the latter being the strongest.

Due to the hydrogen bonding with water molecules, the charges on the halide ions are now decreased compared to the bare ions (Table S1, ESI†). The extent of this charge decrease again depends on the strength of the hydrogen bonding. Of the three anions studied here, the chloride ion is the most electronegative and iodide is the least. Hence, the decrease of the charge on the chloride ion is greater (Cl⁻ = −0.661 e⁻) as compared to its congeners (Br⁻ = −0.715 e⁻ and I⁻ = −0.808 e⁻). The calculated binding energies of the halide ions are 40.0, 32.0 and 25.1 kcal mol⁻¹ for Cl⁻, Br⁻ and I⁻, respectively. The small size and large electronegativity of chloride is responsible for the strongest hydrogen bonding and hence its binding energies are also the largest compared to the larger sized and less electronegative iodide ion.

Important geometric parameters such as the depth (a), and the width at the core (b) and at the portals (c) are shown in Table S2 and Fig S1 in the ESI.† Although the calculated geometric parameters deviate slightly from the crystal structure values, the overall geometric features of CB-[6] such as symmetry (D_6h), cavity diameter and height are reproduced quite well. Furthermore, our calculated geometric parameters are consistent with previously reported values using B3LYP functionals.^22,23

For hm-CB-[6], the optimized distance between the methine carbons of the three glycoluril units are shorter by 0.5 Å (denoted as b₁–b₃ in Table S2, ESI†). Further, the distance between the three oxygen atoms (between o₁, o₂ and o₃ in Fig. S1†, denoted as c₁ to c₃) forming a triangle like arrangement is again larger by 0.5 Å compared to experimental data.¹¹

The portal oxygens of BU-[6] form two triangular arrangements (o₁–o₃ and o₄–o₆ in Fig. S1, ESI†). X-ray data of the chloride bound BU-[6] suggests a small triangle present at the outer portals (∼7.5 Å, c₁–c₃) and a slightly larger triangle formed just above the core (∼8.8 Å, c₃–c₆).²⁶ However in our optimized structures of the bare macrocycle, the triangular arrangements of the oxygen atoms open up significantly and these outer portals are larger than the inner portals, which is in contrast to the X-ray data (Fig. S1, ESI†). Therefore, compared to the experimental data,¹³ our calculated values (c₁–c₃) are larger by more than 2.5 Å, whereas for the inner triangle (c₄–c₆) this value is 0.8 Å shorter than the experimental data. (Table S2, ESI†) This large discrepancy may be due to the role played by the chloride ion in holding the constrained geometry which will be discussed in the forthcoming sections. The inner core formed by the methine carbons is similar to hm-CB-[6] (b₁ to b₃, Table S2, ESI†). The inner triangular oxygen arrangement and the methine core carbons of hm-CB-[6] and BU-[6] are very similar. From Fig. 1, it is very clear that in both hm-CB-[6] and BU-[6], the 12 methine hydrogen atoms are pointing towards inside the core, whereas in CB-[6], the hydrogen atoms are pointing outside.

Our calculated HOMO–LUMO gaps for the three host molecules suggest that CB-[6] is the most stable molecule (6.58 eV), and BU-[6] is most reactive (6.04 eV), whereas hm-CB-[6] falls in between the two hosts (6.29 eV). Our calculated energy gap for CB-[6] is close to the values reported by earlier calculations. ^15,22

(ii) Binding of bare guests

A careful look at the LUMO of the three bare host molecules reveals the possible binding sites of the halide ion (Fig. 2). In CB-[6], a positive potential is created by methine hydrogens outside the CB-[6], whereas in hm-CB-[6] and in BU-[6], the twelve methine hydrogens create a positive potential at the core. Hence, the portals of CB-[6] can be a better binding site for cations such as metal ions and anion binding can occur only outside the CB-[6]. However, for hm-CB-[6] and BU-[6], the central core region is more suitable for the encapsulation of anions, such as halides.

Fig. 2 Lowest unoccupied molecular orbitals of bare (i) CB-[6], (ii) hm-CB-[6] and (iii) BU-[6]. (Color code: yellow = oxygen, bright blue = carbon, green = nitrogen, pale white = hydrogen).

In comparison to hm-CB-[6] and BU-[6], halide ion encapsulation to CB-[6] does not lead to any significant geometrical change. (Table 1, Fig. 3) The halide ions occupy the centre of the core which is 3.14 Å away from the two peripherals. As the portals of CB-[6] are anionic, it is expected that anion encapsulation is difficult due to the lack of stabilization of the electrostatic interactions. In fact, our calculated binding energies using both B3LYP and M06 functionals suggest that irrespective of the nature of the halide ions, encapsulation by CB-[6] is largely unfavorable by more than 20 kcal mol⁻¹ (Table 2). This is due to the fact that the binding of the halide ion in CB-[6] has to overcome the desolvation energy of the halide ions. As there are no stabilizing electrostatic interactions, such as hydrogen bonding, the charges on the halides are not significantly modified compared to the bare ion (Table S1, †). For example, only a ∼0.15–0.10 e⁻ decrease in charge is noted for the three halides upon encapsulation by CB-[6]. It is interesting to note that the binding energies calculated using the B3LYP functional of the three halides falls within ∼7 kcal mol⁻¹ but with the M06 functional this range is rather large (∼20 kcal mol⁻¹, Table 2). We believe that ions with larger ionic radii such as bromide and iodide ions interact with CB-[6] via hydrophobic forces, whereas the smaller ionic radii of the chloride ion interacts with CB-[6] electrostatically. Since the M06 functional accounts for both the electrostatic and dispersion interactions more accurately than the B3LYP functional, iodide species are more stabilized using M06 functional.

Fig. 3 Optimized structures of a halide encapsulated in (i) CB-[6], (ii) hm-CB-[6] and (iii) BU-[6] (yellow = oxygen, bright blue = carbon, green = nitrogen, brown = halide ion, pale white = hydrogen).

Table 1 Structural parameters (Å) of the halide (Cl⁻, (Br⁻), [I⁻]) bound CB-[6], hm-CB-[6] and BU-[6]. Refer to Fig S1, ESI for the captions

	Calculated			Experiment
	CB-[6]	hm-CB-[6]	BU-[6]	CB-[6]	hm-CB-[6]	BU-[6]
b1	7.28 (7.31) [7.35]	4.86, (4.83) [5.05]	4.78, (4.99) [5.21]	—	4.55, 4.88, 5.28	4.75
b2		4.87, (4.95) [5.12]	5.00, (5.05), [5.25]			4.75
b3		4.90, (5.08) [5.28]	5.06, (5.11), [5.25]			4.79
c1	10.11, (10.11), [10.11]	9.02, (8.90) [8.71]	7.82, (8.26), [8.85]	—	8.70	7.46
c2		9.04, (9.07) [8.90]	8.11, (8.46) , [8.85]		8.75	7.49
c3		9.07, (8.94) [8.75]	8.23, (8.38) , [8.92]		9.06	7.81
c4	—	—	8.81, (8.79), [8.63]	—	—	8.82
c5			8.98, (8.85), [8.66]			8.86
c6			9.06, (8.91), [8.68]			8.90

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Table 2 Complexation energies (kcal mol⁻¹) for the formation of host (CB-[6], hm-CB-[6] and BB-[6]) guest (X = Cl⁻, Br⁻ and I⁻) complexes^a

Formation of CB-X^−	CB-6	K^+-CB-6	hm-CB-6	BU-6
a Values in parentheses are using M06/TZVP level.
Desolvated Adducts
Host + Cl^−·6H2O → Host-Cl^− + (H2O)6	+40.9 (+44.8)	−37.1 (−14.9)	−4.4 (−1.9)	−25.3 (−40.2)
Host + Br^−·6H2O → Host-Br^− + (H2O)6	+36.5 (+34.2)	−38.4 (−39.4)	−3.9 (−3.8)	−26.3 (−41.7)
Host + I^−·6H2O → Host-I^− + (H2O)6	+33.2 (+22.2)	−38.2 (−47.8)	−0.8 (−4.8)	−25.2 (−42.5)
Solvated adducts
Host + Cl^−·6H2O → Host-Cl^−·(H2O)6	+19.4 (+11.7)	−51.9 (−59.5)	−15.8 (−26.9)	−34.3 (−76.9)
Host + Br^−·6H2O → Host-Br^−·(H2O)6	+10.3 (−2.7)	−53.2 (−63.9)	−13.9 (−27.0)	−32.2 (−75.4)
Host + I^−·6H2O → Host-I^−·(H2O)6	+5.2 (−15.2)	−53.0 (−71.7)	−9.5 (−28.0)	−26.5 (−71.7)

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Unlike CB-[6], twelve methine hydrogens of the glycoluril units of hm-CB-[6] and BU-[6] point inside the core and hence the binding of halide ions is expected to be significant via hydrogen bonding (Fig. 3, Table S3, ESI†). In the optimized structures of the halide encapsulated complexes of hm-CB-[6], hydrogen bonding is not symmetric but depends upon the nature of the halide ions and the orientation of the methine hydrogen atoms. In hm-CB-[6], the chloride ion is strongly hydrogen bonded to six hydrogens (∼2.65 Å, Table S3, ESI†) and another six hydrogens are only weakly interacting (∼3.18 Å). The calculated hydrogen bond lengths are found to be close to the experimental values. However, in bromide and iodide bound hm-CB-[6], the hydrogen bonding interactions split into two strong (2.85 Å, 2.93 Å for Br⁻), (3.03 Å, 3.07 Å for I⁻) and two weak (3.10 Å, 3.16 Å for Br⁻), (3.18 Å, 3.28 Å for I⁻) ones.

Unlike the bare hm-CB-[6], for chloride bound hm-CB-[6], the calculated values of the width of the core and the portal are now found to be comparable to the corresponding X-ray data (Table 1). For bromide and iodide, the X-ray data are not available and hence we cannot compare our calculated data. Upon replacing the chloride ion by bromide and iodide which have larger ionic radii, the inner core cavities of the host (b₁–b₃ in Table 1) increase and a corresponding decrease in the triangular portal oxygens is noted (c₁–c₃).

As expected in halide bound hm-CB-[6], the charges on the halide ions are found to decrease due to hydrogen bonding (Table S3, ESI†). Although the hydrogen bonding is significant, the calculated binding energies do not reflect its strength. In fact, we cannot confidently say whether the halide ion is bound or not as the error within the theoretical method is ∼5 kcal mol⁻¹. Between the three halide ions, chloride binding is favored by the B3LYP functional, whereas the M06 functional favors iodide binding to hm-CB-6 (Table 2).

Unlike the bare host BU-[6], the geometric parameters of chloride encapsulated BU-[6] are in line with the experimental data (Table 1). Hence, chloride ion encapsulation influences the structural restrictions via favourable hydrogen bonding interactions. The calculated distances between the outer peripheral triangular oxygens (c₁–c₃) are found to be shorter compared to the inner triangular oxygens (c₄–c₆) (Table 1). Similarly the core–core carbon distance (b₁–b₃) is again in agreement with the experimental data, which is encouraging. As is found for hm-CB-[6], with the increasing size of the halide ions, the core–core carbon lengths (b₁–b₃) and the peripheral triangular oxygen lengths (c₁–c₃) also increase, while the inner peripheral triangular oxygen lengths decrease (c₄–c₆). In the halide encapsulated BU-[6], four sets of hydrogen bonding interactions are present (Table S3, †). Irrespective of the nature of halides, BU-[6] methine hydrogens form hydrogen bonds with the halide which are slightly weaker compared to those in hm-CB-[6]. These differing hydrogen bonding strengths are reflected in the calculated Mulliken charges of the anion (Table S1, ESI†). The calculated Mulliken charge of the anion inside the host molecule decreases in the following order, X-BU-[6] > X-hm-CB-[6] > X-CB-[6] (Table S1, ESI†). The strength of the hydrogen bonds and binding energies of the halide ion show variation depending on two factors, the electronegativity and the ionic radii of the halide ion. The calculated binding energies (Table 2) using the M06 functional are ∼15 kcal mol⁻¹ higher than those predicted by the B3LYP functional. We believe that such a large difference is perhaps due to the incorporation of dispersion terms in the M06 functional which are missing in the B3LYP functional. Although the chloride ion has stronger electronegativity compared to the iodide ion, the larger ionic radius of the iodide ion fits the cavity of hm-CB-[6] and BU-[6] better, resulting in stronger binding energies which are consistent with experimental data.

Further, we tried to evaluate the relaxation energy of three host molecules which can reveal how much structural reorganization occurs upon halide encapsulation.

Relaxation Energy = (Host)_optimized − (Host)_{at the halide bound geometry} (3)

Our calculations reveal that the relaxation energies for chloride bound to hm-CB-[6] (8.6 kcal mol⁻¹) and BU-[6] (12.5 kcal mol⁻¹) are larger compared to bromide (8.4. kcal mol⁻¹ for hm-CB-[6] and 10.3 kcal mol⁻¹ for BU-[6]), and iodide (6.8 kcal mol⁻¹ for hm-CB-[6] and 6.3 kcal mol⁻¹ for BU-[6]). These values imply that the host molecules undergo large structural reorganizations when the size of the halide ion is small, which is consistent with our geometry predictions.

(iii) Bonding analysis using AIM

The nature of the interactions present in these complexes has been studied within the framework of the Atoms In Molecules (AIM) theory.⁴⁶ The AIM approach is based on the topological properties of the electron density (denoted by ρ (r)) which is used to examine the bonding interactions present in various chemical systems.^47,48 According to Bader, the presence of a (3,−1) bond critical point (BCP) along the bond path is accepted as the standard criterion for the existence of all types of bonding and non-bonding interactions.^49,50 All the systems investigated here clearly display BCPs indicating the non-bonded interactions that exist between the halide ion and the host molecule (Fig. S1, ESI†). In addition to this, we also note additional critical points such as the ring critical point (RCP) and cage critical point (CCP). Qualitative information on the nature of bonding has been drawn from the electron density at BCPs. In the molecular graph, the big circles correspond to attractors attributed to positions of atoms and critical points such as (3, −1) BCP (red), (3, +1) RCP (yellow) and (3, +3) CCP (green) indicated by small circles (Fig. S2, ESI†).

(a) CB-[6]-halide interactions

A non-covalent interaction between the halide and CB-[6] is apparent from the BCPs (Fig. S2, ESI†). In the CB-[6]-Cl⁻ complex, twelve different bond paths have been observed between the host and the guest ion. Of the 12 bond paths, eight are N⋯Cl type and the remaining four are C⋯Cl type interactions (Fig. S2 (i)-b, ESI†). However for both CB-[6]-Br⁻ and CB-[6]-I⁻ complexes (Fig. S2 (i)-c, d, ESI†), there are twenty four interactions, all arising from N⋯X (X = Br or I) only and no C⋯X interactions are observed. The chloride ion, being more electronegative interacts with the nitrogen and carbon atoms which stabilize the encapsulated guest molecule and the charge on the chloride ion is less than one (Table S1, ESI†). The calculated local topological properties at the BCP between the interacting atoms with the corresponding halide ion suggest that as the size of the halide ion increases, the charge density at BCP also increases (Table S4, ESI†). Although the electronegativity of bromide and iodide is smaller than that of the chloride ion, their ionic radii are larger and therefore they can efficiently interact with the nitrogen atoms of CB-[6] which results in the reduction in charge on them in complexes compared to the bare ion.

(b) hm-CB-[6] and BU-[6] halide complexes. The molecular graphs show the interactions present in hm-CB-[6]-X⁻ and BU-[6]-X⁻ complexes (Fig. S2 (ii) and (iii), ESI†). For a typical hydrogen bond, the values of the electron density at the BCP should be within 0.002–0.035 a.u.⁵¹ Our calculated value for the halide bound hm-CB-[6] falls in this range (Table S5 and S6, ESI†). It is interesting to note that, unlike the CB-[6] complex, there are only H⋯X bonding interactions which stabilize the incoming ions. The ρ values at the H⋯X BCPs suggest that there are twelve such hydrogen bonding interactions that fall into two distinct sets. Among the twelve hydrogen bonds, six are comparatively stronger (Tables S5 and S6 and Fig. S3 and Fig. S4, ESI†) whose BCP values lie around 0.0165 a.u. whereas for the remaining six weak hydrogen bonds, this value lies at ∼0.00424 a.u. These varying degrees are consistent with the geometric parameters (Table 1). From Table S3, ESI† it is clear that the hydrogen bonding between the methine hydrogens of hm-CB-[6] and the halide ions are not symmetric and the strength of the hydrogen bonds are distinguished using the properties of the electron density at BCP (Fig. S3 and S4). It is interesting to find that the six strong hydrogen bonds (H_S) get weakened and other six weak hydrogen bonds (H_W) strengthen gradually as we move from the chloride to iodide in the hm-CB-[6] and BU-[6] complexes. The strong and weak hydrogen bonds can be clearly explained by monitoring the Laplacian of the electron density map and the gradient vector field trajectories obtained for the hm-CB-[6]-Cl complex. It is evident from Fig. 4 (a) that the region of the electron cloud of the chloride ion is well penetrated by hydrogen atoms and the extent to which each hydrogen atom penetrates the chloride ion's electron cloud indicate that there exist two types of hydrogen bonds (H_W and H_S). In the Laplacian of the electron density map, the charge depletion is indicated by an arrow. The gradient vector field of ρ overlaid with the contour of the electron density of the hm-CB-[6]-Cl⁻ is represented in Fig. 4 (b). Here the red circle indicates the (3,−1) BCPs and green circle indicates the (3, +1) RCP, and more importantly the gradient vector field trajectories associated with the BCPs define the boundaries of the atoms. The boundaries of the atoms presented here clearly suggest the presence of strong and weak hydrogen bonds in these complexes. Similar strong and weak hydrogen bonding patterns are also noticed for BU-[6] halide complexes.

Fig. 4 (a) The Laplacian of electron density describing the two types of bonding. (b) Superposition of an electron density contour map and inter atomic surface of the hm-CB-[6]-Cl complex.

(iv) Binding of solvated guests

In three solvated structures of the chloride bound hosts, we find that the bound chloride ions are hydrogen bonded to water molecules. In the optimized structure of the CB-[6]-halide (Fig. 5), we note that three water molecules are anchoring the glycoluril carbonyl oxygens and the chloride ions. Even if the starting geometries are non-hydrogen bonded, the chloride ions are found to move from the hydrophobic core (which is 3.14 Å from the portal oxygens) to the surface of CB-[6] (only 0.7 Å from the portal oxygens) to form hydrogen bonding with the water molecules (2.18 Å). Due to hydrogen bonding with solvent water molecules, the charge on the chloride ion decreases by more than 0.15 e⁻ as compared to the unsolvated chloride bound to CB-[6] (Table S1, ESI†). However, for the case of bromide, the water molecules are hydrogen bonded to themselves and interact only weakly with the guest (3.40 Å) and hence the bromide ion moves slightly inside the cavity (1.58 Å) from the portal oxygens compared to chloride. This decreased interaction result in a decreased change in the charge on the guest molecule compared to the bare ion (Table S1, ESI†). For the iodide ion which is larger, the water molecules are hydrogen bonded to themselves very strongly and the iodide moves back to the hydrophobic core (2.65 Å). Here, the large negative charge on the iodide ion is not stabilized by the water molecules (Table S1, ESI†).

Fig. 5 Optimized structure of the solvated halide encapsulated in (i) CB-[6], (ii) hm-CB-[6] and (iii) BU-[6]. Hydrogen atoms of the host molecules are removed for clarity. (Color code: yellow = oxygen, bright blue = carbon, green = nitrogen, brown = halide, pale white = hydrogen).

We find two different binding energies predicted by the B3LYP and M06 functionals. Using the B3LYP functional, the adduct is stabilized by more than 25 kcal mol⁻¹ with respect to the unsolvated form and the binding energies of the three halide ions remain unfavourable (Table 2). But with the M06 functional, the binding energy is only unfavorable for the chloride ion (by +11 kcal mol⁻¹), for the bromide ion the binding energy is slightly favorable (−3 kcal mol⁻¹) and for iodide ion, the binding energy is favorable by more than 15 kcal mol⁻¹.

We have calculated the effect of basis set superposition error (BSSE) using M06/TZVP for chloride binding to the three host molecule. Although there the binding energies are slightly modified (∼3–6 kcal mol⁻¹), the overall binding energy trend remain the same.

Hence, we have explored alternative models such that binding for halide (particularly chloride ion) encapsulations can be energetically feasible in CB-[6]. We believe that anion encapsulation in CB-[6] is preceded by a cation binding to the portals of CB-[6].^8,9,52 In fact, Nau and co-workers⁵³ proposed this to be the first step based on experimental and molecular mechanics calculations. We find that the formation of such a cation-CB-[6] is favorable by 43.1 kcal mol⁻¹ for the B3LYP functional and 41 kcal mol⁻¹ for the M06 functional when a potassium ion is used. Here, we have solvated the potassium ion with six water molecules (K⁺(H₂O)₆). The six glycoluril carbonyl groups form strong bonds with the metal ion (C=O⋯K⁺ = 3.25 Å) and this metalated CB-[6] is used here for encapsulating halide ions. Minimum energy species for all the three halides were formed (Fig. 6) and all the three guest molecules are found to interact strongly with the cation and occupy the centre of the core of CB-[6]. Due to these additional interactions, the C=O⋯K⁺ interaction is slightly weakened (∼3.40 Å) for the halides. Irrespective of the nature of the halide ion, the binding energy is now much more favorable in both the M06 and B3LYP functionals (Table 2). When both micro-solvation and the potassium ion are incorporated, the movement of the guest molecules towards the water molecules is restricted. The strong electrostatic interaction of the guest with the potassium ion dominates over the hydrogen bonding interactions with the water molecules. Thus, the K⁺–X⁻ bond length change is negligible (less than ∼0.02 Å) and the binding energies are still larger by more than 50 kcal mol⁻¹ (for both functionals).

Fig. 6 Optimized structures of potassium ion mediated encapsulation of (i) bare halide (Cl⁻, (Br⁻), [I⁻]) (ii) Solvated halide species (iii) sealed halide, in CB-[6]. (Color code: yellow = oxygen, bright blue = carbon, green = nitrogen, brown = halide ion, magenta = potassium ion, pale white = hydrogen).

Finally, it was suggested that two potassium ions can be used to seal the portals of CB-[6] such that they can be used as molecular capsules. Indeed we have performed geometry optimization by encapsulating the halide ions inside the sealed portals of CB-[6] with two K⁺ ions (Fig. 6). The addition of a second K⁺ ion to the halide encapsulated K⁺-CB-[6] is found to lead to small changes in the halide K⁺ bond lengths and the resulting binding energies are favourable by more than 60 kcal mol⁻¹ (B3LYP functional).

However, no such complications were observed in the binding of a halide ion to hm-CB-[6] and BU-[6] when the solvation is explicitly taken into account. As noted in the crystal structure of the chloride bound hm-CB-[6], water molecules form rigid network hydrogen bonds with the portals of the host molecule, which motivated us to build a similar water clusters for our present investigation (Fig. 6). As expected, the water molecules form strong hydrogen bonds with the halide ion (2.08 Å (Cl⁻), 2.28 Å (Br⁻) and 2.52 Å (I⁻)) leading to a decrease of the charge on the halide ions compared to their unsolvated counter-parts (Table S1, ESI†). For our calculated structures of chloride bound hm-CB-[6], hydrogen bonding between the water and chloride ion is found to be close to the experimental value of 2.28 Å. The calculated binding energies are also significant (∼20 and 25 kcal mol⁻¹ for B3LYP and M06 functional) as compared to the unsolvated structures where the binding energies are only small.

In the crystal structures of chloride bound BU-[6], a chloroform molecule is hydrogen bonded to outer portals. Hence, we have constructed a similar solvation framework for BU-6 and calculated the binding energies for anion encapsulation. Here again, the hydrogen bonding between the water molecules and the anion is weaker as compared to hm-CB-[6] which is again reflected in the calculated Mulliken charges of the anion (Table S1, ESI†). Due to solvation, the calculated binding energies for chloride and bromide are much more favourable by more than 70 kcal mol⁻¹ using the M06 functional.

Conclusions

Using electronic structure calculations, we have systematically investigated the type of interactions present between three similar host molecules and halide anions. The present study is important to understand the type of interactions present between anions and CBs and related species. Behrend reported that CBs form complexes with toxic heavy metal oxides such as chromate and dichromate (usually anionic) which are potential environmental hazards.¹⁰ To understand the mechanism of binding of such challenging anionic species to CBs, it is necessary to understand the binding of halide ions to CBs which are structurally simpler species. Potential outcomes of our calculations are as follows;

(a) The position of the halide ions inside CB-[6] molecule are largely influenced by water molecules and cations. Our results fall in line with the experimental studies that chloride encapsulation in CB-[5] is achieved only in the presence of a cation.^8,9 However for the other two halide ions, no such cation assistance is need for encapsulation as dispersion effect dominates hydrogen bonding.

(b) Among the three halide bound complexes of hm-CB-[6] and BU-[6], chloride complexes possess the largest relaxation energies of the host. Due to strong electrostatic hydrogen bonding interactions, the geometries of the host molecule need to undergo large structural reorganization. However, the large iodide ion can fit inside the cavity perfectly and hence only small structural changes of the host are required, in line with the experimental data.¹³

(c) The calculated binding energies are very sensitive to the choice of the density functionals. Density functionals which incorporate non-covalent interactions such as dispersion effects predict very strong binding energies compared to the popular ‘B3LYP’ functional. We believe the iodide ion binding to the three host molecules studied here to be mainly dispersive, whereas for the chloride ion it is electrostatic.

(d) AIM calculations clearly bring out the types of interactions present in these complexes and account for the stabilization of the halide ions inside the host molecules. In particular, it unambiguously reveals the presence of two types of hydrogen bonds existing in the halide bound hm-CB-[6] and BU-[6] complexes and their change in strength dependent on the size of the halide ion.

Hence we can conclude that modeling of host guest complexes remains a challenge as one needs to account for many factors including solvation, the role of the cations, the choice of the theoretical and computational method, etc. The present investigation emphasises the importance of the choice of level of theory in handling host–guest complexes in general and in particular the complexes that are stabilized by non-bonded interactions.

Acknowledgements

MS and SKG thank Dr T. Mukherjee for his kind support, KSKRA fellowship for funding and the BARC computer center for providing the high performance parallel computing facility (Ameya and Ajeya Systems). SKG gratefully acknowledges support from the INDO-EU project MONAMI. RVS thanks the University Grants Commission, INDIA for the financial support through Maulana Azad National Fellowship (Ref. No. F.40-17(C/M)/2009(SA-III/MANF) and PV thanks the Council of Scientific and Industrial Research (CSIR), India, & University Grants Commission (UGC), India for their financial support in the form of a major research grants (Ref. No. 02(2158)/07/EMR-II) and (F. No. 33-256/2007(SR)) respectively.

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Footnote

† Electronic supplementary information (ESI) available: Calculated Mulliken charges, hydrogen bonding distances between hm-CB-[6] and BU-[6] with halide ions and calculated local topological properties of the electronic charge density distribution at BCPs are listed in tables. Bond critical points of bare and halide encapsulated to hm-CB-[6] and BU-[6] are given. See DOI: 10.1039/c1ra00266j

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