N-Methyl- and N-Phenylpiperazine Functionalized Styryl Dyes Inside Cucurbiturils: Theoretical Assessment of the Factors Governing the Host–Guest Recognition

The family of cucurbiturils (CBs), the unique pumpkin-shaped macrocycles, has received great attention over the past four decades owing to their remarkable recognition properties. They have found diverse applications including biosensing and drug delivery technologies. The cucurbituril complexation of guest molecules can modulate their pKas, improve their solubility in aqueous solution, and reduce the adverse effects of the drugs, as well as enhance the stability and/or enable targeted delivery of the drug molecule. Employing twelve cationic styryl dyes with N-methyl- and N-phenylpiperazine functionality as probes, we attempted to understand the factors that govern the host–guest complexation of such molecules within CB[7] and CB[8] host systems. Various key factors determining the process were recognized, such as the pH and dielectric constant of the medium, the cavity size of the host, the chemical characteristics of the substituents in the guest entity, and the presence/absence of metal cations. The presented results add to our understanding (at the molecular level) of the mechanism of encapsulation of styryl dyes by cucurbiturils, thus shedding new light on various aspects of the intriguing complexation chemistry and the underlying recognition processes.


Introduction
Ribonucleic acid (RNA) and deoxyribonucleic acid (DNA) attract immense interest from scientists of diverse fields not only because they carry the fundamental genetic information in almost all living organisms, but also due to their irreplaceable functions in catalysis, intracellular recognition, and transport [1].The so-called quadruplexes: noncanonic DNA/RNA motifs of recent finding part of the telomeres have further been recognized as plausible drug targets especially in antitumor therapy [2][3][4].Their complex architecture is formed by folding guanine-rich nucleic acid sequences into square-planar compositions arranged into stacked layers (tetrads) additionally stabilized by the presence of alkali metal cations, most commonly potassium or, less frequently, sodium located in the central channel [5][6][7][8].Selectively binding small heterocyclic molecules to G-quadruplexes could decrease telomerase activity and increase telomere stability, reduce oncogene expression by inhibiting transcription and translation, and increase genome instability, hence, prompting apoptosis (cell death) [9][10][11].In this regard, cyanine dyes have been acknowledged for their beneficial properties, as they exert a dual effect upon polynucleotide binding/cell entering: by triggering specific spectroscopic response, they act simultaneously as imaging and therapeutic agents [12,13].Representatives of the subgroup called hemicyanines-the cationic

Reactions Modeled
The current study is aimed at providing reliable trends concerning the host-guest recognition process between N-methyl-and N-phenylpiperazine functionalized styryl dyes in their monocationic form and cucurbit [7/8]uril, further denoted as CB [7] and CB [8].In order to accomplish the task, the structures presented in Figure 2A and Table 1, first suggested by Zonjić and co-authors in Ref. [40], were considered.Three moieties build the dye molecules: a styryl moiety, which is conserved in all structures; a benzothiazole moiety, containing R1-(being either a hydrogen, a methyl group, or a bromine atom) and R2substituents (a methyl or a benzyl group), and a piperazine moiety, differing in the nature of the R3-substituent being either a methyl-or phenyl group.Thus, the possible combinations result in overall 12 dyes, henceforth referred to as the more generalized dyeN nomenclature, where N stands for the numbers from 1 to 12, e.g., Dye1-12.The N-methylpiperazine functionalized structures correspond to the numbers from 1 to 6, while to their equivalent N-phenylpiperazine dyes have been assigned the numbers from 7 to 12.The chemical structures of the host molecules, their spatial parameters (height, diameter of the inner cavity, and distance between the carbonyl groups of the outer rim), and the glycoluril unit are additionally presented in Figure 2B.

Reactions Modeled
The current study is aimed at providing reliable trends concerning the host-guest recognition process between N-methyland N-phenylpiperazine functionalized styryl dyes in their monocationic form and cucurbit[7/8]uril, further denoted as CB [7] and CB [8].In order to accomplish the task, the structures presented in Figure 2A and Table 1, first suggested by Zonjić and co-authors in Ref. [40], were considered.Three moieties build the dye molecules: a styryl moiety, which is conserved in all structures; a benzothiazole moiety, containing R 1 -(being either a hydrogen, a methyl group, or a bromine atom) and R 2 -substituents (a methyl or a benzyl group), and a piperazine moiety, differing in the nature of the R 3 -substituent being either a methyl-or phenyl group.Thus, the possible combinations result in overall 12 dyes, henceforth referred to as the more generalized dyeN nomenclature, where N stands for the numbers from 1 to 12, e.g., Dye1-12.The N-methylpiperazine functionalized structures correspond to the numbers from 1 to 6, while to their equivalent N-phenylpiperazine dyes have been assigned the numbers from 7 to 12.The chemical structures of the host molecules, their spatial parameters (height, diameter of the inner cavity, and distance between the carbonyl groups of the outer rim), and the glycoluril unit are additionally presented in Figure 2B.

Reactions Modeled
The current study is aimed at providing reliable trends concerning the host-guest recognition process between N-methyl-and N-phenylpiperazine functionalized styryl dyes in their monocationic form and cucurbit[7/8]uril, further denoted as CB [7] and CB [8].In order to accomplish the task, the structures presented in Figure 2A and Table 1, first suggested by Zonjić and co-authors in Ref. [40], were considered.Three moieties build the dye molecules: a styryl moiety, which is conserved in all structures; a benzothiazole moiety, containing R1-(being either a hydrogen, a methyl group, or a bromine atom) and R2substituents (a methyl or a benzyl group), and a piperazine moiety, differing in the nature of the R3-substituent being either a methyl-or phenyl group.Thus, the possible combinations result in overall 12 dyes, henceforth referred to as the more generalized dyeN nomenclature, where N stands for the numbers from 1 to 12, e.g., Dye1-12.The N-methylpiperazine functionalized structures correspond to the numbers from 1 to 6, while to their equivalent N-phenylpiperazine dyes have been assigned the numbers from 7 to 12.The chemical structures of the host molecules, their spatial parameters (height, diameter of the inner cavity, and distance between the carbonyl groups of the outer rim), and the glycoluril unit are additionally presented in Figure 2B.  1 according to the type of R 1 -/R 2 -/R 3 -substituents (A).Chemical structure of the glycoluril unit, CB [7] and CB [8] (B).The dimensions of CB [7] and CB [7] are reported in [29,31].For the assessment of the factors governing the host-guest recognition, the following reactions were taken into account: Reaction R1 illustrates the encapsulation of all the considered dyes in their monocationic form in both cucurbiturils.This approach allows the disclosure of important factors that affect the process, such as the cavity volume, nature of the R 1 -, R 2 -, and R 3 -substituents, and dielectric constant of the environment.Reactions from R2 to R4 consider the complexation of the most intriguing of the representatives of the series-dye9, in regard to obtained results in Ref. [40] and in the current research, and are focused on the assessment of the effect of pH of the medium, charge of the molecule, presence of high-energy water cluster in the host, and of magnesium cations in the solution.Mg 2+ stands for both a bare cation and one surrounded by a hydration shell of six water molecules, in which case the ternary complex has the formula CB [7]@ dye9@Mg_2W ^3+ after the loss of four water molecules (denoted as 4W) in reaction R4.Reaction R3 exemplifies the role of the metal cation as a competitor for binding the CB [7] (substitution), while reaction R4 portrays the formation of a ternary complex (addition).

Effect of the Substituents
The process of encapsulation of Dyes1-6 + in CB [7/8] is depicted in Figure 3 (first/second column, respectively).The optimized structures of the resulting complexes at the M062X/6-31G(d,p) along with the Gibbs energies (in kcal mol −1 ) of their formation at the higher M062X/6-31+G(d,p)//M062X/6-31G(d,p) level are given as well.
The obtained results imply that the formation of CB[7]@dye1-6 ^+ complexes appears thermodynamically favorable for almost all styryl dyes as the Gibbs energies stay firmly on negative ground: the presented data range from −3.5 to −7.2 kcal mol −1 (Figure 3, first column).The only exception is the recognition process between CB [7] and dye6 + , where the calculated ∆G 78 value equals 1.2 kcal mol −1 , which still remains close to zero and is within the acceptable error of the computational method.The inclusion process in the more voluminous CB [8], however, is thermodynamically improbable as the obtained ∆G 78 values are positive and vary between 4.6 and 9.5 kcal mol −1 (Figure 3, second column).The obtained results imply that the formation of CB[7]@dye1-6 Ⴈ+ complexes appears thermodynamically favorable for almost all styryl dyes as the Gibbs energies stay firmly on negative ground: the presented data range from −3.5 to −7.2 kcal mol −1 (Figure 3, first column).The only exception is the recognition process between CB [7] and dye6 + , where the calculated ∆G 78 value equals 1.2 kcal mol −1 , which still remains close to zero and is within the acceptable error of the computational method.The inclusion process in the The following Figure 4 depicts the encapsulation process between the remaining dyes7-12 + and the two host cucurbiturils.more voluminous CB [8], however, is thermodynamically improbable as the obtained ∆G 78 values are positive and vary between 4.6 and 9.5 kcal mol −1 (Figure 3, second column).
The following Figure 4 depicts the encapsulation process between the remaining dyes7-12 + and the two host cucurbiturils.The calculations indicate a similar trend for the N-phenylpiperazine functionalized styryl dyes: the encapsulation in CB [7] is a thermodynamically probable process evidenced by the negative ∆G ε values in almost all cases (except for dye10 and dye12, where the evaluated free energies, although positive, stay close to zero): see the first column in Figure 4. On the other hand, the reactions of formation of CB[8]@dye7-12 Ⴈ+ do not occur The calculations indicate a similar trend for the N-phenylpiperazine functionalized styryl dyes: the encapsulation in CB [7] is a thermodynamically probable process evidenced by the negative ∆G ε values in almost all cases (except for dye10 and dye12, where the evaluated free energies, although positive, stay close to zero): see the first column in Figure 4. On the other hand, the reactions of formation of CB[8]@dye7-12 ^+ do not occur spontaneously under the simulated conditions, as all of the ∆G ε values vary between 1.8 and 11.9 kcal mol −1 : see the second column in Figure 4.
The presented results draw some clear trends in regard to the nature of the substituents in the dyes' molecules.Firstly, the methyl/phenyl group at R 3 position does not substantially affect the outcome of the host-guest recognition in CB [7], as the obtained ∆G ε values fall in close ranges: from 1.2 to −7.2 kcal mol −1 for the formation of complexes CB [7]@dye1-6 ^+, and from 1.6 to −7.7 kcal mol −1 for the formation of the analogous complexes CB [7]@dye7-12 ^+, with a minor preference of up to 0.6 kcal mol −1 for the smaller group.The only odd exception strikes the difference in the recognition between CB [7] and dye4/dye10.These two structures are equivalent in regard to R 1 and R 2 but differ by 7.8 kcal mol −1 in their ∆G ε values.This result can be explained by the position of the dyes in the host cavity: while the N 2 -atom from the piperazine moiety in dye4 is incorporated in relatively close proximity to two carbonyl groups at 3.4/3.2Å, the equivalent N 2 -atom in dye10 interacts with only one C=O group located at 3.3 Å.This composition results in the loss of dipole-dipole interaction and, hence, unfavorably affects the encapsulation of dye10 in CB [7] (positive ∆G 78 = 1.6 kcal mol −1 ).Furthermore, the R 1 substituent more strongly influences the complexation between CB [7] and all the dyes, as expected, since it is the group directly bound to the quaternized N-atom from the benzothiazole moiety.The benzyl group exerts a stronger beneficial impact upon the host-guest recognition, as indicated by the higher absolute values of the calculated ∆G ε .The explanation lies in the greater negative inductive effect of the benzyl moiety as compared to its methyl counterpart, resulting in drawn electronic density from the N + and enhanced ion-dipole interaction with the carbonyl groups from the host.Additionally, the CH 3 -group being smaller manages to insert between the N + ion and the C=O groups from the cucurbituril rim, consequently enhancing the distance between them.Lastly, the R 2 substituents affect the complexation in CB [7] in a clear way: with the substitution of H→CH 3 →Br, the obtained ∆G ε values increase in absolute value (the recognition process becomes more favorable).The only combination that appears disadvantageous is between the benzyl-moiety and the bromine atom: positive Gibbs energies for the formation of CB [7]@dye6/12 ^+ complexes due to the opposite directions of their effects.
Similar (but not necessarily in all cases) trends are observed for the encapsulation of the dyes in CB [8] with regard to the effect of the substituents.Among the R 1 substituents, the direction of the most beneficial is H < CH 3 < Br.The methyl group at R 2 position leads to better results as compared to the benzyl substituent.Overall, the N-methyl functionalized styryl dyes are less affected by the change of the substituents at the other positions since the obtained results fluctuate less in comparison with the calculated ∆G ε values for the formation of CB[8]@dye7-12 ^+: from 4.6 to 9.5 kcal mol −1 vs. from 1.8 to 11.9 kcal mol −1 , respectively.Yet, all the obtained Gibbs energies stand strongly on positive ground, indicating a thermodynamically improbable reaction.

Effect of the Cavity Volume
The effect of the cavity volume is unambiguous-the N-methyland N-phenylpiperazine functionalized styryl dyes under study prefer the smaller cavitand, the preference being indicated by the negative ∆G ε values in almost all cases for their encapsulation in CB [7] as opposed to the positive Gibbs energies obtained for the complexation in CB [8].These results should be attributed to the lost interaction between the host and the guest molecules in the case of the more voluminous representative.Note that this outcome falls in line with experimental observations that CB [7] incorporates dyes in a 1:1 ratio, while CB [8] readily forms complexes but with two dye molecules in the cavity corresponding to a 2:1 or even 2:2 ratio [50-52].

Effect of the Dielectric Constant of the Medium
The presented results are given for two media-gas phase (close to a nonpolar solvent/protein environment) and water.By the implementation of the thermodynamic cycle for calculating the contribution of the solvation energy, the effect of the dielectric constant of the medium can be assessed.The balance between energy gain and de/solvation effects defines the outcome of the complexation process, as seen Figures 3 and 4. For instance, the recognition between CB [8] and the modeled dyes appears possible in the gas phase (negative ∆G 1 values); this trend changes when the reaction takes place in aqueous solution.

Encapsulation of Dye9
^+/2+ in CB [7] in Absence/Presence of Metal Cations 2.3.1.Effect of the pH of the Medium/Charge of the Dye Molecule For the assessment of factors such as the pH of the medium/charge of the dye molecule, reaction R2 was simulated.The optimized structures of dye9 in its mono-(denoted as dye9 + ) and dicationic (denoted as dye9 2+ ) forms participate in the reaction and their structures are explicitly presented in Figure S1.The obtained data-optimized binary host-guest complexes and ∆G ε values in different media are presented in Figure 5A-with an initial "empty" host, and in Figure 5B-when a high-energy water cluster is present in the cavity.
the recognition between CB [8] and the modeled dyes appears possible in the gas phase (negative ∆G 1 values); this trend changes when the reaction takes place in aqueous solution.Ⴈ+/2+ in CB [7] in Absence/Presence of Metal Cations 2.3.1.Effect of the pH of the Medium/Charge of the Dye Molecule For the assessment of factors such as the pH of the medium/charge of the dye molecule, reaction R2 was simulated.The optimized structures of dye9 in its mono-(denoted as dye9 + ) and dicationic (denoted as dye9 2+ ) forms participate in the reaction and their structures are explicitly presented in Figure S1.The obtained data-optimized binary hostguest complexes and ∆G ε values in different media are presented in Figure 5A-with an initial "empty" host, and in Figure 5B-when a high-energy water cluster is present in the cavity.The calculations indicate that the lower pH of the medium corresponding to a higher charge of the dye does not affect the host-guest recognition process significantly as the results differ by 0.8 kcal mol −1 : compare the ∆G ε values for the formation of CB[7]@dye9 Ⴈ+/2+ .This outcome seems somehow peculiar at first sight, because it is expected that the guest with the higher charge would better interact with the host due to the stronger ion-dipole interaction.However, the N1-atom, the bearer of the second positive charge, is located further away from the carbonyl rim of the cucurbituril (at about 3.7 Å) due to the quaternized N-atom from the benzothiazole ring acting as an "anchor" and predisposing the position of the piperazine moiety.Note that the structure with the second charge occupying N1 is, by 12.9 kcal mol −1 , more stable than its N2 counterpart.Additionally, the solvation penalty for the doubly charged construct is greater than for the The calculations indicate that the lower pH of the medium corresponding to a higher charge of the dye does not affect the host-guest recognition process significantly as the results differ by 0.8 kcal mol −1 : compare the ∆G ε values for the formation of CB[7]@dye9 ^+/2+ .This outcome seems somehow peculiar at first sight, because it is expected that the guest with the higher charge would better interact with the host due to the stronger ion-dipole interaction.However, the N 1 -atom, the bearer of the second positive charge, is located further away from the carbonyl rim of the cucurbituril (at about 3.7 Å) due to the quaternized N-atom from the benzothiazole ring acting as an "anchor" and predisposing the position of the piperazine moiety.Note that the structure with the second charge occupying N 1 is, by 12.9 kcal mol −1 , more stable than its N 2 counterpart.Additionally, the solvation penalty for the doubly charged construct is greater than for the monocationic composition, evidenced by the significant difference between the ∆G ε values in the gas phase and in aqueous solution: about 32-34 kcal mol −1 more for the formation of CB [7]@dye9 ^2+ as compared to CB[7]@dye9 ^+ (compare the differences in ∆G 1 /∆G 78 for the modeled reaction in Figure 5, [A]/[B]: 43.8/12.5 (monocation) vs. 77.7/46.4(dication) kcal mol −1 ).Overall, the results still suggest that the formation of both complexes CB[7]@dye9 ^+/2+ is a thermodynamically possible reaction, as the ∆G ε values stay below zero: −6.9/−6.1 kcal mol −1 , respectively.Taking into consideration a high-energy water cluster present in the inner cavity of CB [7] [53] constructed by 8 H 2 O molecules, as previously reported in Ref. [35], adds about 3.1 kcal mol −1 to the energy gained: the calculated ∆G ε values for the formation of both complexes CB[7]@ dye9 ^+/2+ become −10.0/−9.2kcal mol −1 (See Figure 5B).This result is consistent with earlier observations [46,47], suggesting that the hydration of the host is beneficial for the incorporation of metal ions and/or dye guests.

Effect of the Metal Cations
The effect of metal cations present in the solution is a subject of great significance for the supramolecular chemistry of cucurbiturils.Since almost all representatives of this class of cavitands are poorly solvated in an aqueous environment, the discovery that alkali metal cations promote the process [54] was an outstanding success for their use in water.It additionally expands their field of application through the formation of novel constructs such as molecular capsules, tubular polymers and molecular jewelry (bracelets and necklaces) [55][56][57][58][59][60].The metal cation acts as a "lid" that un/blocks the carbonyl portal or can assist with the encapsulation and/or release of the guest molecule under specific conditions, e.g., temperature and/or pH of the medium.Thus, delineating factors of high importance that govern the inclusion of styryl dyes in the CB hosts in the presence of metal cations (in the particular case of Mg 2+ ) is mandatory.Based on our previous calculations [61,62], the magnesium cations participating in reactions R3 and R4 were modeled with either a bare or hydrated cations with a shell of six water molecules.Two modes of magnesium interactions were considered: competitive substitution, where Mg 2+ displaces the bound dye molecule (Figure 6A), and a cooperative addition, where Mg 2+ co-binds to the already formed cucurbituril-dye complex (Figure 6B).The obtained results draw a clear picture of the effect of the magnesium cation: it appears beneficial in all the modeled reactions (negative ∆G ε values).Interestingly, comparing the outcome for the bare Mg 2+ , the cooperative addition appears more probable since the corresponding ∆G 78 are greater in absolute value (−54.1 vs. −31.1 kcal mol −1 ).However, a model closer to reality is the hydrated magnesium cation surrounded by six water molecules.In this case, the Gibbs energies differ by 4.6 kcal mol −1 in favor of the competitive substitution.Noteworthy, this conclusion falls in line with other experimental data with different dyes, showing that metal cations more often compete with the guest for binding the cucurbituril in 1:1 ratio, while they assist in the recognition process if two CB [7] molecules incorporate one dye [51].The obtained results draw a clear picture of the effect of the magnesium cation: it appears beneficial in all the modeled reactions (negative ∆G ε values).Interestingly, comparing the outcome for the bare Mg 2+ , the cooperative addition appears more probable since the corresponding ∆G 78 are greater in absolute value (−54.1 vs. −31.1 kcal mol −1 ).However, a model closer to reality is the hydrated magnesium cation surrounded by six water molecules.In this case, the Gibbs energies differ by 4.6 kcal mol −1 in favor of the competitive substitution.Noteworthy, this conclusion falls in line with other experimental data with different dyes, showing that metal cations more often compete with the guest for binding the cucurbituril in 1:1 ratio, while they assist in the recognition process if two CB [7] molecules incorporate one dye [51].

Methods
The calculations were performed through the utilization of the Gaussian 09 suite of programs [63].The most appropriate combination of a method and basis set was found to be the Minnesota functional M062X [64] with the double zeta 6-31G(d,p) basis set applied, and proven to be reliable in our previous investigations of the physicochemical properties of cucurbiturils [45][46][47]49,65].Initial geometries of the host molecules were derived from TUHGAG (CB [7]) and BATWEA (CB [8]) entries deposited in the Cambridge Crystallographic Data Centre (CCSD) [66,67].The most stable conformations (chair conformation of piperazine moiety and equatorial positioned N 1 /N 2 -substituents) of trans isomers of the dyesN were considered.All structures under study were subjected to full optimization and a vibrational frequency analysis at the lower M062X/6-31G(d,p) level of theory.The latter showed no imaginary frequencies for any of the calculations, thus indicating a local minimum of the potential energy surface (PES).These were used in evaluating the thermal energies, including zero point energy, E th , and the entropy, S, while the electronic energies, E el , were corrected by single point calculations at the higher M062X/6-31+G(d,p)//M062X/6-31G(d,p) level.In order to calculate the Gibbs energies of the modeled Reactions (1) to (4) in the gas phase corresponding to conditions such as room temperature, T= 298.15K, and atmosphere pressure, 1 atm, these data were implemented in the following equation [68]: where ∆E el , ∆E th , and ∆S represent the corresponding differences between the products and the reactants in consistency with Reactions (1) to (4).The change in the number of moles, ∆n, during the reaction is also accounted for in ∆G 1 (∆nRT ≈ P∆V).Additional single point calculations were performed at the M062X/6-31+G(d,p)//M062X/6-31G(d,p) level in a water environment (ε = 78) using the solvation model based on the density (SMD) method [69].The respective electronic energies in aqueous environment (E el 78 ) were used to calculate the solvation energies of the structures as the difference between those in water and those in the gas phase.The overall ∆G 78 of the reactions were finally determined by summing up the Gibbs energy in the gas phase with the Gibbs energies of solvation of the products, and subtracting the corresponding ∆G 78 of the reactants.This is expressed by the equation Note that a positive ∆G 78 value indicates a thermodynamically improbable reaction, while a negative one suggests that the encapsulation process happens spontaneously under the reaction conditions.As the conducted study aims at providing reliable trends concerning the factors of high importance that govern the envisioned host-guest recognition, the most significant conclusions should be based not so much on the sole numbers but more on the change/difference between the Gibbs energies when the conditions differ (volume of the cucurbituril cavity, nature of the substituents, pH and dielectric constant of the medium, presence of metal cations, and solvation of the host).The molecular graphics images were created by applying the PyMOL molecular graphics system [70].

Conclusions
The present calculations shed light on the major factors controlling the encapsulation of styryl dyes by cucurbituril hosts: the smaller cavitand readily binds the modeled guest

Figure 1 .
Figure 1.Schematic presentation of a ternary complex between DNA, a small heterocyclic ligand, and a CB[n].

Figure 1 .
Figure 1.Schematic presentation of a ternary complex between DNA, a small heterocyclic ligand, and a CB[n].

Molecules 2023 , 15 Figure 1 .
Figure 1.Schematic presentation of a ternary complex between DNA, a small heterocyclic ligand, and a CB[n].

Figure 5 .
Figure 5. Optimized structures in the gas phase at the M062X/6-31G(d,p) level of theory of the CB[7]@dye Ⴈ+ (first column) and CB[7]@dye9 Ⴈ2+ (second column) complexes, along with the corresponding ∆G ε values in kcal mol −1 for their formation.The results are obtained by modeling either an "empty" host (A) or a cucurbituril with high-energy water molecules (B) as an initial structure.The upper index indicates a reaction in the gas phase (ε = 1) and in a water environment (ε = 78) yielded at the M062X/6-31+G(d,p)//M062X/6-31G(d,p) level.

Figure 5 .
Figure 5. Optimized structures in the gas phase at the M062X/6-31G(d,p) level of theory of the CB[7]@dye ^+ (first column) and CB[7]@dye9 ^2+ (second column) complexes, along with the corresponding ∆G ε values in kcal mol −1 for their formation.The results are obtained by modeling either an "empty" host (A) or a cucurbituril with high-energy water molecules (B) as an initial structure.The upper index indicates a reaction in the gas phase (ε = 1) and in a water environment (ε = 78) yielded at the M062X/6-31+G(d,p)//M062X/6-31G(d,p) level.

Table 1 .
Structures of the dyes under study according to the type of R 1 -/R 2 -/R 3 -substituents.