Source: https://pubs.rsc.org/en/content/articlehtml/2019/cp/c8cp07705c
Timestamp: 2019-04-18 19:08:20+00:00

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Supramolecular cavities can be found in clathrates and self-assembling capsules. In these computational experiments, we studied the effect of folding planar hydrogen-bonded supramolecules of melamine (M) and cyanuric acid (CA) into stable cage-like quartets. Based on dispersion-corrected density functional theory calculations at the ωB97XD/6-311++G(d,p) level, we show the flexibility of M and CA molecules to form free confined spaces. Our bonding analysis indicates that only CA can form a cage, which is more stable than its planar systems. We then studied the capacity of the complexes to host ionic and neutral monoatomic species like Na+, Cl− and Ar. The encapsulation energies range from −2 to −65 kcal mol−1. A detailed energy decomposition analysis (EDA) supports the fact that the triazine ring of CA is superior to the M one for capturing chloride ions. In addition, the EDA and the topology of the electron density, by means of the Atoms in Molecules (AIM) theory and electrostatic potential maps, reveal the nature of the host–guest interactions in the confined space. The CA cluster appears to be the best multimolecular inclusion compound because it can host the three species and keep its cage structure, and therefore it could also act as a dual receptor of the ionic pair Na+Cl−. We think these findings could inspire the design of new heteromolecular inclusion compounds based on triazines and hydrogen bonds.
Extramolecular, exomolecular, or multimolecular inclusion compounds are special cases within host–guest chemistry, in which more than one molecule creates the cavity for the guest complexation.1 In this context, non-covalent interactions play a fundamental role. Firstly, they are responsible for keeping the cavity, and second, they hold the guest inside it. These systems have prompted a great volume of research2,3 due to their promising applications; for instance, sequestration of small molecules, gases and ionic species.
While metal–organic cages are widely known2 and have found many applications,10–12 hydrogen-bonded capsules are still in the early stages of research. Rebek and coworkers have obtained perhaps the most prominent multimolecular host–guest complex: the tennis ball.13,14 Among others, they have created several self-assembling capsules, with the ability of capturing small molecules like methane,15 and even dimers.16,17 Atwood18,19 and Whitesides20 have also mastered the supramolecular forces to create hydrogen-bonded capsules with enclosed spaces. In this context, triazine rings, like melamine (M) and cyanuric acid (CA), have been shown to be suitable building blocks for creating supramolecular boxes in solution.21 In the solid state, for instance, Mascal et al.22 have obtained a cylindrophane based on two-faced CA rings that effectively captures fluoride ions, while Frontera et al.23 have crystalized complexes of CA molecules, which were previously covalently modified, with chloride ions.
Chemical species have shown different properties when they are confined. For instance, in catalysis27 and hydrogen-bonded systems.28,29 Therefore, in this work, we investigate the impact of folding planar supramolecules of M and CA into cage-shaped complexes. We focus on the stability of hydrogen bonds and the free confined spaces they hold. We then analyze the capacity of the triazine rings and the chemical spaces to capture monoatomic species like Na+, Cl− and Ar. Finally, through our computational experiments, we demonstrate herein that CA is a more robust building block for fabricating supramolecular inclusion compounds.
All computations were performed with dispersion corrected density functional theory (DFT-D) implemented in the Gaussian 03 package,30 by using the ωB97XD hybrid functional from Head Gordon et al.31 with the 6-311++G(d,p) basis set. This method has been proved to show a great performance in similar systems.32–34 The minimum energy nature of the optimized structures was verified using the vibrational frequency analysis.
The bonding energy ΔEbond (eqn (1)) values were obtained at the same level of theory using the approach of Fonseca Guerra et al.,35 calculated as the sum of the interaction energy of the complex ΔEint and the deformation energy ΔEdef.
In this equation, the interaction energy ΔEint is the difference between the energy of the complex and the sum of energies of the monomers with the structures that form in the complex. The deformation energy ΔEdef is the energy needed to deform the structure of monomers from their isolated state to that one they acquire in the complex. The ΔEint of the inclusion compounds was further decomposed into encapsulation energy ΔEenc and hydrogen bonding energy ΔEHB according to eqn (2)–(4).
The non-covalent interactions were analyzed within the framework of the atoms in molecules theory.9 Total electron densities were calculated at the same level of theory. The local properties at the bond critical points were computed using the AIMALL37 and Multiwfn38 programs. Molecular electrostatic potential surfaces were generated by mapping the electrostatic potential V(r) on the electronic density surfaces. We considered an isosurface of ρ(r) = 0.001 a.u., which was suggested by Bader et al.39 and represents the effective molecular volume.
where the term ΔEele describes the classical electrostatic interaction (Coulomb) of the occupied orbitals of one monomer with those of another monomer; ΔEex–rep is the attractive exchange component resulting from the Pauli exclusion principle and the interelectronic repulsion; ΔEpol accounts for polarization and charge transfer components; and ΔEdisp corresponds to the dispersion term.
All images were created with CYLview,42 VMD43 and AIMAll37 software.
We started from the planar complexes. Then, the cage-like clusters were built by folding the planar ones in order to form cyclic quartets, and keeping the original hydrogen bonds (H-bonds). The structures of the systems are shown in Fig. 1, and the corresponding energies are displayed in Table 1. All the cages assume a C2 symmetry. When folding the planar systems into cyclic quartets, two extra H-bonds are formed (or three in the case of M2CA2). Therefore, one may expect a stronger bonding energy in the latter. However, there is an energy penalty related to the acceptor directionality of the H-bond.44 Although the differences in interaction energies are around 5 kcal mol−1, ΔEbond values show there is no extra stabilization. The only exception is the second cage of CA (CA4-2), which is 4.8 kcal mol−1 more stable than its planar counterpart. The formation of the cages also requires a deformation energy, which is almost zero for CA4-2 and relatively high for M4 and M2CA2.
Fig. 1 Optimized geometries at the ωB97XD/6-311++G(d,p) level of theory. Black arrows indicate the folding of the planar systems.
Finally, the Gibbs free energies of bonding show that the planar systems are by far the most stable ones. In the case of CA4-2, the planar and cage systems differ by just 0.8 kcal mol−1. Since this energy difference is very small, we can anticipate that the system will need the help of the guest to favor this cage-like cluster. In the next sections, we will show that the ΔGbond for CA4-2 is notably enhanced due to the presence of ions.
All the cage-shaped quartets form regular cavities with a cup-like shape akin to that of calixarenes. From their molecular electrostatic potential maps shown in Fig. 2(a and b), it can be seen that the inside is more positive than the outside surface. The CA4-1 cage creates the most positive cavity, followed by CA4-2, the mix complex of M2CA2 and M4. In order to gain more information on the cavities, we then obtained sections of the electron density ρ(r), which is also plotted in Fig. 2(c). As shown in Fig. 2, M4, CA4-2 and M2CA2 display a cup-like shape, which is quite similar to some calixarenes.45,46 Furthermore, the CA4-1 complex shows a cage-like cluster with a tubular cavity, alike that observed in the pillarpyridinium molecular box.24 This structure suggests that linear molecules like H2 could fit inside the cavity.
Fig. 2 (a) Side views of molecular electrostatic potential (MEP) maps on the 0.001 a.u. electron density isosurfaces. (b) Top views of MEPs. The values of the MEP vary between −31 kcal mol−1 (red) and 56 kcal mol−1 (blue). (c) Contour plots of cage-shaped complexes superimposed onto molecular graphs. The free space is colored in light blue.
Table 2 reports some meaningful topological parameters of H-Bonds. That is, the electron density ρ at the BCPs, which reflects the strength of a bond. The total energy density H = G + V, where G and V are the kinetic and potential energy densities, respectively. Negative values of H are usually associated with a covalent character. Nevertheless, when H is negative, the hydrogen bonds are stronger than those with positive values.34,47,48 The ellipticity ε measures the extent of the electron density within a plane containing the line path. In addition, it is a direct measure of the stability of a given bond, because it takes infinite large values preceding the coalescence of a ring critical point and a BCP.49 The delocalization [δ(A,B)] index is a measure of the number of electrons that are shared or exchanged between A and B. Finally, the repulsive part of the local potential energy density Vrep accounts for electron–electron and nuclear–nuclear repulsion.
a Due to symmetry reasons, average values are shown. b The sub index up corresponds to the average values of the largest opening. c The sub index down corresponds to the average values of the smallest opening. d Middle corresponds to hydrogen bonds positioned at the middle of the cup-like structure.
When going from the planar systems to the cage-like structures, H-bonds undergo an important bending. This deformation has an impact on the acceptor directionality,50 and it is clearly reflected in their topological values (see Table 2). According to ρ, the strength of the bond decreases with the bending along with a decrease in δ(H,N/O). The ellipticity also increases, except in CA4-1. The fact that the cup-like structure of CA4-2 is more stable than the planar form can be undoubtedly understood by looking at the topological parameters. The CA4-2 cup-shaped complex forms 8 H-bonds, four within the largest opening (H⋯Oup) and four below it (H⋯Odown), having different topological properties. As can be seen from Table 2, the bending does not significantly affect the H-bond properties of the smallest opening, if we compare them with the planar system. Therefore, the two extra H-bonds that are formed in the cage complex are enough to compensate the decrease in interaction energy due to the directionality.
As was shown in the previous section, all the cage-shaped complexes form regular cavities that could host atomic species, or even linear molecules. Therefore, we put them to test with ionic and neutral species like sodium, chloride and argon. All the systems were fully optimized, and those who kept their original shapes are reported. Table 3 shows the bonding analysis of the multimolecular inclusion complexes. Gibbs free energies and bonding energies are more stabilized in the presence of the hosts, except for M4@Ar and CA4-1@Ar. Among all the complexes, just CA4-2 can host a sodium cation and keep its original shape, having the greatest encapsulation energy. The other cages (M4, CA4-1 and M2CA2) are fully deformed in the presence of Na+. This is because the coordinating groups of CA4-2 (C O groups) converge to the metal in the complex, similar to guanine quartets.51 Whilst in the other cases, both endocyclic nitrogens and carbonyl groups are not adequately orientated to coordinate the metal. One should also take into account that the triazine rings cannot interact with metals via the π cloud.
Concerning chloride, the greatest ΔEenc is shown for CA4-1, followed by CA4-2, M2CA2 and M4. This trend suggests that the triazine skeleton of CA is better than the melamine one to capture anions, which could be used for synthesizing new heterocalixarenes. In this context, Frontera et al. have already shown experimental evidence of chloride–π interactions in CA crystals.23 The deformation energies are also more favorable for CA complexes. For the sake of comparison, we computed the corrected interaction energy (ωB97XD/6-311++G(d,p)//BP86/TZ2P) for a heterocalixarene–chloride complex recently reported by Caramori et al.52 (see compound 1·Cl−). The complex has an encapsulation energy of −31.8 kcal mol−1 (BP86/TZ2P energy52 is −37.6 kcal mol−1), which is very close to those in Table 3, and even smaller. Finally, since the second cage of CA can host both Na+ and Cl−, one may think that this system could host both ions at the same time. Indeed, we optimized the CA4-2 system with the NaCl ionic pair and the complex keeps its original shape (see Fig. S1, ESI†). ΔEenc is −55.7 kcal mol−1 (value not included in Table 3), and ΔEdef is even lower than for the isolated ions (1.6 kcal mol−1).
When an argon atom is placed within the cavity, the most favorable values are, again, those for CA complexes, as shown in Table 3. That is, high encapsulation energies and low deformation energies.
Before evaluating the forces that take part in the encapsulation, we must know the nature of the interactions between the atomic species and the isolated triazines. Therefore, we computed a potential energy scan by varying the distance (r) between Cl−/Ar and the triazine ring center. The systems were optimized with C3 symmetry, and the r distance was varied from 2.7 Å to 3.4 Å with a 0.05 Å step (15 optimizations). We then decomposed the interaction energy at every step and the profile for chloride is plotted in Fig. 3 (see energy profile for argon in Fig. S2, ESI†).
Fig. 3 Variation of LMOEDA energy components as a function of r. Chemical structures of the scanned systems are shown, where r is the scanned distance.
At first glance, chloride interacts more strongly with CA than M along the whole scanned distance. At the equilibrium geometry, the interaction energy is −8.7 kcal mol−1 with M and −19.7 kcal mol−1 with CA. Both values are in very good accordance with previous MP2 computations for the same/similar systems. While Berryman et al.53 found a ΔEbond = −8.33 kcal mol−1 for a triazine ring (without –NH2 groups) at the MP2/aug-cc-pVDZ level of theory, Frontera et al.23 obtained a ΔEbond of −22.81 kcal mol−1 (ΔEbond = −16.45 kcal mol−1 with BSSE) for the CA@Cl− complex at the MP2(full)/6–31++G** level of theory. The profile of the energy components indicates that the electrostatic part is the dominant factor of the interaction energy. In addition, the interaction between Cl− and CA has larger charge transfer and dispersion components. These results are in agreement with the trends of encapsulation energies, reaffirming, therefore, the fact that the CA skeleton is a better candidate for synthesizing molecular hosts based on triazines.
Concerning the interactions with argon, the differences in interaction energies are negligible (the energy profiles are shown in the ESI†).
When M⋯Cl−/Ar and CA⋯Cl−/Ar interactions are confined in the cavity, their nature changes drastically. Table 4 collects the LMOEDA analysis of all complexes. In general, the attractive nature of the encapsulation is mostly explained by the charge transfer component. For instance, the interaction of chloride with CA goes from 46% electrostatic in the non-confined state to 5.6% in the CA4-1 complex. The other complexes show repulsive electrostatic interactions, and the trend is shown in Fig. 2 (CA4-2 < M4 < M2CA2). The fact that the M4@Cl− cage shows a larger charge transfer contribution is due to the presence of N-H⋯Cl− H-bonds that hold the anion. Moreover, the Pauli repulsion is again larger for the systems with M, and the dispersion component is almost the same for all the systems.
When either chloride or argon approaches the triazine ring, interactions with the π system are expected.52,56 In the framework of QTAIM, a bond path is a line of maximum electron density that links a pair of nuclei57,58 at the equilibrium geometry. When looking at the L(r) function (−∇2ρ) of M and CA (Fig. 4), a nonbonding charge concentration (NCC) over N atoms and a hole over C can be observed. Note that the NCCs correspond to the Lewis model of lone pairs. In the triazine ring of CA, the lone pairs of N appear delocalized. Therefore, BCPs between either Cl− or Ar and N atoms would likely be present. Fig. 5 shows the molecular graphs of the complexes M⋯Cl−/Ar and CA⋯Cl−/Ar, in which BCPs between Cl−/Ar and N atoms are observed, and Table 5 reports the average properties of those BCPs. The reported values are characteristic of weak closed-shell interactions: low values of ρ, positive laplacian ∇2ρ and H ≈ 0. Since ρ and δ(A,B) are good indicators of the bond strength, their values are in line with the interaction energies. In addition, Vrep is more repulsive for CA⋯Cl−, as was shown in the previous section. Observations regarding Argon indicate that there are no significant differences between M and CA.
Fig. 4 Three-dimensional isosurfaces of L(r) = 1.5 a.u. for (a) melamine and (b) cyanuric acid. Circles A and B correspond to L(r) = 1.03 and 3.0, respectively. Bonding (BCC) and nonbonding charge concentrations (NCC) are indicated with arrows.
Fig. 5 Molecular graphs of M⋯Cl−/Ar and CA⋯Cl−/Ar complexes. Small red dots are BCP, yellow dots are ring critical points and green dots are cage critical points.
a Average values of bond critical points.
It is worth noting that some meaningful QTAIM parameters (ρ, ESP, Vrep and charge transfer) are directly related to LMOEDA terms (ΔEint, ΔEele, ΔEex–rep, ΔEpol and ΔEdisp), as shown in Fig. S3–S6 in the ESI.† These relationships were obtained by computing the local topological properties over the scanned systems, which were discussed above. For instance, among other relationships between EDA components and AIM parameters,59,60 it has been shown that there is a linear relationship between ρ and the interaction energy.48,61 However, we found herein a quadratic relationship between these two parameters. In addition, the sum of the ESPs at the BCPs vs. ΔEele and the charge transfer obtained by QTAIM vs. ΔEpol were found to linearly correlate with both CA⋯Cl− and M⋯Cl− systems. In the case of Argon, the charge transfer values obtained with QTAIM fail to describe its behavior. Previous studies on Voronoi Deformation Densities have shown that Bader's charges fail to describe some systems.62 Nevertheless, according to these relationships, the topological properties can be used to monitor either the strength, electrostatic or repulsive features of the interactions.
Now that we have identified the nature of the interactions between the atomic species and M and CA isolated rings, we analyze the situations within the cavities. Fig. 6 shows the molecular graphs of the multimolecular inclusion compounds, and the topological properties of the inclusion interactions are reported in Table S1 (ESI†). The presence of BCPs between the multimolecular hosts and the guests clearly show the encapsulation effect. They show typical values of weak closed-shell interactions. The values of ρ (BCP) are within the range of 0.004–0.023 a.u. for the systems with chloride and 0.003–0.004 a.u. for the systems with argon. The H-bonds that keep the cavity are also intact, and their topological properties do not change significantly (see Table S2, ESI†). When the M⋯Cl−/Ar and CA⋯Cl−/Ar interactions are confined, their topological properties display a different behavior. These changes are consistent with those observed in the LMOEDA analysis. For example, the interactions with chloride are weaker than those of chloride with the isolated rings. Nevertheless, the presence of multiple bond paths increases the interaction energy. Interestingly, in some cases, the BCPs appear between C atoms and the guests, instead of N (e.g., CA4-2). In the case of M4@Cl−, the anion is also held by N–H⋯Cl− H-bonds. It is also interesting to point out that in most of the cases, the host–guest N⋯Cl− interactions show significantly lower values of ellipticity (ε) when they are compared with the non-confined values. This might indicate that the interactions are more stable within the cage. Furthermore, when comparing CA4-1@Cl− and CA4-2@Cl−, the sum of ρ and δ(A,B) are in line with the encapsulation energy ΔEenc. The repulsion (∑Vrep) is also greater for the CA4-1@Cl− complex, also in agreement with values in Table 4. Even though we cannot form a strong conclusion regarding the character of the interactions, what is evident herein are the differences between the confined and non-confined states. The multimolecular hosts produce a chemical space with an environment that is totally different from the separate triazine rings.
Fig. 6 Molecular graphs of multimolecular inclusion compounds.
On the other hand, the CA4-2 cage is the only system that can capture Na+ without losing the original cup structure. The cation is tetracoordinated, and the BCPs show values that are characteristic of closed-shell interactions as well: low values of ρ, and positive values of ∇2ρ and H. According to Bader, this type of interaction cannot be classified as a metal coordination (relatively low values of ρ, small negative values for H with G/ρ ≅ 1 and small positive values for values ∇2ρ).63 It should also be mentioned that barbituric acid and its derivatives have already been used to coordinate metals and cations in supramolecular compounds.64 In some crystals of barbituric acid65 and 5,5-diethylbarbiturato,66 for example, Na+ and K+ ions have been observed to be hexa-(NaO6) and tetra-coordinated (O2–K–O2–K–O2) by the C O groups. Furthermore, the same system (CA4-2@Na+) can simultaneously hold chloride, that is, CA4-2@NaCl. Its molecular graph (Fig. 7) shows a different topology for chloride. In this complex, the anion is pushed down the cavity because of the presence of the cation. Consequently, the anion interacts less with the π cloud of CA. Note that the encapsulation energies for the separate ions Na+ and Cl− are −64.3 and −46.2 kcal mol−1, respectively (Table 3). However, the encapsulation energy of the ionic pair is −55.7 kcal mol−1. This suggests that the whole encapsulation energy of NaCl might just come from the coordination of the Na+ counter ion.
Fig. 7 Molecular graph of CA cage-shaped cluster acting as a dual receptor of sodium cation and chloride.
In this work, we have conducted a DFT-D analysis over a set of multimolecular inclusion compounds based on M and CA. Our study has shown that these molecules are able to form confined cavities alike calixarenes with the ability to host small atomic species. Whilst the cavity is created by hydrogen bonds, in most of the cases, the guest species are encapsulated due to the interactions with the π systems of melamine and cyanuric acid. Nevertheless, melamine can retain the anion with its amino groups (N–H⋯Cl−), while cyanuric acid can coordinate cations with its keto groups (C O⋯Na+).
Our bonding analysis suggests that the cage-shaped supramolecule of CA is more stable than its open structure by ∼5 kcal mol−1. In the other cases, the extra hydrogen bonds, which are created in the cyclic complexes, are not enough to compensate the weakening of the interactions due to the bending. The triazine skeleton of CA was also shown to be more robust in capturing an ionic guest. In addition, our computations suggest that CA could act as a dual receptor of ionic pairs. Therefore, with proper covalent modifications, CA seems to be the most versatile building block for synthesizing supramolecular inclusion compounds via hydrogen bonds. Nevertheless, the other cage-shaped structures could serve as model sets for constructing new heteromolecular hosts.
The authors gratefully acknowledge the financial support from the Secretaría de Ciencia y Tecnología, Universidad Tecnológica Nacional, Facultad Regional Resistencia. A. N. P. thanks the National Scientific and Technical Research Council (CONICET), Argentina, for a doctoral fellowship. N. M. P. is a CONICET career researcher.
Encyclopedia of Spramolecular Chemistry, ed. J. L. Atwood and J. W. Steed, CRC Press, Boca Raton, 2004, vol. 1 Search PubMed.
M. Yoshizawa, J. K. Klosterman and M. Fujita, Functional molecular flasks: new properties and reactions within discrete, self-assembled hosts, Angew. Chem., Int. Ed., 2009, 48, 3418–3438 CrossRef CAS PubMed.
O. Dumele, N. Trapp and F. Diederich, Halogen Bonding Molecular Capsules, Angew. Chem., Int. Ed., 2015, 54, 12339–12344 CrossRef CAS PubMed.
B. T. Birchall, C. S. Frampton, G. J. Schrobilgen and J. Valsdóttir, b-Hydroquinone Xenon Clathrate, Acta Crystallogr., Sect. C: Cryst. Struct. Commun., 1989, 45, 944–946 CrossRef.
J. C. a. Boeyens and J. a. Pretorius, X-ray and neutron diffraction studies of the hydroquinone clathrate of hydrogen chloride, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem., 1977, 33, 2120–2124 CrossRef.
J.-P. Torré, R. Coupan, M. Chabod, E. Pere, S. Labat, A. Khoukh, R. Brown, J.-M. Sotiropoulos and H. Gornitzka, CO2–Hydroquinone Clathrate: Synthesis, Purification, Characterization and Crystal Structure, Cryst. Growth Des., 2016, 16, 5330–5338 CrossRef.
E. Eikeland, M. K. Thomsen, J. Overgaard, M. A. Spackman and B. B. Iversen, Intermolecular Interaction Energies in Hydroquinone Clathrates at High Pressure, Cryst. Growth Des., 2017, 17, 3834–3846 CrossRef CAS.
M. Ilczyszyn, M. Selent and M. M. Ilczyszyn, Participation of xenon guest in hydrogen bond network of β-hydroquinone crystal, J. Phys. Chem. A, 2012, 116, 3206–3214 CrossRef CAS PubMed.
R. F. W. Bader, Atoms in Molecules. A Quantum Theory, Clarendon, Oxford, UK, 1990 Search PubMed.
P. Mal, B. Breiner, K. Rissanen and J. R. Nitschke, White phosphorus is air-stable within a self-assembled tetrahedral capsule, Science, 2009, 324, 1697–1699 CrossRef CAS PubMed.
S. H. A. M. Leenders, R. Gramage-Doria, B. de Bruin and J. N. H. Reek, Transition metal catalysis in confined spaces, Chem. Soc. Rev., 2015, 44, 433–448 RSC.
N. Ahmad, H. A. Younus, A. H. Chughtai and F. Verpoort, Metal–organic molecular cages: applications of biochemical implications, Chem. Soc. Rev., 2015, 44, 9–25 RSC.
R. Wyler, J. de Mendoza and J. Rebek, A Synthetic Cavity Assembles Through Self-Complementary Hydrogen Bonds, Angew. Chem., Int. Ed. Engl., 1993, 32, 1699–1701 CrossRef.
T. Szabo, G. Hilmersson and J. J. Rebek, Dynamics of Assembly and Guest Exchange in the Tennis Ball, J. Am. Chem. Soc., 1998, 120, 6193–6194 CrossRef CAS.
F. Hof, L. C. Palmer and J. J. Rebek, Synthesis and Self-Assembly of the Tennis Ball and Subsequent Encapsulation of Methane, J. Chem. Educ., 2001, 78, 1519–1521 CrossRef CAS.
D. Tzeli, G. Theodorakopoulos, I. D. Petsalakis, D. Ajami and J. Rebek, Theoretical study of hydrogen bonding in homodimers and heterodimers of amide, boronic acid, and carboxylic acid, free and in encapsulation complexes, J. Am. Chem. Soc., 2011, 133, 16977–16985 CrossRef CAS.
D. Tzeli, I. D. Petsalakis, G. Theodorakopoulos, D. Ajami and J. Rebek, Theoretical study of free and encapsulated carboxylic acid and amide dimers, Int. J. Quantum Chem., 2013, 113, 734–739 CrossRef CAS.
L. R. MacGillivray and J. L. Atwood, Achiralsphericalmolecular assemblyheldtogetherby 60 hydrogenbonds, Nature, 1997, 389, 469–472 CrossRef CAS.
J. L. Atwood, L. J. Barbour and A. Jerga, Organization of the interior of molecular capsules by hydrogen bonding, Proc. Natl. Acad. Sci. U. S. A., 2002, 99, 4837–4841 CrossRef CAS PubMed.
G. M. Whitesides, E. E. Simanek, J. P. Mathias, C. T. Seto, D. N. Chin, M. Mammen and D. M. Gordon, Noncovalent synthesis: using physical-organic chemistry to make aggregates, Acc. Chem. Res., 1995, 28, 37–44 CrossRef CAS.
J. M. C. A. Kerckhoffs, M. G. J. Ten Gate, M. A. Mateos-Timoneda, F. W. B. Van Leeuwen, B. Snellink-Ruël, A. L. Spek, H. Kooijman, M. Crego-Calama and D. N. Reinhoudt, Selective self-organization of guest molecules in self-assembled molecular boxes, J. Am. Chem. Soc., 2005, 127, 12697–12708 CrossRef CAS.
M. Mascal, I. Yakovlev, E. B. Nikitin and J. C. Fettinger, Fluoride-selective host based on anion–π interactions, ion pairing, and hydrogen bonding: synthesis and fluoride-ion sandwich complex, Angew. Chem., Int. Ed., 2007, 46, 8782–8784 CrossRef CAS.
A. Frontera, F. Saczewski, M. Gdaniec, E. Dziemidowicz-Borys, A. Kurland, P. M. Deyà, D. Quiñonero and C. Garau, Anion–π interactions in cyanuric acids: A combined crystallographic and computational study, Chem. – Eur. J., 2005, 11, 6560–6567 CrossRef CAS.
S. Kosiorek, B. Rosa, T. Boinski, H. Butkiewicz, M. P. Szymański, O. Danylyuk, A. Szumna and V. Sashuk, Pillarpyridinium: A square-shaped molecular box, Chem. Commun., 2017, 53, 13320–13323 RSC.
T. D. Della and C. H. Suresh, Anion Encapsulated Fullerenes Behave as Large Anions: A DFT Study, Phys. Chem. Chem. Phys., 2018, 20, 24885–24893 RSC.
M. B. Hillyer, H. Gan and B. C. Gibb, Precision Switching in a Discrete Supramolecular Assembly: Alkali Metal Ion-Carboxylate Selectivities and the Cationic Hofmeister Effect, ChemPhysChem, 2018, 19, 2285–2289 CrossRef CAS.
M. F. Zalazar, E. N. Paredes, G. D. Romero Ojeda, N. D. Cabral and N. M. Peruchena, Study of Confinement and Catalysis Effects of the Reaction of Methylation of Benzene by Methanol in H-Beta and H-ZSM-5 Zeolites by Topological Analysis of Electron Density, J. Phys. Chem. C, 2018, 122, 3350–3362 CrossRef CAS.
O. Shameema, C. N. Ramachandran and N. Sathyamurthy, Blue shift in X–H stretching frequency of molecules due to confinement, J. Phys. Chem. A, 2006, 110, 2–4 CrossRef CAS.
R. Musat, J. P. Renault, M. Candelaresi, D. J. Palmer, S. Le Caër, R. Righini and S. Pommeret, Finite size effects on hydrogen bonds in confined water, Angew. Chem., Int. Ed., 2008, 47, 8033–8035 CrossRef CAS.
M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, A. Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez and J. A. Pople, Gaussian 03, Revision C.02, Gaussian, Inc., Wallingford CT, 2004 Search PubMed.
J.-D. Chai and M. Head-Gordon, Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections, Phys. Chem. Chem. Phys., 2008, 10, 6615–6620 RSC.
Z. Li, G. Chen, Y. Xu, X. Wang and Z. Wang, Study of the Structural and the Spectral Characteristics of [C3N3(NH2)3]n (n = 1–4) Clusters, J. Phys. Chem. A, 2013, 117, 12511–12518 CrossRef CAS.
A. N. Petelski, D. J. R. Duarte, S. C. Pamies, N. M. Peruchena and G. L. Sosa, Intermolecular perturbation in the self-assembly of melamine, Theor. Chem. Acc., 2016, 135, 65 Search PubMed.
A. N. Petelski, N. M. Peruchena, S. C. Pamies and G. L. Sosa, Insights into the self-assembly steps of cyanuric acid toward rosette motifs: a DFT study, J. Mol. Model., 2017, 23, 263 CrossRef.
C. Fonseca Guerra, H. Zijlstra, G. Paragi and F. M. Bickelhaupt, Telomere Structure and Stability: Covalency in Hydrogen Bonds, Not Resonance Assistance, Causes Cooperativity in Guanine Quartets, Chem. – Eur. J., 2011, 17, 12612–12622 CrossRef CAS.
S. F. Boys and F. Bernardi, The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors, Mol. Phys., 1970, 19, 553–559 CrossRef CAS.
T. A. Keith, AIMAll (Version 11.12.19), TK Gristmill Software, Overland Park KS, USA, 2011, http://aim.tkgristmill.com Search PubMed.
T. Lu and F. Chen, Multiwfn: A multifunctional wavefunction analyzer, J. Comput. Chem., 2012, 33, 580–592 CrossRef CAS.
R. F. W. Bader, M. T. Caroll, J. R. Cheeseman and C. Chang, Properties of atoms in molecules: atomic volumes, J. Am. Chem. Soc., 1987, 109, 7968–7979 CrossRef CAS.
P. Su and H. Li, Energy decomposition analysis of covalent bonds and intermolecular interactions, J. Chem. Phys., 2009, 131, 014102 CrossRef.
M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis and J. A. Montgomery, General Atomic and Molecular Electronic Structure System, J. Comput. Chem., 1993, 14, 1347–1363 CrossRef CAS.
C. Y. Legault, CYLview, 1.0b, Université de Sherbrooke, 2009, http://www.cylview.org Search PubMed.
W. Humphrey, A. Dalke and K. Schulten, VMD - Visual Molecular Dynamics, J. Mol. Graphics, 1996, 14, 33–38 CrossRef CAS.
T. Steiner, The Hydrogen Bond in the Solid State, Angew. Chem., Int. Ed., 2002, 41, 48–76 CrossRef CAS.
D. N. Lande and S. P. Gejji, Exploring Chimeric Calixtetrolarene Molecular Scaffolds: Theoretical Investigations, J. Phys. Chem. A, 2018, 122, 4189–4197 CrossRef CAS.
P. Murphy, S. J. Dalgarno and M. J. Paterson, Transition Metal Complexes of Calixarene: Theoretical Investigations into Small Guest Binding within the Host Cavity, J. Phys. Chem. A, 2016, 120, 824–839 CrossRef CAS.
A. N. Petelski, N. M. Peruchena and G. L. Sosa, Evolution of the hydrogen-bonding motif in the melamine–cyanuric acid co-crystal: a topological study, J. Mol. Model., 2016, 22, 202 CrossRef PubMed.
N. J. M. Amezaga, S. C. Pamies, N. M. Peruchena and G. L. Sosa, Halogen bonding: a study based on the electronic charge density, J. Phys. Chem. A, 2010, 114, 552–562 CrossRef.
C. F. Matta, J. Hernández-Trujillo, T. H. Tang and R. F. W. Bader, Hydrogen–Hydrogen bonding: A stabilizing interaction in molecules and crystals, Chem. – Eur. J., 2003, 9, 1940–1951 CrossRef CAS.
F. H. Allen, C. M. Bird, R. S. Rowland and P. R. Raithby, Resonance-Induced Hydrogen Bonding at Sulfur Aeceptors in R1R2C = S and R1CS2 Systems, Acta Crystallogr., Sect. B: Struct. Sci., 1997, 53, 680–695 CrossRef.
F. Zaccaria, G. Paragi and C. Fonseca Guerra, The Role of Alkali Metal Cations in the Stabilization of Guanine Quadruplexes: Why K+ is the best, Phys. Chem. Chem. Phys., 2016, 18, 20895–20904 RSC.
A. O. Ortolan, I. Østrøm, G. F. Caramori, R. L. T. Parreira, E. H. Da Silva and F. M. Bickelhaupt, Tuning Heterocalixarenes to Improve Their Anion Recognition: A Computational Approach, J. Phys. Chem. A, 2018, 122, 3328–3336 CrossRef CAS.
O. B. Berryman, V. S. Bryantsev, D. P. Stay, D. W. Johnson and B. P. Hay, Structural criteria for the design of anion receptors: The interaction of halides with electron-deficient arenes, J. Am. Chem. Soc., 2007, 129, 48–58 CrossRef CAS.
F. Hettche, P. Reiβ and R. W. Hoffmann, Effect of conformational preorganization of a three-armed host on anion binding and selectivity, Chem. – Eur. J., 2002, 8, 4946–4956 CrossRef CAS.
C. T. Seto and G. M. Whitesides, Molecular self-assembly through hydrogen bonding: supramolecular aggregates based on the cyanuric acid-melamine lattice, J. Am. Chem. Soc., 1993, 115, 905–916 CrossRef CAS.
A. O. Ortolan, G. F. Caramori, F. Matthias Bickelhaupt, R. L. T. Parreira, A. Muñoz-Castro and T. Kar, How the electron-deficient cavity of heterocalixarenes recognizes anions: Insights from computation, Phys. Chem. Chem. Phys., 2017, 19, 24696–24705 RSC.
R. F. W. Bader, A Bond Path: A Universal Indicator of Bonded Interactions, J. Phys. Chem. A, 1998, 102, 7314–7323 CrossRef CAS.
F. Guo, E. Y. Cheung, K. D. M. Harris and V. R. Pedireddi, Contrasting Solid-State Structures of Trithiocyanuric Acid and Cyanuric Acid, Cryst. Growth Des., 2006, 6, 846–848 CrossRef CAS.
E. L. Angelina, D. J. R. Duarte and N. M. Peruchena, Is the decrease of the total electron energy density a covalence indicator in hydrogen and halogen bonds?, J. Mol. Model., 2013, 19, 2097–2106 CrossRef CAS PubMed.
D. J. R. Duarte, G. L. Sosa and N. M. Peruchena, Nature of halogen bonding. A study based on the topological analysis of the Laplacian of the electron charge density and an energy decomposition analysis, J. Mol. Model., 2013, 19, 2035–2041 CrossRef CAS PubMed.
J.-W. Zou, M. Huang, G.-X. Hu and Y.-J. Jiang, Toward a uniform description of hydrogen bonds and halogen bonds: correlations of interaction energies with various geometric, electronic and topological parameters, RSC Adv., 2017, 7, 10295–10305 RSC.
C. F. Guerra, J. Handgraaf, E. J. Baerends and F. M. Bickelhaupt, Voronoi Deformation Density (VDD) Charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD, J. Comput. Chem., 2003, 25, 189–210 CrossRef PubMed.
F. Cortés-Guzmán and R. F. W. Bader, Complementarity of QTAIM and MO theory in the study of bonding in donor – acceptor complexes, Coord. Chem. Rev., 2005, 249, 633–662 CrossRef.
K. T. Mahmudov, M. N. Kopylovich, A. M. Maharramov, M. M. Kurbanova, A. V. Gurbanov and A. J. L. Pombeiro, Barbituric acids as a useful tool for the construction of coordination and supramolecular compounds, Coord. Chem. Rev., 2014, 265, 1–37 CrossRef CAS.
J. Martin-Gil, F. J. Martin-Gil, M. Perez-Mendez and J. Fayos, Structure of K2(Pt2I6)·2C4H4N2O3, Z. Kristallogr., 1985, 173, 179 CrossRef CAS.
V. T. Yilmaz, F. Yilmaz, H. Karakaya, O. Büyükgüngör and W. T. A. Harrison, Silver(I)-barbital based frameworks: Syntheses, crystal structures, spectroscopic, thermal and antimicrobial activity studies, Polyhedron, 2006, 25, 2829–2840 CrossRef CAS.

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