- Email: [email protected]
On the encapsulation of halide anions by bambus[6]uril
Computational and Theoretical Chemistry 1023 (2013) 5–9
Contents lists available at ScienceDirect
Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
On the encapsulation of halide anions by bambus[6]uril Pablo A. Denis a,⇑, Jorge S. Gancheff b a b
Computational Nanotechnology, DETEMA, Facultad de Química, Universidad de la República, CC 1157, 11800 Montevideo, Uruguay Cátedra de Química Inorgánica, Departamento ‘‘Estrella Campos’’, Universidad de la República, Montevideo, Uruguay
a r t i c l e
i n f o
Article history: Received 6 June 2013 Received in revised form 2 August 2013 Accepted 29 August 2013 Available online 7 September 2013
a b s t r a c t The relative affinity of the recently synthesized receptor bambus[6]uril (BU[6]) towards halides in encapsulation processes was theoretically studied by means of M06-2X and B3LYP calculations. The gas-phase results do not follow the affinity experimentally observed in solution, as the largest encapsulation energy was obtained for fluoride, and the smallest one for iodide. Nevertheless, this finding is in agreement with the gas phase hydrogen bond energies determined for the CH4 X– complexes, X = F–, Cl–, Br–, I–. The structural changes experienced by the receptor when the halide is inside decrease as we move from fluoride to iodide. Thus, the relative affinity is due to a balance between the hydrogen-bond energies between the methine groups inside the cavity and the anions (CH X–) and the deformation of the receptor induced by the anion. When solvents effects are considered, the affinity of BU[6] for halides is in line with experimental evidence. In effect, the difference between the DG298 computed for iodide and bromide is 1 kcal/mol, just 0.5 kcal/mol smaller than the experimental value. The effect of the counter ion was evaluated using Na+, but inclusion of the latter worsens the agreement with experiment. Finally, we discuss methodological problems observed for the BU[6]X– complexes. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Cucurbituril (CB) was synthetized in 1905 [1] but it was until 1981 when its pumpkin structure was reported by Mock et al. [2] Once the large space available inside CB was revealed, its applications as host in supramolecular chemistry started to grow at exponential rate. The properties and applications of the cucurbit[n]uril family have been recently reviewed by Lagona et al. [3]. Some examples of the host–guest inclusion complexes of the CB family include: viologen derivatives [4], CO2, [5] styryl dye, [6] imidazole derivatives, [7] and even small CB molecules [8]. Although the list of guests able to be hosted by the CB family is quite large, the search for new receptors derived from CB is still open. In effect, recent work by Svec et al. [9] reported the synthesis of bambus[6]uril (BU[6]). This macrocyle has six glycouril units connected through methylene bridges and can be viewed as a structure derived from cucurbit[6]uril and hemicucurbit[6]uril. BU[6] binds halides, using its twelve C–H interior units. In this line, 1 H NMR studies indicated that such anions are hosted preferentially in the following order: I–, >Br–, >Cl–> and F– [9,10]. In a second report, it was shown that anion free BU[6] is insoluble in various solvents. However, when tetramethylammonium and a suitable anion are added, BU[6] can be suspended in methanol:chloroform (1:1) [10]. Isothermal tritration calorimetry was
⇑ Corresponding author. E-mail address: [email protected] (P.A. Denis). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.08.023
utilized to quantitatively determine the preference of dodecabenzyl-BU[6] for halides, the observed selectivity being in this case for I–: 4400, 1200 and 12 times over F–, Cl– and Br– [11]. Regarding the gas-phase behavior of BU[6], it was found that the affinity for halide anions follow the same order as in solution, but more than one halide anion interacts with one BU[6] unit [12]. Theoretical calculations can be used to shed light into the interaction of receptors like BU[6] [7–17]. In effect, Dixit et al. [7] employed density functional theory (DFT) to study the interaction of imidazole derivatives with cucurbit[6]uril derivatives. They found that the part of the cucurbituril-based receptor which interacts with the imidazole-containing compound depended on the functional groups attached to the imidazole fragment. Toman et al. [13] employed the B3LYP/LANL2DZ method to show that Cl , Br and I are bound to BU[6] by 12 weak CH X– hydrogen bonds with the methine hydrogen atoms located on the interior of BU[6]. However, in a second work [14] they showed that fluoride forms a complex having C3 symmetry and is bound by 6 weak CH X– hydrogen bonds. In contrast with this result, Gobre et al. [15] reported that F interacts with BU[6] via 8 weak CH X– hydrogen bonds. In addition to this, in this landmark investigation they reported the electronic structure, vibrational spectra and 1H NMR of BU[6]X– and X = fluoride, chloride and iodide. They also reported the encapsulation energies at the B3LYP/6-31G(d,p) and B3LYP/6-31+G(d,p) levels of theory. At the latter level of theory, the interaction energies (kcal/mol) followed the order: Br (78.6) > F (71.3) > Cl (59.0). Finally their analysis of the 1H NMR spectra was in good agreement with experiment.
6
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9
Motivated by the high selectivity of BU[6] towards halide anions we decided to study the process of encapsulation of halides by means of first-principle calculations. Our study is focused on the interaction energies and Gibbs free energy changes in gas phase and in solution. We have found that it is extremely difficult to reproduce the experimental results in the gas and solution phases. The problems faced are discussed in detail. We expect that our results may assist experimentalists in designing receptors to selectively host ionic species. Our intention is to explore the feasibility of high-level DFT methods in studying the interactions BU[6] halide, and in doing so, to develop a reliable theoretical tool for the prediction of the affinity in guest-encapsulation processes. 2. Methods The M06-2X [18] and B3LYP [19,20] functionals as implemented in Gaussian 2009 [21] were employed. Even though the interaction between halides and BU[6] is expected to be dominated by electrostatic interactions, we selected M06-2X because of its well documented performance in the investigation of non-bonded interactions [18,22,23]. The basis sets employed for all atoms were the 6-311G, 6-311+G and 6-311++G⁄⁄ [24]. No ECP was used for iodide and all electrons were considered in the calculations. We have included basis set superposition error (BSSE) as suggested by Boys and Bernardi. Although M06-2X slightly underestimates dispersion interactions we expect a good performance because the binding in BU[6]X– is dominated by electrostatic interactions. Solvent effects were taken into account using the Polarizable Continuum Model (PCM) developed by Tomasi and coworkers [25–30]; the solvents considered were acetonitrile and water. Geometries were optimized when including solvent but vibrational frequencies were calculated only for the gas phase optimized complexes. 3. Results and discussion 3.1. Gas phase results The gas phase structure of BU[6] is presented in Fig. 1. This receptor has D3d symmetry and guests can be hosted in its internal space involving its twelve CH units. These units are divided in two
groups of six and define a circumference with 5.9 Å diameter, at the M06-2X/6-311+G level of theory. The height of the macrocycle is 9.0 Å, as defined by Svec et al. [10]: the distance between the planes that contain the oxygen atoms at the portal. When the halides are inside BU[6], we observed important structural changes. The deformation energies (DE) induced by the encapsulation are presented in Table 1. They show a large variation when different basis sets are employed. However, iodide has the smallest DE, whereas fluoride and chloride display the largest ones. This results means that the macrocyle has an optimal cavity for the encapsulation of iodide in the gas phase. At the M06-2X/6-311G level of theory, we found that the D3d symmetry of BU[6] is maintained only for bromide. When using the M06-2X/6-311+G and M06-2X/6311++G⁄⁄ methodologies the complexes of BU[6] with chloride and iodide have S6 symmetry but that of bromide belongs to the C2h group. Fluoride is the most extreme case for which the symmetry of BU[6] is completely lost for all basis set employed. Our results are in line with those reported by Gobre et al. [15] which suggested the fluoride interacts with 8 H atoms when it is inside BU[6]. The D3d structure is a transition state for BU[6]Cl– and BU[6]F–. The d1 diameter is contracted by 1 Å for the encapsulation of iodide and the d4 diameter is 0.6 Å smaller in order to facilitate with the formation of the weak CH-halide hydrogen bonds. For bromide, d1 contracts by 1.3 Å and d4 is reduced by 0.7 Å. The smaller size of chloride as compared with Br– and I– significantly reduces the size of the receptor. The d1 diameter goes from 10.2 Å for the empty macrocyle to 8.6 Å and d4 is contracted by 1 Å. As it can be seen in Fig. 2, the structure of BU[6]F– is markedly different from that of Cl–, Br– and I–. The strong interactions exerted by F– promote such an important deformation on the macrocyle geometry that we are not in position of talking any more about d1 and d4 as metric variables into account, since the spherical structure at the portals is replaced by an almost rectangular cross-section The interaction energies (IE) are presented in Table 1. At the M06-2X/6-311G level and including BSSE the IE are 85.4, 77.5, 74.6 and 72.0 kcal/mol, for F–, Cl–, Br– and I–, respectively. If free energy corrections are included we obtained the following results for DG298 : 70.9, 64.2, 65.7 and 61.9 kcal/mol, respectively. These values differ from those experimentally obtained in solution [9–11] and in the gas phase [12], which point I– to be the preferred guest. The IE computed at the B3LYP/6-311G level of theory are
Fig. 1. Gas phase optimized structure and IR spectrum of bambus[6]uril, at the M06-2X/6-311+G level of theory.
7
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9 Table 1 Gas phase interaction energies, enthalpies and free energies calculated at the B3LYP and M06-2X levels of theory for the complexes BU[6]X–X = F–, Cl–, Br–, I–.
DE
a b
M06-2X
6-311G
M06-2X
6-311+G
M06-2X
6-311++G⁄⁄
B3LYP
6-311G
–
F Cl– Br– I– F– Cl– Br– F– Cl– Br– I– F– Cl– Br– I–
120.4 80.4 80.1 77.4 96.8 85.1 84.0 96.2 82.9 76.2 73.9 107.6 60.4 61.0 53.5
DEzpe
DH298
DG298
118.5 79.0 80.0 77.0 93.2 82.7 82.8
120.0 79.8 80.0 77.8 96.4 84.7 83.6
105.9 66.1 71.2 67.3 82.3 64.4 70.0
87.6 56.8 53.5 48.0
107.3 59.3 59.7 52.9
93.8 49.3 48.9 40.8
DE + BSSE 85.4 77.5 74.6 72.0 93.5 83.2 79.0 93.9 81.1 74.5 72.4 87.6 56.8 53.5 48.0
DG + BSSE 70.9 64.2 65.7 61.9 79.0 62.5 65.0 79.4a 67.1a 65.6a 62.3a 73.8 46.1 42.0 35.3
BSSE
Def.b
35.0 2.9 5.5 5.4 3.3 2.5 5.0 2.3 1.8 1.7 1.5 20.0 3.2 6.9 5.5
17.6 13.6 9.2 6.1 12.8 11.2 8.0 7.0 7.4 6.3 3.1 22.3 11.8 10.1 6.5
Computed using the DE ? DG298 corrections computed at the M06-2X/6-311G level. Deformation energies experienced by the receptor hosting halide ions.
Fig. 2. Gas-phase optimized structure for BU[6]X– (X– = F–, Cl–, Br–, I–) at the M06-2X/6-311+G level of theory (bond distances, d, in Å).
even more deviated from the condensed phase results. Indeed, the IE for I– is 5.5 kcal/mol smaller than the one of bromide and the whole trend along the halide series is in contraposition to the one observed in solution. From a methodological stand-point the lack of diffuse functions is a problem because we are dealing with anions. For this reason, we computed IE using the 6-311+G and 6311++G⁄⁄ basis sets. The IE determined using the latter basis set are 93.9, 81.1, 74.5 and 72.4 kcal/mol for F–, Cl–, Br– and I–, respectively. As we observed for the 6-311G basis set, the M062X/6-311++G⁄⁄ results also differ with experiment. Interestingly, the agreement between M06-2X/6-311G and M06-2X/6-311++G⁄⁄ is improved as we move down in the periodic table. For iodide and bromide the IE computed with the 6-311G basis set are less than 0.5 kcal/mol smaller than those computed with the 6311++G⁄⁄ basis set (both BSSE corrected). However, for fluoride and chloride the deviations are larger because the inclusion of BSSE in the M06-2X/6-311G calculations underestimates IE. Finally, for comparative purposes, we performed M06-2X/aug-cc-pVDZ single point calculations for bromide and iodide. The IE were 77.9 and 73.8 kcal/mol, respectively, both in excellent agreement with the results obtained using the 6-311++G⁄⁄ basis set. This, being said, for all basis sets employed, qualitative agreement with experiment is not reached.
The strong bonding observed for fluoride is not surprising if we consider that this anion has the largest complexation energy with methane. Indeed, at the M06-2X/6-311G+ BSSE level of theory the hydrogen bond energies for CH4::X , X = F–, Cl–, Br–, I–, are 7.7, 2.9, 2.3 and 1.8 kcal/mol, respectively. Although the methine groups are a bit different than methane, a simple electrostatic analysis suggests a similar trend as that observed for methane. We note that for this system BSSE is relevant only for fluorine and also the use of diffuse functions makes a real difference for this atom. As we move down in the periodic table BSSE is reduced. Before analyzing the effect of the solvent it is important to discuss methodological and chemical issues that complicate the study of energetic aspects of the complexes BU[6]X–, namely: (a) symmetry of the complexes, (b) relative affinities. (a) The first problem faced was that the complexes do not have D3h symmetry, which is the expected result. For iodide the D3h and S6 (lower symmetry) structures are local minima but that with lower symmetry is by 0.14 kcal/mol more stable. For chloride, the D3h structure is a first-order transition state which is located 1.6 kcal/mol above the S6 structure. In the case of bromide the symmetry is D3h at the M06-2X/6-311G level of theory, but it is reduced to C2h when the basis set is extended to 6-311+G or 6311++G⁄⁄. The most severe situation is observed for fluoride for
8
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9
which the complex has no symmetry and the D3h structure is rather a fourth order saddle point. Although the energetic differences between the high- and low-symmetry structures are small, they become more important when the thermodynamic corrections are calculated (ZPE, entropy, etc.). These results indeed affect the order of relative affinity of BU[6] hosting halide ions. For example the DE ? DG298 corrections are 14.5, 14.3, 8.9 and 10.1 kcal/mol for F–, Cl–, Br– and I–, respectively, at the M06-2X/6-311G level of theory. These values can be compared with those computed at the M06-2X/6-311+G level of theory, namely, 14.5, 20.7 and 14.0 kcal/mol, for F–, Cl– and Br–, respectively. Thus, important differences emerge for bromide and chloride. The correction determined for Cl using the 6-311+G basis set seems to be too large. For this reason, we evaluated the free energy changes at the M06-2X/6-311++G⁄⁄ level of theory, using the DE ? DG298 corrections computed at the M06-2X/6-311G level. In this way, the free energy changes at the M06-2X/6-311++G⁄ level are 96.8, 75.7 and 70.0 kcal/mol for F , Cl– and Br–, respectively. Thus, at the highest level of theory employed, i.e. M06-2X/6-311++G⁄⁄+BSSE, the strongest interaction is obtained for BU[6]F–. Much work is needed to accurately estimate the DE ? DG298 corrections for this system. (b) Even though the observed relative selectivity of BU[6] towards halide anions seems to be very important, (for I– was 4400, 1200 and 12 times over the ones of F–, Cl– and Br–, respectively [11]) the differences in DG298 are small. In effect, employing the association constants experimentally determined [11] we found that the DG298 corresponding to I– is only 1.51, 2.74 and 13.0 kcal/mol larger than those corresponding to Br–, Cl– and F–, respectively. The differences between the free energy changes for encapsulation I–, Br– and Cl– are within 2.74 kcal/mol. This value is extremely small and thus requires very accurate methodologies in order to deal with such energetic difference by means of first principle calculations. The use of these techniques is prohibitively expensive because the systems contain 139 atoms. Up to know we have compared our gas phase results with those obtained in gas and condensed phase. On the basis of the results presented in the previous paragraph, we concluded that in the gas phase the affinity of BU[6] follows this trend F– > Cl– > Br– > I–, in disagreement with experiment [12], but in agreement with the gas phase hydrogen bond energies determined for the CH4 X- complexes. In the next section we analyze if the inclusion of solvent effects reverses this trend. 3.2. Solvent effects The complexes of BU[6] with halide anions were reoptimized including solvent effects. In Table 2 we list the IE computed in water and acetonitrile. We used these two solvents because a mixture of them was employed in the experiments. At the M06-2X/6311G level the affinity towards all halides except F– follows the same trend as in experiment: I– > Br– > Cl–. However, for F– the IE is still remarkable larger. Although BSSE is expected to be less important in solution, for fluoride it can still be significative. In ef-
Table 2 Interaction energies in solution calculated at the M06-2X and B3LYP levels of theory for the BU[6]X– complexes, X = F–, Cl–, Br–, I–.
F Cl Br I
H2O M06-2X 6-311G
H2O B3LYP 6-311G
CH3CN M06-2X 6-311G
42.4 15.6 19.2 21.4
34.1 1.0 3.0 0.7
17.2 20.6 22.8
H2O M06-2X 6-311+G
CH3CN M06-2X 6-311+G
15.4 18.8 23.2
20.0 25.0
Table 3 Interaction energies in gas phase and solution calculated at the M06-2X level of theory for the Na+BU[6]X– complexes, X = Cl–, Br–, I–.
Cl Br I
Gas M06-2X 6-311G
Gas M06-2X 6-311+G
H2O M06-2X 6-311+G
CH3CN M06-2X 6-311+G
146.4 126.1 101.0
143.7 135.0
138.8 131.7
146.8 134.5
fect, in the previous section we observed that the BSSE for fluoride is larger than for the rest of the halides (recall the agreement observed for Br- and I- when using the 6-311G and 6-311++G⁄⁄ basis sets). By adding a diffuse function we found that the IE of fluoride complex is dramatically decreased. At the M06-2X/6-311+G level of theory the IE are 15.4, 18.8, 23.2 kcal/mol, for F–, Cl–, Br–, respectively. Thus, if the 6-311+G complexation energy is considered for fluoride, and the 6-311G ones are used for the rest, we are able to reproduce the order of affinities observed experimentally, i.e. I– > Br– > Cl– > F–. When acetonitrile is considered as solvent the IE computed for chloride, bromide and iodide also follow the order observed experimentally. The free energy corrections calculated at the M06-2X/6-311G level are: 14.5, 14.3, 8.9 and 10.1 kcal/mol for F–, Cl–, Br– and I–, respectively. We can combine our complexation energies in solution with the free energy corrections determined in the gas phase. If that procedure is employed we obtain that DG298 in solution are: 11.3, 10.3 and 8.5 kcal/mol for and I–, Br–, Cl– respectively. The difference between the DG298 computed in water for iodide and bromide is 1 kcal/mol, only 0.5 kcal/mol lower than the value derived from the association constants reported experimentally. 3.3. Effect of the cation The halide encapsulation by BU[6] experimentally proceeds in the presence of a cation that can be for example: Na+, Cs+ or tetrabutylamonium (TBA+). In the case of Cl– the equilibrium constants for the encapsulation process were similar in the presence of the three cations. For the sake of completeness, we investigated the energetics of this process for all halides with the inclusion of Na+, at the M06-2X/6-311G level of theory. The results are presented in Table 3. In the gas-phase, the interaction energy of the complex NaBU[6]Br is 126.1 kcal/mol, the charges supported by Na and Br being +0.71 and 0.72 (Natural population results). For the analogous of iodide, the interaction energy is 101.1 kcal/mol and the charges of Na and I are 0.72 and 0.72, respectively. Finally, for chloride the complexation energy is 146.4 kcal/mol and the charges of Na and Cl are +0.78 and 0.87 respectively. Therefore, when the cation is included, the relative affinity decreases in the following order for Cl > Br > I . When a diffuse function is included the interaction energies follow the same order as discussed above. These results were not corrected by BSSE because it is expected to be similar for the three halides as was observed in Sections 3.1 and 3.2. Finally, when the latter two complexes are studied in solution, we found that the IE follow the same order as in the gas phase. This result is in disagreement with those obtained by us in solution in absence of sodium and also with experiment. 4. Conclusions M06-2X and B3LYP calculations were employed to study the encapsulation of halides (X–) by the recently synthetized receptor bambus[6]uril. The following are considered to be the most important findings of the work:
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9
(1) The gas phase results do not follow the affinity experimentally observed, as the largest encapsulation energy was obtained for fluoride and the smallest one for iodide. However, this finding is in agreement with the gas phase hydrogen bond energies calculated for the CH4 X complexes. (2) The halide encapsulation energy (relative affinity) is a balance between the CH X– hydrogen bond energies inside the receptor and its deformation. (3) When solvents effects are considered, the selectivity of the receptor is the same as that observed in solution. (4) The effect of the counter ion was evaluated using Na+, but inclusion of the latter worsens the agreement with experiment. (5) Two methodological problems emerged during this study: (a) basis sets must be quite large to obtain meaningful results, (b) the symmetry D3d of the BU[6] is lost upon encapsulation for most of the halides and this alters the evaluation of the thermodynamic properties such as free energy change.
Acknowledgment The authors thank PEDECIBA Quimica for financial support. The authors thank Walter Shands from Intel for his help with Intel Cluster Studio. References [1] R. Behrend, E. Meyer, F. Rusche, J. Liebigs, Condensations producte aus glycoluril und formaldehyd, Ann. Chem. 339 (1905) 1–37. [2] W.A. Freeman, W.L. Mock, N.-Y. Shih, Cucurbituryl, J. Am. Chem. Soc. 103 (1981) 7367–7368. [3] J. Lagona, P. Mukhopadhyay, S. Chakrabarti, L. Isaacs, The cucurbit[n]uril family, Angew. Chem. Int. Ed. 44 (2005) 4844–4870. [4] X. Xiao, Q.H. Hu, Z. Tao, Y.-Q. Zhang, S.-F. Xue, Q.-J. Zhu, G. Wei, Host–guest inclusion complexes of viologen derivative and tetramethyl cucurbit[6]uril with multiple interaction models, Chem. Phys. Lett. 514 (2011) 317. [5] J. Tian, S. Ma, P.K. Thallapally, D. Fowler, B.P. McGraila, J.L. Atwood, Cucurbit[7]uril: an amorphous molecular material for highly selective carbon dioxide uptake, Chem. Commun. 47 (2011) 7626–7628. [6] D.A. Ivanov, N.K. Petrov, E.A. Nikitina, M.V. Basilevsky, A.I. Vedernikov, S.P. Gromov, M.V. Alfimov, The 1:1 hostguest complexation between cucurbit[7]uril and styryl dye, J. Phys. Chem. A 115 (2011) 4505–4510. [7] P.H. Dixit, R.V. Pinjari, S.P. Gejji, Electronic structure and 1H NMR chemical shifts in host-guest complexes of cucurbit[6]uril and sym-tetramethyl cucurbit[6]uril with imidazole derivatives, J. Phys. Chem. A 114 (2010) 10906–10916. [8] A.I. Day, R.J. Blanch, A.P. Arnold, S. Lorenzo, G.R. Lewis, I. Dance, Angew. Chem. Int. Ed. 41 (2002) 275–277. [9] J. Svec, M. Necas, V. Sindelar, Bambus[6]uril, Angew. Chem. Int. Ed. 49 (2010) 2378–2381. [10] J. Svec, M. Dusek, K. Fejfarova, P. Stacko, P. Klan, A.E. Kaifer, W. Li, E. Hudeckova, V. Sindelar, Anion-free bambus[6]uril and Its supramolecular properties, Chem. Eur. J. 17 (2011) 5605–5612. [11] V. Havel, J. Svec, M. Wimmerova, M. Dusek, M. Pojarova, V. Sindelar, Bambus[n]urils: a new family of macrocyclic anion receptors, Org. Lett. 13 (2011) 4000–4003.
9
[12] A. Revesz, D. Schroder, J. Svec, M. Wimmerova, V. Sindelar, Anion binding by bambus[6]uril probed in the gas phase and in solution, J. Phys. Chem. A 115 (2011) 11378–11386. [13] P. Toman, E. Makrlík, P. Vanura, Theoretical study on the complexation of bambus[6]uril with the chloride, bromide, and iodide anions, Monatsh Chem. 142 (2011) 881–884. [14] P. Toman, E. Makrlík, P. Vanura, Theoretical study on the complexation of bambus[6]uril with the fluoride anion, Comput. Theor. Chem. 989 (2012) 97– 99. [15] V.V. Gobre, P.H. Dixit, J.K. Khedkar, S.P. Gejji, Electronic structure, vibrational spectra and 1H NMR of halide ion (F-, Cl- and Br-) encapsulated bambus[6]uril from density functional theory, Comput. Theor. Chem. 976 (2011) 76–82. [16] P. Toman, E. Makrlík, P. Vanura, DFT Study on the complexation of bambus[6]uril with the perchlorate and tetrafluoroborate anions, Acta Chim. Slov. 58 (2011) 846–849. [17] P. Toman, E. Makrlík, P. Vanura, Bambus[6]uril as a novel macrocyclic receptor for the cyanide anion, Chem. Phys. Lett. 547 (2012) 63–65. [18] Y. Zhao, D.G. Truhlar, The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 120 (2008) 215. [19] A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648. [20] C. Lee, L. Yang, R.B. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785. [21] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, 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, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian Inc., Wallingford, CT, 2009. [22] Y. Zhao, N.E. Schultz, D.G. Truhlar, Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions, J. Chem. Theor. Comput. 2 (2006) 364. [23] Y. Zhao, D.G. Truhlar, Size-selective supramolecular chemistry in a hydrocarbon nanoring, J. Am. Chem. Soc. 129 (2007) 8440. [24] R. Ditchfeld, W.J. Hehre, J.A. Pople, Self-consistent molecular-orbital methods. IX. An extended gaussian-type basis for molecular-orbital studies of organic molecules, J. Chem. Phys. 54 (1971) 724. [25] J. Tomasi, B. Mennucci, R. Cammi, Quantum mechanical continuum solvation models, Chem. Rev. 105 (2005) 2999–3094. [26] B. Mennucci, J. Tomasi, Continuum solvation models: a new approach to the problem of solute’s charge distribution and cavity boundaries, J. Chem. Phys. 106 (1997) 5151. [27] B. Mennucci, E. Cances, J. Tomasi, Evaluation of solvent effects in isotropic and anisotropic dielectrics and in ionic solutions with a unified integral equation method: theoretical bases, computational implementation, and numerical applications, J. Phys. Chem. B 101 (1997) 10506–10517. [28] R. Cammi, B. Mennucci, J. Tomasi, Second-order Møller Plesset analytical derivatives for the polarizable continuum model using the relaxed density approach, J. Phys. Chem. A 103 (1999) 9100–9108. [29] R. Cammi, B. Mennucci, J. Tomasi, Fast evaluation of geometries and properties of excited molecules in solution: a Tamm–Dancoff Model with application to 4-dimethylaminobenzonitrile, J. Phys. Chem. A 104 (2000) 5631. [30] M. Cossi, G. Scalmani, N. Rega, V. Barone, New developments in the polarizable continuum model for quantum mechanical and classical calculations on molecules in solution, J. Chem. Phys. 117 (2002) 43.
Contents lists available at ScienceDirect
Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
On the encapsulation of halide anions by bambus[6]uril Pablo A. Denis a,⇑, Jorge S. Gancheff b a b
Computational Nanotechnology, DETEMA, Facultad de Química, Universidad de la República, CC 1157, 11800 Montevideo, Uruguay Cátedra de Química Inorgánica, Departamento ‘‘Estrella Campos’’, Universidad de la República, Montevideo, Uruguay
a r t i c l e
i n f o
Article history: Received 6 June 2013 Received in revised form 2 August 2013 Accepted 29 August 2013 Available online 7 September 2013
a b s t r a c t The relative affinity of the recently synthesized receptor bambus[6]uril (BU[6]) towards halides in encapsulation processes was theoretically studied by means of M06-2X and B3LYP calculations. The gas-phase results do not follow the affinity experimentally observed in solution, as the largest encapsulation energy was obtained for fluoride, and the smallest one for iodide. Nevertheless, this finding is in agreement with the gas phase hydrogen bond energies determined for the CH4 X– complexes, X = F–, Cl–, Br–, I–. The structural changes experienced by the receptor when the halide is inside decrease as we move from fluoride to iodide. Thus, the relative affinity is due to a balance between the hydrogen-bond energies between the methine groups inside the cavity and the anions (CH X–) and the deformation of the receptor induced by the anion. When solvents effects are considered, the affinity of BU[6] for halides is in line with experimental evidence. In effect, the difference between the DG298 computed for iodide and bromide is 1 kcal/mol, just 0.5 kcal/mol smaller than the experimental value. The effect of the counter ion was evaluated using Na+, but inclusion of the latter worsens the agreement with experiment. Finally, we discuss methodological problems observed for the BU[6]X– complexes. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Cucurbituril (CB) was synthetized in 1905 [1] but it was until 1981 when its pumpkin structure was reported by Mock et al. [2] Once the large space available inside CB was revealed, its applications as host in supramolecular chemistry started to grow at exponential rate. The properties and applications of the cucurbit[n]uril family have been recently reviewed by Lagona et al. [3]. Some examples of the host–guest inclusion complexes of the CB family include: viologen derivatives [4], CO2, [5] styryl dye, [6] imidazole derivatives, [7] and even small CB molecules [8]. Although the list of guests able to be hosted by the CB family is quite large, the search for new receptors derived from CB is still open. In effect, recent work by Svec et al. [9] reported the synthesis of bambus[6]uril (BU[6]). This macrocyle has six glycouril units connected through methylene bridges and can be viewed as a structure derived from cucurbit[6]uril and hemicucurbit[6]uril. BU[6] binds halides, using its twelve C–H interior units. In this line, 1 H NMR studies indicated that such anions are hosted preferentially in the following order: I–, >Br–, >Cl–> and F– [9,10]. In a second report, it was shown that anion free BU[6] is insoluble in various solvents. However, when tetramethylammonium and a suitable anion are added, BU[6] can be suspended in methanol:chloroform (1:1) [10]. Isothermal tritration calorimetry was
⇑ Corresponding author. E-mail address: [email protected] (P.A. Denis). 2210-271X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2013.08.023
utilized to quantitatively determine the preference of dodecabenzyl-BU[6] for halides, the observed selectivity being in this case for I–: 4400, 1200 and 12 times over F–, Cl– and Br– [11]. Regarding the gas-phase behavior of BU[6], it was found that the affinity for halide anions follow the same order as in solution, but more than one halide anion interacts with one BU[6] unit [12]. Theoretical calculations can be used to shed light into the interaction of receptors like BU[6] [7–17]. In effect, Dixit et al. [7] employed density functional theory (DFT) to study the interaction of imidazole derivatives with cucurbit[6]uril derivatives. They found that the part of the cucurbituril-based receptor which interacts with the imidazole-containing compound depended on the functional groups attached to the imidazole fragment. Toman et al. [13] employed the B3LYP/LANL2DZ method to show that Cl , Br and I are bound to BU[6] by 12 weak CH X– hydrogen bonds with the methine hydrogen atoms located on the interior of BU[6]. However, in a second work [14] they showed that fluoride forms a complex having C3 symmetry and is bound by 6 weak CH X– hydrogen bonds. In contrast with this result, Gobre et al. [15] reported that F interacts with BU[6] via 8 weak CH X– hydrogen bonds. In addition to this, in this landmark investigation they reported the electronic structure, vibrational spectra and 1H NMR of BU[6]X– and X = fluoride, chloride and iodide. They also reported the encapsulation energies at the B3LYP/6-31G(d,p) and B3LYP/6-31+G(d,p) levels of theory. At the latter level of theory, the interaction energies (kcal/mol) followed the order: Br (78.6) > F (71.3) > Cl (59.0). Finally their analysis of the 1H NMR spectra was in good agreement with experiment.
6
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9
Motivated by the high selectivity of BU[6] towards halide anions we decided to study the process of encapsulation of halides by means of first-principle calculations. Our study is focused on the interaction energies and Gibbs free energy changes in gas phase and in solution. We have found that it is extremely difficult to reproduce the experimental results in the gas and solution phases. The problems faced are discussed in detail. We expect that our results may assist experimentalists in designing receptors to selectively host ionic species. Our intention is to explore the feasibility of high-level DFT methods in studying the interactions BU[6] halide, and in doing so, to develop a reliable theoretical tool for the prediction of the affinity in guest-encapsulation processes. 2. Methods The M06-2X [18] and B3LYP [19,20] functionals as implemented in Gaussian 2009 [21] were employed. Even though the interaction between halides and BU[6] is expected to be dominated by electrostatic interactions, we selected M06-2X because of its well documented performance in the investigation of non-bonded interactions [18,22,23]. The basis sets employed for all atoms were the 6-311G, 6-311+G and 6-311++G⁄⁄ [24]. No ECP was used for iodide and all electrons were considered in the calculations. We have included basis set superposition error (BSSE) as suggested by Boys and Bernardi. Although M06-2X slightly underestimates dispersion interactions we expect a good performance because the binding in BU[6]X– is dominated by electrostatic interactions. Solvent effects were taken into account using the Polarizable Continuum Model (PCM) developed by Tomasi and coworkers [25–30]; the solvents considered were acetonitrile and water. Geometries were optimized when including solvent but vibrational frequencies were calculated only for the gas phase optimized complexes. 3. Results and discussion 3.1. Gas phase results The gas phase structure of BU[6] is presented in Fig. 1. This receptor has D3d symmetry and guests can be hosted in its internal space involving its twelve CH units. These units are divided in two
groups of six and define a circumference with 5.9 Å diameter, at the M06-2X/6-311+G level of theory. The height of the macrocycle is 9.0 Å, as defined by Svec et al. [10]: the distance between the planes that contain the oxygen atoms at the portal. When the halides are inside BU[6], we observed important structural changes. The deformation energies (DE) induced by the encapsulation are presented in Table 1. They show a large variation when different basis sets are employed. However, iodide has the smallest DE, whereas fluoride and chloride display the largest ones. This results means that the macrocyle has an optimal cavity for the encapsulation of iodide in the gas phase. At the M06-2X/6-311G level of theory, we found that the D3d symmetry of BU[6] is maintained only for bromide. When using the M06-2X/6-311+G and M06-2X/6311++G⁄⁄ methodologies the complexes of BU[6] with chloride and iodide have S6 symmetry but that of bromide belongs to the C2h group. Fluoride is the most extreme case for which the symmetry of BU[6] is completely lost for all basis set employed. Our results are in line with those reported by Gobre et al. [15] which suggested the fluoride interacts with 8 H atoms when it is inside BU[6]. The D3d structure is a transition state for BU[6]Cl– and BU[6]F–. The d1 diameter is contracted by 1 Å for the encapsulation of iodide and the d4 diameter is 0.6 Å smaller in order to facilitate with the formation of the weak CH-halide hydrogen bonds. For bromide, d1 contracts by 1.3 Å and d4 is reduced by 0.7 Å. The smaller size of chloride as compared with Br– and I– significantly reduces the size of the receptor. The d1 diameter goes from 10.2 Å for the empty macrocyle to 8.6 Å and d4 is contracted by 1 Å. As it can be seen in Fig. 2, the structure of BU[6]F– is markedly different from that of Cl–, Br– and I–. The strong interactions exerted by F– promote such an important deformation on the macrocyle geometry that we are not in position of talking any more about d1 and d4 as metric variables into account, since the spherical structure at the portals is replaced by an almost rectangular cross-section The interaction energies (IE) are presented in Table 1. At the M06-2X/6-311G level and including BSSE the IE are 85.4, 77.5, 74.6 and 72.0 kcal/mol, for F–, Cl–, Br– and I–, respectively. If free energy corrections are included we obtained the following results for DG298 : 70.9, 64.2, 65.7 and 61.9 kcal/mol, respectively. These values differ from those experimentally obtained in solution [9–11] and in the gas phase [12], which point I– to be the preferred guest. The IE computed at the B3LYP/6-311G level of theory are
Fig. 1. Gas phase optimized structure and IR spectrum of bambus[6]uril, at the M06-2X/6-311+G level of theory.
7
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9 Table 1 Gas phase interaction energies, enthalpies and free energies calculated at the B3LYP and M06-2X levels of theory for the complexes BU[6]X–X = F–, Cl–, Br–, I–.
DE
a b
M06-2X
6-311G
M06-2X
6-311+G
M06-2X
6-311++G⁄⁄
B3LYP
6-311G
–
F Cl– Br– I– F– Cl– Br– F– Cl– Br– I– F– Cl– Br– I–
120.4 80.4 80.1 77.4 96.8 85.1 84.0 96.2 82.9 76.2 73.9 107.6 60.4 61.0 53.5
DEzpe
DH298
DG298
118.5 79.0 80.0 77.0 93.2 82.7 82.8
120.0 79.8 80.0 77.8 96.4 84.7 83.6
105.9 66.1 71.2 67.3 82.3 64.4 70.0
87.6 56.8 53.5 48.0
107.3 59.3 59.7 52.9
93.8 49.3 48.9 40.8
DE + BSSE 85.4 77.5 74.6 72.0 93.5 83.2 79.0 93.9 81.1 74.5 72.4 87.6 56.8 53.5 48.0
DG + BSSE 70.9 64.2 65.7 61.9 79.0 62.5 65.0 79.4a 67.1a 65.6a 62.3a 73.8 46.1 42.0 35.3
BSSE
Def.b
35.0 2.9 5.5 5.4 3.3 2.5 5.0 2.3 1.8 1.7 1.5 20.0 3.2 6.9 5.5
17.6 13.6 9.2 6.1 12.8 11.2 8.0 7.0 7.4 6.3 3.1 22.3 11.8 10.1 6.5
Computed using the DE ? DG298 corrections computed at the M06-2X/6-311G level. Deformation energies experienced by the receptor hosting halide ions.
Fig. 2. Gas-phase optimized structure for BU[6]X– (X– = F–, Cl–, Br–, I–) at the M06-2X/6-311+G level of theory (bond distances, d, in Å).
even more deviated from the condensed phase results. Indeed, the IE for I– is 5.5 kcal/mol smaller than the one of bromide and the whole trend along the halide series is in contraposition to the one observed in solution. From a methodological stand-point the lack of diffuse functions is a problem because we are dealing with anions. For this reason, we computed IE using the 6-311+G and 6311++G⁄⁄ basis sets. The IE determined using the latter basis set are 93.9, 81.1, 74.5 and 72.4 kcal/mol for F–, Cl–, Br– and I–, respectively. As we observed for the 6-311G basis set, the M062X/6-311++G⁄⁄ results also differ with experiment. Interestingly, the agreement between M06-2X/6-311G and M06-2X/6-311++G⁄⁄ is improved as we move down in the periodic table. For iodide and bromide the IE computed with the 6-311G basis set are less than 0.5 kcal/mol smaller than those computed with the 6311++G⁄⁄ basis set (both BSSE corrected). However, for fluoride and chloride the deviations are larger because the inclusion of BSSE in the M06-2X/6-311G calculations underestimates IE. Finally, for comparative purposes, we performed M06-2X/aug-cc-pVDZ single point calculations for bromide and iodide. The IE were 77.9 and 73.8 kcal/mol, respectively, both in excellent agreement with the results obtained using the 6-311++G⁄⁄ basis set. This, being said, for all basis sets employed, qualitative agreement with experiment is not reached.
The strong bonding observed for fluoride is not surprising if we consider that this anion has the largest complexation energy with methane. Indeed, at the M06-2X/6-311G+ BSSE level of theory the hydrogen bond energies for CH4::X , X = F–, Cl–, Br–, I–, are 7.7, 2.9, 2.3 and 1.8 kcal/mol, respectively. Although the methine groups are a bit different than methane, a simple electrostatic analysis suggests a similar trend as that observed for methane. We note that for this system BSSE is relevant only for fluorine and also the use of diffuse functions makes a real difference for this atom. As we move down in the periodic table BSSE is reduced. Before analyzing the effect of the solvent it is important to discuss methodological and chemical issues that complicate the study of energetic aspects of the complexes BU[6]X–, namely: (a) symmetry of the complexes, (b) relative affinities. (a) The first problem faced was that the complexes do not have D3h symmetry, which is the expected result. For iodide the D3h and S6 (lower symmetry) structures are local minima but that with lower symmetry is by 0.14 kcal/mol more stable. For chloride, the D3h structure is a first-order transition state which is located 1.6 kcal/mol above the S6 structure. In the case of bromide the symmetry is D3h at the M06-2X/6-311G level of theory, but it is reduced to C2h when the basis set is extended to 6-311+G or 6311++G⁄⁄. The most severe situation is observed for fluoride for
8
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9
which the complex has no symmetry and the D3h structure is rather a fourth order saddle point. Although the energetic differences between the high- and low-symmetry structures are small, they become more important when the thermodynamic corrections are calculated (ZPE, entropy, etc.). These results indeed affect the order of relative affinity of BU[6] hosting halide ions. For example the DE ? DG298 corrections are 14.5, 14.3, 8.9 and 10.1 kcal/mol for F–, Cl–, Br– and I–, respectively, at the M06-2X/6-311G level of theory. These values can be compared with those computed at the M06-2X/6-311+G level of theory, namely, 14.5, 20.7 and 14.0 kcal/mol, for F–, Cl– and Br–, respectively. Thus, important differences emerge for bromide and chloride. The correction determined for Cl using the 6-311+G basis set seems to be too large. For this reason, we evaluated the free energy changes at the M06-2X/6-311++G⁄⁄ level of theory, using the DE ? DG298 corrections computed at the M06-2X/6-311G level. In this way, the free energy changes at the M06-2X/6-311++G⁄ level are 96.8, 75.7 and 70.0 kcal/mol for F , Cl– and Br–, respectively. Thus, at the highest level of theory employed, i.e. M06-2X/6-311++G⁄⁄+BSSE, the strongest interaction is obtained for BU[6]F–. Much work is needed to accurately estimate the DE ? DG298 corrections for this system. (b) Even though the observed relative selectivity of BU[6] towards halide anions seems to be very important, (for I– was 4400, 1200 and 12 times over the ones of F–, Cl– and Br–, respectively [11]) the differences in DG298 are small. In effect, employing the association constants experimentally determined [11] we found that the DG298 corresponding to I– is only 1.51, 2.74 and 13.0 kcal/mol larger than those corresponding to Br–, Cl– and F–, respectively. The differences between the free energy changes for encapsulation I–, Br– and Cl– are within 2.74 kcal/mol. This value is extremely small and thus requires very accurate methodologies in order to deal with such energetic difference by means of first principle calculations. The use of these techniques is prohibitively expensive because the systems contain 139 atoms. Up to know we have compared our gas phase results with those obtained in gas and condensed phase. On the basis of the results presented in the previous paragraph, we concluded that in the gas phase the affinity of BU[6] follows this trend F– > Cl– > Br– > I–, in disagreement with experiment [12], but in agreement with the gas phase hydrogen bond energies determined for the CH4 X- complexes. In the next section we analyze if the inclusion of solvent effects reverses this trend. 3.2. Solvent effects The complexes of BU[6] with halide anions were reoptimized including solvent effects. In Table 2 we list the IE computed in water and acetonitrile. We used these two solvents because a mixture of them was employed in the experiments. At the M06-2X/6311G level the affinity towards all halides except F– follows the same trend as in experiment: I– > Br– > Cl–. However, for F– the IE is still remarkable larger. Although BSSE is expected to be less important in solution, for fluoride it can still be significative. In ef-
Table 2 Interaction energies in solution calculated at the M06-2X and B3LYP levels of theory for the BU[6]X– complexes, X = F–, Cl–, Br–, I–.
F Cl Br I
H2O M06-2X 6-311G
H2O B3LYP 6-311G
CH3CN M06-2X 6-311G
42.4 15.6 19.2 21.4
34.1 1.0 3.0 0.7
17.2 20.6 22.8
H2O M06-2X 6-311+G
CH3CN M06-2X 6-311+G
15.4 18.8 23.2
20.0 25.0
Table 3 Interaction energies in gas phase and solution calculated at the M06-2X level of theory for the Na+BU[6]X– complexes, X = Cl–, Br–, I–.
Cl Br I
Gas M06-2X 6-311G
Gas M06-2X 6-311+G
H2O M06-2X 6-311+G
CH3CN M06-2X 6-311+G
146.4 126.1 101.0
143.7 135.0
138.8 131.7
146.8 134.5
fect, in the previous section we observed that the BSSE for fluoride is larger than for the rest of the halides (recall the agreement observed for Br- and I- when using the 6-311G and 6-311++G⁄⁄ basis sets). By adding a diffuse function we found that the IE of fluoride complex is dramatically decreased. At the M06-2X/6-311+G level of theory the IE are 15.4, 18.8, 23.2 kcal/mol, for F–, Cl–, Br–, respectively. Thus, if the 6-311+G complexation energy is considered for fluoride, and the 6-311G ones are used for the rest, we are able to reproduce the order of affinities observed experimentally, i.e. I– > Br– > Cl– > F–. When acetonitrile is considered as solvent the IE computed for chloride, bromide and iodide also follow the order observed experimentally. The free energy corrections calculated at the M06-2X/6-311G level are: 14.5, 14.3, 8.9 and 10.1 kcal/mol for F–, Cl–, Br– and I–, respectively. We can combine our complexation energies in solution with the free energy corrections determined in the gas phase. If that procedure is employed we obtain that DG298 in solution are: 11.3, 10.3 and 8.5 kcal/mol for and I–, Br–, Cl– respectively. The difference between the DG298 computed in water for iodide and bromide is 1 kcal/mol, only 0.5 kcal/mol lower than the value derived from the association constants reported experimentally. 3.3. Effect of the cation The halide encapsulation by BU[6] experimentally proceeds in the presence of a cation that can be for example: Na+, Cs+ or tetrabutylamonium (TBA+). In the case of Cl– the equilibrium constants for the encapsulation process were similar in the presence of the three cations. For the sake of completeness, we investigated the energetics of this process for all halides with the inclusion of Na+, at the M06-2X/6-311G level of theory. The results are presented in Table 3. In the gas-phase, the interaction energy of the complex NaBU[6]Br is 126.1 kcal/mol, the charges supported by Na and Br being +0.71 and 0.72 (Natural population results). For the analogous of iodide, the interaction energy is 101.1 kcal/mol and the charges of Na and I are 0.72 and 0.72, respectively. Finally, for chloride the complexation energy is 146.4 kcal/mol and the charges of Na and Cl are +0.78 and 0.87 respectively. Therefore, when the cation is included, the relative affinity decreases in the following order for Cl > Br > I . When a diffuse function is included the interaction energies follow the same order as discussed above. These results were not corrected by BSSE because it is expected to be similar for the three halides as was observed in Sections 3.1 and 3.2. Finally, when the latter two complexes are studied in solution, we found that the IE follow the same order as in the gas phase. This result is in disagreement with those obtained by us in solution in absence of sodium and also with experiment. 4. Conclusions M06-2X and B3LYP calculations were employed to study the encapsulation of halides (X–) by the recently synthetized receptor bambus[6]uril. The following are considered to be the most important findings of the work:
P.A. Denis, J.S. Gancheff / Computational and Theoretical Chemistry 1023 (2013) 5–9
(1) The gas phase results do not follow the affinity experimentally observed, as the largest encapsulation energy was obtained for fluoride and the smallest one for iodide. However, this finding is in agreement with the gas phase hydrogen bond energies calculated for the CH4 X complexes. (2) The halide encapsulation energy (relative affinity) is a balance between the CH X– hydrogen bond energies inside the receptor and its deformation. (3) When solvents effects are considered, the selectivity of the receptor is the same as that observed in solution. (4) The effect of the counter ion was evaluated using Na+, but inclusion of the latter worsens the agreement with experiment. (5) Two methodological problems emerged during this study: (a) basis sets must be quite large to obtain meaningful results, (b) the symmetry D3d of the BU[6] is lost upon encapsulation for most of the halides and this alters the evaluation of the thermodynamic properties such as free energy change.
Acknowledgment The authors thank PEDECIBA Quimica for financial support. The authors thank Walter Shands from Intel for his help with Intel Cluster Studio. References [1] R. Behrend, E. Meyer, F. Rusche, J. Liebigs, Condensations producte aus glycoluril und formaldehyd, Ann. Chem. 339 (1905) 1–37. [2] W.A. Freeman, W.L. Mock, N.-Y. Shih, Cucurbituryl, J. Am. Chem. Soc. 103 (1981) 7367–7368. [3] J. Lagona, P. Mukhopadhyay, S. Chakrabarti, L. Isaacs, The cucurbit[n]uril family, Angew. Chem. Int. Ed. 44 (2005) 4844–4870. [4] X. Xiao, Q.H. Hu, Z. Tao, Y.-Q. Zhang, S.-F. Xue, Q.-J. Zhu, G. Wei, Host–guest inclusion complexes of viologen derivative and tetramethyl cucurbit[6]uril with multiple interaction models, Chem. Phys. Lett. 514 (2011) 317. [5] J. Tian, S. Ma, P.K. Thallapally, D. Fowler, B.P. McGraila, J.L. Atwood, Cucurbit[7]uril: an amorphous molecular material for highly selective carbon dioxide uptake, Chem. Commun. 47 (2011) 7626–7628. [6] D.A. Ivanov, N.K. Petrov, E.A. Nikitina, M.V. Basilevsky, A.I. Vedernikov, S.P. Gromov, M.V. Alfimov, The 1:1 hostguest complexation between cucurbit[7]uril and styryl dye, J. Phys. Chem. A 115 (2011) 4505–4510. [7] P.H. Dixit, R.V. Pinjari, S.P. Gejji, Electronic structure and 1H NMR chemical shifts in host-guest complexes of cucurbit[6]uril and sym-tetramethyl cucurbit[6]uril with imidazole derivatives, J. Phys. Chem. A 114 (2010) 10906–10916. [8] A.I. Day, R.J. Blanch, A.P. Arnold, S. Lorenzo, G.R. Lewis, I. Dance, Angew. Chem. Int. Ed. 41 (2002) 275–277. [9] J. Svec, M. Necas, V. Sindelar, Bambus[6]uril, Angew. Chem. Int. Ed. 49 (2010) 2378–2381. [10] J. Svec, M. Dusek, K. Fejfarova, P. Stacko, P. Klan, A.E. Kaifer, W. Li, E. Hudeckova, V. Sindelar, Anion-free bambus[6]uril and Its supramolecular properties, Chem. Eur. J. 17 (2011) 5605–5612. [11] V. Havel, J. Svec, M. Wimmerova, M. Dusek, M. Pojarova, V. Sindelar, Bambus[n]urils: a new family of macrocyclic anion receptors, Org. Lett. 13 (2011) 4000–4003.
9
[12] A. Revesz, D. Schroder, J. Svec, M. Wimmerova, V. Sindelar, Anion binding by bambus[6]uril probed in the gas phase and in solution, J. Phys. Chem. A 115 (2011) 11378–11386. [13] P. Toman, E. Makrlík, P. Vanura, Theoretical study on the complexation of bambus[6]uril with the chloride, bromide, and iodide anions, Monatsh Chem. 142 (2011) 881–884. [14] P. Toman, E. Makrlík, P. Vanura, Theoretical study on the complexation of bambus[6]uril with the fluoride anion, Comput. Theor. Chem. 989 (2012) 97– 99. [15] V.V. Gobre, P.H. Dixit, J.K. Khedkar, S.P. Gejji, Electronic structure, vibrational spectra and 1H NMR of halide ion (F-, Cl- and Br-) encapsulated bambus[6]uril from density functional theory, Comput. Theor. Chem. 976 (2011) 76–82. [16] P. Toman, E. Makrlík, P. Vanura, DFT Study on the complexation of bambus[6]uril with the perchlorate and tetrafluoroborate anions, Acta Chim. Slov. 58 (2011) 846–849. [17] P. Toman, E. Makrlík, P. Vanura, Bambus[6]uril as a novel macrocyclic receptor for the cyanide anion, Chem. Phys. Lett. 547 (2012) 63–65. [18] Y. Zhao, D.G. Truhlar, The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals, Theor. Chem. Acc. 120 (2008) 215. [19] A.D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98 (1993) 5648. [20] C. Lee, L. Yang, R.B. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37 (1988) 785. [21] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H.P. Hratchian, A.F. Izmaylov, J. Bloino, G. Zheng, J.L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J.A. Montgomery, Jr., J.E. Peralta, F. Ogliaro, M. Bearpark, J.J. Heyd, E. Brothers, K.N. Kudin, V.N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J.C. Burant, S.S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J.M. Millam, M. Klene, J.E. Knox, 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, R.L. Martin, K. Morokuma, V.G. Zakrzewski, G.A. Voth, P. Salvador, J.J. Dannenberg, S. Dapprich, A.D. Daniels, O. Farkas, J.B. Foresman, J.V. Ortiz, J. Cioslowski, D.J. Fox, Gaussian Inc., Wallingford, CT, 2009. [22] Y. Zhao, N.E. Schultz, D.G. Truhlar, Design of density functionals by combining the method of constraint satisfaction with parametrization for thermochemistry, thermochemical kinetics, and noncovalent interactions, J. Chem. Theor. Comput. 2 (2006) 364. [23] Y. Zhao, D.G. Truhlar, Size-selective supramolecular chemistry in a hydrocarbon nanoring, J. Am. Chem. Soc. 129 (2007) 8440. [24] R. Ditchfeld, W.J. Hehre, J.A. Pople, Self-consistent molecular-orbital methods. IX. An extended gaussian-type basis for molecular-orbital studies of organic molecules, J. Chem. Phys. 54 (1971) 724. [25] J. Tomasi, B. Mennucci, R. Cammi, Quantum mechanical continuum solvation models, Chem. Rev. 105 (2005) 2999–3094. [26] B. Mennucci, J. Tomasi, Continuum solvation models: a new approach to the problem of solute’s charge distribution and cavity boundaries, J. Chem. Phys. 106 (1997) 5151. [27] B. Mennucci, E. Cances, J. Tomasi, Evaluation of solvent effects in isotropic and anisotropic dielectrics and in ionic solutions with a unified integral equation method: theoretical bases, computational implementation, and numerical applications, J. Phys. Chem. B 101 (1997) 10506–10517. [28] R. Cammi, B. Mennucci, J. Tomasi, Second-order Møller Plesset analytical derivatives for the polarizable continuum model using the relaxed density approach, J. Phys. Chem. A 103 (1999) 9100–9108. [29] R. Cammi, B. Mennucci, J. Tomasi, Fast evaluation of geometries and properties of excited molecules in solution: a Tamm–Dancoff Model with application to 4-dimethylaminobenzonitrile, J. Phys. Chem. A 104 (2000) 5631. [30] M. Cossi, G. Scalmani, N. Rega, V. Barone, New developments in the polarizable continuum model for quantum mechanical and classical calculations on molecules in solution, J. Chem. Phys. 117 (2002) 43.