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Cooperative Interaction of Hydronium Ion with an Ethereally Fenced Hexaarylbenzene-Based Receptor: An NMR and Theoretical Study Jaroslav Krˇ´ızˇ,*,† Petr Toman,† Emanuel Makrlı´k,‡ Jan Budka,§ Ruchi Shukla,| and Rajendra Rathore| Institute of Macromolecular Chemistry AS CR, V. V. i., HeyroVske´ho Sq. 2, 162 06 Prague, Czech Republic, Faculty of Applied Sciences, UniVersity of West Bohemia, HusoVa 11, 306 14 Pilsen, Czech Republic, Institute of Chemical Technology, Technicka´ 5, 166 28 Prague, Czech Republic, and Marquette UniVersity, P.O. Box 1881, Milwaukee, Wisconsin 53201-1881 ReceiVed: February 4, 2010; ReVised Manuscript ReceiVed: March 25, 2010
Using 1H and 13C NMR and DFT calculations, the structure and interactions of the symmetric ethereally fenced hexaarylbenzene receptor 1 with hydronium ions were studied. Both 1 and its equimolecular complex 1 · H3O+ exhibit C3V symmetry. According to DFT, two similar optimal structures of the complex exist, the more stable one being 15.4 kJ/mol lower in energy. The equilibrium between 1 and 1 · H3O+ complexes is characterized by the stabilization constant K ) 1.97 × 106 (i.e., the binding constant η ) 6.3) according to both proton and carbon NMR spectra. The exchange dynamics between 1 and the complex measured by the delay-varied CPMG sequence had to be corrected for the internal exchange processes in both 1 (conformation change) and the complex (vacillation between the two minima). After this correction, the correlation time of exchange was found to be 4.76 × 10-5 s. Such relatively fast exchange can be explained only by it being mediated by the excess water molecules present in the system. Introduction In recent years, quite a number of molecular receptors often tailored to bind specific ions were prepared and studied. In most of them, cations are bound in some kind of molecular cavity having a defined shape and usually bearing multiple polar groups with electron-donating ability. Modified calixarenes were shown1-10 to be an important class of such receptors for metal cations and so were crown ethers11-16 either purely aliphatic or fortified with benzo groups. In recent years, an interesting receptor based on a hexaarylbenzene platform with an ethereal fence was prepared,17-19 and it was shown that it binds potassium ion with remarkable efficiency.17 In this receptor, the molecular cavity has a rim formed by three -O-(CH2)4-Ogroups, each attached to two neighboring aromatic rings and a central aromatic ring at its bottom (structure 1, Scheme 1). Like in some calixarenes, the metal ion is thought to be partially bound by cation-π interactions with the aromatic π-orbitals, although donor-acceptor interactions between the oxygen atoms of the cavity rim and the cation surely are at play as well. Because we have already shown in a number of studies20-26 on both calixarenes and crown ethers, the ligands binding alkali metal cations bind some form of hydrated proton (HP), usually the hydronium ion, H3O+. Although the stabilization energies of the complexes are quite comparable to those with metal cations (provided that the metal cation has an appropriate size to fit into the cavity), the binding mode is different. As we have shown both by experimental techniques and theoretical calculations, the hydronium ion is preferentially bound to the ligand by hydrogen bonds fortified by the positive charge of the ion. * To whom correspondence should be addressed. E-mail: kriz@ imc.cas.cz. Tel: +420-296809382. Fax: +420-296809410. † Institute of Macromolecular Chemistry. ‡ University of West Bohemia. § Institute of Chemical Technology. | Marquette University.
SCHEME 1: Structure of 1 and the Numbering of Carbon and Hydrogen Atoms
Because this specific binding mode of HPs is probably operable in many natural receptors, the verification of the hydronium ion binding in various types of receptors has a more than only theoretical value. Accordingly, the main motive of our hydronium ion binding study to the receptor 1 is driven by its unique bipolar receptor site, which contains a polar ethereal fence (a structural feature similar to crown ethers) and a hydrophobic central benzene ring that can participate in the binding even via cation-π interactions. There is another interesting feature of the binding of various ions to the receptors. Despite the usually high stabilization constants (g105), which suggest a very high energy barrier against the liberation of the ion from the complex, surprisingly fast exchange of the ions with unbound receptor molecules has been observed, and in some cases, exotic explanations such as quantum tunneling16 are proposed for the fast ion-exchange processes. Such rapid exchange of H3O+ as well as other forms of HPs and various receptors has been extensively studied in
10.1021/jp101080h 2010 American Chemical Society Published on Web 04/05/2010
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Figure 1. 1H NMR spectrum (300.13 MHz) of (a) 1.0 mmol/L 1 and its mixtures with (b) 0.5 and (c) 1.0 equiv HDCC in nitrobenzene-d5 at 296 K. The broad signal of water + hydrated protons was removed by presaturation and relaxation filter, in part b, the intensity of the signals 8a + 8e is lowered because of saturation near these signals.
Experimental Section
for 1H and 13C NMR, respectively. 13C NMR measurements were performed using the 1H-13C DEPT45 sequence28 (collecting 6000 scans). Exponential weighting (lb ) 1 Hz) was used before Fourier transform in 13C NMR. For the exchange dynamics, the Carr-Purcell-Meiboom-Gill sequence29-31 was used on the 1 H NMR resonance with the delay between π pulses tp being 2.0, 1.0, 0.5, 0.25, and 0.125 ms. (The length of the π pulse was 31.2 µs.) We measured 32 experimental points with the total time of the sequence gradually increased by 40 ms in one experiment with the given tp. Each measurement was repeated at least three times. The error of the obtained R2 was lower than 3% rel. Quantum Mechanical Calculations. The calculations were performed using the Gaussian 03 suite of programs.32 Molecular geometry was fully optimized at the B3LYP level of density functional theory (DFT) with the 6-31G(d) basis set. In both the free molecule 1 and its complexes with H3O+, the optimization was unconstrained, without any assumption of molecular geometry.
Materials and Samples. The receptor 1 was prepared by the previously published method.16 HDCC was prepared from cesium bis(1,2-dicarbollyl)cobaltate (HDCC) by the method published elsewhere27 and dried under vacuum for several weeks. In its final state, it still contained 3.5 mol H2O/1 mol HDCC. Nitrobenzene-d5 was purchased from Sigma-Aldrich and dried over molecular sieves before use. All samples for NMR measurements contained 1 mmol/L of 1 and various amounts of HDCC dissolved in nitrobenzene-d5. The samples were stored and measured at 296 K. NMR Spectroscopy. 1H and 13C NMR spectra were measured at 300.13 and 75.45 MHz, respectively, with an upgraded Bruker Avance DPX300 spectrometer. We measured 32 and 64 k points
Results and Discussion 1. Structure of the Free Receptor 1 and Its Complex With H3O+. Because of very low solubility of 1 in nitrobenzene, we had to work with a very low concentration of it, namely, 1 mmol/L. This somewhat limited the variety of the NMR experimental methods, especially in the realm of 13C NMR spectra, where only experiments utilizing {1H f 13C} polarization transfer (such as in DEPT45 sequence) were successful on grounds of sensitivity as well as solvent-to-solute signal ratio. Figure 1 shows examples of 1H NMR spectra of the original 1 and its mixtures with HDCC, molar ratio β ) [HDCC]/[1]0 being 0.5 and 1.0. Figure 2 shows examples of {1H f 13C}
our laboratories, and any possibility of quantum tunneling was ruled out by closer scrutiny.21 Instead, a cooperative exchange mechanism involving excess water molecules was suggested. In the case of the present receptor, the bound potassium ion shows no sign of fast exchange in their NMR spectra.17 We therefore question if H3O+ with a similar ion radius will demonstrate an analogous behavior with receptor 1. As in most of our previous studies,20-26 we performed the present study of interaction between 1 and HPs in nitrobenzene, a relatively polar organic medium ascertaining ionization by its dielectric constant (ε > 35). As a reliable source of wellionized protons,20 a superacid hydrogen bis(1,2-dicarbollyl)cobaltate (HDCC) was used. In our experiments, HDCC contained 3.5 mol/mol of H2O per one proton, as a result of which HP could be present in various hydration states up to H7O3+. As we shall demonstrate herein, without doubt the bound form of HP in the complex of receptor 1 is H3O+.
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Figure 2. 13C DEPT45 NMR spectrum (75.45 MHz) of (a) 1.0 mmol/L 1 and (b) its mixture 1.0 equiv HDCC in nitrobenzene-d5 at 296 K (nb means residual nitrobenzene signals).
DEPT45 NMR spectra of 1 and its equimolar mixture with HDCC. As for 1 in the free state, both 1H and 13C NMR spectra (for signal assignment, done using 2D COSY, HSQC, and HMBC spectra; see Scheme 1 where protons and the attached carbon atoms have the same number) with only one set of signals for each type of 1H or 13C nuclei strongly indicate a C3V symmetry of the molecule. Small and very fast deviations from this symmetry cannot be excluded, but they could only be of a type of symmetric oscillations around the symmetric ground state. Large differences between the chemical shifts of the protons and carbons 4 and 6 cannot be explained merely by the electron density redistributions caused by the oxygen next to carbon 5; it is much more likely that they are due to the propeller-like orientation of the six aromatic rings,17,18 which exerts various long-range shielding by the neighboring aromatic ring. Interestingly, this phenomenon also makes both protons and carbons in the methyl groups 1 and 2 slightly nonequivalent, an effect slightly more pronounced in the case of the complex. The narrow signals 1 to 6 in 1H NMR indicate that the corresponding protons assume relatively rigid positions relative to the rest of the molecule; that is, the propeller conformation does not change significantly and thereby renders the molecular cup of the receptor rather rigid. The broadening of the signals 7a,e and 8a,e in the 1H NMR spectrum (as well as fast relaxation, vide infra) indicates larger relative mobility of the ethereal loop. The features of the structure of 1, which can be read from the NMR spectra, are in accord with the DFT calculation. The ground-state structure optimized under assumption of the C3V symmetry is reproduced in Figure 3. A usual objection to this and further calculations is possible, namely, that the calculations are done in vacuo, that is, without respect to the relatively polar medium. Our long experience with analogous studies20-26 has shown that DFT calculations on this level correspond remarkably well with our experimental results notwithstanding the polarity of the medium.
In accord with NMR spectra, the six aromatic rings in the wreath around the central ring are arranged in a propeller-like configuration. The diameter of the cavity, that is, the distance of any two opposite oxygen atoms, is found to be 6.195 Å, thus allowing even larger cations to enter the cavity. The distance of the plane containing the centers of all six oxygen atoms from the plane of the central aromatic ring is ∼2.15 Å. Therefore, any ion held in the plane of the oxygen atoms makes significant contact with the π-electron cloud of the central aromatic ring. As documented in the next paragraph, the NMR evidence leaves no doubt that 1 binds with 1 equiv HP. The evident C3V symmetry of the complex strongly indicates that HP is in the form of H3O+: the next C3V symmetric HP is H7O3+, which is too large for the cavity, and its binding would be too weak to secure the high stabilization constant of the complex. (See the next paragraph.) In 1H NMR, the largest relative chemical shifts between 1 and 1 · H3O+ are observed for signals 5, 7, and 8, which further attests that H3O+ is mainly bound by chargereinforced hydrogen bonds to the oxygen atoms: either to three ethereal oxygen atoms by strong binding while leaving the other three oxygen atoms essentially free or by bifurcated hydrogen bonds to all six oxygen atoms.18 A somewhat similar case of binding to dibenzo-18-crown-6 suggests the first possibility to be preferred26 because there is no visible doubling of the signals of the adjacent nuclei in the complex (5, 7, 8), and the hydronium ion most likely rotates in the plane of oxygen atoms with a fast velocity (the rotational barrier being ∼15 kJ/mol, see below). DFT calculations are in a full accord with these NMR results. Two structural minima were found by optimization of the structure of 1 · H3O+ complex. The lower and probably global energy minimum is depicted in Figure 4, which shows that 1 retains most of the features of its free state including the propeller-like structure. The hydronium ion H3O+ sits over the
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Figure 3. Two projections of the free substance 1 as optimized by the B3LYP/6-31G(d) quantum chemical DFT calculation (hydrogen atoms are omitted for better lucidity).
center of the central aromatic ring, and its positively charged oxygen atom sits 2.83 Å above the aromatic plane. The hydrogen atoms of the hydronium ion point to three of the six oxygen atoms of 1 with a distance of 1.756 Å, indicating fairly strong hydrogen bonds. At the same time, their distances to the other oxygen of the same ethereal loop and to the nearest next oxygen are 2.685 and 2.841 Å, respectively, that is, on the very border of substantial bonding. The nearest and still realizable minimum shown in Figure 5 has somewhat lower difference in binding to the oxygen atoms of the same loop; namely, the distances are 1.902 and 2.618 Å, whereas that to the next nearest oxygen is 2.689 Å. In this case, the prominent hydrogen bonds are markedly weaker. Also, as shown in Table 1, the total binding energy in this structure is ∼15.4 kJ/mol lower than that in the former one, thus showing that the main interactions in the complex are due to the hydrogen bonds, as predicted by NMR spectroscopy. 2. Equilibrium. In the interval of β )[H3O+ ]0/[1]0 from 0 to 1.0, both 1H and 13C NMR signals of 1 show shifts to various degrees. Their proportional shift without multiplying their number, which stops at β ) 1.0, shows that (i) only one H3O+ ion binds to the molecule of 1 and (ii) there is a fast exchange between 1 and 1 · H3O+. Under such conditions, the chemical shift δ of the given signal is a weighted mean of those of 1 and
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Figure 4. Two projections of the complex 1 · H3O+ (global minimum) as optimized by the B3LYP/6-31G(d) quantum-chemical DFT calculation. (Hydrogen atoms are omitted for better lucidity.)
1 · H3O+, and the equilibrium constant of binding is thus assumed to be
K)
[1 · H3O+] [1][H3O+]
(1)
The relative shift ∆δ of a given signal can be shown20-26 to obey the following relationship
∆δ ) ∆δmax
1 + K[1]0(1 + β) -
√{1 + K[1]0(1 + β)}2 - 4K2[1]20β 2K[1]0
(2)
where ∆δmax is the maximum relative shift of the given signal that corresponds to the complex 1 · H3O+. Figure 6 shows the relative shifts of selected 1H NMR signals and their fitting by eq 2, whereas Figure 7 shows the same fitting for the selected 13 C NMR signals. (In both cases, signals with highest relative shifts were selected.) Table 2 summarizes the results of fittings in Figures 6 and 7. The scatter in the obtained K values reflects only the fact that their magnitudes lie toward the upper limit of the equilibrium constants that can be determined by NMR methods. The mean of the equilibrium constant values obtained
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Figure 6. Dependence of the relative chemical shifts of the indicated 1 H NMR signals of 1 on the molar ratio β (nitrobenzene-d5, 296 K).
Figure 5. Two projections of the complex 1 · H3O+ (nearest second minimum) as optimized by the B3LYP/6-31G(d) quantum-chemical DFT calculation. (Hydrogen atoms are omitted for better lucidity.)
TABLE 1: Calculated Energies and Binding Energies of 1, H3O+, and Two Lowest-Energy Structures of 1 · H3O+ (B3LYP/6-31G(d)) energy of 1 (au) energy of H3O+ (au) energy of 1 · H3O+ (au) binding energy (kJ/mol)
minimum I
minimum II
-3245.61377370 -76.6890841785 -3322.45671343 403.95
-3245.61377370 -76.6890841785 -3322.45083257 388.507
Figure 7. Dependence of the relative chemical shifts of the indicated 13 C NMR signals of 1 in dependence on the molar ratio β (nitrobenzened5, 296 K).
TABLE 2: Maximum Relative Chemical Shifts, ∆δmax (ppm), of the selected 1H and 13C NMR Signals and the Fitted Values of Equilibrium Constants, K (mol-1) 1
-1
is K ) 1.97 × 10 mol or, as it is more customary to express, log K ) 6.3. The magnitude of K on the order of 106 mol-1 corresponds well to the large binding energy obtained by theoretical calculations. (See Table 1.) 3. Dynamics of the System. The experimentally measured large equilibrium constant (Table 2) together with a hefty stabilization energy of the complex obtained by theoretical calculations (Table 1) suggest a high energy barrier for the release of H3O+ from its complex (i.e., 1 · H3O+), which should be the first step of its exchange between the complex and the free molecule of 1. Therefore, a very low, if any, frequency of exchange should be observed. However, contrary to this expectation, as already stated above, the shape of both 1H and 13 C NMR spectra leaves little doubt that the exchange is fast, at least on the NMR time scale. Before starting to speculate about the possible reasons of this phenomenon, quantitative data for the exchange process are called for. 6
13
H NMR
signal
∆δmax
K × 10
5 6 7a 7e 8a 8e
0.123 0.013 0.252 0.202 0.353 0.201
1.49 2.33 1.99 2.60 1.45 2.02
-6
C NMR
signal
∆δmax
K × 10-6
1 4 5 6 7 8
0.460 1.991 0.943 -1.028 -0.401 -0.371
1.54 2.12 1.87 1.65 2.45 2.13
As is well known, the exchange rate can be established by measuring the dependence of transverse relaxation rate on the interpulse delay, tp, between the π pulses in the Carr-PurcellMeiboom-Gill sequence (CPMG).29 The actually measured relaxation rate, R2(tp), can be expressed30 as
R2(tp) ) R02 + p1p2δω2τex[1 - (τex /tp) tanh(tp /τex)]
(3)
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where R20 is the part of relaxation rate independent of exchange, p1 and p2 are the probabilities of finding the nucleus at the sites 1 (free 1 in our case) and 2 (1 · H3O+), respectively, δω is the relative chemical shift between the two sites (δω ) 2π∆δmax), and τex is the correlation time of exchange. Assuming that τex , tp, we can use the approximation31
R2(tp) ) ζ - ξ/tp
(4)
ζ ) R02 + p1p2δω2τex
(4a)
ξ ) p1p2δω2τ2ex
(4b)
with
and
However, as already indicated in previous paragraphs and documented below, the present situation is complicated by the fact that both 1 (site 1) and 1 · H3O+ (site 2) undergo their specific intramolecular exchanges (e.g., conformation changes of the ethereal loops in the first case and probable jumps between the two energy minima in the second one), which contribute not only to the transverse relaxation rate but also to its dependence on tp. Therefore, we have to reformulate eq 4, partially modifying the approach already used in our recent study26 in the following way
Figure 8. Dependence of transverse relaxation rates, R2, of indicated signals of 1 (0.8 is added to R2 of signal 5) with the inverse of tp (nitrobenzene-d5, 296 K).
2
R2(tp) ) λ - κ/tp )
∑ (pi2ζi) + i)1
2
p1p2ζ12 - [
∑ (pi2ξi) + p1p2ξ12]/tp
(5)
i)1
where ζi and ξi are the abscissa and the slope of the R2/tp dependence in the ith pure state, that is, 1 (i ) 1) and 1 · H3O+ (i ) 2), whereas ζ12 and ξ12 are the analogous quantities specific for the exchange between 1 and 1 · H3O+, explicitly
ζ12 )
δω212τex
ζ12 )
δω212τ2ex
(5a) (5b)
where δω12 is the relative chemical shift of the given signal between both pure sites, expressed in rad/s, and τex is the corresponding correlation time of exchange in seconds. We are able to measure ζi and ξi in the pure states, and although we cannot express them explicitly because we have no means of establishing the corresponding relative shift, δωi, eq 5 gives us the necessary relation for obtaining τex for the exchange between 1 and the complex. The experimental dependences of transverse relaxation rates of selected signals on 1/tp are shown in Figure 8 for free 1 and in Figure 9 for the complex 1 · H3O+. The fitted abscissas 0.25ζi and slopes 0.25ξi are compiled in Table 3. The dependence of R2 on tp-1 shows that some chemical exchange is going on in both pure sites: in 1, it probably is merely a slowed-down conformation change in the system of atoms 7 and 8; in the complex, the somewhat more marked dependence almost certainly reflects the jumps between the
Figure 9. Dependence of transverse relaxation rates, R2, of indicated signals of 1 (0.6 is added to R2 for signal 5) in equimolar mixture with HDCC with the inverse of tp (nitrobenzene-d5, 296 K).
TABLE 3: Abscissas 0.25ζi and Slopes 0.25ξi×105 of the Dependences of R2 on 1/tp for Selected Signals in 1 and 1 · H3O+ (Nitrobenzene, 296 K) signal
0.25ζ1
0.25ξ1 × 105
0.25ζ2
0.25ξ2 × 105
5 7a 7e 8a 8e
0.85 1.87 1.92 2.23 2.24
0.84 2.12 2.18 3.24 3.32
1.37 2.86 2.97 3.48 3.54
2.14 4.15 4.34 5.14 5.32
somewhat different molecular geometries corresponding to the two energy minima mentioned above. The important fact is that both exchange processes contribute to the dependence of R2 on tp-1 and thus must be taken into account. The experimental dependences of R2 on tp-1 for the β ) 0.5 mixture are shown in Figure 10. (3.0 was added to R2 of signal 5 for graphical reasons.) The values of κ and λ obtained by fitting and the calculated values of ζ12, ξ12, and, consequently, τex are given in Table 4.
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Figure 10. Dependence of transverse relaxation rates, R2, of indicated signals of 1 in 1:0.5 mol/mol mixture with HDCC with the inverse of tp (nitrobenzene-d5, 296 K).
TABLE 4: Experimental Values of δω (rad/s), λ (s-1), and K and Calculated Values of ζ12 (s-1), ξ12, and τex (s) for Selected Signals of 1 in its 1:0.5 mol/mol Mixture with HDCC (Nitrobenzene-d5, 296 K) signal δω × 10-3 5 7a 7e 8a 8e
0.232 0.475 0.381 0.666 0.379
λ
ζ12
2.81 2.35 7.62 11.55 6.53 6.55 10.96 20.98 7.61 7.31
κ × 104 ξ12 × 104 τex × 105 0.554 2.106 1.390 3.319 1.794
1.023 5.915 2.953 9.924 3.721
4.36 5.12 4.51 4.73 5.09
According to the NMR spectra, only one hydronium ion binds to 1. The equilibrium between 1 and 1 · H3O+ was examined using relative chemical shifts of both proton and 13C NMR signals of 1. The measurement of the equilibrium constants was on the upper limit of the possibilities of such measurements by NMR spectroscopy, but the results were sufficiently coherent to determine the reliable equilibrium constant K ) 1.97 ( 0.63 × 106 mol-1 (i.e., log K ) 6.3). The measurement of the exchange dynamics between 1 and 1 · H3O+ using transverse relaxation measurements by the CPMG sequence with varied delays between π pulses was complicated by the intramolecular exchange in both 1 (conformational change of the ethereal links) and the complex (jumps between the two optimal structures). We solved the problem by measuring the internal exchange in 1 and in the complex (β ) 1) and then, using equations derived in this article, in the equimolar mixture of 1 with 1 · H3O+ (β ) 0.5). The mean value of the exchange correlation time, τex ) 4.76 × 10-5 s, can be explained only by a cooperative mediation of the exchange by the excess water molecules present in the system. Acknowledgment. This work was supported by the Grant Agency of the Czech Republic, project 203/09/1478, and the Czech Ministry of Education, Youth and Sports, projects MSM 4977751303 and MSM 6046137301. The computer time at the MetaCentrum (project MSM 6383917201), as well as at the Institute of Physics (computer Luna/Apollo), Academy of Sciences of the Czech Republic, is gratefully acknowledged. Also, R.R. thanks the National Science Foundation for financial support. References and Notes
The seemingly surprising fact that some of the ξ12 values are larger than the corresponding values of κ is due to eq 5, where, inherently, ξ12 )(0.5)-2[κ - 0.25(ζ1 + ζ2)] and analogously for ζ12. The mean value of τex in Table 4 is 4.76 × 10-5 s, the individual values being scattered within 10% rel, which is probably the best precision we could hope for. The relative coherence of these values shows that they all correspond to chemical exchange 1 T 1 · H3O+. Recalling that the above indicated huge energy barrier of dissociation 1 · H3O+ f 1 + H3O+, it is clear that the exchange must be mediated by a cooperative mechanism, which most likely involves the excess water molecules. Such mechanism proved26 in an analogous case of dibenzo-18-crown-6 is supported in our case by the fact that there is a swift exchange between protons of H3O+ and water so that there is only one signal of both species. (In Figure 1, it is suppressed so that other aliphatic signals can be seen.) The bound H3O+ and excess water are expected to be in a dynamic contact, which enables the mediation of its exchange between the two molecules of 1. Conclusions The structure and interactions of the symmetric ethereally fenced hexaarylbenzene-based receptor 1 (Scheme 1) with HPs provided by HDCC in nitrobenzene-d5 were studied using 1H and 13C NMR techniques and ab initio DFT calculations. It was found that both 1 and its complex with HP exhibit C3V symmetry. The calculations as well as NMR spectroscopic evidence strongly indicate that the form of the bound HP to receptor 1 is the hydronium ion, H3O+. DFT calculations further suggest that there are two similar optimal structures of the complex, one of them being 15.4 kJ/mol lower in energy than the other.
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