Structure and Dynamics of [3.3] Paracyclophane As Studied by

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Structure and Dynamics of [3.3]Paracyclophane As Studied by Nuclear Magnetic Resonance and Density Functional Theory Calculations Helena Dodziuk,*,† Sławomir Szyman´ski,*,†,‡ Jarosław Jaz´win´ski,‡ Maciej E. Marchwiany,†,# and Henning Hopf§ Institute of Physical Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Kasprzaka 44/52, Poland, Institute of Organic Chemistry, Polish Academy of Sciences, 01-224 Warsaw, Kasprzaka 44/52, Poland, and Institute of Organic Chemistry, ICM, Warsaw UniVersity, Pawinskiego 5a, 02-106 Warsaw, Poland, Technical UniVersity Braunschweig, Hagenring 30, 38106 Braunschweig, Germany ReceiVed: July 14, 2010; ReVised Manuscript ReceiVed: August 17, 2010

Strained cyclophanes with small (-CH2-)n bridges connecting two benzene rings are interesting objects of basic research, mostly because of the nonplanarity of the rings and of interference of π-electrons of the latter. For title [3.3]paracyclophane, in solutions occurring in two interconverting cis and trans conformers, the published nuclear magnetic resonance (NMR) data are incomplete and involve its partially deuterated isotopomers. In this paper, variable-temperature NMR studies of its perprotio isotopomer combined with DFT quantum chemical calculations provide a complete characterization of the solution structure, NMR parameters, and interconversion of the cis and trans isomers of the title compound. Using advanced methods of spectral analysis, total quantitative interpretation of its proton NMR spectra in both the static and dynamic regimes is conducted. In particular, not only the geminal but also all of the vicinal JHH values for the bridge protons are determined, and for the first time, complete Arrhenius data for the interconversion process are reported. The experimental proton and carbon chemical shifts and the nJHH, 1JCH, and 1JCC coupling constants are satisfactorily reproduced theoretically by the values obtained from the density functional theory calculations. Introduction Highly strained cyclophanes with small bridges such as [2.2]paracyclophane 1, (1,2,3)-, (1,3,5)-, (1,2,4)-, and (1,2,4;1,2,5)[2.2.2]cyclophanes 2-5, respectively,1 and hexahydrosuperphane 6,2 which we have recently studied, are interesting objects of basic research for several reasons.3-5 First, as opposed to benzene, they have nonplanar aromatic ring(s). Second, the aromatic rings in 1-5 are closely situated, enabling interaction of π-electrons of the rings. Third, according to high-level quantum chemical calculations, the saturated ring in hypothetical 6 adopts a planar conformation that is unusual for the cyclohexane structure. Because of the longer bridges in comparison to those of 1-6, there is less strain in [3.3]paracyclophane 7 (Figure 1) and its aromatic rings are less distorted from planarity and are more distant. However, a certain interaction between the aromatic π-electrons is also expected in this case. An X-ray study by Gantzel and Trueblood6 showed that in the solid state 7 assumes trans conformation 7a with slightly nonplanar aromatic rings (C2-C1-C6-C5 torsional angle of ca. 8° and interring C1-C7 and C4-C10 distances of ∼3.1 Å), while later studies in solution7,8 showed 7 to exist in a dynamic equilibrium between trans-7a and cis-7b conformers, with 7b prevailing. At low temperatures, the dynamic process could be frozen on the nuclear magnetic resonance (NMR) time scale and the NMR spectra exhibited separated resonances of the two conformers. The reported NMR studies involved isotopomers of 7 deuterated in various positions. Selective deuterations were performed to * To whom correspondence should be addressed. E-mail: dodziuk@ ichf.edu.pl or [email protected]. † Institute of Physical Chemistry, Polish Academy of Sciences. ‡ Institute of Organic Chemistry, Polish Academy of Sciences. § Technical University Braunschweig. # Present address: ICM, Warsaw University.

render both the static and dynamic 1H spectra amenable to interpretation with approximate methods.

In this paper, quantum chemical calculations of the structure and NMR parameters together with variable-temperature NMR studies of the perprotio isotopomer of 7 are reported. They are aimed at the possibility of obtaining complete characteristics of the solution structure of 7, of its NMR parameters, and of the interconversion of 7a and 7b. Because of the use of advanced methods of spectral analysis, fully quantitative interpretation of both the static and dynamic proton NMR spectra of 7 is conducted. In particular, not only the geminal but also all of the vicinal JHH values for the bridge protons are determined. For the first time, complete Arrhenius data for the interconversion process are reported. The experimental proton chemical shifts and coupling constants are in a good agreement with the values obtained from density functional theory (DFT) quantum chemical calculations. The rates of interconversion extracted from the spectra of the aromatic and aliphatic protons in 7 are

10.1021/jp106533n  2010 American Chemical Society Published on Web 09/03/2010

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Figure 1. Atom numbering in trans-[3.3]paracyclophane 7a (left) and cis-[3.3]paracyclophane 7b (right).

consistent, but in the latter case, the data cover a wider temperature range (220-275 K as opposed to 220-303 K). Because successful handling of the dynamic spectra of the aliphatic protons appears to exceed the capabilities of standard programs for line shape analysis, relevant details of our nonstandard procedure are described. Experimental and Computational Procedures Computational Method. Geometry optimization was performed using the Gaussian’03 molecular modeling package.9 Calculations were conducted using the GIAO DFT method9 with the B3LYP functionals and 6-311G(d,p), cc-pVDZ, and ccpVTZ basis sets. The NMR parameters were determined using Gaussian’03 for GIAO B3LYP and 6-311G(d,p), cc-pVDZ, and cc-pVTZ basis sets for the structures optimized at the same level. To enable a comparison of the computed chemical shifts with the experimental shifts, the isotropic screening constants of the 13 C nuclei (184.4 ppm) and protons (31.74 ppm) in TMS were calculated using the GIAO B3LYP/cc-pVTZ method for the structure optimized at the B3LYP/cc-pVTZ level of theory. NMR Measurements. All NMR experiments were conducted on a BRUKER DRX-500 Avance spectrometer with XWINNMR acquisition and processing software. The measurements were taken in CDCl3 (99.8% D atoms, Ag-stabilized). Variable-temperature (VT) one-dimensional (1D) 1H NMR spectra for 3.5 mg of 7 dissolved in 0.7 mL of CDCl3 were recorded with a relaxation delay sufficient to achieve a complete sample relaxation. Sample temperatures were measured with an accuracy of (1 K using a methanol chemical shift thermometer; the temperatures were kept stable within 0.1 K. Conventional 1D (1H and 13C) and two-dimensional (2D) (COSY, 13C-1H gHSQC, and 13C-1H gHMBC) spectra were recorded applying standard parameter sets and procedures, using a 5 mm triple broadband inverse probe (TBI) with a z-gradient coil. Nuclear Overhauser effect (NOE) measurements were performed using the DPFGSE-NOE 1D technique (Bruker’s “selnogp.3” pulse program). All 13C chemical shifts were read out from 1D spectra; the signal assignments were determined on the basis of 2D correlation spectra and NOE results. 1 13 1 J( C, H) coupling constants were read from the 1H-coupled 13 C NMR spectrum. One-bond 13C-13C coupling constants were read out from 13C satellites in the 13C{1H} spectrum measured at room temperature for a saturated solution of 7 in CDCl3, to achieve a high signal-to-noise ratio. Line Shape Analysis of NMR Spectra. “Static” Spectra. 1 H chemical shifts and, whenever possible, J(1H,1H) coupling constants were extracted from the 1H NMR static spectrum recorded at 208 K where interconversion of 7a and 7b is frozen on the NMR time scale. For this purpose, a home-written, line shape fitting procedure was used, designed to handle overlapping spectra of several differently populated species, where, in addition to chemical shifts, coupling constants, and natural line

widths, the population fractions can also be adjusted in an iterative process. Dynamic Spectra. As explained below, the proton systems in the aliphatic bridges of the two interconverting isomers of 7 could not be handled with commercial programs for line shape analysis. Thus, the dynamic 1H spectra were analyzed with a home-written program based on the conventional Liouville space approach, but employing unconventional concepts (more specifically, double cosets of molecular symmetry groups) in the description of spin exchange.10-12 Protons in the bridge are spincoupled only among themselves and form a six-spin system (AA′BB′CD). In different isomers, these systems will be denoted by different letters, A-D for 7a and E-H for 7b. The corresponding spin exchange scheme involves interconversions of four fictitious conformers or “permutamers”, AA′BB′CD and BB′ AA′DC for 7a and EE′FF′GH and FF′EE′HG for 7b, as shown in Figure 2. Because of the respective symmetries C2V and C2h, the bridges in 7a as well as in 7b are equivalent, and hence, each permutamer represents both bridges. In an exchange event, one of the bridges from, for instance, 7a, is converted into such a bridge in 7b with simultaneous interchange of the equatorial and axial proton positions (see Figure 1), while protons in the other bridge retain their positions, e and a, on conversion. Hence, in Figure 2, each such event is represented by two arrows coming out of the same permutamer of, for instance, 7a, and aiming at two different permutamers of 7b. In the Liouville space formalism, the feasibility of line shape calculations is critically dependent on the size of complex, nonHermitian matrices entering the line shape equation. For S ) 1 /2 spins, with a growing number, n, of interacting spins and that, N, of species engaged in exchange, the size increases roughly as N × 4n. In the calculations, the eigenvalues and eigenvectors of such “spectral matrices” are needed. Our own experience is that with the use of an advanced, double-precision diagonalization routine zgeev from the LAPACK library (http:// www.netlib.org/lapack/complex16/) exact evaluation of the eigenvectors is possible for such matrices up to dimensions of ∼300 × ∼300. To the best of our knowledge, the existing commercial programs for line shape analysis are based on the Stephenson and Binsch (SB) formalism employed once in their DNMR5 program.13 In such programs, interconversion of the aliphatic protons in 7 would have to be treated as an exchange among four (i.e., N ) 4) fictitious, six-spin “species”, as shown in Figure 2. In the standard basis of Liouville space, the relevant spectral matrix would be decomposed onto diagonal blocks, of which the largest would have dimensions of 1200 × 1200. In the SB approach, the block sizes could be reduced because of the conservation in the exchange process of Cs symmetry of the aliphatic protons. Specifically, the 1200 × 1200 block would be replaced with two subblocks, with dimensions of 192 × 192 and 432 × 432. Such a reduction in matrix size is still insufficient for the performance of line shape calculations.

Structure and Dynamics of [3.3]Paracyclophane

Figure 2. Exchange scheme for the aliphatic protons in 7 (see the text).

In our program, the use of double cosets of the relevant molecular symmetry groups in the description of spin exchange enables each of the interconverting species to be represented by only one of its permutamers.10 Interconversions of such representative permutamers may need to be described by several nuclear permutation schemes. In the case considered, instead of four, only two permutamers, for instance, AA′BB′CD and EE′FF′GH, are needed, interconverting according to two permutation schemes. Accordingly, instead of a 1200 × 1200 block, the largest block of the spectral matrix now has dimensions of 600 × 600. Conservation of Cs symmetry allows one to reduce its size and to ultimately replace it with two subblocks, with dimensions of 216 × 216 and 96 × 96, which renders the problem numerically tractable. In a recent approach to line shape calculations for exchanging many-spin systems, the Liouville formalism, so sensitive to the number of interacting spins, was not used.14-16 In that treatment, Monte Carlo simulations of the fates of the individual spin systems suffering sudden changes in their NMR Hamiltonians are performed. From the reported material, it is clear that the feasibility of such calculations is no longer so severely limited by the number of spins in the system. A still open question is how this novel approach will perform for systems like the aliphatic bridges in 7, where random trajectories of the individual spin systems must sample in a peculiar way as many as four different instantaneous configurations. Results and Discussion Geometry. The optimal structures calculated for all used basis sets give, within the accuracy level, close values of geometrical parameters of both isomers. Therefore, only the data calculated at the B3LYP/6-311G(d,p) level (for which the most accurate values of coupling constants were obtained) are presented in Figure 3 and compared with the available experimental values of bond lengths. The corresponding calculated values of bond and torsional angles for the trans and cis isomers of the titled compound are listed in Table 1. The calculated values of bond lengths and angles for all used basis sets for both isomers and the corresponding experimental values for the trans form are listed in Tables ESI-1 and ESI-2 of the Supporting Information. It should be stressed that the experimental structure of the trans conformer8 has a lower C2 symmetry than the calculated one, D2h. As mentioned in the Introduction, [3.3]cyclophane represents an intermediate case between highly strained [2.2]cyclophane and less strained cyclophanes with longer bridges. As we will discuss below, short bridges force nonplanar distortions of the aromatic rings and lengthening of some bonds while the proximity of the rings implies interactions of π-electron clouds in the molecule.

J. Phys. Chem. A, Vol. 114, No. 38, 2010 10469 The calculated distance between the aromatic rings, interconnected by the bridges, is very close in both isomers (3.238 and 3.243 Å for the trans and cis isomers, respectively) and is in a fair agreement with the experimental value of 3.137 Å determined for the first one in the solid state. Importantly, the calculated distance between the rings is smaller than the sum of the van der Waals radii of carbon atoms (∼3.4 Å). Thus, in agreement with expectation, in both isomers the cyclophane benzene rings are significantly deformed. The C2-C1-C6-C5 torsional angles in both isomers, characterizing nonplanar distortions of the aromatic rings, are equal to ∼8.0° for either isomer, regardless of the basis set used, and are in a good agreement with the experimental value of 7.0° for the trans one. In both isomers, the benzylic carbon atoms in the bridges lie close to the C2-C3-C5-C6 plane and the C13-C1-C4-C16 torsional angle is equal to 0.9°, 1.2°, or 0.6° at the 6-311G(d,p), cc-pVDZ, or cc-pVTZ level, respectively, in fair agreement with the experimental value of 2.4° for the trans conformer. The corresponding angle is equal to 0.0° in all basis sets used for the cis one. The calculated values of C13-C14 bond length [1.551 Å for the 6-311G(d,p) and cc-pVDZ basis sets and 1.548 Å for the cc-pVTZ basis set] are for both isomers slightly larger than the standard value of 1.533 Å for the unstrained hydrocarbons17 and considerably larger than the experimental C13-C14 and C14-C15 bond lengths of 1.537 and 1.525 Å, respectively, for the trans isomer. The experimental values of the C1-C13 and C4-C16 bond lengths are equal to 1.518 and 1.507 Å, respectively, while the values calculated at the B3LYP/6311G(d,p), cc-pVDZ, and cc-pVTZ levels are equal to 1.517, 1.518, and 1.513 Å, respectively. Thus, in agreement with expectation, almost all bridge bonds are elongated. Understandably, in both conformers, the calculated values of the C1-C2-C3 and C1-C6-C5 bond angles are equal to 121.2° for all used basis sets, and in agreement with the experimental values of 121.19° and 121.24° for the trans one, the value for the cis isomer is equal to 121.0° for the 6-311G(d,p) basis set and 121.1° for the other used basis sets. The calculated C2-C1-C6 angle is 117.3° for the trans (experimental values of 117.0° and 116.8°) and 117.4° for the 6-311G(d,p) basis set and 117.3° for the cis isomer for the other basis sets used. Characterization of cis-trans Interconversion in 7 on the Basis of VT NMR Spectra. Examples of VT 1H NMR spectra of 7 in the aliphatic region are shown in Figure 4. The experimental spectra are superimposed with theoretical ones obtained from iterative least-squares fits. The fits are virtually perfect. Fits to the aromatic proton spectra (not shown) are equally good. The spectrum at 208 K is a static superposition of contributions from 7a and 7b. It was analyzed with the static program mentioned above. The values of 1H chemical shifts and J(1H,1H) coupling constants determined in the static limit will be discussed later, together with the corresponding values involving carbon atoms and the calculated values of all NMR parameters. Equilibrium Constant. At 208 K, the [7b]/[7a] ratio (Kba) is 1.53, which is the average of the values of 1.55 and 1.51, obtained in the fits to the spectra of the aromatic and aliphatic protons, respectively. The value reported previously is equal to 2.0 at 185 K for a solution of 7 in a mixture of CDCl3 and CDCl2F.7 In CD2Cl2 solutions, when the isomer exchange is completely frozen on the NMR time scale, Sako et al. found the [7b]/[7a] ratio to depend on the concentration because, as a result of preferential crystallization of 7a, at 203 K its

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Figure 3. Experimental bond lengths and bond lengths calculated at the B3LYP/6-311G(d,p) level (in parentheses) for 7a and 7b.

TABLE 1: Experimental Bond and Torsional Angles and Those Calculated at the B3LYP/6-311G(d,p) Level trans-7a exptl Csp3Csp3Csp3 C13-C14-C15 Csp2Csp3Csp3 C1-C13-C14 C7-C14-C15 Csp2Csp2Csp2 C1-C2-C3 C1-C6-C5 C2-C1-C6 C3-C4-C5 C4-C5-C6

cis-7b calcd

trans-7a

calcd

116.8

118.2

118.2

113.6 115.9

115.2 115.2

115.1 115.2

121.6 121.2 116.8 117.0 121.4

121.2 121.0 117.3 117.3 121.2

121.0 121.1 117.4 117.4 121.1

concentration decreases nearly twice with a 5-fold increase in the concentration of 7.8 Above 210 K, 7a and 7b interconvert, leading to motional averaging of the resonances. In this range, the spectra were analyzed using the “dynamic” line shape program described in Experimental and Computational Procedures. In the analysis, the J coupling parameters were not optimized but fixed at the values obtained from the static spectra at 208 K. Apart from the rate constant kba of interconversion of 7b into 7a, the equilibrium constant Kba could be extracted from spectra up to 235 K. The values of Kba decrease slightly with temperature

Csp3Csp2Csp2Csp3 C13-C1-C4-C16 Csp2Csp2Csp2 Csp2 C1-C2-C3-C4 C3-C4-C5-C6 C2-C3-C4-C5 C2-C1-C6-C5

cis-7b

exptl

calcd

calcd

2.4

0.9

0.0

1.0 1.1 7.1 7.0

0.9 0.8 8.5 8.5

0.0 0.0 8.0 8.0

(decreasing to 1.46 at 235 K). The value of 1.53 at 208 K, obtained from the static spectra, essentially fits the trend. A leastsquares fit of the van’t Hoff equation to these values from the range of 208-235 K, assuming a ∆Sba of 0, delivers an enthalpy difference ∆Hba of 0.17 kcal/mol, where the standard error is on the third decimal digit. Thus, in a CDCl3 solution for the concentration of 7 as given in Experimental and Computational Procedures, preferential crystallization of 7a is not observed even if the solvent is slightly overcooled (freezing point of CHCl3 being 209.7 K).

Figure 4. VT 1H NMR spectra of 7 in the aliphatic region superimposed with theoretical spectra obtained from iterative least-squares fits. The fits are virtually perfect to such an extent that some differences between the experimental and theoretical lines are visible only for the impurity signals in the 2.2-2.3 ppm region.

Structure and Dynamics of [3.3]Paracyclophane

Figure 5. Arrhenius plot for the values of kab in 7. Over the range from 220 to 275 K, arithmetic averages of the values extracted from the aromatic and aliphatic proton spectra are given. The straight line corresponds to an Ea of 12.29 ( 0.08 kcal/mol and a kba0 of (9.6 ( 4.5) × 1012 s-1.

For all basis sets and functionals used, the calculated energy difference between the cis and trans conformers of 7 is equal to ∼0.25 kcal/mol in favor of the cis form, in fair agreement with the evaluation based on the VT NMR spectra. Interestingly, experimentally it is the trans isomer that crystallizes.6 InterconWersion Dynamics. In the 210-235 K range, apart from kba and Kba, the chemical shifts of the individual protons could also be extracted from the spectra. The observed temperature trends of the chemical shifts are fairly linear. In the fits to the spectra above 235 K, linearly extrapolated values of these parameters were used and not optimized. Similarly, the values of Kba were extrapolated using the van’t Hoff equation. These extrapolations were necessary for obtaining possibly unbiased estimates of the interconversion rate constant also above 235 K. As shown in Figure 4, the line shape fits also remain perfect in this temperature range. Over the whole range from 220 to 303 K, the delivered values of kba show linear behavior in Arrhenius coordinates, as shown in Figure 5. Of the Arrhenius parameters determined here [EA ) 12.29 ( 0.08 kcal/mol and kba0 ) (9.6 ( 4.5) × 1012 s-1], the energy of activation fairly compares with the previous assessments of the free energy of activation (∆Gq of 12.0 kcal/mol at 258.2 K in a CD2Cl2 solution8 and 11.7 ( 0.5 kcal/mol at 243.2 K in a toluene-d8 solution,7 both obtained from coalescence temperatures of the apparent J-coupled AB patterns of the benzylic protons in 7 deuterated selectively at positions 14 and 17). Such an agreement is presumably due to the fact that in both isomers of 7 the chemical shift difference of ∼0.6 ppm between the benzylic protons at the a and e positions is substantially greater than that between the benzylic proton positions a in 7a and 7b (ca. -0.014 ppm) and e in 7a and 7b (ca. 0.012 ppm). With such a pattern of chemical shift differences, at coalescence temperatures the observed signals are essentially populationweighted averages of the resonances of protons at positions a and e in 7a and 7b. Noteworthy is the fact that the ∆Gq values evaluated in this way represent neither the forth nor back processes, but a combination of both. These results have a welldefined meaning and for the first time describe the interconversion of 7b into 7a in a complete way.

J. Phys. Chem. A, Vol. 114, No. 38, 2010 10471 NMR Parameters. The 1H and 13C chemical shift values calculated for 7a and 7b are listed in Table 2 together with the corresponding experimental data. The values for all used basis sets are given in Table ESI-1 of the Supporting Information. The signals assigned in this work agree with those of Sako et al.8 The experimental and calculated nJHH, 1JCH, and 1JCC coupling constants are listed in Tables 3-5, respectively. The 3 JHH data are presented together with theoretical values of the corresponding torsional angles. Complete results of coupling constant calculations are listed in Tables ESI-2-ESI-4 of the Supporting Information. The calculated values of all NMR parameters for all used basis sets reflect geometrical symmetries of the 7a and 7b isomers. 1 H Chemical Shifts. The values of proton chemical shifts calculated using all basis sets mentioned in Experimental and Computational Procedures are very close to each other and reproduce satisfactorily the experimental results. With regard to the experimental values of chemical shift differences between the 7a and 7b isomers, the only considerable one of 0.112 ppm was obtained for the H14a and H17a bridgehead protons. 13 C Chemical Shifts. The experimental shifts are best represented by the theoretical values obtained using the ccpVDZ basis set. These values are consistently smaller than the experimental ones. The results obtained for the 6-311G(d,p) basis set are very similar to those for the cc-pVTZ basis set and are consistently larger than the experimental values. For all basis sets, the calculated values exhibit the same trend as the experimental results. Carbon chemical shifts for the 7a and 7b conformers are very close. Understandably, the largest difference of 0.5 ppm was obtained for the C14 and C17 bridgehead atoms. Coupling Constants. As mentioned above, experimental JHH coupling constants were determined by line shape analysis. For the aliphatic protons, not only the geminal but also all of the vicinal coupling constants could be extracted from the static spectrum at 208 K. Of the long-range (i.e., across four bonds) coupling constants, only those between proton e of C13 and proton e of C15 (or C16 and C18) are significantly different from zero, which is typical for planar or nearly planar zigzag arrangements of the paths of formal bonds connecting these protons. For the aromatic protons, all of the coupling values could be extracted only for 7a; for 7b, the two potentially different values of Jortho could not be determined. In the fits, they were assumed to be equal and fixed at 8.20 Hz, the value obtained for 7a. This assumption does not significantly influence the values of other coupling constants determined by the procedure. For all used basis sets, all calculated values of 1J and 3J coupling constants are positive for both isomers while most of those through two bonds are negative. The 1JCC and 1JCH values for carbon atoms of the benzene ring, calculated for the 6-311G(d,p) basis set, are close to the values obtained for the cc-pVTZ basis set. 1J values exhibit the same trend in all used basis sets. The long-range (i.e., across four bonds) JHH coupling constants between protons at C13 and C15 (and C16 and C18), with the zigzag arrangnment of the mediating bonds, could not be reproduced at the theoretical levels presently tested. In Table 3, the JHH values obtained from line shape fits are compared with the values calculated at the 6-311G(d,p) level. These are most close to the experimental data, a fact that also holds true for the theoretical 1JCH (Table 4) and 1JCC (Table 5) values. Like the chemical shifts, most experimentally determined values of coupling constants of both isomers are very close. Understandably, the largest differences of 0.7 Hz have been

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TABLE 2: Experimental 1H and 13C Chemical Shifts (parts per million) and Those Calculated at the cc-pVDZ Level for trans and cis Isomers of 7 trans-7a C1, C4, C7, C10 C2, C5, C8, C11 C3, C6, C9, C12 C13, C15, C16, C18 C14, C17 H2, H5, H8, H11 H3, H6, H9, H12 H13a, H15a, H16a, H18a H13e, H15e, H16e, H18e H14a, H17a H14e, H17e a

cis-7b

exptlc

exptl a

calcd

138.9 128.7 131.5 35.9 29.3 6.74 6.63 2.36 2.99

138.2 128.0a 130.9a 35.5a 29.2a 6.735b 6.630b 2.360b 3.021b 2.074b 2.036b

exptl

131.0 120.3 122.7 31.9 27.1 7.14 6.98 3.35 2.49 2.35 2.24

C1, C4, C7, C10 C2, C3, C8, C9 C5, C6, C11, C12 C13, C15,C16, C18 C14, C17 H2, H3, H8, H9 H5, H6, H11, H12 H13a, H15a, H16a, H18a H13e, H15e, H16e, H18e H14a, H17a H14e, H17e

a

138.3 128.2a 130.9a 35.7a 29.7a 6.775b 6.617b 2.374b 3.009b 1.962b 2.053b

exptlc

calcd

139.0 128.9 131.6 36.1 29.3 6.78 6.62 2.38 2.98

131.0 120.1 122.9 32.2 27.3 6.94 7.16 2.31 2.33 2.25 2.23

Readout from the 13C{1H} spectrum measured at ∼210 K. b From line shape analysis. c From ref 8.

TABLE 3: Experimental JHH Coupling Constants (in hertz) and Those Calculated at the B3LYP/6-311G(d,p) Level through Two to Five Bonds for the trans and cis Isomers of 7a and the Difference between the Corresponding Experimental Values of the Constants for the cis and trans Isomers trans-7a exptl

calcd

-14.36b (-)14.2c -14.51b

-13.06

cis-7a torsional angle 2

H13a-C13-H13e H14a-C14-H14e

JHH

-13.30

torsional angle

∆Jexpt1(cis-trans)

exptl

calcd

-13.90b (-)13.9c -14.32b

-12.95

0.46

-13.28

0.19

8.20d

7.11

0.0

0.04

8.20d 2.64 13.13 4.81 2.94

6.69 2.47 11.18 4.78 2.83

0.0 65.8 179.8 48.7 65.3

0.04 0.05 0.36 0.45 -0.30

1.35 2.61

2.84 0.15

-0.15 -0.72

1.86

0.33

-0.71

3

8.16b 7.8c 8.16b 2.42b 12.77b 4.36b 3.24b

6.93 2.50 11.22 4.72 2.90

H2-C2-C1-C6-H6 H13e-C13-C14-C15-H15e

1.50b 3.33b

1.31 0.17

H2-C2-C1-C6-C5-H5

2.57b

0.37

H2-C2-C3-H3 H5-C5-C6-H6 H13a-C13-C14-H14e H13a-C13-C14-H14a H13e-C13-C14-H14e H13e-C13-C14-H14a

JHH 0.3

6.93

65.5 179.5 48.9 65.0 4

5

JHH

JHH

a For n > 3, the data are given only in the instances where experimental values are known. b From line shape analysis; at convergence, the J coupling values are delivered with the same signs as assumed for the approximate input values. c Values from ref 9, with the sign added. d Assumed values (see the text).

TABLE 4: Experimental JCH Coupling Constants (in hertz) and Those Calculated at the B3LYP/6-311G(d,p) Level for the trans and cis Isomers of 7 trans-7a exptla,b

cis-7b exptla,b

calcd 1

C2-H2 C3-H3 C13-H13a C13-H13e C14-H14e C14-H14a

155,a 157,a 125,a 125,a 127,a 127,a

156.5b 156.5b 125.3b 125.3b 126.5b 126.5b

C14-C13-H13a C14-C13-H13e

(-)4.5b,c (-)4.5b,c

JCH

146.3 144.7 121.6 121.5 122.9 121.5 2

-3.6 -3.5

calcd

C2-H2 C5-H5 C13-H13a C13-H13e C14-H14e C14-H14a

154,a 157,a 125,a 125,a 127,a 127,a

156.5b 156.5b 125.3b 125.3b 126.5b 126.5b

C14-C13-H13a C14-C13-H13e

(-)4.5b,c (-)4.5b,c

JCH

144.6 146.4 121.5 121.6 121.6 123.0 -3.6 -3.5

a Readout, with the accuracy of (1 Hz, from the proton-undecoupled 13C spectrum recorded at ∼210 K. b Exchange-averaged values read out from the proton-undecoupled 13C room-temperature spectrum. c The signs of the experimental 2JCH values have not been determined.

obtained for the long-range 4JHH constants (H13e-C13-C14C15-H15e) and 5JHH constants (H2-C2-C1-C6-C5-H5). Differences of >0.4 Hz were also observed for 2JHH (H13aC13-H13e) and 3JHH (H13e-C13e-C14e). Unfortunately, the calculated values do not reproduce these trends.

Within the accuracy with which the 1JCH and 1JCC coupling constants could be measured ((1 Hz), both geometry distortions of the aromatic rings and other internal strains in isomers 7a and 7b are not displayed in the experimental values of these quantities. For instance, the 1JCC value of 58 Hz for the C1-C2

Structure and Dynamics of [3.3]Paracyclophane

J. Phys. Chem. A, Vol. 114, No. 38, 2010 10473

TABLE 5: Experimental 1JCC Coupling Constants (in hertz) and Those Calculated at the B3LYP/6-311G(d,p) Level for the trans and cis Isomers of 7 trans-7a exptl C1-C2 C1-C6 C2-C3 C5-C6 C1-C13 C13-C14

58 58 44 34

a

cis-7b

calcd 64.3 65.1 65.9 65.9 45.1 34.6

C1-C2 C1-C6 C2-C3 C5-C6 C1-C13 C13-C14

exptla

calcd

58 58

63.8 65.5 67.0 64.9 45.1 34.6

44 34

a Exchange-averaged J values read out from 13C satellites at a high signal-to-noise ratio, 13C{1H} room-temperature spectrum of a saturated solution of 7 in CDCl3.

bond is close to the one-bond C-C coupling in benzene, 57.0 Hz, and the 1JCC value of 44 Hz for the C1-C13 bond is almost equal to 44.2 Hz, the value for the C1-Cmethyl bond in toluene.18 The value of 34 Hz for the C13-C14 bond can be compared with that of 34.6 Hz in ethane.18 As discussed below, for the vicinal JHH values in the strained aliphatic bridges, the situation is essentially similar. In Table 3, these vicinal coupling values are presented in relation to the theoretical dihedral angles between the corresponding C-H bonds. It may be of interest to compare the experimental J values with the predictions of the Karplus equation19 in its canonical parametrization by Haasnoot et al.20 For 7a and 7b, the root-mean-square deviations between the experimental vicinal couplings and the values calculated from the theoretical dihedral angles of Table 3 are 0.56 and 0.42 Hz, respectively. These deviations are close to that of 0.5 Hz reported by Haasnoot et al.20 for a large collection of data. In that collection, compounds with low internal strain must prevail. Therefore, of some significance may be the fact that the deviation is smaller for the isomer 7b, which in solution is less strained than 7a. Conclusions Quantum chemical calculations at a DFT level using Gaussian’03 confirm that [3.3]paracyclophane 7 is a considerably strained hydrocarbon containing nonplanar benzene rings. Exact VT NMR studies confirm that, at variance with the solid state where only the trans 7a conformer occurs, in chlorophorm solution the other conformer, cis-7b, is present and prevails. Below 210 K, a dynamic equilibrium between the isomers is frozen on the NMR time scale. Advanced line shape analysis methods afforded for the first time a fully quantitative interpretation of the VT proton spectra of 7 in the regime of frozen exchange and in the dynamic range. Accurate values of practically all proton-proton coupling constants, proton chemical shifts, and temperature-dependent values of both the equilibrium constant and the interconversion rate constant are evaluated in this way over broad temperature ranges. From these temperature dependencies, for the first time both the enthalpy difference (∆Hba ) 0.17 kcal/mol) and the Arrhenius parameters (EA ) 12.29 kcal/mol, and kba0 ) 9.6 × 1012 s-1) for the conversion of 7b to 7a are determined. It may be somewhat surprising that the experimental JHH, 1JCH, and 1JCC values fall

in ranges typical for “unstrained” aromatic and aliphatic hydrocarbons, despite the significant nonplanarity of the benzene rings and strain in the aliphatic bridges in 7. For 7a and 7b, only the accurately measured values of JHH coupling constants exhibit significant differences, which may reflect the different internal strain in these isomers. Although these differences proved to be too small to be reproduced at the theoretical levels explored here, the experimental NMR parameters are generally in fair agreement with the theoretical values obtained using the cc-pVDZ basis set for chemical shifts and the 6-311G(d,p) and cc-pVTZ basis sets for coupling constants. Acknowledgment. H.D. and M.E.M. received financial support from Grant 204 3752 33 for the research project from 2007 to 2010. We thank the Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw (Warsaw, Poland), for Computational Grant C28-7. Supporting Information Available: Additional experimental and calculated results. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Dodziuk, H.; Ostrowski, M.; Ruud, K.; Jaz´win´ski, J.; Hopf, H. Magn. Reson. Chem. 2009, 47, 407–414. (2) Dodziuk, H.; Ostrowski, M. Eur. J. Org. Chem. 2006, 5231. (3) Hopf, H. In Strained hydrocarbons. Beyond Van’t Hoff and LeBel hypothesis; Dodziuk, H., Ed.; Wiley-VCH: Weinheim, Germany, 2009. (4) Gleiter, R., Hopf, H., Eds. Modern Cyclophane Chemistry; WileyVCH: Weinheim, Germany, 2004. (5) Bickelhaupt, F. Pure Appl. Chem. 1990, 62, 373. (6) Gantzel, P. K.; Trueblood, K. N. Acta Crystallogr. 1965, 18, 958. (7) Anet, F. A. L.; Brown, M. A. J. Am. Chem. Soc. 1969, 91, 2389– 2391. (8) Sako, K.; Meno, T.; Takemura, H.; Shinmyozu, T.; Inazu, T. Chem. Ber. 1990, 123, 639–642. (9) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Lyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian’03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (10) Szymanski, S. Mol. Phys. 1985, 55, 763–798. (11) Szymanski, S.; Binsch, G. In Annual Report on NMR Spectroscopy; Webb, G. A., Ed.; Academic Press: London, 1990; Vol. 23, pp 209-288. (12) Szymanski, S. J. Magn. Reson., Ser. A 1994, 108, 151–159. (13) Stephenson, D. S.; Binsch, G. J. Magn. Reson. 1978, 32, 145–152. (14) Szalay, Z.; Rohonczy, J. J. Magn. Reson. 2008, 191, 56–65. (15) Szalay, Z.; Rohonczy, J. J. Magn. Reson. 2009, 197, 48–55. (16) Szalay, Z.; Rohonczy, J. J. Magn. Reson. 2010, 197, 48–55. (17) Vilkov, L. V.; Mastryukov, V. S.; Sadova, N. I. Determination of the geometrical structure of free molecules; Mir: Moscow, 1978; p 75. (18) Krivdin, L. B.; Kalabin, G. A. Prog. Nucl. Magn. Reson. Spectrosc. 1989, 21, 293–448. (19) Karplus, M. J. Am. Chem. Soc. 1963, 85, 2870–2871. (20) Haasnoot, C. G. A.; De Leeuw, F. A. A. M.; Altona, C. Tetrahedron 1980, 36, 2783–2792.

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