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Interconversion Study in 1,4-Substituted Six-Membered Cyclohexane-Type Rings. Structure and Dynamics of trans-1,4-Dibromo-1,4-dicyanocyclohexane Alex D. Bain,*,† Maximo Baron,‡ Steven K Burger,† Valdemar J. Kowalewski,§ and Marina Belen Rodríguez‡ †
Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada Facultad de Ciencias Exactas y Naturales, Universidad de Belgrano, Villanueva 1324, 1426 Buenos Aires, Argentina § Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Pabellon 1, Ciudad Universitaria, 1426 Buenos Aires, Argentina ‡
bS Supporting Information ABSTRACT: Cyclohexane is an extremely flexible molecule that oscillates, at room temperature, between two clearly distinct and extreme conformations that cannot be distinguished at room temperature; so much so that the NMR spectrum is a single line that includes all 12 protons be they axial or equatorial. This raises the interesting question as to what happens when there are equal substituents at the 1 and 4 carbon atoms of the ring. Therefore substitution in the 1,4-positions in the cyclohexane ring has been the subject of considerable interest because some form of interconversion between extreme conformations could lead to the existence of a rather unusual behavior. To study this problem, the interconversion in (di- or tetra-1,4)-substituted six-membered cyclohexane-type rings, trans-1,4-dibromo-1,4-dicyanocyclohexane, was found to be a particularly suitable candidate. Although X-ray diffraction studies on the crystalline solid found the molecule to be centrosymmetric, it still shows a significant dipole moment μ in solution, as determined with a procedure that leads to the vapor phase values of μ. Furthermore, the low magnetic field proton NMR spectrum at ambient temperature appears as a single line, a situation that changes with increasing field intensity and different solvents. Both these effects are attributed to dynamics, because small distortions can easily disrupt the exact cancellation of the individual dipoles (which are quite strong) associated with each end of the molecule. The molecule can exist in two forms, with both the bromines in an axial geometry or both in an equatorial position. Interconversion between these forms is observed, as in the parent cyclohexane. The single NMR line observed at low magnetic fields is due to fast exchange and requires that the two forms have roughly equal populations. Spectra obtained at low temperature confirm this, and variable-temperature studies allow measurement of the rates, leading to an enthalpy of activation of 62 kJ mol1. More details of the interconversion are provided by some new calculation methods. Even for a relatively small molecule like this, calculation of a full potential energy surface is prohibitive. However, methods are now available to follow the molecule along the reaction coordinate in quite an efficient way. The results of these calculations lead to an extremely detailed picture of chairchair interconversion in a diand tetrasubstituted six-membered ring of the cyclohexane family.
’ INTRODUCTION In the chair form of cyclohexanes, the hydrogens or other substituents on the ring can be of two types: axial or equatorial.1 The ring is quite flexible, so many substituents can be accommodated without excessive crowding. Any particular molecule will have a specific conformation, and there is an extensive literature on rationalizing these stereochemical preferences.27 Furthermore, the ring is often flexible enough that it can readily interconvert from one chair form to another.814 This process takes a group in an axial position and puts it in an equatorial position in the new chair form and vice versa. The parent molecule, cyclohexane, undergoes this interconversion quickly enough at room temperature that the proton NMR spectrum shows a single line, especially at 60 MHz. The axial and equatorial protons are rendered magnetically equivalent by this fast exchange process, as has been described in detail.15 Indeed, NMR has been a major tool in the study of the dynamics of cyclohexane rings,11 but even if the fundamentals are well-known, there are still a number of interesting and challenging systems to be examined. r 2011 American Chemical Society
Interconversion in cyclohexane itself has been thoroughly studied. This reaction starts from the chair form and proceeds through a transition state to a twist-boat intermediate. By symmetry, the reaction then goes through the same transition state to the flipped chair form. However, there is little detailed information about the more important substituted systems. How much do perturbations change the familiar picture? The molecule trans-1,4-dibromo-1,4-dicyanocyclohexane (Figure 1) was considered to be a good candidate for this kind of investigation. The basic reaction is the same, but there are two different ground states, and two transition states. As well, it has a number of interesting and unexpected properties which have remained in the literature without explanation for a long time. Modern computers and advanced NMR spectrometers now permit revisiting this system, partly as a structural and spectroscopic Received: June 8, 2011 Revised: July 22, 2011 Published: July 25, 2011 9207
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Figure 1. trans-1,4-Dibromodicyanocyclohexane.
problem but also as a framework for studying the details of the important chairchair interconversion in di- and tetrasubstituted six-membered cyclohexane-type rings. Also of particular interest is the possibility to calculate the strongly coupled NMR spectra and compare the experimental spectra with the simulated ones. The first somewhat-unexpected observations were a substantial nonzero dipole moment (μ = 1.05 ( 0.02 D) and a single NMR peak, at 60 MHz16 (Figure 2a). This was also observed more recently at 330 K and 500 MHz (Figure.2b). The single peak at 60 MHz was later attributed, as a result of theoretical calculations,17 to the significant presence of interconverting conformers. This appeared to be confirmed by the 500 MHz NMR spectrum. To these intriguing results was added the fact that in the solid state the molecule is centrosymmetric.18 NMR spectra at 100 MHz of the molecule around room temperature are still less than enlightening, as can be seen in Figure 2c. This made it necessary first to increase the magnetic field (to 300 and 500 MHz) to see fine structure and protonproton couplings and second to find a solvent that would enable to work at temperatures low enough to see possible interconversion (acetone and toluene). All these conflicting facts raise a number of questions. Is the conformation in the crystalline solid the same as in solution? If this is not the case what are the details of the dynamics? Are the Br and CN substituents axial or equatorial? What causes the observed nonzero dipole moment? How does this molecule fit into the family of six-membered rings? Why are the answers to these questions important? The six-membered chair-form cyclohexane-type ring is a fundamental substructure in chemistry. It is the smallest ring that will accommodate all singly bonded atoms in their natural tetrahedral geometry. The interconversion between the two extreme conformations, or isomerization, in cyclohexane has been studied under various conditions of temperature, pressure, and in solution both theoretically through molecular dynamics and simulations as well as experimentally.1921 Therefore we consider that it is of interest to examine the behavior of substituted cyclohexanes, especially with the substituents on carbons 1 and 4 because some resemblance regarding interconversion could be expected, similar to what has been found in the parent cyclohexane. The reason for this is that calculations of structure, reactions paths, and transitional states of this particular compound would allow us to compare behavior with the parent cyclohexane and open interesting possibilities toward understanding the behavior of similar structures with other substituents in the same positions. This small six-membered ring has excellent stability, so it occurs in many organic molecules,1,2,22,23 perhaps most famously in steroids.24,25 Heteroatoms do not disturb this stability very much, so carbohydrates in their pyranose ring forms, with one oxygen atom in the ring, also adopt chair conformations,2629 and there are many more examples.3041 Common network solids, such as diamond, quartz, and silicon carbide,42,43 are also based on tetrahedral coordination, so the structures can be viewed as fused
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six-membered rings. This is a small sample of the vast literature on these six-membered ring systems. Although from the cited available information the interconversion, at room temperature and pressure, between two extreme conformations in cyclohexane-like molecules is a general situation, it has not been studied in detail for other molecules than cyclohexane. Consequently the present molecule, trans-1,4-dibromo-1,4-dicyanocyclohexane, can provide further information about the details of the exchange process in a six-membered ring. As in cyclohexane, the reaction goes through a twist-boat intermediate, but the two transition states on either side of the intermediate will not be the same. One transition state leads from the intermediate to the final form in which the bromines are axial, whereas the other transition state leads to the form with the bromines equatorial. The molecule is small enough to make good electronic structure calculations possible, so the experimental data can be enhanced with calculations of structures along the reaction path. Stationary points along the reaction coordinate for six-membered rings have been calculated,23,36 but even for a relatively small molecule such as this, a full potential energy surface, giving more details about the trajectory, is out of the question.29,41 In this paper we calculate the progress of the molecule all along the reaction coordinate by applying recent theoretical methods.4446 It was expected that this would give us a picture of chairchair interconversion with unprecedented detail. To address the above-mentioned questions, the availability of NMR techniques involving 300 and 500 MHz instruments, additional dipole moment determinations, recent methods for electronic structure studies, and advanced NMR simulation programs have opened the possibility to a more complete examination of the unusual behavior of this molecule.
’ EXPERIMENTAL SECTION The dipole moments were determined at two temperatures (298 and 308 K) by a previously described procedure,17,47,48 using CCl4 as solvent, in a newly developed instrument.49 A nonpolar solvent is essential here and CCl4 was used because, from previous experience,16 it appeared to interact less with the solute, as was the case with benzene. Solvent permittivities (ε1), solvent and solute densities (d1 and d2 in g mL1), solute refractive index (n2), solute p/p concentration, and solution permittivities (ε12) are shown in Table 1. NMR spectra of this system (Figure 2) were taken at a number of magnetic fields in a number of solvents. Most showed effectively a single line near 300 K, with the exception of 300 MHz spectra in DMSO. In this case, the solvent appears to affect the spectrum significantly. The 500 MHz spectra of a sample dissolved in toluene-d8 (at temperatures from 230 to 298 K (Figure 4) and in acetone-d6 at 228 K (Figure 5) were obtained on a Bruker Avance 500 MHz NMR spectrometer equipped with a 5 mm inverse-geometry room temperature probe. NMR spectra were obtained first at room temperature (∼300 K) to see if there is any significant solvent influence. To this effect benzene-d6 and acetone-d6 were used, at 60 and 100 MHz. In both cases either a single peak (at 1.58 and 1.69 ppm at 60 MHz in both solvents) or a closely packed multiplet (sextuplet in fact, centered at 1.82 ppm at 100 MHz in benzene-d6) were observed. A single peak was also observed at 2.35 ppm in pyridine-d5. These results suggested that different solvents at low magnetic fields 9208
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Figure 2. Proton NMR spectra of trans-1,4-dibromodicyanocyclohexane at or near 300 K: (a) spectrum at 60 MHz; (b) spectrum at 500 MHz in toluene-d8 at 330 K; (c) spectrum at 100 MHz in pyridine-d5; (d) spectrum at 300 MHz in DMSO-d6. The peaks centered at 2.50 ppm are from residual protons in the solvent. The upper spectrum is a simulation.
were unable to show any fine structure indicating the need to proceed at higher fields.
At higher fields in these and other solvents, at substantially room temperature, the spectra showed notable differences at 9209
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Table 1. Data Used in the Dipole Moment Calculations temp, K
ε1
d1
d2
n2
concn (p/p)
ε12
μ (D)
298
2.2279 1.58439 1.7544 1.53992
0.00158
2.2296 0.59 ( 0.02
308
2.2079 1.5840
0.00493
2.2197 1.50 ( 0.02
1.7544 1.5342
Table 2. Spin Parameters Used in Simulation of the 500 MHz Proton Spectrum in Figure 7ba bromine eq νA
789
741
νB
676
575
3
12.0
12.0
2
JAB 3 JAB0
16.0 3.0
16.0 3.0
3
4.0
4.0
JAA0
JBB0
a
bromine ax
All values in Hz.
Figure 4. Experimental 500 MHz proton NMR spectra of trans-1,4dibromodicyanocyclohexane in toluene-d8 as a function of temperature (on the left of each spectrum).
Figure 3. Simulated spectra at 60 (a) and 100 MHz (b).
500 MHz. In both Figures 4 and 5 it can be seen that the relative amounts of both conformers are almost the same. NMR spectra were then obtained at room temperature in DMSO-d6, acetoned6, and toluene-d8. While the latter two solvents at 500 MHz
showed single peaks at 1.4 and 1.54 ppm, respectively, the former at 300 MHz showed two sets of quadruplets centered at 2.43 and 2.63 ppm, respectively. The two sets are substantially identical with a small difference in intensities. Although this will be discussed later in detail, it can now be anticipated that the low field group corresponds to all equatorial protons while the high field group corresponds to the axial ones. This assignment can be done on the basis of the NMR spectrum of trans-1,4-dicyanocyclohexane,16 wherein the axial protons on carbons 1 and 4 appear as a 15 Hz broad signal with a peak at 2.28 ppm in acetone-d6, 2.5 ppm in benzene-d6 and pyridine-d5, and 2.78 ppm in CDCl3. These results clearly suggest that there is an influence of the solvent on the NMR spectra of this type of compounds. Since acetone and toluene appeared to be good solvents for this compound and can be used for low temperature studies, NMR spectra were obtained in both solvents at temperatures 9210
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Figure 5. Experimental 500 MHz proton NMR spectra of trans-1,4dibromodicyanocyclohexane in acetone-d6 at 230 K.
between 228 and 298 K (Figures 4 and 5). The spectra were not integrated, because the shapes of the traces are quite clear and they could be simulated by the Mexico program.50 They show that in DMSO-d6, acetone-d6, and toluene-d8 the signals of both axial and equatorial hydrogen atoms are similar. The simulations of the static NMR spectra were obtained with the SpinWorks 3.1 program (http://www.umanitoba.ca/chemistry/nmr/spinworks/) using chemical shift and J-coupling values, such as those shown in Table 2, that were obtained from experimental spectra. All these values were used in the various simulations since the program easily allows us to do this by changing the values of the spectrometer frequency (60 and 100 MHz are shown in Figure 3). High-level calculations of the structure in the two ground states, the twist-boat intermediate and the two transition states were carried out with the Gaussian03 program at the B3LYP/ 6-311++G(3df,2p) level of theory. The two transition states obeyed the rule that only one vibrational frequency was negative.
’ DISCUSSION Structure and Dipole Moments. The structure of trans-1,4dibromo-1,4-dicyanocyclohexane can now be described as a result of the experimental findings. The molecule, in the crystalline solid, possesses an inversion center, so it should have a zero dipole moment, but measurements gave a value of 1.05 D at 298 K in benzene solution.49 Determinations in CCl4 at two temperatures (298 and 308 K) not only confirmed this value but also showed a distinct increase in the μ value (from μ = 0.59 D to μ = 1.50 D) indicating the existence of orientation polarization, which can only arise from the absence of a center of symmetry. The difference observed in the μ values when determined in benzene and CCl4 solutions at 298 K is not unexpected because it has been observed previously in trans-1,4-dicyanocyclohexane (μ(C6H6) = 0.49 ( 0.02 D; μ(CCl4) = 0.27 ( 0.02 D).16 On the other hand the substantial increase in the dipole moment value in a temperature range of only 10 K is by no means unexpected: a detailed examination of the literature51 indicates clearly that this is a quite general phenomenon, with even large differences in as little as a 5 K increase in temperature. At this point it should be
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remembered that the dipole moment calculations with the BaronMechetti47 equation leads to the vapor phase values of the dipole moment so that any solvent effects can be disregarded in this determination. The electronic semiempirical structure calculations with the AMPAC program indicated that although there is a center of symmetry both in the ground state conformations and in the metastable intermediate, there is a twisted nonsymmetric ground state conformation.17 A symmetric state means a zero dipole moment, but only because the relatively large local dipoles at each end of the molecule exactly cancel out. Calculations on 2-bromo-2-cyanopropane, a model of half the molecule, indicate a dipole of almost 4 D. A misalignment of less than 10° would cause two opposing 4 D dipoles to give a net 1 D dipole moment. The calculations suggest that there are close to 10 vibrations with energies of less than 200 cm1, so there is ample scope for these symmetrybreaking motions, suggesting an explanation of our experimental determinations. The question of the ground-state geometry is still open. The surprisingly large dipole moment suggests an asymmetry, but the calculations point to a symmetrical ground state. In either case, the molecule is very flexible, so what we see is an average over an ensemble of geometries, symmetrical and not. This matter of a possible orientation polarization as the cause of a nonzero dipole moment in apparently centrosymmetric molecules has received considerable attention over the years and it has even been claimed to originate in an abnormally high atom polarization.52 If the latter would be the case, there should be no change in the dipole moment value with temperature but our experimental results show a very different picture with a clear increase in the value of μ. Therefore the substantial increase in the dipole moment value is a clear indication of the absence of centrosymmetry in this molecule. The crystal structure of this molecule has been determined and published.53 It was found that the cyano groups are axial in the crystal and the bromines are equatorial, suggesting that the bromo group is bulkier. Studies on the 1,4-dihalogenocyclohexane derivatives, with just two identical groups trans to each other, reveal only a small preference for axial over equatorial positions.2,5456 The A value57 for a bromo substituent is approximately 2 kJ mol1, and for a cyano it is about 0.8 kJ mol1. Favorable dipolar interactions are the basis of the rationalization of the fact that a bulky, but polar, substituent like bromine will readily adopt an axial position. NMR Spectroscopy. There are two possible conformations: one with the two bromines equatorial (and the cyano groups axial) and the other with the bromines axial. If either conformation dominated, then the NMR spectrum would be expected to show separate signals for the axial and equatorial protons, an AA0 BB0 system even in fast exchange. This is probably the reason that the DMSO-d6 spectra (Figure 2d) shows such a pattern. The fact that we see one line in the other solvents implies not only dynamics but also the populations of the two conformers must be similar. If the populations were exactly equal, all the NMR parameters would be averaged and a single line would be observed, as in cyclohexane itself. The structure is probed by running the NMR spectra at low temperature in toluene-d8 and acetone-d6, where the exchange is frozen out (Figures 4 and 5). In toluene-d8 at low temperatures (
