J . Phys. Chem. 1985, 89, 258-261
258
Multinuclear NMR Relaxation Studies of Crown Ethers and Alkali Cation Crown Ether Complexes Bertil Eliasson, Department of Organic Chemistry, University of UmeP, S-901 87 UmeA, Sweden
Kerstin M. Larsson, and Jozef Kowalewski* Division of Physical Chemistry, Arrhenius Laboratory, University of Stockholm, S - 106 91 Stockholm, Sweden (Received: July 24, 1984) Multinuclear spin relaxation data are reported for three crown ethers and their complexes with alkali metal ions. Quadrupole coupling constants in systems modeling the complexes are estimated by ab initio SCF MO calculations. The calculations indicate that the quadrupole coupling constant for I7O is only weakly influenced by complex formation. The comparison of I3C and I7O relaxation rates leads to the conclusion that the complex formation not only slows the overall reorientation of the crown ether molecules but also reduces the segmental motion of the CH2 groups. The relaxation rates of the alkali metal nuclei are used to estimate the quadrupole coupling constants, which are also compared to the calculated results. or 39K.8-10In the l3C/I7O study of the crown ethers 12-crown-4 (12C4), 15-crown-5 (15C5), and 18-crown-6 (18C6) and their Crown ethers constitute a class of compounds that show an complexes with Li', Na+, and K', it was concluded that "0 line exciting development since their discovery less than two decades width modifications result mainly from changes of the effective ago.'S2 Due to their solubility properties and their tendency to correlation time.8 However, the different ratios Tl(free ligselectively form strong electrostatic complexes with cations, they and)/ T,(complex) obtained from the 13Cand I7O measurements have been used as phase transfer catalysts, for salt solubility were not discussed. It was also concluded that I7O line broadening enhancement, and for anion activation in synthesis.* Their occurs when a crown ether forms a complex with a cation that properties have also made them interesting as models for studies fits well into the cavity, while line narrowing results from comof biological complexation proce~ses.~ plexation with a cation much smaller than the cavity. Although A number of investigations have been concerned with structures they clearly are of importance for the explanation of the 170line of both uncomplexed systems and complexes, their related thernarrowing process, the I3C relaxation times corresponding to the modynamics, and the multitude of factors influencing these 170 line narrowing cases were not measured. e q ~ i l i b r i a .In~ ~general, ~ ~ ~ the selectivity toward a cation and the In order to get a firm picture of the microdynamics of the free stability of a complex can be described from the fit between the and complexed crown ethers 12C4(Li+), 1SCS(Li+,Na+,K+),and cation and the crown ether cavity sizes. However, proper con18C6(Na+,K+) in CD3CN and (CD3)2C0,a relaxation time study sideration of other factors such as changed conformations and enthalpy and entropy effects must be taken into a ~ c o u n t . ~ ~of~the ~ ~nuclei 13C, 170,7Li, 23Na,and 39Khas been performed. The field gradients at oxygen and cations have been estimated by ab Studies dealing with complexation rates and microdynamics of initio calculations. The results are interpreted in terms of crown the free "crowns" and the complexes are considerably less frequent. ether segmental motions, overall molecular tumbling, and cation Insight into the microscopic region clearly is of importance for mobility within the complexes. The field gradients/quadrupole the understanding of the interaction between cation and ligcoupling constants are also discussed. and/solvent, and the phase diffusion processes. Information on the structures and the motions can be obtained Experimental Section from N M R relaxation time ( T I )measurements. Studies of Compounds. The substances used were of commercial origin. crown-type compounds using this method have focused on the 'H To ensure a low water content, 12C4 and 15C5 were treated with or the I3Cnucle~s,6.~ or a combination of 13Cand either 170,23Na activated 4 8, molecular sieves, while 18C6 was dried in vacuo at 50 OC overnight. CD3CN was dried over P20s and distilled. Finely dispersed alkali metal perchlorates and iodides were dried in an oven at 150 O C for several days. Weighted amounts of crown ether or crown ether + salt were mixed with a small amount of solvent and subsequently diluted to 0.28 M, except for 18C6 in CD3CN, where a maximum concentration of 0.16 M was obtained. All work was performed in a drybox under a nitrogen atmosphere. The samples were degassed (1) (a) Pedersen, C. J. J. Am. Chem. SOC.1967,89, 7017. (b) Pedersen, by one freeze-pump-thaw cycle and sealed under vacuum. C. J. Ibid. 1967, 89, 2495. (c) Pedersen, C. J. Ibid. 1970, 92, 386. N M R Measurements. The NMR spectra were recorded on (2) For reviews see: (a) Pedersen, C. J.; Frensdorff, H. K. Angew. Chem., Int. Ed. Engl. 1972, I I , 16. (b) Gokel, G. W.; Durst, H. D. Synthesis, 1976, a JEOL GX 400 spectrometer at 30 OC. Field/frequency lock 168. (c) VGgtle, F.; Weber, E., In 'The Chemistry of Ethers, Crown Ethers, was set at the deuterium signal in the solvents. Relaxation times Hydroxyl Groups and Their Sulphur Analogues", Part 1; Patai, S., Ed.; ( T I )for I3C,'Li, and 23Nawere measured at least twice with the Wiley-Interscience: New York, 1980; Chapter 2. (d) Weber, E.; Vogtle, F. fast inversion-recovery pulse sequence" and calculated with a Top. Curr. Chem. 1981, 98, 1. (e) Viout, P. J . Mol. C a r d . 1981, I O , 231. Introduction
(3) Dietrich, B.; Lehn, J.-M.; Sauvage, J.-P. Chem. Zeit. 1973, 7 , 120. (4) Goldberg, I. In 'The Chemistry of Ethers, Crown Ethers, Hydroxyl Groups and Their Sulphur Analogues", Part 1; Patai, S.,Ed.; Wiley Interscience: New York, 1980; p 175. ( 5 ) (a) Michaux, G.; Reisse, J. J. Am. Chem. SOC.1982, 104, 6895. (b) Sugawara, T.; Yudasaka, M.; Yokoyama, Y.; Fujiyama, T.; Iwamura, H. J . Phys. Chem. 1982,86,2705. (c) Dishong, D. M.; Gokel, G. W. J. Org. Chem. 1982, 47, 147. (d) Wipff, G.; Weiner, P.; Kollman, P. J. Am. Chem. SOC. 1982, 104, 3249. (e) Perrin, R.; Decoret, C.; Bertholon, G.; Lamartine, R. Nouu. J . Chim. 1983, 7, 263. (0 EIBasyony, A.; Brfigge, H. J.; von Deuten, K.; Dickel, M.; Knochel, A.; Koch, K. U.; Kopf, J.; Melzer, D.; Rudolph, G. J. Am. Chem. SOC.1983, 105, 6568.
0022-3654/85/2089-0258$01.50/0
(6) Nosaka, Y.; Akasaka, K.; Hatano, H. J . Phys. Chem. 1978,82, 2829 (7) (a) Fedarko, M.-C. J. Magn. Reson. 1973, 12, 30. (b) Durst, H. D.; Echegoyen, L.; Gokel, G. W.; Kaifer, A. Tetrahedron Lett. 1982, 23, 4449 (c) Live, D.; Chan, S. I. J . Am. Chem. SOC.1976, 98, 3769. (8) Popv, A. I.; Smetana, A. J.; Kintzinger, J.-P.; NguyCn, T. T.-T. Helu. Chim. Acta 1980, 63, 668. (9) (a) Kintziner, J.-P.; Lehn, J.-M. J . Am. Chem. SOC.1974, 96, 3313. (b) Bisnaire, M.; Detellier, C.; Nadon, D. Can. J . Chem. 1982, 60,3071. (IO) Neurohr, K. J.; Drakenberg, T.; ForsCn, S.; Lilja, H. J. Magn. Reson. 1983, 5 1 , 460.
0 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 2, 1985 259
N M R of Crown Ether Complexes
eq 2 to the T1values (7Li, Z3Na)and to the line widths (39K,170).
three-parameter fitting program.12 Relaxation times for 170and 39K were determined from their line widths, obtained by using a Lorentzian curve-fitting r 0 ~ t i n e . I ~The experimental error in the T I values (I3C, 7Li, 23Na) and line widths (170, 39K) was estimated a t less than 5%. A natural abundance 170N M R experiment was typically run overnight.
Results and Discussion Theoretical Background. Under 'H decoupling and extreme narrowing conditions, a relationship between the dipole-dipole relaxation rate (l/TIDD)and the effective correlation time ( T ~ of a proton bearing spin l/z 13Cnucleus is given by the equation14
where po is the permeability of the vacuum, nH the number of attached hydrogens, rCHthe C-H distance, and the other symbols have their usual meaning. For a rigid molecule undergoing isotropic reorientation, the rotational correlation time, T ~is equal ~ , to 1/6D1, where D,is the rotational diffusion constant. For most molecules in solution, anisotropic tumbling and conformational flexibility of the molecule give rise to an "effective" correlation time, whose physical interpretation is rather complicated. The relaxation of quadrupolar nuclei, e.g., 'Li, 23Na,and 39K with 1 = 3/2 and I7O with 1 = 5/z, is induced by fluctuations in the electric field gradient at the nucleus.'5 For the extreme narrowing case, the rate of spin-lattice and spinspin relaxation is given by
3r2
21
+3
( ;)( 1+-
e2;Q)'iFG (2)
10 P ( 2 1 - 1) where e is the asymmetry parameter (0 < E < l), q = qzzis the largest principal component of the field gradient tensor, and Q is the nuclear quadrupole moment. rFGrepresents the correlation time for reorientation of q and is identical with rCHfor isotropic t ~ m b l i n g . ' ~ . However, '~ in the case of anisotropic or internal motion, the two correlation times may differ. The product ezqzzQ/his known as the quadrupole coupling constant (QCC). Hence, if is small or constant, the relaxation rate is proportional to Experimental values of QCC's can be derived from N M R or NQR solid-state studies, or from gas-phase rotational or molecular beam spectroscopy. Approximate QCC's may also be calculated by M O methods. Experimental Domain. The dominance of the dipole-dipole mechanism for the I3C relaxation is demonstrated by dynamic NOE experiments on the 18C6-KC104 complex, where 95-100% NOE is found. This is in agreement with NOE experiments on similar c o m p l e x e ~ . ~Hence, ~ , ~ ~ the measured I3C T l values can safely be used as TIDDvalues. Since no hydrogen is present in the solvent (CD3CN), an intermolecular dipoldipole contribution to the relaxation of the quadrupolar nuclei can be excluded even for the 'Li nucleus, which has a rather small quadrupole moment.16 We also neglect the intramolecular DD contribution and apply (11) Canet, D.; Levy, G. C.; Peat, I. R. J. Magn. Reson. 1975, 18, 199. (12) Kowalewski, J.; Levy, G. C.; Johnson, L. R.; Palmer, L. J . Magn. Reson. 1977, 26, 533. (13) Levy, G. C. Curve fitting program 'NMR l", NMR Laboratory, Syracuse University, 1983. (14) Harris, R. K. "Nuclear Magnetic Resonance Spectroscopy";Pitman: London, 1983; Chapter 3. (1 5) Hams, R. K. "Nuclear Magnetic Resonance Spectroscopy";Pitman: London, 1983; Chapter 5. (16) (a) Lindman, B.; ForsEn, S. In 'NMR and the Periodic Table"; Harris, R. K.; Mann, B. E., Eds.; Academic Press: London, 1978; Chapter 6. (b) Laszlo, P. In 'The multinuclear Approach to NMR Spectroscopy"; Lambert, J. B., Riddell, F. G., Ed.;Reidel: Dordrccht, Holland, 1983; Chapter 12. (c) Mishustin, A. I.; Kessler, Yu. M. J. Sol. Chem. 1975, 4, 779.
~ )
Our choice of CD3CN as solvent is based on its polarity properties," which should be high enough to eliminate counterion (C10,) effects on the N M R parameters of the cation-ligand system.7c*1SJ9A constant 170chemical shift of the Clod- ion observed for the crown ether complexed perchlorate salts in CD3CN and other solvents indicates that these systems exist as solvent-separated ion pairs.s The polarity of CD3CN is, however, low enough to avoid solvent competition with the crown ether for cation solvation. Hence, high formation constants ( K ) of the 1:l crown ethercation complexes should be obtained. For the Li+/ 12C4, 15C5 and Na+/ 15C5, 18C6 complexes in CD3CN, the log K values are >3.8.18*'9 To our knowledge, no K values for the K+/ 15C5,18C6 complexes in CD3CN have been reported. Since the log K values for Na+/cyclohexano-l5C5 and Na+/18C6 in MeOH are similar to those mentioned above (>3.7), it seems reasonable to approximate the log K values of K+/15C5, 18C6 with the corresponding values of K+/cyclohexano-15C5 and K+/ 18C6 in MeOH, which are 3.6 and 6.1, respectively.z0 For the crown ether/cation combinations in this investigation, the amount of free ions or ligands should thus be negligible (
