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684 J. Chem. SOC. (B), 1968 Nuclear Magnetic Resonance Studies of Six-membered Rings. Part 1.l Ring Inversion in Heterocyclic Compounds By R. K. Harris * and R. A. Spragg. School of Chemical Sciences, University of East Anglia, Norwich NOR 88C Free energies of activation, AG:, for ring inversion are reported for a number of heterocycles. These values are obtained from coalescence temperatures observed for 'H n.m.r. spectra. The observed variations in AGI are correlated with differences in barriers to internal rotation in analogous acyclic compounds. The limitations and anomalies of the correlation are mentioned. and the implications are discussed. THE rates of ring inversion for a number of compounds containing six-membered rings have been studied by n.m.r.2 There is considerable variation between the rates for different compounds, and a corresponding variation in the values of the free energy of activation for ring inversion, AGZ.The dependence of this para- meter on the nature of the ring substituents has not been clearly established, and requires rationalisation. In this work we have obtained AG: values for a number of morpholine and piperazine derivatives. The results for these and other six-membered saturated heterocycles are considered in terms of a half-chair transition state for the ring inversion. Hendrickson calculated that the principal contribution to the inversion barrier in cyclohexane arises from torsional strain, and we have attempted to relate the observed variation in AGt to the variation in the torsional strain in the transition state.The torsional contribution to the inversion barrier is estimated by use of the same geometrical model as used by Hendrick~on,~ and by use of the barriers to methyl group rotation in compounds of the type MeXMe to obtain the substituent dependence. The variation in the estimated torsional contributions to the inversion barrier is sufficiently large to account for the observed variation in AGj, and some correlation is found. In some cases other factors are important. EXPERIMENTAL The compounds studied are all derivatives of piperazine and morpholine. The parent amines, N-methylpiperazine, NN'-diniethylpiperazine, N-methylniorpholine, N-phenyl- morpholine, N-acetylmorpholine, cis-2,5-dimethylpiper- azine, and tvans-2,6-dimethylmorpholine were all com- mercially available; they were dried and used without further purification. NN-Dimethylpiperazinium chloride hydrochloride was prepared by the method of Harfeni~t.~ NN-Dimethylmorpholinium iodide was obtained by treat- ing N-methylmorpholine with methyl iodide ; morpholine hydrochloride and piperazine dihydrochloride were obtained from the amines and hydrochloric acid.The amine salts were recrystallised from methanol and water. l-Methyl- 4-nitrosopiperazine was commercially available. The amines were studied in solution in methylene chloride, f.p. - 96.7", which was dried before use. As solutions of secondary amines in methylene chloride deposit crystalline material when set aside for a few days, all solu- tions were freshly prepared. hTo changes in the room Preliminary communication, R.K. Harris and R. A. Spragg, Chem. Comm., 1966, 314. 2 (a) J. E. Anderson, Quart. Rev., 1965, 19, 426; (b) F. G. Riddell, ibid., 1967, 21, 364. temperature spectra were noted after the time required for the low temperature measurements. Some solutions in methanol, f.p. - 97.8", and methylcyclohexane, f.p. - 126.4"C, were also studied. Tetramethylsilane (TMS) was used as an internal reference a t a concentration of ca. 3% v/v. The amine salts were studied in solution in sulphur dioxide, f.p. -75-5", with benzene as internal reference, since TMS was insufficiently soluble to provide a signal for the internal lock system of the spectrometer. All spectra were recorded on a Varian Associates HA- 100 Spectrometer a t 100 Mc./sec.The lowest temperature accessible was ca. - 100". The temperatures were esti- mated from the separation of the methyl and hydroxy- resonances of methanol; estimated accuracy & 2 O , though the consistency is higher. RESULTS All the compounds studied had spectra corresponding to rapid ring inversion at room temperature. Low temperature spectra corresponding to slow ring inversion, with separate signals from axial and equatorial protons, were observed for the following compounds : piperazine, N-methylpiperazine, NN'-dimethylpiperazine, morpho- line, AT-methylmorpholine, cis-2,5-dimethylpiperazine, trans-Z,6-dimethyl morpholine, and NN-dimethyl piper- azinium chloride hydrochloride. The case of N-methyl- piperazine is illustrated in Figure 1. N-Phenyl- and N-acetyl-morpholine gave spectra corresponding to rapid ring inversion even a t -95".No well-defined changes were observed in the low temperature spectra of the remaining amine salts; in these cases the tern- perature range was restricted because of the higher freezing point of sulphur dioxide. For compounds containing N-methyl groups the signal from this group was always a sharp singlet at room temperature. For solutions in methylene chloride and in methylcyclohexane the signal remains a sharp singlet down to -95", when ring inversion is slow. This indicates either that the methyl group is in only one conformation, or that interconversion between axial and equatorial positions caused by inversion of the configur- ation at nitrogen is rapid. In methanol solutions, how- ever, the N-methyl signal broadens appreciably below -70"; for N-methylmorpholine it has Wn 6 c./sec.at -95". This broadening presumably arises rrom a slow- ing of the inversion at nitrogen, and shows that the N-methyl group must exist in a significant proportion in both axial and equatorial positions. Hydrogen bonding 3 J . B. Hendrickson, J . Amev. Chem. Soc., 1961, 83, 4537. M. Harfenist, J . Amev. Chem. Soc., 1957, 79, 2211.Phys. Org. to the nitrogen atom will slow the rate of inversion at nitrogen, since such hydrogen bonds must be broken in the inversion process. Bottini and Roberts observed that N-inversion in aziridines occurred ca. times more slowly in hydroxylic than in non-hydroxylic sol- vents. Studies6 of the pH-dependence of the n.m.r. spectrum of lJ2,6-trimethylpiperidine have led to the suggestion that the rate of N-inversion may not always be fast compared to the ring-inversion rate for N-hetero- cyclic amines.However , complications arising from N-inversion are ignored in the present paper. The analysis of the low temperature spectra of the amines, and the chemical shifts and coupling constants FIGURE 1 'H N.m.r. spectra (100 Mc./sec.) of N-methylpiper- azine in CH,Cl, as a function of temperature; A, +30°; B, -226"; C, -558". The low-field group of lines in A and B is due to the protons of the CH, group u t o NH. The full intensity of the NMe line (and that of the NH line in B) is not shown obtained will be discussed in detail in a subsequent paper. In the cases of cis-2,5-dimethylpiperazine and trans-2,6-dimethylmorpholine the low temperature spectra were not analysed completely, as the resolution was inadequate.The separate signals from axial and equatorial methyl groups were, however, readily ob- served, and the chemical shift difference and coalescence temperature of these signals were obtained. In NN- 80, 5203. 1188. A. T. Bottini and J . D. Roberts, J . Amer. Chem. SOC., 1958, ti J. J. Delpuech and M. N. Deschamps, Chem. Comm., 1967, dimethylpiperazinium hydrochloride the splitting of the NH, signal into a broad doublet was observed, but the rest of the spectrum was too complicated for observation of the separation of signals from axial and equatorial positions. As the spectra are complex, the inversion rate can be readily estimated only at the temperature of coalescence of the signals from the axial and equatorial positions.This coalescence was clearly observed in all cases, and the temperature of coalescence was well defined. It could be estimated generally to ca. &Z"; the transition from one signal to two was observed within a range of about 5". In Table 1 are listed the chemical shift differences between axial and equatorial positions, and the observed coalescence temperatures. Preliminary results for mor- pholine, N-methylmorpholine and NN'-dimethylpiper- azine have already been rep0rted.l ESTIMATION OF AG: For the case of two equally populated sites with no coupling (and with the linewidth in the absence of exchange neglected) the mean lifetime in one site when the two signals coalesce is given by: SA = 2'(x80)-' (1) where 6w is the chemical shift difference between the sites in c./sec.In the spectra observed here there are two factors to be considered: the coupling between the nuclei in the exchanging sites, and the coupling of these to other nuclei. For an AB system, with coupling between the sites, the mean lifetime when the A and B signals coalesce is given by: In general the effect of coupling to other nuclei on the exchange rate required to cause coalescence cannot be readily estimated. However, in certain cases it can be taken into account as a line-broadening phenonien~n.~ For a linewidth a t half height of 0.40 60 the lifetime a t coalescence is 0.57 q,, where T,, is the lifetime for coalescence with narrow lines. In the examples studied here, however, the broadening resulting from coupling to other nuclei generally takes the form of multiplet structure which is modified by the exchange process.Nevertheless the exchange rate for coalescence will probably not differ from that which would be observed in the absence of this coupling by much more than a factor of two, unless the magnitude of the coupling approaches half the chemical shift difference between the sites. The free energy of activation, AG$, may be obtained from the exchange rate a t the coalescence temperature, Tc, by application of the absolute-rate theory equation. It is generally accepted that the ring inversion process involves surmounting an energy barrier which leads to a twist-boat J. A. Pople, W. G. Schneider, and H. J. Bernstein, ' High R.J. Kurland, M. B. Rubin, and W. B. Wise, J . Chem. H. S . Gutowsky and C. H. Holm, J . Chem. Prays., 1956, 25, Resolution N.M.R.,' McGraw-Hill, New York, 1959. Phys., 1964, 40, 2426. 1228.J. Chem. SOC. (B), 1968 form, from which the molecule passes over an equivalent barrier leading either to the form with an inverted con- formation, or back to the original forni.1° The observed rate of chair to chair interconversion is therefore exactly half the rate at which molecules surmount the initial barrier, since they are equally likely to end in the inverted or the original conformation. The free energy of activation for rate a t the coalescence temperature is less than that assumed in the equation for AGI. If the exchange rate differs from that assumed by a factor of two, the calculated value of AGI, for a coalescence temperature of 2 5 0 " ~ , will be in error by about 0.3 ltcal.mole-'. In Table 1 are listed values of AGf for the compounds studied here a t the coalescence temperatures given. A TABLE 1 Axial-equatorial chemical shift differences, coalescence temperatures, and free energies of activation for ring inversion obtained at 100 Mc./sec. a,, Tc AG t (I) Piperazine CH,Cl, 57; W/V N-CH, 16 208 10.3 (111) NN'-Dimethylpiperazine CH,Cl, 20% v/v N-CH, 62 265 12.5 MeOH 20:b v/v N-CH, 68 270 12.7 (IV) N-Methylpiperazine CH,Cl, 20q4 v/v MeNCH, 80 247 11.5 MeOH 20y0 v/v MeNCH, 80 252 11.7 (Y) N-Methylmorpholine CH,Cl, 2004 v/v N-CH, 56 242 11.5 O-CH, 22 233 11.5 RkOH 20Oj, V/V N-CH, 56 243 11.5 Solvent Conc.Signal (c./sec.) ( O K ) (kcal./mole) ................................................... ................................................... (11) Morpholine CH,Cl, 57$ V/V O-CH, 2 3 203 9.9 ................................. ....................................... ....................................... C,H,,i\le 10% v/v S-CH, 50 236 11.2 (VI) tvans-2,6-Dimethylmorpholine CH,Cl, 5O4, v/v C-Me 30 187 9.0 ........................... .............................. (VII) cis-2,5-Dimethylpiperazine CH,Cl, 5% w/v C-Me 26 199 9-6 (VIII) NN-Dimethylpiperazinium chloride hydrochloride SO, NH, 34 214 10.3 0 AG: is calculated from equation 4 with 80 = a,,, i.e., ignoring coupling effects. TABLE 2 coalescence temperatures Free energies of activation a for ring inversion, calculated from literature values of asial- (IX) Cyclohexane .......................................(X) Pentamethylene sulphide ........................ (XI) Thian l-oxide ....................................... (XII) Tetrahydropyran ................................. (XIIT) Piperidine .......................................... (XIV) N-Methylpiperidine .............................. (XV) 1,3-Dioxan .......................................... (XVI) 1,3-DimethyIhexahydropyrimidine ............ (XVII) 1,3,5-Trimethylhexahydrotriazine ............ Solvent Cs2 CH,CI, CH,CI, CD,OD :?,OD CD,,OD Me,CO Me,CO CDCl, CDCl,, CDCl, CHFCI, Signal CHI> S-CH, S-CH, O-CH, O-CH, N-CH, N-CH, 2-CH2 2-CH2 2-CH2 N-CH, N-CH, N-CH, (c. /sec.) 28-7 30 52.2 33 d 55 26.1 56.5 19.3 20 73.8 54.7 52-8 53.8 -equatorial shift differences and T c ( "4 212 180 203 193 208 210 252 188 193 244 268 269.5 268.1 AG: 10.3 11 8.7 12 9.8 12 9.3 12 9.9 13 10.4 14 11.9 14 9.3 15 9.5 16 11.3 17 12.7 18 12.8 19a 12.8 19b (kcal./mole) Ref.0 AGt Calculated from the coalescence of AB spectra in all cases except cyclohexane. b Spectrometer frequency 60 Mc./sec. in d The value is assumed t o We have obtained a AGt value of ca. 11.4 kcal. molc-l for an undeuteriated sample some cases and 100 Mc./sec. in others. be the same (in p.p.m.) as in solution l3 in CS,. of this compound in CH,CI, solution. Value estimated from comparison with other compounds. chair to twist-boat conversion is therefore given [from equation (l)] by AGI = 4.58TJ9.97 +- log (TJSw)] cal. mole-l The result of ignoring coupling between the exchanging sites and to other nuclei is that the estimated AGS values will be lower than the true values, since the true exchange (3) 10 E.L. Eliel, N. L. Allinger, S. J. Angyal, and G. A. Morrison, l1 F. A. L. Anet and A. J . R. Bourn, J . Amer. Chem. SOC., l 2 J. B. Lambert and R. G. Keske, J , Ovg. Cheilz., 1966, 31, l3 G. Gatti, A. L. Segre, and C. Morandi, J . Chem. Sac. ( B ) , J. B. Lambert, R. G. Keske, R. E. Cahart, and A. P. ' Conformational Analysis,' Interscience, New York, 1965. 1967, 89, 760. 3429. 1966, 1203. Jovanovich, J . Amev. Chem. SOC., 1967, 89, 3761. reasonable estimate of the accuracy of these values is 0.4 kcal. mole-" the relative values will be more accurate since the error due to neglcct of coupling is always in the same direction.Errors as large as 5" in T , lead typically to errors of only ca. k0.2 kcal. mole-l in AGf. In Table 2 are given the values of AGS obtained from values of coalescence temperatures and axial/equatorial shift differences quoted l5 J . E. Anderson and J . C. D. Brand, Tvaias. Faraduy SOC., 1966, 62, 39. l6 H. Friebolin, S. Kabuss, W. Maier, and A. Luttringhaus, Tetvahedvon Lettevs, 1962, 683. l7 ( a ) F. G. Riddell and J. M. Lehn, Chem. Comm., 1966, 375; (b) F. G. Kiddell, J . Chem. SOC. ( B ) , 1967, 560. J. M. Lehn, F. G. Riddell, B. J. Price, and I. 0. Sutherland, J . Chem. SOC. ( B ) , 1967, 387. l9 ( a ) I<. F. Farmer and J. Hamer, Chem. Comm., 1966, 866; ( b ) H. S. Gutowsky and P. A. Temussi, J . Amev. Chem. Soc., 1967, 89, 4358.Phys.Org. 687 in the literature. In these cases the spectra are all of the simple AB type, and the value of AGS at the coalescence temperature is obtained using a modification of equation (3) to incorporate (2). THEORETICAL CONSIDERATIONS An estimate of the barrier to inversion in cyclohexane has been made by Hendrick~on.~ He considered three contributions to the energy of a particular conformation : torsional energy resulting from changing the dihedral angles between bonds to neighbouring carbon atoms from the 60" of a staggered conformation; bond angle strain due to distortion of valency angles away from the tetrahedral angle ; and repulsions between non-bonded hydrogen atoms. The energy of the half-chair transition state was calculated to be 12.7 kcal.mole-l above that of the chair form, cf. the experimental value of 10.8 kcal. mole-l for the eizthalpy of activation for ring inversion.ll It has been suggested8 that the calculated value is too high because the chair form does not have exactly tetra- hedral internal angles.20 A more recent calculation by Allinger et aL21 gives 12-00 kcal. mole-' for the excitation energy froin the chair to the half-chair form. The principal contribution to the barrier was found to be the torsional strain, calculated to be 7-6 kcal. mole-l using a cosine potential of the form : I' = (V0/2)(l + cos 34) with a value of 2-80 kcal. mole-l for Vo, taken from the torsional barrier in ethane. This value of Yo is likely to be too low (the value 22a in propane is 3.2 kcal. mole-l) but there is no adequate model compound for estimation of the torsional barrier about a C-C bond in cyclohexane.suggests that torsional strain accounts for ca. 60% of the inversion barrier; the work of Allinger et aZ.21 does not affect this conclusion. We shall there- fore consider here the variation in this contribution to the barrier which will occur when a ring carbon atom is replaced by a hetero-atom. In order to do this we shall assume that the ring geometry, both of the chair and the half-chair conformation, is not greatly changed by the replacement. The replacement of a methylene group by nitrogen or oxygen has only a small effect on the geometry of the chair form, but replacement by sulphur has a much larger effect. Typical bond lengths and angles are given in refs.21 and 23. The torsional strain in the half-chair state is obtained here by use of a cosine potential of the form given above, where 4 is the dihedral angle between bonds to neighbouring atoms in the ring. The values of V0 are taken from the barriers to methyl group torsion in the acyclic compounds of the type MeXMe. The dihedral angles are those given by Hendrickson for the half-chair state of cyclohexane, shown in Scheme 1. The use of the compounds MeXMe Hendrickson * It is assumed that enthalpy differences may be equated to differences in energy obtained from potential energy curves ; this procedure ignores contributions of volume (PV term) and temperature to H or assumes cancellation of such contributions when AH is considered. ignores any effects on the torsional barrier from ring atoms p and y to X.5 I SCHEME 1 The geometry of the half-chair form of cyclo- hexane 4 9, 9, f14 8, 6, 41 4 2 4 3 4 4 4 5 4 6 CCC Angle 113.5 118.8 118.5 113.5 106.0 106.0 Dihedral angle 19.1 0.0 19-1 56.2 75.0 56.2 For a precise definition of the dihedral angle + see ref. 3. In this way we can obtain the torsional contribution to the enthalpy of formation of each half-chair form of a substituted cyclohexane. I t will be more convenient to consider in what follows the difference in enthalpy of formation between a half-chair state of the substituted cyclohexane and that of cyclohexane. This is obtained by considering those dihedral angles involving bonds to hetero-atoms, and, for an individual half-chair form, i, is given * by where AHc$ is the enthalpy of activation for cyclo- hexane, AVO= is the difference between the barriers to methyl group torsion in MeXMe and propane, and 4si is the appropriate dihedral angle about a bond in the ring to the heteroatom X.The summation is over all such bonds to hetero-atoms (each heteroatom involves two bonds). None of the examples discussed here has two adjacent hetero-atoms. The values of AH& - AH,: for the half-chair states of some substituted cyclohexanes are given in Scheme 2. A substituent occupying position 5 or 6 in the half-chair (see Scheme 1) has little effect on the enthalpy of form- ation; the dihedral angles about these positions are close to those in the chair form. The greatest effect occurs when the substituent is in position 2 or 3 as there is complete eclipsing across the 2-3 bond, and the dihedral angles across the 1-2 and 3-4 bonds are also small.To estimate the relative rates of inversion for the different compounds it is necessary to make some as- sumption about the entropy changes involved. I t will be assumed that the entropy change caused by formation of a single half-chair from a chair form is the same in all cases. This procedure neglects variations in the con- tributions of rotation and vibration to AS:; this is a reasonable assumption, since the change in geometry is 20 hl. Davis and 0. Hassel, Act. Chem. Scand., 1960, 17, 1181. 21 N. L. Allinger, 31. A. Miller, F. A. Vancatledge, and J. A. Hirsch, J . Amev. Chem. SOC., 1967, 89, 4325. 22 (a) G. B. Kistiakowsky and W. W.Itice, .J. Chem. Ph-ys., 1940, 8, 610; (b) E. Hirota, C. Matsumura, and Y. Morino, Bull. Chem. SOC. Japan. 1967, 40, 1124. 23 K. E. Marsh, Acta Ctyst., 1955, 8, 91.688 J. Chem. SOC. (B), 1968 may also be used to define an overall difference in the free energies of activation for ring inversion, AGS - AGc$ : k/k, = exp[-(AGS - AGc$)/RT] The quantity AGJ is that normally reported from n.m.r. measurements of rates of inversion. Thus AGc$ - AGS may be calculated from the estimated enthalpies of formation for the half-chair states: exp[-(AG$ - AG,f:)/RT] = The calculated values may then be compared to experi- mental ones to test the validity of the simple model used. In Table 3 are listed values of the barriers to methyl group torsion for a number of compounds of the type MeXMe; values of AVox are also given.Table 4 shows values of ni exp[-(AHiJ - AHCS)/Rq and of (AGf: - AG,I) calculated at the coalescence temperature for each compound. As the torsional barriers in propane and &Zni exp[ - ( AHiS - AHcS)/RT] similar for all the substituted cyclohexanes. The ob- served ASS for the inversion of cyclohexane differs somewhat from that calculated on a simple baskf1 Mono- lf3-Di- 1,4-Di- 1,3,5-Tri- substituted substituted substituted substituted A J x 1' x-x v 0. I6 AV,x 0.94 AVOX 0.78 AVOx + 0.78 AV0y 2-71 AV,x I *77 AV0x I .93 AV0x 1-77 AVOx + 0. I6 AV,y SCHEME 2 The possible half-chair states of ring-substituted cyclohexanes, and the torsional contribution to the enthalpy of formation from the corresponding chair forms, relative to that in cyclohexane The rate of formation of any half chair state from the chair form is given by ki = kT - exp[ - (AGif:/RT)] h where AGit is the free energy of formation of the half- chair state.With the assumption that the entropy change in this process is always the same, the relative rates of formation of different half-chair states can be obtained from the difference in the enthalpies of form- ation. For two states with enthalpies of formation AHiS and AHjS: ki'/kj' = exp[-(AH& - AHjf:)/RT] Thus the rate of formation of any half chair state, relative to the rate of formation of a half-chair state in cyclo- hexane at the same temperature, is given by ki'/k,' == exp[ - ( AHi'i - AH,$)/RT] The overall rate of ring inversion is obtained by sum- ming over all the six half-chair forms which are obtained directly from a given chair (mirror-image half-chairs may be ignored).For cyclohexane there are six equivalent half-chair forms, and for the substituted cyclohexane there are ni half-chair states with the same value of AHi$. The relative rates of ring inversion are then given by: k/k, = Q Cni exp[-(AHiS - AHcS)/RT] 1 The relative rates of ring inversion for the two compounds 24 P. H. Kasai and R. J. Myers, J . Chem. Phys., 1959, 30, 1096. 25 W. G. Fateley and F. A. MiIler, Spectrochim. Acta, 1962, 18, 977. 26 D. R. Lide, jun. and D. E. Mann, J . Chem. Phys., 1958, 28, 572. TABLE 3 Barriers a to methyl group torsion type MeXMe v4l A VO, MeCH,Meb ...... 3.2 0.00 MeOMe ............ 2.72 -0.48 MeNHMe .........3.28 +0.08 MeN(Me)Me ...... 4.40 +1.20 MeSMe ............ 2.13 - 1.07 MeS(0)Me ......... 2.94 -0.26 MeCH(Me)Me ... 3-90 +Om70 MeC(0)Me ...... 0.78 -2.42 in compounds of the Method Ref. Specific heat 22a Microwave 24 25 Far i.r. Microwave 26 Microwave 27 Microwave 28 Microwave 29 Microwave 3.0 0 Values of Vo and AVOx are in kcal. mole-'. A recent microwave determination 22b of the barrier in propane, includ- ing interaction between the two tops and therefore quoting two parameters, gives results comparable to the thermo- dynamic value of Vo given here; small variations in this quantity would not affect our general conclusions. dimethylamine are so similar, separate data are not given for compounds differing only by replacement of CH, by NH. The values of ni exp -(AHit - AH,X)/RT show the relative contribution of the different half-chair forms to the overall inversion rate.There are generally several different routes available for ring inversion, and this leads to differences in the entropy of activation for ring inversion in different compounds, even though the entropy of formation of a single half-chair state is treated as constant. Consider the two extreme cases: cyclohexane, in which there are six equivalent half-chair forms through which the inversion proceeds, and a substituted compound in which one half-chair is of much lower energy than the others so that inversion proceeds almost exclusively through this one form. The entropy 27 L. Pierce and M. Hayashi, J . Chew. Phys., 1961, 35, 479. 28 H. Dreizler and G.Dendl, 2. Naturforsch., 1965, 20a, 1431. 29 D. R. Lide, jun. and D. E. Mann, J . Chem. Phys., 1958, 29, 3O J. D. Swalen and C . C. Costain, J . Cltem. Pltys., 1959, 31, 914. 1562.Phys. Org. of activation for ring inversion for cyclohexane will be more positive by Rln6 than that for the substituted compound. In other cases the overall entropy and TABLE 4 Energies of the various half-chair states of heterocyclic compounds relative to that for cyclohexane a Hi (XII) 9 - 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 6 Form A B C A B C A B C A B C G (X = 0) H ( X = O ) G H D E F D E F I (X = 0) J ni exp[ - (AH+ - AH,*) /RTcl 2.60 5.86 1.34 0.34 0.02 2.22 3.26 6.84 3.5 24.6 20.6 394 0.64 0.04 8.62 0.07 0.03 7.0 51.8 24.4 0.21 0.004 0.02 AGt - AGC (kcal./mole) - 0.60 -+ 0.63 - 0.29 - 1.53 -0.21 -+ 2.08 - 1-05 + 1.67 -+ 3.6 Values are given for the coalescence temperatures listed See text for explanation of the notation.in Tables 1 and 2. b See Scheme 2. c ,4t Tc (193"~). enthalpy of activation are not so readily defined, but are given by the general expression : exp( - AGZIRT) = exp( ASJ/R) exp( - AHJ/-RT) = 2 ni exp( - AHi'/RT) 1 Measured values of AS: and AHt are available for a number of compounds, but are not considered31 as reliable as the values of AGZ. Moreover the inter- pretation of absolute values of AS: is often obscure (though differences in A S between related compounds may be of more as we have indicated above). Values of AGX are more commonly available than AH: or A S values and, for all the above reasons, we feel that at the present stage it is best to consider the variations of AG:, rather than those of AH: or AS:.The free energy of activation is often only known at T,, which is different for each molecule; our estimations of AGt are also made the appropriate coalescence temperatures. In many cases several non-equivalent half-chair forms will contribute significantly to the observed inversion rate. Recently34 it has been suggested that for sub- stituted cyclohexanes only the half-chair transition 31 A. Allerhand, F-M. Chen, and H. S. Gutowsky, J . Chew. 32 R. J. *4braham and D. B. McDonald, Chem. Comni., 1966, Phys., 1965, 42, 3040. 188. state of lowest energy needs to be considered. Such statements must be treated with caution unless it can be demonstrated that the various half-chair forms differ significantly in ene1-gy.3~ The procedure developed here emphasises the ill-defined nature of the reported values of AH$ and AS$.If the half-chair forms differ only slightly in energy, these parameters (as defined above) will be temperature dependent. and AH: is to plot the logarithm of the inversion rate constant k& (or, as has been suggested,33 k,&) against T-l. It is assumed that there is a linear relationship between these quantities (deviations from linearity are in practice not easy to observe); this is equivalent to assuming that AS$ and AH: are independent of tempera- ture. Fortunately, use of typical values for ring in- version energies (Table 4) shows that the temperature- variations of AH: and AS: from the cause cited above are slight (ca.0.1 kcal./mole and 0.4 e.u. respectively for a temperature change of 100" in the region of T , and room temperature). However the values of AH: ob- tained by the normal procedure may be up to 0.2 kcal./ mole higher than the lowest AHi: value. The normal procedure for evaluating AS DISCUSSION Figure 2 shows the result of plotting the calculated value of (AGX - AG,:) against the difference between the measured free energy of activation for ring inversion and that for cyclohexane at the same temperature. The calculated variation in the torsional contribution to the barrier is sufficiently large to account for the observed range of AGI values, Furthermore, certain trends are described qualitatively ; replacement of CH, by NH has little effect on AG:, but the presence of an N-methyl group causes a marked increase, and oxygen and sulphur both reduce AGJ.Agreement between the observed and calculated values is surprisingly close for most compounds, but there are marked deviations for some of the compounds with N-methyl substituents. The barriers for N-methylpiperidine, N-niethylpiperazine and N-methylmorpholine are all higher than predicted. It is surprising that the barrier in N-methylmorpholine is not lower than that in N-methylpiperazine, despite the presence of the oxygen atom; the barriers in morpholine and tetrahydropyran are appreciably lower than those in piperazine and piperidine respectively. The inadequacies of the model used to estimate AGI are of two types: those arising from the calculation of the torsional contribution (discussed in the preceding section), and those resulting from neglect of other effects.The importance of non-bonded interactions and angle-bending strain in determining the barrier is not readily ascertained. In considering the barrier we are concerned with the difference between the interactions in the chair and half-chair forms. -4lthough the 33 R. K. Harris and N. Sheppard, J . iMol. Spectroscopy, 1967, 23, 231. 34 S. Wolfe and J. R. Campbell, Chern. Cottiin., 1967, 874; 1967, 877.690 J. Chem. SOC. (B), 1968 magnitude of the non-bonded interactions for a parti- cular conformation will change with different sub- stituents, there may be some cancellation of this variation in taking the difference between the interactions in two 3O t 2.0L x m / txm) / - 2.0 I I t -2.0 -1.0 0 I.0 2.0 3.0 FIGURE 2 The observed free energies of activation to ring inversion, relative t o cyclohexane, plotted against values calculated as in the text.The numbering of the points is that used in Tables 1 and 2. Both calculated and observed values of AG: - AG,: are for the coalescence temperatures given in the Tables. In cases where several values are given in the Tables, an average has been used for this Figure. Compounds (VI), (VII), and (1;III) have not been included because of lack of knowledge about the appropriate torsional barriers forms. Hendrickson estimated that the effect of non- bonded interactions in cyclohexane is small, and it is unlikely that the variation in this effect contributed much to the observed variation in AGZ values, except for the compounds containing methyl groups, to be discussed later. The variation in angle-bending strain may be estimated for oxygen and nitrogen substituents from the relative case of deformation of CCC, COC, and CNC angles, since the geometry is very similar in all these cases.For sulphur tlie bond angles are rather different, and the angle strain is not readily estimated. The vibrational frequencies for CXC bending in com- pounds of the type MeXMe range from 283 cm-l for Me,S to 426 cm.-l for Me,N.25'35p36 In general the vibrational frequencies increase in the same order as do tlie torsional barriers, with the exception of the case of dimethyl ether, which has the highest bending frequency but a comparatively low torsional barrier.The vari- ation in the contribution of angle-bending strain to tlie barrier will therefore generally reinforce the variation of the torsional contribution,* the angle bending strain being greatest at those positions for which the torsional strain is greatest (Scheme 1). Solvent-solute inter- actions may affect the barrier. There is evidence that these may be important in the case of nitrogen-containing compounds. For N-methylmorpholine AG: is about 0.3 kcal. mole-l lower in methylcyclohexane than in methyl- * While this paper was in preparation, an article appeared 2b which discussed the various contributions t o the energy of six- membered heterocycles and suggested that much of the potential energy of the transition state to inversion must be in the form of angle strain.For reasons discussed in the text we believe this t o be unlikely. 7 We thank a referee for this suggestion. ene chloride or methanol. Similarly, for 1,3,5-trimethyl- hexahydrotriazine AG* is about 0.5 kcal. molep1 lower in hydrocarbon solvents than in deuteriochloroform or deuterium oxide. Most of the AGt values given here are for solutions in chloroform, niethylene chloride, or methanol. The values for nitrogen-containing com- pounds would all probably be slightly lower if ' non- interacting ' solvents were used. The relative AGt values for different compounds, however, are unlikely to change greatly. For the majority of these nitrogen- containing compounds tlie variation in AG: for ring inversion follows the pattern expected from consider- ation simply of the torsional contribution to the barrier.I t is possible that solvent effects may account for the high values of AGZ noted above for N-methylpiperidine, N-methylpiperazine and N-met hylmorpholine. How- ever, it is difficult to see why, if this is the case, the values for the other nitrogen-containing compounds are not correspondingly high. Perhaps these anomalies merely illustrate the inadequacy of the simple model used. Other complicating factors not considered here are ( a ) that the transition state may not be of the form illustrated in Scheme 2, (b) that nitrogen-inversion may affect the observed barrier in some cases,lSb and (c) that in compounds with two heterocyclic atoms there may be effects from bond dipole interactions.7 The possibility that twist-boat forms have energies closer than ca.1 kcal. mole-l to that of the chair form is also neglected. The data for compounds with methyl groups in the ring are of some interest, since non-bonded interactions are likely to be important. In the chair form a methyl group in an axial position experiences a repulsive interaction of about 1.7 kcal. mole-l with the axial protons in the 3- and 5-positions.lO In the half-chair form there are six different positions which a methyl group can occupy [formula (l)]. Only two positions, 5 b 6 ' 4 and 6, are sufficiently close to other positions, 6' and 4' respectively, to experience interactions as large as those for an axial methyl group in the chair form. The re- pulsions in these positions will in fact be slightly larger than in the chair form, as the interacting positions are slightly closer together.Thus if a methyl group which occupies an axial position in the chair form is in position 4 or 6 in the half-chair, the non-bonded interactions will increase the barrier relative to that in an unsubstituted compound (unless there are compensating changes for 35 N. Sheppard and D. M. Simpson, Quart. Rev., 1953, 7, 19. 36 ( a ) A. I<. Salonen, A n n . Acad. Sci. Fennicae, 1961, 67, 1; (b) W. D. Horrocks, jun. and I;. A. Cotton, Spectvochim. Acta, 1961, 17, 134.Phys. Org. 691 non-bonded interactions involving other substituents) . If the methyl group occupies any other position in the half-chair the barrier will be reduced relative to that in an unsubstituted compound.The value 3' of AGS for 1,l-dimethylcyclohexane is 10.2 kcal. mole-', close to that for cyclohexane. The methyl groups can occupy positions 1 and 2 in the half- chair, whereas one must be axial in the chair form. The value of AGS might therefore be expected to be less than that for cyclohexane. There are, however, two factors increasing AG: relative to that for cyclohexane. The torsional contribution will probably be larger, as the barrier to methyl group rotation in isobutane, 3.9 kcal. mole-l, is appreciably larger than that in propane. In addition, there are only two equivalent half-chair forms, compared with six for cyclohexane. This reduces the inversion rate by a factor of three, equivalent to an increase of about 0.5 kcal. mole-l in AG:.The situation is very similar for 1,l -dimethylpiperazinium chloride hydrochloride, and the value of AG:, 10.3 ltcal. mole-l, is again close to that for cyclohexane. trans-2,6-Dimet h ylmorpholine and cis-2,5-dime t hyl- piperazine have values of AG$ lower than those for the unsubstituted amines by 0-9 kcal. mole-l and 0.6 kcal. molep1, respectively. In the chair form of both coin- pounds there is an axial methyl group, but in the half- chair there are several forms in which the steric inter- action is reduced, see Scheme 3. In these cases the steric interactions are important in reducing the barrier to inversion. trans-2,6- cis-2,5- D~n~ethylniorpholii~e Dimethylpiperazine Half- 1 chair H 6 V H N H SCHEME 3 The chair and half-chair forms of compounds with methyl groups in the ring The presence of an sp2-hybridised atom in the ring appears to lower the inversion barrier ; cyclohexanone, for example, has a spectrum which is unchanged38 at -84".The torsional contribution to the barrier is expected to be much reduced in this case; the barrier to methyl group rotation in acetone is only 0-78 kcal. mole-l. A further cause of the low barrier is the large 37 H. Friebolin, W. Faisst, H. G. Schmid, and S. Kabuss, letvahedvon Letters, 1966, 1317. 38 P. Grander and Ill. 31. Claudon, Bzdl. SOC. chim. France, 1966, 763. CCC angle at the carbonyl group in the chair form, which will reduce the angle-bending strain in the half-chair. N-Acetyl- and N-phenyl-morpholine both show rapid ring inversion at -95", indicating that the inversion barriers are appreciable lower than in morpholine.In both these compounds the unshared electron pair on the nitrogen atom is probably partially delocalised into the substituent group, with acquistion of some double-bond character by the N-C bond. (The spectrum of the AT-acetyl compound shows that rotation about the N-C bond is slow below O".) The hybridisation of the nitrogen atom will then be intermediate between s$* and s $ ~ , so that there will be an increase in the CNC angle and some flattening of the ring compared with morpholine. The barrier will therefore be lowered in the same way as that in cyclohexanone. l-Methyl-4- nitrosopiperazine is similar in that the N-N bond to the nitroso-group has some double-bond character. The spectrum shows broadening below -60" but the spectrum corresponding to a fixed chair form is not observed even at -95".The inversion is clearly well below that for N-niethylpiperazine, which has a coalescence temperature of - 26". CONCLUSIONS Figure 2 indicates that torsional effects probably dominate for the ring-inversion barrier. In order to confirm this, it would be useful to have more accurate data for AGX at a single temperature; alternatively, full data for AH: and AS: would pave the way for a more complete understanding of the effects discussed here. Such data can probably only be obtained reliably from the study of heavily deuteriated compounds, where there are no problems from long-range spin-spin coupling. A more thorough study of solvent effects on barriers for nitrogen-containing compounds should throw some light on the anomalies mentioned above.However, the general trends of Figure 2 are clear, and these may be used in a predictive fashion. For instance, it may be suggested that the barrier for 1,4-dioxan is significantly lower than that for cyclohexane (by ca. 0.9 kcal. mole-l). This seems to be true, since the spectrum corresponding to slow inversion has not been obtained; l3 however, in this case the situation is complicated because the axial- equatorial chemical shift is predicted to be Recently it has been reported 40 that a derivative, cis- 2,3-dimethyl-l,4-dioxan shows two methyl peaks at low temperatures. It has also been reported lgl, that ring inversion for s-trioxane is too fast for measurement by n.m.r.; our theory would indicate a value of ca.9.0 kcal. mole-l for AG: for this molecule. The predicted value for AGI for 1,3,5-trithian is 7.4 kcal. mole-I; spin-echo measurements lgb indicate that the free energy of activation for hexamethyl-1,3,5-trithian is ca. 7.8 kcal. mole-1. [8/053 Received, Janztary 15th, 19681 39 R. A. Spragg, Ph.D. Thesis, University of East Anglia, 40 G. Gatti, A. L. Segre, and C. Morandi, Tetvahedron, 1967, 1967. 23, 4385. 684 J. Chem. SOC. (B), 1968 Nuclear Magnetic Resonance Studies of Six-membered Rings. Part 1.l Ring Inversion in Heterocyclic Compounds By R. K. Harris * and R. A. Spragg. School of Chemical Sciences, University of East Anglia, Norwich NOR 88C Free energies of activation, AG:, for ring inversion are reported for a number of heterocycles.These values are obtained from coalescence temperatures observed for 'H n.m.r. spectra. The observed variations in AGI are correlated with differences in barriers to internal rotation in analogous acyclic compounds. The limitations and anomalies of the correlation are mentioned. and the implications are discussed. THE rates of ring inversion for a number of compounds containing six-membered rings have been studied by n.m.r.2 There is considerable variation between the rates for different compounds, and a corresponding variation in the values of the free energy of activation for ring inversion, AGZ. The dependence of this para- meter on the nature of the ring substituents has not been clearly established, and requires rationalisation. In this work we have obtained AG: values for a number of morpholine and piperazine derivatives.The results for these and other six-membered saturated heterocycles are considered in terms of a half-chair transition state for the ring inversion. Hendrickson calculated that the principal contribution to the inversion barrier in cyclohexane arises from torsional strain, and we have attempted to relate the observed variation in AGt to the variation in the torsional strain in the transition state. The torsional contribution to the inversion barrier is estimated by use of the same geometrical model as used by Hendrick~on,~ and by use of the barriers to methyl group rotation in compounds of the type MeXMe to obtain the substituent dependence. The variation in the estimated torsional contributions to the inversion barrier is sufficiently large to account for the observed variation in AGj, and some correlation is found.In some cases other factors are important. EXPERIMENTAL The compounds studied are all derivatives of piperazine and morpholine. The parent amines, N-methylpiperazine, NN'-diniethylpiperazine, N-methylniorpholine, N-phenyl- morpholine, N-acetylmorpholine, cis-2,5-dimethylpiper- azine, and tvans-2,6-dimethylmorpholine were all com- mercially available; they were dried and used without further purification. NN-Dimethylpiperazinium chloride hydrochloride was prepared by the method of Harfeni~t.~ NN-Dimethylmorpholinium iodide was obtained by treat- ing N-methylmorpholine with methyl iodide ; morpholine hydrochloride and piperazine dihydrochloride were obtained from the amines and hydrochloric acid.The amine salts were recrystallised from methanol and water. l-Methyl- 4-nitrosopiperazine was commercially available. The amines were studied in solution in methylene chloride, f.p. - 96.7", which was dried before use. As solutions of secondary amines in methylene chloride deposit crystalline material when set aside for a few days, all solu- tions were freshly prepared. hTo changes in the room Preliminary communication, R. K. Harris and R. A. Spragg, Chem. Comm., 1966, 314. 2 (a) J. E. Anderson, Quart. Rev., 1965, 19, 426; (b) F. G. Riddell, ibid., 1967, 21, 364. temperature spectra were noted after the time required for the low temperature measurements. Some solutions in methanol, f.p. - 97.8", and methylcyclohexane, f.p.- 126.4"C, were also studied. Tetramethylsilane (TMS) was used as an internal reference a t a concentration of ca. 3% v/v. The amine salts were studied in solution in sulphur dioxide, f.p. -75-5", with benzene as internal reference, since TMS was insufficiently soluble to provide a signal for the internal lock system of the spectrometer. All spectra were recorded on a Varian Associates HA- 100 Spectrometer a t 100 Mc./sec. The lowest temperature accessible was ca. - 100". The temperatures were esti- mated from the separation of the methyl and hydroxy- resonances of methanol; estimated accuracy & 2 O , though the consistency is higher. RESULTS All the compounds studied had spectra corresponding to rapid ring inversion at room temperature.Low temperature spectra corresponding to slow ring inversion, with separate signals from axial and equatorial protons, were observed for the following compounds : piperazine, N-methylpiperazine, NN'-dimethylpiperazine, morpho- line, AT-methylmorpholine, cis-2,5-dimethylpiperazine, trans-Z,6-dimethyl morpholine, and NN-dimethyl piper- azinium chloride hydrochloride. The case of N-methyl- piperazine is illustrated in Figure 1. N-Phenyl- and N-acetyl-morpholine gave spectra corresponding to rapid ring inversion even a t -95". No well-defined changes were observed in the low temperature spectra of the remaining amine salts; in these cases the tern- perature range was restricted because of the higher freezing point of sulphur dioxide. For compounds containing N-methyl groups the signal from this group was always a sharp singlet at room temperature.For solutions in methylene chloride and in methylcyclohexane the signal remains a sharp singlet down to -95", when ring inversion is slow. This indicates either that the methyl group is in only one conformation, or that interconversion between axial and equatorial positions caused by inversion of the configur- ation at nitrogen is rapid. In methanol solutions, how- ever, the N-methyl signal broadens appreciably below -70"; for N-methylmorpholine it has Wn 6 c./sec. at -95". This broadening presumably arises rrom a slow- ing of the inversion at nitrogen, and shows that the N-methyl group must exist in a significant proportion in both axial and equatorial positions. Hydrogen bonding 3 J .B. Hendrickson, J . Amev. Chem. Soc., 1961, 83, 4537. M. Harfenist, J . Amev. Chem. Soc., 1957, 79, 2211.Phys. Org. to the nitrogen atom will slow the rate of inversion at nitrogen, since such hydrogen bonds must be broken in the inversion process. Bottini and Roberts observed that N-inversion in aziridines occurred ca. times more slowly in hydroxylic than in non-hydroxylic sol- vents. Studies6 of the pH-dependence of the n.m.r. spectrum of lJ2,6-trimethylpiperidine have led to the suggestion that the rate of N-inversion may not always be fast compared to the ring-inversion rate for N-hetero- cyclic amines. However , complications arising from N-inversion are ignored in the present paper. The analysis of the low temperature spectra of the amines, and the chemical shifts and coupling constants FIGURE 1 'H N.m.r.spectra (100 Mc./sec.) of N-methylpiper- azine in CH,Cl, as a function of temperature; A, +30°; B, -226"; C, -558". The low-field group of lines in A and B is due to the protons of the CH, group u t o NH. The full intensity of the NMe line (and that of the NH line in B) is not shown obtained will be discussed in detail in a subsequent paper. In the cases of cis-2,5-dimethylpiperazine and trans-2,6-dimethylmorpholine the low temperature spectra were not analysed completely, as the resolution was inadequate. The separate signals from axial and equatorial methyl groups were, however, readily ob- served, and the chemical shift difference and coalescence temperature of these signals were obtained. In NN- 80, 5203.1188. A. T. Bottini and J . D. Roberts, J . Amer. Chem. SOC., 1958, ti J. J. Delpuech and M. N. Deschamps, Chem. Comm., 1967, dimethylpiperazinium hydrochloride the splitting of the NH, signal into a broad doublet was observed, but the rest of the spectrum was too complicated for observation of the separation of signals from axial and equatorial positions. As the spectra are complex, the inversion rate can be readily estimated only at the temperature of coalescence of the signals from the axial and equatorial positions. This coalescence was clearly observed in all cases, and the temperature of coalescence was well defined. It could be estimated generally to ca. &Z"; the transition from one signal to two was observed within a range of about 5". In Table 1 are listed the chemical shift differences between axial and equatorial positions, and the observed coalescence temperatures. Preliminary results for mor- pholine, N-methylmorpholine and NN'-dimethylpiper- azine have already been rep0rted.l ESTIMATION OF AG: For the case of two equally populated sites with no coupling (and with the linewidth in the absence of exchange neglected) the mean lifetime in one site when the two signals coalesce is given by: SA = 2'(x80)-' (1) where 6w is the chemical shift difference between the sites in c./sec.In the spectra observed here there are two factors to be considered: the coupling between the nuclei in the exchanging sites, and the coupling of these to other nuclei. For an AB system, with coupling between the sites, the mean lifetime when the A and B signals coalesce is given by: In general the effect of coupling to other nuclei on the exchange rate required to cause coalescence cannot be readily estimated.However, in certain cases it can be taken into account as a line-broadening phenonien~n.~ For a linewidth a t half height of 0.40 60 the lifetime a t coalescence is 0.57 q,, where T,, is the lifetime for coalescence with narrow lines. In the examples studied here, however, the broadening resulting from coupling to other nuclei generally takes the form of multiplet structure which is modified by the exchange process. Nevertheless the exchange rate for coalescence will probably not differ from that which would be observed in the absence of this coupling by much more than a factor of two, unless the magnitude of the coupling approaches half the chemical shift difference between the sites.The free energy of activation, AG$, may be obtained from the exchange rate a t the coalescence temperature, Tc, by application of the absolute-rate theory equation. It is generally accepted that the ring inversion process involves surmounting an energy barrier which leads to a twist-boat J. A. Pople, W. G. Schneider, and H. J. Bernstein, ' High R. J. Kurland, M. B. Rubin, and W. B. Wise, J . Chem. H. S . Gutowsky and C. H. Holm, J . Chem. Prays., 1956, 25, Resolution N.M.R.,' McGraw-Hill, New York, 1959. Phys., 1964, 40, 2426. 1228.J. Chem. SOC. (B), 1968 form, from which the molecule passes over an equivalent barrier leading either to the form with an inverted con- formation, or back to the original forni.1° The observed rate of chair to chair interconversion is therefore exactly half the rate at which molecules surmount the initial barrier, since they are equally likely to end in the inverted or the original conformation.The free energy of activation for rate a t the coalescence temperature is less than that assumed in the equation for AGI. If the exchange rate differs from that assumed by a factor of two, the calculated value of AGI, for a coalescence temperature of 2 5 0 " ~ , will be in error by about 0.3 ltcal. mole-'. In Table 1 are listed values of AGf for the compounds studied here a t the coalescence temperatures given. A TABLE 1 Axial-equatorial chemical shift differences, coalescence temperatures, and free energies of activation for ring inversion obtained at 100 Mc./sec.a,, Tc AG t (I) Piperazine CH,Cl, 57; W/V N-CH, 16 208 10.3 (111) NN'-Dimethylpiperazine CH,Cl, 20% v/v N-CH, 62 265 12.5 MeOH 20:b v/v N-CH, 68 270 12.7 (IV) N-Methylpiperazine CH,Cl, 20q4 v/v MeNCH, 80 247 11.5 MeOH 20y0 v/v MeNCH, 80 252 11.7 (Y) N-Methylmorpholine CH,Cl, 2004 v/v N-CH, 56 242 11.5 O-CH, 22 233 11.5 RkOH 20Oj, V/V N-CH, 56 243 11.5 Solvent Conc. Signal (c./sec.) ( O K ) (kcal./mole) ................................................... ................................................... (11) Morpholine CH,Cl, 57$ V/V O-CH, 2 3 203 9.9 ................................. ....................................... ....................................... C,H,,i\le 10% v/v S-CH, 50 236 11.2 (VI) tvans-2,6-Dimethylmorpholine CH,Cl, 5O4, v/v C-Me 30 187 9.0 ......................................................... (VII) cis-2,5-Dimethylpiperazine CH,Cl, 5% w/v C-Me 26 199 9-6 (VIII) NN-Dimethylpiperazinium chloride hydrochloride SO, NH, 34 214 10.3 0 AG: is calculated from equation 4 with 80 = a,,, i.e., ignoring coupling effects. TABLE 2 coalescence temperatures Free energies of activation a for ring inversion, calculated from literature values of asial- (IX) Cyclohexane ....................................... (X) Pentamethylene sulphide ........................ (XI) Thian l-oxide ....................................... (XII) Tetrahydropyran ................................. (XIIT) Piperidine .......................................... (XIV) N-Methylpiperidine ..............................(XV) 1,3-Dioxan .......................................... (XVI) 1,3-DimethyIhexahydropyrimidine ............ (XVII) 1,3,5-Trimethylhexahydrotriazine ............ Solvent Cs2 CH,CI, CH,CI, CD,OD :?,OD CD,,OD Me,CO Me,CO CDCl, CDCl,, CDCl, CHFCI, Signal CHI> S-CH, S-CH, O-CH, O-CH, N-CH, N-CH, 2-CH2 2-CH2 2-CH2 N-CH, N-CH, N-CH, (c. /sec.) 28-7 30 52.2 33 d 55 26.1 56.5 19.3 20 73.8 54.7 52-8 53.8 -equatorial shift differences and T c ( "4 212 180 203 193 208 210 252 188 193 244 268 269.5 268.1 AG: 10.3 11 8.7 12 9.8 12 9.3 12 9.9 13 10.4 14 11.9 14 9.3 15 9.5 16 11.3 17 12.7 18 12.8 19a 12.8 19b (kcal./mole) Ref. 0 AGt Calculated from the coalescence of AB spectra in all cases except cyclohexane. b Spectrometer frequency 60 Mc./sec.in d The value is assumed t o We have obtained a AGt value of ca. 11.4 kcal. molc-l for an undeuteriated sample some cases and 100 Mc./sec. in others. be the same (in p.p.m.) as in solution l3 in CS,. of this compound in CH,CI, solution. Value estimated from comparison with other compounds. chair to twist-boat conversion is therefore given [from equation (l)] by AGI = 4.58TJ9.97 +- log (TJSw)] cal. mole-l The result of ignoring coupling between the exchanging sites and to other nuclei is that the estimated AGS values will be lower than the true values, since the true exchange (3) 10 E. L. Eliel, N. L. Allinger, S. J. Angyal, and G. A. Morrison, l1 F. A. L. Anet and A. J . R. Bourn, J . Amer. Chem. SOC., l 2 J. B. Lambert and R. G.Keske, J , Ovg. Cheilz., 1966, 31, l3 G. Gatti, A. L. Segre, and C. Morandi, J . Chem. Sac. ( B ) , J. B. Lambert, R. G. Keske, R. E. Cahart, and A. P. ' Conformational Analysis,' Interscience, New York, 1965. 1967, 89, 760. 3429. 1966, 1203. Jovanovich, J . Amev. Chem. SOC., 1967, 89, 3761. reasonable estimate of the accuracy of these values is 0.4 kcal. mole-" the relative values will be more accurate since the error due to neglcct of coupling is always in the same direction. Errors as large as 5" in T , lead typically to errors of only ca. k0.2 kcal. mole-l in AGf. In Table 2 are given the values of AGS obtained from values of coalescence temperatures and axial/equatorial shift differences quoted l5 J . E. Anderson and J . C. D. Brand, Tvaias. Faraduy SOC., 1966, 62, 39.l6 H. Friebolin, S. Kabuss, W. Maier, and A. Luttringhaus, Tetvahedvon Lettevs, 1962, 683. l7 ( a ) F. G. Riddell and J. M. Lehn, Chem. Comm., 1966, 375; (b) F. G. Kiddell, J . Chem. SOC. ( B ) , 1967, 560. J. M. Lehn, F. G. Riddell, B. J. Price, and I. 0. Sutherland, J . Chem. SOC. ( B ) , 1967, 387. l9 ( a ) I<. F. Farmer and J. Hamer, Chem. Comm., 1966, 866; ( b ) H. S. Gutowsky and P. A. Temussi, J . Amev. Chem. Soc., 1967, 89, 4358.Phys. Org. 687 in the literature. In these cases the spectra are all of the simple AB type, and the value of AGS at the coalescence temperature is obtained using a modification of equation (3) to incorporate (2). THEORETICAL CONSIDERATIONS An estimate of the barrier to inversion in cyclohexane has been made by Hendrick~on.~ He considered three contributions to the energy of a particular conformation : torsional energy resulting from changing the dihedral angles between bonds to neighbouring carbon atoms from the 60" of a staggered conformation; bond angle strain due to distortion of valency angles away from the tetrahedral angle ; and repulsions between non-bonded hydrogen atoms.The energy of the half-chair transition state was calculated to be 12.7 kcal. mole-l above that of the chair form, cf. the experimental value of 10.8 kcal. mole-l for the eizthalpy of activation for ring inversion.ll It has been suggested8 that the calculated value is too high because the chair form does not have exactly tetra- hedral internal angles.20 A more recent calculation by Allinger et aL21 gives 12-00 kcal.mole-' for the excitation energy froin the chair to the half-chair form. The principal contribution to the barrier was found to be the torsional strain, calculated to be 7-6 kcal. mole-l using a cosine potential of the form : I' = (V0/2)(l + cos 34) with a value of 2-80 kcal. mole-l for Vo, taken from the torsional barrier in ethane. This value of Yo is likely to be too low (the value 22a in propane is 3.2 kcal. mole-l) but there is no adequate model compound for estimation of the torsional barrier about a C-C bond in cyclohexane. suggests that torsional strain accounts for ca. 60% of the inversion barrier; the work of Allinger et aZ.21 does not affect this conclusion. We shall there- fore consider here the variation in this contribution to the barrier which will occur when a ring carbon atom is replaced by a hetero-atom.In order to do this we shall assume that the ring geometry, both of the chair and the half-chair conformation, is not greatly changed by the replacement. The replacement of a methylene group by nitrogen or oxygen has only a small effect on the geometry of the chair form, but replacement by sulphur has a much larger effect. Typical bond lengths and angles are given in refs. 21 and 23. The torsional strain in the half-chair state is obtained here by use of a cosine potential of the form given above, where 4 is the dihedral angle between bonds to neighbouring atoms in the ring. The values of V0 are taken from the barriers to methyl group torsion in the acyclic compounds of the type MeXMe.The dihedral angles are those given by Hendrickson for the half-chair state of cyclohexane, shown in Scheme 1. The use of the compounds MeXMe Hendrickson * It is assumed that enthalpy differences may be equated to differences in energy obtained from potential energy curves ; this procedure ignores contributions of volume (PV term) and temperature to H or assumes cancellation of such contributions when AH is considered. ignores any effects on the torsional barrier from ring atoms p and y to X. 5 I SCHEME 1 The geometry of the half-chair form of cyclo- hexane 4 9, 9, f14 8, 6, 41 4 2 4 3 4 4 4 5 4 6 CCC Angle 113.5 118.8 118.5 113.5 106.0 106.0 Dihedral angle 19.1 0.0 19-1 56.2 75.0 56.2 For a precise definition of the dihedral angle + see ref. 3. In this way we can obtain the torsional contribution to the enthalpy of formation of each half-chair form of a substituted cyclohexane.I t will be more convenient to consider in what follows the difference in enthalpy of formation between a half-chair state of the substituted cyclohexane and that of cyclohexane. This is obtained by considering those dihedral angles involving bonds to hetero-atoms, and, for an individual half-chair form, i, is given * by where AHc$ is the enthalpy of activation for cyclo- hexane, AVO= is the difference between the barriers to methyl group torsion in MeXMe and propane, and 4si is the appropriate dihedral angle about a bond in the ring to the heteroatom X. The summation is over all such bonds to hetero-atoms (each heteroatom involves two bonds).None of the examples discussed here has two adjacent hetero-atoms. The values of AH& - AH,: for the half-chair states of some substituted cyclohexanes are given in Scheme 2. A substituent occupying position 5 or 6 in the half-chair (see Scheme 1) has little effect on the enthalpy of form- ation; the dihedral angles about these positions are close to those in the chair form. The greatest effect occurs when the substituent is in position 2 or 3 as there is complete eclipsing across the 2-3 bond, and the dihedral angles across the 1-2 and 3-4 bonds are also small. To estimate the relative rates of inversion for the different compounds it is necessary to make some as- sumption about the entropy changes involved. I t will be assumed that the entropy change caused by formation of a single half-chair from a chair form is the same in all cases.This procedure neglects variations in the con- tributions of rotation and vibration to AS:; this is a reasonable assumption, since the change in geometry is 20 hl. Davis and 0. Hassel, Act. Chem. Scand., 1960, 17, 1181. 21 N. L. Allinger, 31. A. Miller, F. A. Vancatledge, and J. A. Hirsch, J . Amev. Chem. SOC., 1967, 89, 4325. 22 (a) G. B. Kistiakowsky and W. W. Itice, .J. Chem. Ph-ys., 1940, 8, 610; (b) E. Hirota, C. Matsumura, and Y. Morino, Bull. Chem. SOC. Japan. 1967, 40, 1124. 23 K. E. Marsh, Acta Ctyst., 1955, 8, 91.688 J. Chem. SOC. (B), 1968 may also be used to define an overall difference in the free energies of activation for ring inversion, AGS - AGc$ : k/k, = exp[-(AGS - AGc$)/RT] The quantity AGJ is that normally reported from n.m.r.measurements of rates of inversion. Thus AGc$ - AGS may be calculated from the estimated enthalpies of formation for the half-chair states: exp[-(AG$ - AG,f:)/RT] = The calculated values may then be compared to experi- mental ones to test the validity of the simple model used. In Table 3 are listed values of the barriers to methyl group torsion for a number of compounds of the type MeXMe; values of AVox are also given. Table 4 shows values of ni exp[-(AHiJ - AHCS)/Rq and of (AGf: - AG,I) calculated at the coalescence temperature for each compound. As the torsional barriers in propane and &Zni exp[ - ( AHiS - AHcS)/RT] similar for all the substituted cyclohexanes. The ob- served ASS for the inversion of cyclohexane differs somewhat from that calculated on a simple baskf1 Mono- lf3-Di- 1,4-Di- 1,3,5-Tri- substituted substituted substituted substituted A J x 1' x-x v 0.I6 AV,x 0.94 AVOX 0.78 AVOx + 0.78 AV0y 2-71 AV,x I *77 AV0x I .93 AV0x 1-77 AVOx + 0. I6 AV,y SCHEME 2 The possible half-chair states of ring-substituted cyclohexanes, and the torsional contribution to the enthalpy of formation from the corresponding chair forms, relative to that in cyclohexane The rate of formation of any half chair state from the chair form is given by ki = kT - exp[ - (AGif:/RT)] h where AGit is the free energy of formation of the half- chair state. With the assumption that the entropy change in this process is always the same, the relative rates of formation of different half-chair states can be obtained from the difference in the enthalpies of form- ation.For two states with enthalpies of formation AHiS and AHjS: ki'/kj' = exp[-(AH& - AHjf:)/RT] Thus the rate of formation of any half chair state, relative to the rate of formation of a half-chair state in cyclo- hexane at the same temperature, is given by ki'/k,' == exp[ - ( AHi'i - AH,$)/RT] The overall rate of ring inversion is obtained by sum- ming over all the six half-chair forms which are obtained directly from a given chair (mirror-image half-chairs may be ignored). For cyclohexane there are six equivalent half-chair forms, and for the substituted cyclohexane there are ni half-chair states with the same value of AHi$. The relative rates of ring inversion are then given by: k/k, = Q Cni exp[-(AHiS - AHcS)/RT] 1 The relative rates of ring inversion for the two compounds 24 P.H. Kasai and R. J. Myers, J . Chem. Phys., 1959, 30, 1096. 25 W. G. Fateley and F. A. MiIler, Spectrochim. Acta, 1962, 18, 977. 26 D. R. Lide, jun. and D. E. Mann, J . Chem. Phys., 1958, 28, 572. TABLE 3 Barriers a to methyl group torsion type MeXMe v4l A VO, MeCH,Meb ...... 3.2 0.00 MeOMe ............ 2.72 -0.48 MeNHMe ......... 3.28 +0.08 MeN(Me)Me ...... 4.40 +1.20 MeSMe ............ 2.13 - 1.07 MeS(0)Me ......... 2.94 -0.26 MeCH(Me)Me ... 3-90 +Om70 MeC(0)Me ...... 0.78 -2.42 in compounds of the Method Ref. Specific heat 22a Microwave 24 25 Far i.r. Microwave 26 Microwave 27 Microwave 28 Microwave 29 Microwave 3.0 0 Values of Vo and AVOx are in kcal.mole-'. A recent microwave determination 22b of the barrier in propane, includ- ing interaction between the two tops and therefore quoting two parameters, gives results comparable to the thermo- dynamic value of Vo given here; small variations in this quantity would not affect our general conclusions. dimethylamine are so similar, separate data are not given for compounds differing only by replacement of CH, by NH. The values of ni exp -(AHit - AH,X)/RT show the relative contribution of the different half-chair forms to the overall inversion rate. There are generally several different routes available for ring inversion, and this leads to differences in the entropy of activation for ring inversion in different compounds, even though the entropy of formation of a single half-chair state is treated as constant.Consider the two extreme cases: cyclohexane, in which there are six equivalent half-chair forms through which the inversion proceeds, and a substituted compound in which one half-chair is of much lower energy than the others so that inversion proceeds almost exclusively through this one form. The entropy 27 L. Pierce and M. Hayashi, J . Chew. Phys., 1961, 35, 479. 28 H. Dreizler and G. Dendl, 2. Naturforsch., 1965, 20a, 1431. 29 D. R. Lide, jun. and D. E. Mann, J . Chem. Phys., 1958, 29, 3O J. D. Swalen and C . C. Costain, J . Cltem. Pltys., 1959, 31, 914. 1562.Phys. Org. of activation for ring inversion for cyclohexane will be more positive by Rln6 than that for the substituted compound. In other cases the overall entropy and TABLE 4 Energies of the various half-chair states of heterocyclic compounds relative to that for cyclohexane a Hi (XII) 9 - 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 6 Form A B C A B C A B C A B C G (X = 0) H ( X = O ) G H D E F D E F I (X = 0) J ni exp[ - (AH+ - AH,*) /RTcl 2.60 5.86 1.34 0.34 0.02 2.22 3.26 6.84 3.5 24.6 20.6 394 0.64 0.04 8.62 0.07 0.03 7.0 51.8 24.4 0.21 0.004 0.02 AGt - AGC (kcal./mole) - 0.60 -+ 0.63 - 0.29 - 1.53 -0.21 -+ 2.08 - 1-05 + 1.67 -+ 3.6 Values are given for the coalescence temperatures listed See text for explanation of the notation.in Tables 1 and 2. b See Scheme 2. c ,4t Tc (193"~). enthalpy of activation are not so readily defined, but are given by the general expression : exp( - AGZIRT) = exp( ASJ/R) exp( - AHJ/-RT) = 2 ni exp( - AHi'/RT) 1 Measured values of AS: and AHt are available for a number of compounds, but are not considered31 as reliable as the values of AGZ.Moreover the inter- pretation of absolute values of AS: is often obscure (though differences in A S between related compounds may be of more as we have indicated above). Values of AGX are more commonly available than AH: or A S values and, for all the above reasons, we feel that at the present stage it is best to consider the variations of AG:, rather than those of AH: or AS:. The free energy of activation is often only known at T,, which is different for each molecule; our estimations of AGt are also made the appropriate coalescence temperatures. In many cases several non-equivalent half-chair forms will contribute significantly to the observed inversion rate.Recently34 it has been suggested that for sub- stituted cyclohexanes only the half-chair transition 31 A. Allerhand, F-M. Chen, and H. S. Gutowsky, J . Chew. 32 R. J. *4braham and D. B. McDonald, Chem. Comni., 1966, Phys., 1965, 42, 3040. 188. state of lowest energy needs to be considered. Such statements must be treated with caution unless it can be demonstrated that the various half-chair forms differ significantly in ene1-gy.3~ The procedure developed here emphasises the ill-defined nature of the reported values of AH$ and AS$. If the half-chair forms differ only slightly in energy, these parameters (as defined above) will be temperature dependent. and AH: is to plot the logarithm of the inversion rate constant k& (or, as has been suggested,33 k,&) against T-l.It is assumed that there is a linear relationship between these quantities (deviations from linearity are in practice not easy to observe); this is equivalent to assuming that AS$ and AH: are independent of tempera- ture. Fortunately, use of typical values for ring in- version energies (Table 4) shows that the temperature- variations of AH: and AS: from the cause cited above are slight (ca. 0.1 kcal./mole and 0.4 e.u. respectively for a temperature change of 100" in the region of T , and room temperature). However the values of AH: ob- tained by the normal procedure may be up to 0.2 kcal./ mole higher than the lowest AHi: value. The normal procedure for evaluating AS DISCUSSION Figure 2 shows the result of plotting the calculated value of (AGX - AG,:) against the difference between the measured free energy of activation for ring inversion and that for cyclohexane at the same temperature.The calculated variation in the torsional contribution to the barrier is sufficiently large to account for the observed range of AGI values, Furthermore, certain trends are described qualitatively ; replacement of CH, by NH has little effect on AG:, but the presence of an N-methyl group causes a marked increase, and oxygen and sulphur both reduce AGJ. Agreement between the observed and calculated values is surprisingly close for most compounds, but there are marked deviations for some of the compounds with N-methyl substituents. The barriers for N-methylpiperidine, N-niethylpiperazine and N-methylmorpholine are all higher than predicted.It is surprising that the barrier in N-methylmorpholine is not lower than that in N-methylpiperazine, despite the presence of the oxygen atom; the barriers in morpholine and tetrahydropyran are appreciably lower than those in piperazine and piperidine respectively. The inadequacies of the model used to estimate AGI are of two types: those arising from the calculation of the torsional contribution (discussed in the preceding section), and those resulting from neglect of other effects. The importance of non-bonded interactions and angle-bending strain in determining the barrier is not readily ascertained. In considering the barrier we are concerned with the difference between the interactions in the chair and half-chair forms.-4lthough the 33 R. K. Harris and N. Sheppard, J . iMol. Spectroscopy, 1967, 23, 231. 34 S. Wolfe and J. R. Campbell, Chern. Cottiin., 1967, 874; 1967, 877.690 J. Chem. SOC. (B), 1968 magnitude of the non-bonded interactions for a parti- cular conformation will change with different sub- stituents, there may be some cancellation of this variation in taking the difference between the interactions in two 3O t 2.0L x m / txm) / - 2.0 I I t -2.0 -1.0 0 I.0 2.0 3.0 FIGURE 2 The observed free energies of activation to ring inversion, relative t o cyclohexane, plotted against values calculated as in the text. The numbering of the points is that used in Tables 1 and 2. Both calculated and observed values of AG: - AG,: are for the coalescence temperatures given in the Tables.In cases where several values are given in the Tables, an average has been used for this Figure. Compounds (VI), (VII), and (1;III) have not been included because of lack of knowledge about the appropriate torsional barriers forms. Hendrickson estimated that the effect of non- bonded interactions in cyclohexane is small, and it is unlikely that the variation in this effect contributed much to the observed variation in AGZ values, except for the compounds containing methyl groups, to be discussed later. The variation in angle-bending strain may be estimated for oxygen and nitrogen substituents from the relative case of deformation of CCC, COC, and CNC angles, since the geometry is very similar in all these cases.For sulphur tlie bond angles are rather different, and the angle strain is not readily estimated. The vibrational frequencies for CXC bending in com- pounds of the type MeXMe range from 283 cm-l for Me,S to 426 cm.-l for Me,N.25'35p36 In general the vibrational frequencies increase in the same order as do tlie torsional barriers, with the exception of the case of dimethyl ether, which has the highest bending frequency but a comparatively low torsional barrier. The vari- ation in the contribution of angle-bending strain to tlie barrier will therefore generally reinforce the variation of the torsional contribution,* the angle bending strain being greatest at those positions for which the torsional strain is greatest (Scheme 1). Solvent-solute inter- actions may affect the barrier. There is evidence that these may be important in the case of nitrogen-containing compounds.For N-methylmorpholine AG: is about 0.3 kcal. mole-l lower in methylcyclohexane than in methyl- * While this paper was in preparation, an article appeared 2b which discussed the various contributions t o the energy of six- membered heterocycles and suggested that much of the potential energy of the transition state to inversion must be in the form of angle strain. For reasons discussed in the text we believe this t o be unlikely. 7 We thank a referee for this suggestion. ene chloride or methanol. Similarly, for 1,3,5-trimethyl- hexahydrotriazine AG* is about 0.5 kcal. molep1 lower in hydrocarbon solvents than in deuteriochloroform or deuterium oxide.Most of the AGt values given here are for solutions in chloroform, niethylene chloride, or methanol. The values for nitrogen-containing com- pounds would all probably be slightly lower if ' non- interacting ' solvents were used. The relative AGt values for different compounds, however, are unlikely to change greatly. For the majority of these nitrogen- containing compounds tlie variation in AG: for ring inversion follows the pattern expected from consider- ation simply of the torsional contribution to the barrier. I t is possible that solvent effects may account for the high values of AGZ noted above for N-methylpiperidine, N-methylpiperazine and N-met hylmorpholine. How- ever, it is difficult to see why, if this is the case, the values for the other nitrogen-containing compounds are not correspondingly high.Perhaps these anomalies merely illustrate the inadequacy of the simple model used. Other complicating factors not considered here are ( a ) that the transition state may not be of the form illustrated in Scheme 2, (b) that nitrogen-inversion may affect the observed barrier in some cases,lSb and (c) that in compounds with two heterocyclic atoms there may be effects from bond dipole interactions.7 The possibility that twist-boat forms have energies closer than ca. 1 kcal. mole-l to that of the chair form is also neglected. The data for compounds with methyl groups in the ring are of some interest, since non-bonded interactions are likely to be important. In the chair form a methyl group in an axial position experiences a repulsive interaction of about 1.7 kcal. mole-l with the axial protons in the 3- and 5-positions.lO In the half-chair form there are six different positions which a methyl group can occupy [formula (l)].Only two positions, 5 b 6 ' 4 and 6, are sufficiently close to other positions, 6' and 4' respectively, to experience interactions as large as those for an axial methyl group in the chair form. The re- pulsions in these positions will in fact be slightly larger than in the chair form, as the interacting positions are slightly closer together. Thus if a methyl group which occupies an axial position in the chair form is in position 4 or 6 in the half-chair, the non-bonded interactions will increase the barrier relative to that in an unsubstituted compound (unless there are compensating changes for 35 N.Sheppard and D. M. Simpson, Quart. Rev., 1953, 7, 19. 36 ( a ) A. I<. Salonen, A n n . Acad. Sci. Fennicae, 1961, 67, 1; (b) W. D. Horrocks, jun. and I;. A. Cotton, Spectvochim. Acta, 1961, 17, 134.Phys. Org. 691 non-bonded interactions involving other substituents) . If the methyl group occupies any other position in the half-chair the barrier will be reduced relative to that in an unsubstituted compound. The value 3' of AGS for 1,l-dimethylcyclohexane is 10.2 kcal. mole-', close to that for cyclohexane. The methyl groups can occupy positions 1 and 2 in the half- chair, whereas one must be axial in the chair form. The value of AGS might therefore be expected to be less than that for cyclohexane. There are, however, two factors increasing AG: relative to that for cyclohexane.The torsional contribution will probably be larger, as the barrier to methyl group rotation in isobutane, 3.9 kcal. mole-l, is appreciably larger than that in propane. In addition, there are only two equivalent half-chair forms, compared with six for cyclohexane. This reduces the inversion rate by a factor of three, equivalent to an increase of about 0.5 kcal. mole-l in AG:. The situation is very similar for 1,l -dimethylpiperazinium chloride hydrochloride, and the value of AG:, 10.3 ltcal. mole-l, is again close to that for cyclohexane. trans-2,6-Dimet h ylmorpholine and cis-2,5-dime t hyl- piperazine have values of AG$ lower than those for the unsubstituted amines by 0-9 kcal. mole-l and 0.6 kcal.molep1, respectively. In the chair form of both coin- pounds there is an axial methyl group, but in the half- chair there are several forms in which the steric inter- action is reduced, see Scheme 3. In these cases the steric interactions are important in reducing the barrier to inversion. trans-2,6- cis-2,5- D~n~ethylniorpholii~e Dimethylpiperazine Half- 1 chair H 6 V H N H SCHEME 3 The chair and half-chair forms of compounds with methyl groups in the ring The presence of an sp2-hybridised atom in the ring appears to lower the inversion barrier ; cyclohexanone, for example, has a spectrum which is unchanged38 at -84". The torsional contribution to the barrier is expected to be much reduced in this case; the barrier to methyl group rotation in acetone is only 0-78 kcal. mole-l. A further cause of the low barrier is the large 37 H. Friebolin, W. Faisst, H. G. Schmid, and S. Kabuss, letvahedvon Letters, 1966, 1317. 38 P. Grander and Ill. 31. Claudon, Bzdl. SOC. chim. France, 1966, 763. CCC angle at the carbonyl group in the chair form, which will reduce the angle-bending strain in the half-chair. N-Acetyl- and N-phenyl-morpholine both show rapid ring inversion at -95", indicating that the inversion barriers are appreciable lower than in morpholine. In both these compounds the unshared electron pair on the nitrogen atom is probably partially delocalised into the substituent group, with acquistion of some double-bond character by the N-C bond. (The spectrum of the AT-acetyl compound shows that rotation about the N-C bond is slow below O".) The hybridisation of the nitrogen atom will then be intermediate between s$* and s $ ~ , so that there will be an increase in the CNC angle and some flattening of the ring compared with morpholine. The barrier will therefore be lowered in the same way as that in cyclohexanone. l-Methyl-4- nitrosopiperazine is similar in that the N-N bond to the nitroso-group has some double-bond character. The spectrum shows broadening below -60" but the spectrum corresponding to a fixed chair form is not observed even at -95". The inversion is clearly well below that for N-niethylpiperazine, which has a coalescence temperature of - 26". CONCLUSIONS Figure 2 indicates that torsional effects probably dominate for the ring-inversion barrier. In order to confirm this, it would be useful to have more accurate data for AGX at a single temperature; alternatively, full data for AH: and AS: would pave the way for a more complete understanding of the effects discussed here. Such data can probably only be obtained reliably from the study of heavily deuteriated compounds, where there are no problems from long-range spin-spin coupling. A more thorough study of solvent effects on barriers for nitrogen-containing compounds should throw some light on the anomalies mentioned above. However, the general trends of Figure 2 are clear, and these may be used in a predictive fashion. For instance, it may be suggested that the barrier for 1,4-dioxan is significantly lower than that for cyclohexane (by ca. 0.9 kcal. mole-l). This seems to be true, since the spectrum corresponding to slow inversion has not been obtained; l3 however, in this case the situation is complicated because the axial- equatorial chemical shift is predicted to be Recently it has been reported 40 that a derivative, cis- 2,3-dimethyl-l,4-dioxan shows two methyl peaks at low temperatures. It has also been reported lgl, that ring inversion for s-trioxane is too fast for measurement by n.m.r.; our theory would indicate a value of ca. 9.0 kcal. mole-l for AG: for this molecule. The predicted value for AGI for 1,3,5-trithian is 7.4 kcal. mole-I; spin-echo measurements lgb indicate that the free energy of activation for hexamethyl-1,3,5-trithian is ca. 7.8 kcal. mole-1. [8/053 Received, Janztary 15th, 19681 39 R. A. Spragg, Ph.D. Thesis, University of East Anglia, 40 G. Gatti, A. L. Segre, and C. Morandi, Tetvahedron, 1967, 1967. 23, 4385.

ISSN:0045-6470    

DOI:10.1039/J29680000684

出版商:RSC    

年代:1968

数据来源: RSC