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THE PROTON MAGNETIC RESONANCE SPECTRUM OF CYCLOPROPYLAMINE THE A2.42'X CASE WITH STRONG CROSS-COUPLING: A PSEUDO FIRST-ORDER SPECTRUM WITH COMBINATION LINES Department of Chemistvy, Vniuersity of Manitoba, Fl'innipeg, Manitoba Received July 2, 1963 Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 ABSTRACT By means of the anisotropic solvent effect of benzene on the ring protons of cyclopropylamine the proton spectrum is converted to a12A2'X. Since the cross-coupling from the A2 to the Az' protons is large the spectrunl does not approximate to a pseudo first-order AX4 spectrum. Instead, it is one which may be described as pseudo first-order with combination lines. The presence of the latter allo~vsa fairly complete set of coupling constants to be derived in a simpler way than by a computer attack on the general -12B2X spectrum. Conversely, the approach developed here, when applicable, allows the derivation of reliable input parameters for a computer program. From the temperature dependence of the A2Xz'X case the A2 and ,Aa' protons can be distinguished and it is found t h a t the protons trans to the amino group are preferentially shifted to high field by the beilzeile molecules. IKTRODUCTIOS Sometinles many of the theoretical transitions in high-resolution n.m.r. spectra For personal use only. effectively coalesce or may be too weak to be observed. Since the analysis of the spectra usually reduces to the problem of assigning the observed peaks, there may then be more than one assignment and, therefore, more than one set of coupling constants which fits the observed spectrum. Abraham and Bernstein have discussed this situation for the ABX, A2X2,and ABXY spectra in some detail (1). In practice it is usually found that only sums or differences of coupling constants can be obtained from the observed pseudo first-order spectra. In general, such deceptively simple spectra are expected for the ABC. . . X Y Z . . . systems when quantities of the type J A B ,JXY are large compared t o the chemical shift differences a,,! ax, plus quantities of the type JAx-JAY. Separations between the lines in each group are then given by the average of constants of the type JAX, J A Y When the system has some symmetry the general statements have to be modified slightly (1). Exainples of deceptively simple spectra are discussed in reference 1 and misinter- pretations in the literature are also discussed. A similar discussion for the ABX case was given by Schaefer ( 2 ) , by Grant and Gutowsky for the AzBzcase (3), and by llusher and Corey for the three-spin system (4). 14-e discuss here the ring-proton spectrum of cyclopropylamine. The proton on the substituted carbon atom is shifted far enough to low field by the inductive effect of the amino group that, in general, an A2BzX system is obtained a t 60 i\Ic/s. This case was first discussed by Richards and Schaefer ( 5 ) . By means of solvent effects we bring about a zero shift between the A and B protons and hence obtain an A2A2'X system. A pseudo first-order spectrum is not found, however, but rather what may be described as a pseudo first-order spectrum with combination lines. As we shall show, this is due to a strong cross-coupling between A and A' protons. Such a situation could have been qualitatively lHolder of a C.I.L. Fellowship, 1966-1965. Canadian Journal of Chemistry. Volume 41 (1963) HUTTON AND SCHAEFER: CYCLOPROPI'LAMINE SPECTRUM 2775 predicted from the discussion in reference 1. I t appears that our example is the first of this type. I t will also appear t h a t the existence of the few extra lines in the Az,42'X spectrum allows one to place quite stringent limits on the values of the coupling con- stants. This is important in obtaining good starting values for the parameters in the computer solutions for systems as coinplex as a strongly coupled A2B2X. EXPERIMENTAL Proton spectra were taken oil a Varian DP6O i1.m.r. Spectrometer and calibrations were carried out by t h e side-band technique relative to internal tetramethylsilane (TMS). Spectra were taken in a number of solvents but in none of them except benzene were they strikingly different from the standard spectrutll in CDC1, Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 recorded by Bhacca et al. (6). I n benzeile it was possible to obtain a spectrum of simple appearance a t a concentration of about 1:4 by volun~e.This conceiltration was very critical and the collapsed peaks mere found t o separate rapidly with concentration on either side of the critical one. Spectra of this critical solution in benzene were run a t various temperatures up to 131' C. Dissociation of the very weak complex formed with b e n ~ e n e(7) allowed the separation of the collapsed peaks to be followed in a sensitive way. I n this way the assignments of the peaks could be checked and it was also possible t o obtain the relative order of the shifts of the two sets of equivalent protons in the uncollapsed region. RESGLTS AXD DISCUSSIOY T h e proton spectrum of the critical solution in benzene is shown together with calcu- lated spectra in Fig. 1. In Fig. 2 the spectrum of the same solution a t 64' C is shown. I . The Case A2A2'X T h e critical solution spectrum of the ring protons corresponds to the case A2AztX.* For personal use only. The limiting case where the couplings from A z and A2' to X are equal has already been discussed by one of us ( 8 ) . None of the possible 46 combination lines were considered i n t h a t treatment. Because some of these play a major role in our discussion and for reasons of clarity we discuss here a rather general case, including the combination lines. T h e ring-p-roton system for the critical solution can be characterized as in I : We shall assume that Jlz = J34 This is the only approximation we make and from the analysis of cyclopropylcarboxylic acid (9, 10) this approximation is considered t o be valid to a t least 0.5 c.p.s. Thirty-six of the line positions are independent of J12 and J34and from the analysis i t is clear t h a t the error in many other line positions will be about half t h a t of the difference in J l z and JS4or about 0.25 c.p.s. T h e matrix elements in the F, representation are given in reference 8. In the A2AZtX case the matrix is factored to eight 1 X 1, eight 2 X2, and two 4 x 4 submatrices. Positive quantities A , B , C, D and angles 6, 4, $, y are defined by [I] 4 A cos 20 = J35-J15 4 B cos 24 = J15-J3.5 2A sin 26 = J23fJ13 2B sin 24 = JZ3+Jl3 4C cos 2P = J35 -J15 4 0 cos 2 y = J15 -J35 2C sin 2$ = J23-J13 2 0 sin 27 = J13-J23 *The amine protons gave a broad peak. Apart from a slight broadening of the neighboring proton there was n o evidence of a n y coupling with the ring protons by either the amine protons ou the nitrogen nucleus. CANADIAN JOURNAL OF CHEMISTRY. O. V L 41, 1963 Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 For personal use only. I 64 OC 'I X PROTON 1 I I 140 130 I20 10 1 40 30 20 10 C PS. from TMS H 2 FIG. 1. Proton magnetic resonance spectrum a t 60 Mc/s of cyclopropylalnine in benzene a t room temperature. Calibration is in c.p.s. with respect to vo(1-UA) and vo(1-ux), which are a t 16.2 c.p.s. and 123.2 c.p.s. to low field of internal TMS, respectively. I n the calculated spectrum, the two large pseudo triplets in the region are drawn to one-third the intensity of the other transitions. The amino group resonance a t 84.8 c.p.s. to low field of internal T M S is not shown. FIG.2. Proton lnagnetic resonance spectrum a t 60 R.Ic/s of cyclopropylamine in benzene a t 64' C; calibration is to lo\\- field of internal TMS. T h e amino group resonance a t 90 c.p.s. is not shown. The transitions of the X proton which do not vary in position on introduction of a shift between A2 and A2' are indicated by the arrows. The indicated orthogonal transformations were carried out on the eight 2x2 matrices and the statioilary spin functions and energies are given in Tables I11 and 117 of refer- ence s.* "Repuint requests for this paper will also receive a r e p ~ i n of reference 8. t HUTTON A N D SCHAEFER: CYCLOPROPYLAMINE SPECTRUM 2777 Selection rules allow a maxinlum of 110 transitions for the five nuclei. Of these, 46 are coinbination lines which were not considered in reference 8 but which will be taken into account here. Of the 46 combination lines, 18 are zero under all circumstances. This leaves 92 transitions for the general case. At this point we cease to distinguish between combination and other lines since for strong cross-coupling there is no longer a real distinction in the A2A2'X limit. The S protons give rise to a ~naximumof 36 lines of which 16 involve the two 4 x 4 submatrices. For the other 20, explicit energies and intensities are given in Table I. The X2 and -A2' protons give rise to 56 lines of which 32 involve the 4 x 4 submatrices. Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 Explicit energies and intensities for the other 24 are given in Table 11. TABLE I Transitions and intensities of proton X Energy, relative t o eo(1-ux) Relative intensity 1. Jt6fJ3j 1 2. 1/2(Jij+J3j) - A +B (COS 0 cos 4 + + sin 4 sin e)2 e cos 4 sin 4 sin 0)" 3. 1/2(J15+J3s)+ A - B (COS 4. -1/2(Jij+J30)+A -B + (cos B cos + sin 4 sin 8)2 5. -1/2(Jls+J36)-A+B (co~Bcos++sin~sin8)~ 6. - (J15+J36) 1 (COS y cos $ - sin y sin $)= 8 7 I . 1/2(Jlj+J36) - C+D 8. 1/2(Jle+Jaj)+C-D (COS y cos $ - sin y sin $ ) 2 For personal use only. 9. 0 1 10. 0 1 11. -1/2(J15+J3u)+C-D (COS -, cos $ - sin y sin $ ) 2 (COS y cos $ - sin y sin $ ) 2 12. 13. 14. .-1/2(J15+J3~)- C+D 1/2(Jle+Jas) +A +B 1/2(Jis+J35) - A - B (sin 0 cos 4 - sin 4 cos 8)2 (sin 4 cos 0 - sin 0 cos 4 ) 2 15. -1/2(Jla+Jss)-A-B (sin 4 cos 8 - sin 8 cos c$)~ 16. -1/2(Jij+J36)+A+B (sin e cos 4 - sin 4 cos e)2 17. 1/2(J16+J35) +C+D + (sin y cos $ sill $ cos r ) 2 18. 1/2(Jlj+J35) - C-D (sin $ c o s y+ + sin y cos $ ) 2 (sin $ cos y s!n y cos $ ) 2 19. -1/2(Jlj+J~~)-C-D 20. -1/2(Ji5+J~s)+C+D ( s m y cos $ + sln $ cos y ) 2 KOTE:Transitions 21-36 involve the 4 x 4 submatrices. 2. Tlze Proton Spectrum of Fig.I ( a ) The X Region If the six weakest lines in the region are disregarded there are left five equally spaced lines with a separation of 5.10 c.p.s.* Comparison with Table I indicates that we have jJ15+J351 = 10.2 C.P.S.In a pseudo first-order spectrum these five lines would be expected to have intensities in the ratio of 1:4:6:4:1. I t is obvious that this is not so and, clearly, the six weak lines derive their intensitis from the inner three of the main lines. In Table I eight lines are listed (lines 13-20) which become combination lines in the limit of a large shift between the A2 and A2' protons. We assign lines 13-16 to the two pairs flanking the main pealis a t f5.10 c.p.s. From equation [I] it immediately follows that il = B = 1.25 c.p.s., and using the experimental intensities in Fig. 1 we can place the following limits on the parameters: 1/4(J35- J15) = 0.7 + 0.8 c.P.s., 1/2(J23+JI3) = 1.0 -+ 0.9 c.P.s., 4-6' = 41' -+ 44O. *The intensities of these lines increase slightly towards high field, indicating that the X approxinzation i s not quite valid. Howezjev, P ~ ( U A - U X ) = 107.0 6.p.s. compared with the largest off-diagonal element, expected to be no larger than about 1% c.p.s. I t i s well known that the line positions are not nearly as sensitzve to the spin functions as are the intensities and we can proceed with the analysis with some confidence. CANADIAN JOURNAL O F CHEMISTRY. VOL. 41, 1963 TABLE I1 Transitions and intensities of A and 4' protons Energy, relative t o vo(1-oa) Relative intensity 37. 1/4(2Ji3+2J23+Jij+J3s) - A + 2(1 sin 28) 38. 1/4(-2Ji3-2J23+Ji5+J35) -A 2(1 - sin 20) 39. 1/4(-2Ji3-2J23- Jib- J35) - B 2(1 - sin 24) 40. 1/4(2Ji3+2Je3-J15-J3j) - B + 2(1 sin 24) 41. 1/4(-2J13+2J23+Ji5+J35) - C 1 + sin 211. 42. 1/4(2Ji3-2J23+Ji~,+J3~)-C 1 - sin 211. 43. 1 - sin 27 Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 1/4(-2Jl3+2J23-Jis-J35)-D 44. 1/4(2Ji3-2J~3-Jla-J35) -D + 1 sin 27 45. 1/4(-2J13+2J23+Ji5+J3j) - C 1 + sin 2$ 46. 1/4(2J13-2J23+Ji~+J35) - C 1 - sin 2$ 47. 1/4(2Jia-2J23+J1s+J3~?-D 1 + sin 27 48. 1/4(-2Ji3+2J23-Ji~-J35) -D 1 - sin 2y 49. 1/4(2Ji3+2J23+Ji~+J35)+A 2(1 - sin 20) 50. 1/4(2Ji3+2J~3-Ji5-J3j) +B 2(1 - sin 24) 51. 1/4(-2Jia-2J2a+J15+J35) + A + 2(1 sin 20) 52. 53. 1/4(-2J13-2J23-Jlj-J3j)+B 1/4(-2J13+2J23+J1s+J35) +C + 2(1 sin 29) 1 - sir1 2$ 54. 55. 1/4(2Ji3-2J23+Ji~+J~j)+C 1/4(-2Ji3+2J23-Ji~-J3s) +D 1 + + sin 2$ 1 sin 2y 56. 1/4(2Ji~-2J23-Ji~-J3s) +D 1 - sin 2 y 57. 1/4(2Ji3-2J2a+Ji5+J35)+C 1 + sin 211. 58. 1/4(-2J13+2123+Jis+Ja5)+C 1 - sin 211. 59. 1/4(-2J13+2J23-Jis-J35) +D + 1 sin 27 60. 1/4(2113-2J23-J15-J35)+ D 1 - sin 2r For personal use only. NOTE: Transitions 61-92 involve the 4 x 4 submatrices. We have assumed here that J23 is smaller than and of opposite sign to J13 and that J15 and J 3 5are of the same sign with J35 > J15.This agrees with a considerable set of data (10-13). The same sign of J23 and J13 would simply interchange the constants A , B with C, D so that the relative signs of Jz3 and J13 cannot be obtained from the spectrum a t this point. Opposite signs of J15 and J35 can, however, be ruled out a t this point. If they did have opposite signs then the spectrum would not be simple unless 1/4(IJ351 /J15/) + < < 1/21J23+J13/,which is hardly likely. On the other hand, if J13were very small (cross- < coupling small) and 1/4/J35- J15\ < 1/2(J23j then the spectrum would be completely pseudo first-order as has been shown, in effect, in reference 8. From the additional demand that C and D be large enough to have sin2 ($+r)5 0.01 (lines 17-20 in Table I are then unobservable), it follows that C = D = 6.5 -+ 6.6 c.p.s. with 1/2/J13-J231 = 6.5-6.6 c.p.s. Hence we obtain J23 = -5.5f 0.1 c.p.s. and J13 = 7 . 5 f 0 . 1 C.P.S. With this set of data the intensities and positions of all the lines in Table I can be calculated. The positions of the two weak lines overlapping the main lines a t f 5.10 c.p.s. are still to be accounted for. We note that the pairs of lines a t f 10.2 c.p.s. are of unit intensity and should not vary in position on introduction of a shift between A2 and Apt. The same holds for the position of the six lines falling a t 0 c.p.s. I n Fig. 2 the spectrum verifies these statements. The separation of the three peaks in the X region is temperature independent. ( b ) The A Region The partial set of parameters derived from the X region allows the calculation of intensities and positions of the 24 lines in Table 11. None of the intense lines deviate by more than 0.2 c.p.s. from the expected positions a t v o ( l - a J f 2 . 5 5 c.p.s. HUTTON A N D SCHAEFER: CYCLOPROPYLAMINE SPECTRUM 2779 (c) The 4 X 4 Submatrices and J l z We must now solve the two 4 x 4 submatrices. The energy levels of the one will differ from the energy levels of the others only by vo(1-ux). Hence four transitions between the two sets will fall a t vo(l -u,), no matter what parameters are used for the solution, but the other transitions involving these eight energy levels will depend on the input parameters. J15 and J35 enter in the same way as in equation [I].J z 3and J13 enter separately and we take the values obtained above. J12 enters also, for the first time, and we chose it as an adjustable parameter. The 4 x 4 submatrices were solved for the values of Jlz = 8.0, 9.0, 10.0, 11.0, and 12.0 c.p.s. The positions of the weak lines a t h 4 . 6 c.p.s. - Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 in the X region were smooth and fairly sensitive functions of J12,although their inten- sities were not very sensitive to J12. In this way we found J l z 1 2 . 5 f 0.5 c.p.s., a reasonable value (10). The complete calculated spectrum of 92 lines is shown in Fig. 1. Note that additional intensity accrues to the lines a t ~ ~ ( 1 - u X )2.7 c.p.s. from transitions involving the 4 x 4 % submatrices. Note also that all lines separated by 0.25 c.p.s. or less have been collapsed in order to take the finite resolution of the observed spectrum into account. The agree- ment found is thought to be satisfactory. I t indicates also that JZ3 is indeed negative since it enters diagonally and off-diagonally into the 4 x 4 submatrices. In Fig. 1 it is seen that the lines in the A region which fall off the f 2.55 c.p.s, doublet calculated in pseudo first-order are relatively weak compared to the analogous lines in the X region. If the A region is run a t an instrument gain such that the doublet just fills the paper no For personal use only. evidence of any other lines is noticeable. (d,) Summary of Results We feel that the following sets of parameters in c.p.s. are reliable within the limits stated : The last two values have been derived by considering the data in references 10-13, which suggest that the ratio of J,,, to J,,,,, falls between 1.5 and 1.8, increasing as the electronegativity of the substituent increases. The geminal coupling constant is desig- nated as negative with respect to the vicinal coupling constants. 3. The Solvent and Temperature Dependence of the Shift o the A and A' Protons f The effect of the benzene is to shift one pair of protons to high field more effectively than the other. For steric reasons (7, 14) we would expect the protons trans to the NH2 group to be shifted most rapidly t o high field by the anisotropic benzene molecules. If this is actually an association effect, similar to the one we studied for bis(2,2-dichloro- cyclopropyl) ether (7), then increasing temperature should cause the fastest low-field shift for these protons. In Fig. 2 the low-field line of the intense doublet in the A region has split up while the high-field line has not. In equation [I] each of the cosine expressions has added to it a shift term on the right-hand side for the AzBzX case. From the values of the coupling constants given above we can calculate the values of A , B, C and D as 2780 - CANADIAS JOURNAL O F CHEMISTRY. O. V L 41, 1963 a function of the shift between the 4 and A' protons. I t follows easily that only A changes rapidly in the region of small shift. For instance, when the shift is 1 c.p.s., A has changed from 1.3 to 2.1 c.p.s. while the others have changed by about 0.2 c.p.s. We expect lines like 37 and 51 in Table I1 t o change their positions most rapidly and these are both originally centered on the low-field line of the intense doublet. Now it is clear that in the limit of large shift the splitting in the group of lines arising from the protons trans to the amino group, i.e., cis to the X proton, will be largest: JCj, > J.,,. Hence, as the shift decreases to zero this group of lines will collapse last. This set of lines appears a t low field as shown above and moves to low field as the Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 temperature increases. We have shown, therefore, that it is the protons trans to the amino group which are most solvent dependent and experience the largest high-field shift on dilution in benzene. This is consistent with a preferred interaction with benzene molecules a t this position. The low-field shift of the trans protons can be understood in terms of Buckingham's electric field calculations (15). The cis protons would also be shifted to low field by the dipole whose negative end poi~lts the C-N direction but, due to the angular factor, in would be expected to be less, as observed. A quantitative estimate demands a ltnowledge of the magnitude of this dipole and also, perhaps, whether the contribution of the lone pair on the nitrogen is important. ACKSOIVLEDGMESTS For personal use only. One of us (H. AI. H.) would like to thank Canadian Industries Limited for fellowship support. The financial support of the National Research Council was essential to this study. REFERENCES 1. R. J. ABRAHAU and H. J. BERXSTEIX. Can. J. Chem. 39, 216 (1961). 2. T . SCHAEFER. Can. T. Chem. 40. 1678 11962). 3. D. GRAYT and H. S."GUTOWSKY.' J . Chem. Phys. 34, 699 (1961). 4. J . I. MUSHER and E. J . COREY. Tetrahedron, 18, 791 (1962). 5. R. E. I~ICHARDS T. SCHAEFER.Proc. Roy. Soc. (London), Ser. A, 246, 429 (1958). aild 6. h. S. BHACCA, F. J O H ~ S O N , J . N. SHOOLERY.N M R Spectra Catalog, Trarian Associates. L. and Spectru~llS o . 37. 1962. 7 . H. h4. H ~ T T O and T. SCHAEFER. Can. T. Chem. 41. 1857 11963). N \ , 8. T . SCHAEFER.Can. J . Chem., 37,. 882 (19"59). 9. K. \TIBERG. Private commurncation. 10. H. ILI. HUTTON and T . SCHAEFER.Can. J . Chem. 41, 684 (1963). 11. H. M . HUTTON and T. SCHAEFER.Can. J. Chem. 41, 1623 (1963). 12. D. SEYFEKTH, YAWAZAKI, D. L. XLLESTO~. . Org. Chem. 28, 703 (1963). H. and J 13. J. D. GR4HA11 and M. T. ROGERS. J. Am. Chem. Soc. 84, 2249 (1962). 14. T . SCHAEFER.Can. J. Chem. 39, 1864 (1961). 15. A. D. BUCKIXGHA~I. J. Chem. 38, 300 (1960). Can. This article has been cited by: 1. G. Fritz, J. Maas. 1980. Bildung siliciumorganischer Verbindungen, 79. NMR-spektroskopische Untersuchung der 1,3,5- Trisilacyclohexane und 1,3,5,7-Tetrasilaadamantane. Zeitschrift f#r anorganische und allgemeine Chemie 460:1, 144-158. [CrossRef] 2. Paul D. Ellis, Gary E. Maciel. 1971. Molecular orbital calculations of hydrogen-hydrogen coupling constants in substituted cyclopropanes. Molecular Physics 20:3, 433. [CrossRef] 3. Paul D. Ellis, Gary E. Maciel. 1971. Molecular orbital calculations of hydrogen-hydrogen coupling constants in substituted cyclopropanes. Molecular Physics 20:3, 433-448. [CrossRef] 4. Harold Booth. 1969. Chapter 3 Applications of 1H nuclear magnetic resonance spectroscopy to the conformational analysis of cyclic compounds. Progress in Nuclear Magnetic Resonance Spectroscopy 5, 149-381. [CrossRef] 5. G Schrumpf. 1969. Nmr spectra of three-membered ring compounds. II. Bromo- and iodocyclopropane. Tetrahedron Letters Can. J. Chem. Downloaded from www.nrcresearchpress.com by 41.238.236.45 on 07/09/12 10:31, 2635-2638. [CrossRef] 6. Pierre Laszlo. 1967. Chapter 6 Solvent effects and nuclear magnetic resonance. Progress in Nuclear Magnetic Resonance Spectroscopy 3, 231-402. [CrossRef] 7. R COOKSON. 1966. Geminal coupling constants in methylene groups. Tetrahedron 22, 355-390. [CrossRef] For personal use only.