In the Laboratory
An Experiment To Demonstrate Magnetic Nonequivalence in Proton NMR Christopher J. Welch Department of Pharmaceutical Chemistry, Organic Pharmaceutical Chemistry, Uppsala Biomedical Centre Uppsala University, Box 574, S-751 23 Uppsala, Sweden
Most undergraduate chemistry students first encounter NMR spectroscopy during organic chemistry courses. The knowledge gained is often restricted to factors affecting chemical shift and simple coupling patterns. Students can quite easily recognize an ethyl group through the presence of the characteristic triplet and quartet in the proton NMR spectrum. Similarly, parasubstituted aromatics present little problem. Unfortunately, by the time students progress to synthetic problems at a more advanced level, the spectra obtained are more complicated than those previously presented. The presence of protons that couple to up to five other protons or the presence of magnetically nonequivalent protons often makes interpretation difficult, resulting in excessive use of the term multiplet in the reports submitted. In this article a bicyclic compound 1, synthesized in a one-step reaction, is used to highlight the presence of magnetically nonequivalent protons. Geminal coupling can be seen for two different spin systems. Furthermore, through the use of either ball-and-stick or CPK models, it can be seen that the nonequivalence of one of the pairs of protons is due not to restricted rotational freedom, a common misconception, but to the different environments protons experience during free rotation. General Procedure 3a,6a-Diethoxycarbonyl-2,5-dimethyl-1,4-dioxooctahydropyrrolo[3,4-c]pyrrole (1) is prepared from tetraethyl ethane-1,1,2,2-tetracarboxylate (2) and 1,3,5trimethylhexahydro-1,3,5-triazine (3), using the procedure reported by Knowles and Harris (Fig. 1) (1). This reaction uses commercially available reagents and requires no special equipment; it may be performed in an open test tube. Solvent is required only for the work-up procedure. A sample of the product (10–15 mg dissolved in deuterated chloroform is sufficient) may then be submitted for NMR analysis.
obtained consists of a triplet at 1.18 ppm, a singlet at 2.86 ppm, doublets at 3.74 and 3.98 ppm, and a multiplet at 4.12 ppm (Fig. 2). The triplet shows a coupling constant of 7.2 Hz and is assigned as the CH3 of the ethyl ester; the singlet is assigned as the CH3 attached to nitrogen. The two doublets arise from the endocyclic CH2, which behaves as a typical AB system with a geminal coupling constant, J = 10.2 Hz. Use of models at this stage will show how the cis or trans relationship to the ester functions causes the magnetic nonequivalence of these protons. Finally, the multiplet at 4.12 ppm is assigned as the CH 2 of the ethyl group. The topography of this multiplet will vary with the field strength of the NMR spectrometer used. The spectra reported here were recorded at 270 MHz (Fig. 2). These assignments can be confirmed by a combination of COSY, HETCOR and DEPT experiments. Analysis of the multiplet may be performed by a number of different methods, one of which is described here. The coupling constant for the CH2 to the CH3 is measured directly on the triplet and found to be 7.2 Hz.
O
O
EtO EtO
O OEt + OEt
O
N
N
OEt N
N
N EtO
O
2
H+
O
3
O
O
1
Figure 1. Synthesis of 3a,6a-diethoxycarbonyl-2,5-dimethyl-1,4dioxooctahydropyrrolo[3,4-c]pyrrole.
Evaluation of Results The reaction performed requires acid catalysis. The role of the acid is to facilitate generation of the Mannich base from the hexahydrotriazine. Despite the addition of trifluoroacetic acid, the reaction mixture is basic owing to the excess of the hexahydrotriazine. Generation of stabilized enolates is therefore possible, allowing the reaction to proceed with good results. The mechanism for this reaction can be used as a difficult problem for advanced students to solve. The first observation concerning the proton NMR spectrum is that the data reported in the literature are not consistent with the data obtained experimentally (1). This should initiate a discussion of the reliability of reported data and perhaps help in the development of critical evaluation of scientific reports. The NMR spectrum
Figure 2. 270 MHz NMR spectrum of compound 1.
Vol. 74 No. 2 February 1997 • Journal of Chemical Education
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In the Laboratory
Figure 3. Algorithm for determination of the coupling pattern applied to a spectrum measured at 300 MHz. The coupling constant 7.2 Hz is assumed correct from the triplet found at 1.18 ppm. From the spectrum a coupling constant of 10.8 Hz is measured and the difference between the signals, ∆δ, is determined to be 0.053 ppm.
Assuming that the multiplet is caused by the magnetic nonequivalence of the two protons, one would expect a quartet for each proton that would be further split by the geminal coupling. The signals are so close together that considerable overlap occurs. The problem remaining is to determine the magnitude of the geminal coupling constant and the chemical shifts of the signals for the two protons. Reduction of the multiplet by all couplings equal to 7.2 Hz leaves a single coupling which is the geminal coupling constant. In this case, this is found to be 10.8 Hz, exactly 1.5 times the vicinal coupling constant. The example shown in Figure 3 is for the spectrum obtained at 300 MHz. The multiplicity is quite complicated. However, using this algorithm both the geminal coupling constant and the chemical shifts can be determined. Spectra obtained at 200 or 270 MHz are particularly interesting because the chemical shift difference, 0.053 ppm, corresponds very closely to an exact multiple of the coupling constants, 10.7 and 14.4 Hz, respectively. This causes some of the peaks to coincide, reducing the multiplicity and increasing the difficulty in determining the chemical shifts. Application of the same algorithm for the coupling constants yields the geminal coupling constant. However, to determine the position of the individual signals it would be necessary to perform a spin simulation experiment. Since both the vicinal and geminal coupling constants are known, a coupling diagram for one signal may be constructed. This shows the 8 signals expected in a ratio of 1:3:1:3:3:1:3:1. A duplicate of this pattern may be inverted and placed edge-to-edge with the original. By sliding these two coupling patterns laterally against each other, it is possible to simulate the situation as the resonance frequency varies (Fig. 4). Thus the position where signals coincide may be found. From this it is simple to determine the chemical shift of the two protons in question. Having demonstrated that the methylene protons of the ethyl groups of compound 1 are magnetically nonequivalent, molecular models can be used to consider the freedom with which rotation is allowed about the C–O–C–C and O–C–C–H bonds Conclusions The experiments presented in this article highlight a number of points useful for students’ knowledge and understanding of organic chemistry and NMR spectroscopy. The synthesis may be used to illustrate the generation of an imine or iminium ion. This leads to a discussion of the mechanism of the Mannich reaction, re-
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Figure 4. Determination of overlap and chemical shifts for the signal observed at 270 MHz. Moving the calculated multiplets as indicated by the arrows simulates the effect of changing the field strength of the spectrometer.
quiring knowledge of enolate stabilization and of the reaction of a secondary amine with an ester—in this case, forming a γ-lactam. There is a large geminal coupling (J = 10.2 Hz) and a large difference in chemical shift for the first set of magnetically nonequivalent hydrogen atoms, the endocyclic methylene group. This can be explained by the different magnetic environments experienced by the two protons held in place by the rigidity of the ring system. For the second set of magnetically nonequivalent hydrogen atoms, the methylene of the ethyl group, the multiplicity is greater whilst the difference in chemical shift is smaller. The student is required to understand and use a number of different methods to solve this spectrum. The nonequivalence is caused by the different magnetic environments each hydrogen atom experiences during free rotation about the various bonds. This may be well understood through use of models. In both cases, it will be necessary to discuss the diastereotopic nature of the methylene groups. A paper by Hoye et al. (2) provides useful information on subjects addressed here and is recommended for further reading. Literature Cited 1. Knowles, P.; Harris, N. V. J. Chem. Soc. Perkin Trans. 1 1983, 1475. 2. Hoye, T. R.; Hanson, P. R.; Vyvyan, J. R. J. Org. Chem. 1994, 4096.
Journal of Chemical Education • Vol. 74 No. 2 February 1997
