Theory of the Chemical Shift in Aromatic Heterocycles BY G. G. HALL,* A. HARDISSON * AND L. M. JACKMAN I>ept. of Mathematics, and Dept. of Chemistry (Organic Chemistry Research Laboratories), Imperial College, London, S. W.7 Received 7th June, 1962 An extension of the self-consistent form of the molecular orbital theory, to enable the chemical shifts associated with ring currents in aromatic molecules to be calculated, is discussed. The theory is used to predict the shifts of the aromatic protons in aza derivatives of alternant hydrocarbons and the results of the self-consistent calculations are compared with those of the Huckel theory. Calcula- tions for some other molecules are also presented and used to discuss the different effects of a hetero- atom on ring current. The ring current contributions to diamagnetic anisotropy are also tabulated. A ring current is induced among its mobile electrons when a conjugated mole- cule having at least one ring is subjected to a magnetic field.This current produces two effects which enable it to be observed, the diamagnetic anisotropy and the chemical shift. Unfortunately, both effects are influenced by other contributions and the calculated ring current contributions can be compared with experiment only when due account has been taken of these other effects. In general, the chemical shift is a more useful indicator of ring current than the anisotropy, partly because it is easier to isolate the ring current contribution 1 and partly because there are experimental results for each proton.The development of a theory of ring current using the self-consistent form of molecular orbital theory with the external magnetic field and the nuclear magnetic dipole treated as perturbations has been given recently 2 and described in relation to earlier theories by the present authors.3 Their paper also discussed a number of heterocycles and showed that the differences between the self-consistent results and the Hiicltel ones could become large and significant. This contrasts with the alternant hydrocarbons for which the results are almost the same. This discussion is continued in the present paper and some general conclusions drawn about the factors governing ring current. EFFECTS O F NITROGEN SUBSTITUTION In table 1 is given the calculated chemical shifts, due to ring current, for pyridine, pyrimidine and S-triazine.These are expressed as ratios to the corresponding effect in benzene and, since these are single ring systems, the same ratio is found for the ring current contribution to the diamagnetic anisotropy. Since the value of the electronegativity parameter 6~ is not precisely known the calculations have been repeated for thee possible values of &. This also facilitates the general dis- cussion of substitution. Two main effects can be seen in table 1. First, the ring current decreases as increases. This is due to the increased localization of electrons on the nitrogens and is parallel to the increase in formal charge there. It is least in pyridine, which has only one hetero-atom and greatest in S-triazine which * present address : Department of Mathematics, University of Nottingham.t present address : Department of Chemistry, University of Melbourne, Australia. 1516 CHEMICAL SHIFT I N HETEROCYCLES has three. The second effect is that the self consistent results for & = 0.2 show a ring current larger than in benzene. This can be attributed to larger value of PCN, which is 1.076 PCC, and increases the ring current. In the Huckel theory the first effect always predominates. To demonstrate that this B effect is genuine the cal- culation was repeated for pyridine with the same & and PCN equal to PCC. The result is 0.99 which is now less than benzene and also less than the Huckel value. TABLE 1.-cALClJLATED CHEMICAL SHIFTS AND DIAMAGNETIC ANISOTROPIES (RELATIVE TO BENZENE) IN PYRIDINE, PYR~MIDINE AND S-TRIAZINE pyridine pyrimidine S-triazine % Huckel S.C.F. Hiickel S.C.F.Huckel S.C.F. 0.20 1.00 1-02 0.99 1 -03 0.98 1 -04 0.50 0.98 0.99 0.95 0.96 0.90 0.89 0.80 0.96 0.95 0.87 0.83 0.76 0.67 The chemical shifts and diamagnetic anisotropies of the more elaborate hetero- cycles 4-( 1 -1ndenylidene)- 1 methyl- ly4-dihydropyridine (I) and cyclazine (11) are shown in table 2. For purposes of calculation, (I) is assumed to be planar. The results for (I) show that the chemical shift is considerably reduced from the benzene TABLE 2.-cALCULATED CHEMICAL SHIFTS AND DIAMAGNETIC ANISOTROPIM (RELATIW TO BENZENE) IN HETEROCYCLES (I) AND OI) chemical shifts T II ak 1 -02 1-52 2.02 position A B C D A B C D A B C D Huckel S.C.F.Hiickel S.C.F. 0.79 0-36 1.41 1.44 0.81 0.38 1.51 1.54 1-20 1.22 1.08 1.09 0.70 0.27 1.44 1-47 0.72 0.29 1-55 1.59 1-31 1-36 1.19 1.M 0-61 0.21 1.46 1.48 0.64 0-22 1-58 1-61 1.39 1-45 1.27 1-33 diamagnetic anisoiropies I II Huckel S.C.F. Hlickel S.C.F. 2-28 1.49 2.53 2-58 2.15 1.33 2-69 2-78 2-04. 1-20 2.80 2.89 value. This is due to the combined effect of the nitrogen, with its large value of 6iY and the substituent. The large difference between the Hiickel results and the self-consistent ones, already mentionedy3 is again to be noted. The effect of an increase in the electronegativity of a group attached to a ring is to counteract more and more the localizing effect of a nitrogen in the ring and hence to increase the ring current. (This effect is illustrated in table 2 of the previous paper.3) The experimental shifts4 suggest that there is virtually no ring current and hence that the planar model is incorrect.One explanation might be that the steric effect of the hydrogens attached to the two rings would produce a large twist about the inter-ring bond. This non-planarity would require a smaller p for the inter-ring bond and hence a smaller ring current. The results for (II) show an effect of nitrogen substitution which is of a quite different character. For this molecule the increase in produces a steadyG. G. HALL, A. HARDISSON AND L. M. JACKMAN 17 increase in the chemical shift and also a reduction in the range of values for the different protons. This can be explained by the fact that, as 6, increases, the molecule approaches closer to the 10 electron ring formed by the peripheral carbons because two electrons are becoming localized on the central nitrogen.To confirm z? A I 1 & C 0 U A Q; m FIG. 1. this interpretation the hypothetical molecule whose configuration is the same as this periphery was calculated. The results agree well with those obtained by extra- polating the results in table 2 to an infinite value for i3i. Effects of this kind can be expected in similar polycyclic molecules provided that the periphery is of Huckel type with (4n+2) electrons. Such perimeters have singlet ground states and are diamagnetic with large ring currents. THE PERINAPHTHENYLIUM ION The calculated chemical shifts and diamagnetic anisotropy of the perinaph- thenylium ion (111) are shown in table 3.It is hoped that experimental shifts will be available soon. One feature of this molecule is that the self-consistent results show much larger effects than the Huckel ones. This is in striking contrast with TABLE 3.<ALCULATED CHEMICAL SHIFTS AND DIAMAGNETIC AMSOTROPES (RELATIVE TO BENZENE) N THE PERINAPHTHENYLIUM ION chemical shifts diamagnetic anisotropies position Hiickel S.C.F. Hiickel S.C.F. A 0.77 0.92 2.01 2.41 B 0.85 1 -02 the corresponding results for the single ring systems discussed above. It agrees, however, with the results for (11) though the effect there is much smaller. The probable reason is that the central carbon, which has a negative charge of 0.024 in the self-consistent treatment and is neutral in the Huckel treatment, is increasing the ring current by making the periphery more nearly of type (4n + 2). One of us (A. H.) has to thank the C.S.I.C. of Madrid for a grant and we are indebted to the English Electric Company and staff of the DEUCE Department for computing facilities. 1 Elvidge and Jackman, J. Chem. Suc., 1961, 859. 2 Hall and Hardisson Proc. Roy. Suc., A, 1962, 268, 328. 3 Hall, Hardisson and Jackman, Tetrahedron, 1962, 268, 328. 4 Boyd and Jackman, unpublished results,