ORIGIN OF LINEARITY OF CARBON-13 SHIFT WITH CHARGE . CALCULATIONS FOR AZINES

Carbon-13 chemical shifts in the azines pyridine, pyrazine, pyrimidine, pyridazine, s-triazine, and s-tetrazine have been calculated at several levels of approximation in the theory of chemical shifts with a variety of π and σ wave functions and the results examined with respect to the proposed linearity of shift with charge. The Ramsey tensor, without approximation, using the methods of Karplus and Kern to evaluate the multicenter integrals, gives only qualitative agreement with the observed shifts. Use of the average energy approximation only accounts for about half of the shift in each case, though they do follow the correct order. It is found that explicitly including the terms involving the lower excitation energies (n→π*) in the expression for XpA and using the average energy approximation for the others give excellent agreement between calculated and observed shifts and different excitation energy, DEE. The CNDO-MO's of Bene and Jaffé were used in this scheme. Both the observed shifts and the σ + π charges calculated with these CNDO wave functions for the azines are linear functions of the corresponding values for pyridine. The observed shifts are linear with the total charge on carbon, 160 ppm/electron. It is proposed that atomic terms dominate the shifts and charges. Decomposition of the expression for Δσ, with respect to benzene, B, gives-N−1[XBΔ(r−3) + (r−3)BΔX + ΔXΔ(r−3)]. The first term is known to be proportional to charge, 86 ppm/electron; the second is roughly linear, 73 ppm/electron. Together they account for the observed dependence of shift on charge. The first term alone corresponds to the results in the Pople-Karplus approximation. Aromatic systems whose carbon-13 shifts are expected to be proportional to charge should have exchange interactions little different from those in benzene. Altogether in these calculations it is critical that the wave function predicts the correct lower electronic excitation energies and takes account of the polarity of the σ framework. © 1969, American Chemical Society. All rights reserved.