Proton Nuclear Magnetic Shielding and the Diamagnetic Anisotropy of C–C and C–H Bonds in Propane

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Abstract
The nuclear magnetic resonance shielding σ of a proton in a molecule can be written as the sum of two contributions, namely, (a) the local or primary shielding σ l due to the surrounding electron cloud, and (b) the distant or secondary shielding σ d due to magnetically anisotropic charge distributions farther away from the nucleus. An internal chemical shift Δσ between two protons A and B may originate from differences in σ l and/or σ d (Δσ l and Δσ d , respectively). Using the hindered rotation model for propane (A6B2) an expression for Δσ d between the methyl and methylene group protons has been derived in terms of the magnetic anisotropy (Δχ) of the C–H and C–C bonds in this molecule. If it is assumed that σ l for both methyl and methylene group protons is the same, the internal chemical shift can be expressed solely in terms of the bondanisotropies. The value of the ratio Δχ CC /Δχ CH of the bondanisotropies thus obtained using the experimental value of Δσ is much larger than the theoretical value of Δχ CC /Δχ CH obtained by Tillieu. To the extent then that the theoretical studies of Tillieu on bond susceptibilities may be relied on, our calculations would indicate that there is a difference between the local shielding σ l of the methyl and methylene group protons in propane. Since this difference in local shielding values may logically be related to an electronegativity difference between the CH3 and CH2 groups we have evaluated Δσ l empirically from a modified form of the Dailey‐Shoolery equation. Using this value along with the observed Δσ an estimate of Δσ d was obtained which then led by our method to a value of Δχ CC /Δχ CH which is in reasonable agreement with the theoretical results of Tillieu. A semi‐quantitative treatment for Δσ l using theoretically calculated `atom charges' of methyl and methylene group protons also yields a value of Δχ CC /Δχ CH in satisfactory agreement with the theoretical value for this quantity. Our results may therefore be taken to indicate that both the local and distant shielding terms contribute to the total internal chemical shift in propane and that the former term is probably the more important.

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