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

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 σl due to the surrounding electron cloud, and (b) the distant or secondary shielding σd 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 σl and/or σd (Δσl and Δσd, respectively). Using the hindered rotation model for propane (A6B2) an expression for Δσd 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 σl for both methyl and methylene group protons is the same, the internal chemical shift can be expressed solely in terms of the bond anisotropies. The value of the ratio ΔχCC/ΔχCH of the bond anisotropies thus obtained using the experimental value of Δσ is much larger than the theoretical value of ΔχCC/ΔχCH 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 σl 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 Δσl empirically from a modified form of the Dailey-Shoolery equation. Using this value along with the observed Δσ an estimate of Δσd was obtained which then led by our method to a value of ΔχCC/ΔχCH which is in reasonable agreement with the theoretical results of Tillieu. A semi-quantitative treatment for Δσl using theoretically calculated `atom charges' of methyl and methylene group protons also yields a value of ΔχCC/ΔχCH 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.