A Comparison between Classical Theory of Motional Narrowing and Narrowing Due to Quantum Mechanical Tunnelling Motion
At low temperature hindered molecular motion must be treated quantum mechanically introducing the concept of a tunnelling frequency which characterises the motional rate in place of the correlation time Tç which is a feature of classical theory. To illustrate the relationship between the two theories the n.m.r. spectrum is calculated for a proton moving between two sites having different resonance frequencies (a) when the motion is described as random hopping (b) when the proton tunnels between the sites. The central part of the spectrum is narrowed in each case but spectrum (a) has broad wings while spectrum (b) has weak tunnelling sidebands. The interaction of tunnelling groups with nearby paramagnetic centres is shown to offer the best means of studying the tunnelling motion.
KeywordsCoherence Sine Cose Para Hydrogen
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