Chemical Exchange in Nuclear Magnetic Resonance

Citation

Mueller, Leonard John (1997) Chemical Exchange in Nuclear Magnetic Resonance. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/fx7d-jf45. https://resolver.caltech.edu/CaltechTHESIS:02212018-140937311

Abstract

Nuclear magnetic resonance spectra of molecules undergoing chemical exchange have traditionally been quantified using a theory that combines a quantum-mechanical treatment of the spin dynamics with a kinetic model for the molecular exchange. This implicit factorization of spin and spatial degrees of freedom is without theoretical justification and yet it has been widely relied upon in chemical studies. In this thesis, a quantum-statistical theory of chemical exchange is presented for the calculation of lineshapes in dynamic nuclear magnetic resonance. In this treatment, the rates describing the exchange of spin coherence are shown to be complex valued due to the incomplete cancellation of the imaginary components of the spectral density of purely spatial perturbations. These imaginary components give rise to the previously unrecognized phenomena of exchange shifts, new contributions to the line positions which depend on spatial rates even in the fast-exchange limit. These shifts can be orders of magnitude greater than the experimental resolution. The same purely spatial fluctuations responsible for chemical exchange determine these shifts through a Hilbert-transform relationship.

New measurements on the ¹³C NMR of methylcyclohexane show that, indeed, the traditional theory fails to relate spectra obtained in the regimes of fast and slow exchange. If interpreted using the traditional theory, the fast-exchange line positions in methylcyclohexane lead to an extracted equilibrium constant with an error of up to 30% and differing between isotopomers by up to 30%. With plausible assumptions on the temperature dependence of the chemical shifts and free energy, an overall fit of the fast­ and slow-exchange methylcyclohexane data is unsatisfactory, rigorously excluding the traditional theory. The exchange-shift theory indicates why additional information is needed to fit the fast-exchange line positions and allows a fit consistent with the observed experimental data on methylcyclohexane using a single conformer free energy difference linear in temperature over the entire experimental range.

Thesis Files