Quantum-mechanical chemical exchange. Stochastic averaging in magnetic resonance

Citation

Jones, Daniel Hall (1993) Quantum-mechanical chemical exchange. Stochastic averaging in magnetic resonance. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/nr9w-1k51. https://resolver.caltech.edu/CaltechTHESIS:12172012-092540697

Abstract

I. Quantum-Mechanical Chemical Exchange

A quantum-mechanical treatment of both spin and space degrees of freedom is derived which accounts for both tunnelling splittings and lineshape behavior in the observed NMR of exchanging proton pairs. In this self-consistent treatment, the chemical exchange rate is expressed in terms of a correlation function of the operator which couples space and spin. A master equation formulation of the correlation function is presented which can be solved for any model of discrete rovibrational states. In contrast to previous descriptions of intramolecular chemical exchange, which either use transition state theory and the notion of molecular tunnelling or ad hoc ideas of incoherent tunnelling, the present treatment places chemical exchange among the class of transport and relaxation rates described by the quantum-statistical fluctuation-dissipation theorem. Results from simple models of the tunnelling system are analyzed in order to relate the observed NMR lineshape of certain transition metal hydrides to the underlying Born-Oppenheimer potential for the quantized nuclear motion.

II. Stochastic Averaging in Magnetic Resonance

As a result of the typical smallness of spin Hamiltonian parameters relative to the rates of relaxation of spatial degrees of freedom, many magnetic resonance spectra are understood to be stochastic averages over thermally accessible molecular configurations or spatial (e.g., rovibrational) eigenstates. The temperature dependence of the average spin parameters is widely used to provide information on the potential energy functions which determine molecular conformation. It is universal practice in computing these averages that the energies (or free energies) multiplying β(=1/kT) in the Boltzmann probability factors are the spatial contributions only. It is argued that any such averaging procedure is inconsistent with statistical mechanics and an alternative procedure is presented for calculating the stochastically-averaged spin Hamiltonian. The experimental conditions and possible test systems for validating the traditional or alternative forms of the stochastic average are discussed.

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