Exchange of Interacting Nuclear Spins in Nuclear Magnetic Resonance. I. Intramolecular Exchange

The effect of internal-exchange processes in a molecule on high-resolution nuclear magnetic resonance spectra is investigated. A Boltzmann equation governing the behavior of the nuclear spin density matrix is derived. This equation is valid for arbitrary coupling strengths and exchange rates. The methods of solving this equation are discussed and, in particular, it is shown that the calculation of the steady-state (slow-passage) NMR spectrum can be reduced to the solution of a set of simultaneous linear algebraic equations. Explicit approximation formulas for the slow- and fast-exchange limits are derived and a number of examples discussed in detail.