Theory of Chemical Exchange Effects in Magnetic Resonance

Abstract

The Anderson—Weiss formalism is used to develop a general theory for calculating the effects of chemical exchange and spin coupling on echo amplitudes in Carr—Purcell pulse sequences on spin systems in the liquid phase. The theory is shown to involve the matrix integral solution of the Hahn—Maxwell—McConnell equations, generalized to include spin coupling, and of Alexander's equations for the relevant density matrix elements, subject to the boundary conditions imposed by the pulses. Some specific systems are treated in detail, and closed formulas are given for the decay of the echo train in several situations, including the coupled and uncoupled AB systems, and the coupled ABX and ABXq systems. We show that if the natural relaxation rates of nuclei in exchanging sites are identical, then in general effects of both exchange and spin coupling can be removed by pulsing sufficiently rapidly. Modulation of the echo train by spin coupling is removed by rapid exchange between the coupled sites. The Carr—Purcell experiment on an equivalent set of spins affords effective decoupling from another equivalent set unaffected by the pulses, in the absence of exchange between the sets. An analogy is drawn between chemical exchange and quadrupolar relaxation, and a method is outlined which in principle should provide an indirect determination of quadrupolar or other fast relaxation rates. We illustrate the applicability of the theory to the calculation of line shapes in steady-state spectra by treating the exchanging coupled AB system in detail, and show that in the fast exchange limit the theory predicts weak broad resonances not previously described.

Nuclear magnetic relaxation by the manganese in aqueous suspensions of chloroplasts

“…Nuclei in the solvation sphere of the Mn(I1) have greatly enhanced relaxation rates (eq 1 with p q = 1). Sharing of the enhancement with the other solvent nuclei depends upon the exchange rates among the three fractions and upon their relative populations (Gutowsky et al, 1965). Current models of chloroplast thylakoids place the manganese associated with oxygen evolution on the inside of the chloroplast vesicles (Trebst, 1974).…”

“…The exchange across the membranes will not average out the difference in the relaxation rates provided that (Gutowsky et al, 1965) the average rate constant for exchange is less than the difference between external and internal relaxation rates; that is where k = 1 f 7 is a rate constant for exchange across the membrane, the subscripts e and i refer to nuclei external to and inside of the vesicles, and the subscript av designates an average over the two fractions. The exchange rate across the membrane is the same in both directions, P c I T e = PJ.1…”

Ligand exchange and complex formation kinetics studied by NMR exemplified on fac-[(CO)3M(H2O)]+ (M=Mn, Tc, Re)

“…Since the beginning of the application of NMR in chemistry it has been used for quantitative determination of reaction rate constants [1][2][3][4]. The theory and reams of examples for exchange rate measurements by NMR can be found in books [5][6][7][8] review articles [9][10][11][12].…”

Determination of transverse relaxation rates in systems with scalar-coupled spins: The role of antiphase coherences

“…When the repetition rate m rep = 1/(s + s p + s), where s p is the duration of the 180°pulse, becomes high compared to the chemical shift of the off-resonance spin S (m rep ) X S /(2p)), echo modulations are quenched. This idea, first described by Gutowsky et al [11] and by Allerhand [12], exploits the property that two magnetically equivalent nuclei lead to a singlet, since the J-coupling between them has no effect on their evolution, even when it does not vanish. A CPMG sequence with a sufficiently fast repetition rate leads to a similar effect as spin-locking with a continuous-wave (cw) rf irradiation [13].…”