A general theory of the effect of dynamics (relaxation and (or) exchange) on NMR spectra is presented. This theory is based on a reexamination of the transition probability. The classic expression for this is as the square of the transition moment, but we feel it is useful to separate the square into two separate terms. In the generalization presented here, we show that one of these terms corresponds to the share of the initial magnetization that each spin coherence receives at the start of the experiment. The second term is how much that coherence contributes to the total detected signal. The final intensity is the product of these two factors. For a static spectrum, these two terms are complex conjugates, so the product is real and we recover the standard transition probability. When there is dynamics, the product becomes complex, so the time evolution includes oscillatory and dispersive terms. This means that a dynamic spectrum is still a sum of individual transitions, but the lineshapes are distorted in phase, intensity, position, and linewidth by the dynamic process. In this paper we develop the general theory, and illustrate it with a calculation of the classic problem of mutual exchange in an AB spin system.Key words: NMR spectroscopy, transition probability, chemical exchange, kinetics.RCsumC : On prCsente une thCorie gCnCrale de l'effet des processus dynamiques (relaxation et (ou) Cchange) sur les spectres RMN. Cette thCorie est basCe sur un rkexamen de la probabilitk de transition. L'expression classique pour ceci implique le cam6 du moment de transition; toutefois, on croit qu'il est utile de sCparer le carrC en deux termes. Dans la gCnCralisation prCsentCe ici, on montre que I'un de ces termes correspond h la partie de la magnktisation initiale que chaque coherence de spin reqoit au dCbut de l'expkrience. Le second terme est un reflet de la partie de cette cohtrence qui contribue au signal qui est dCtectC. L'intensitC finale est le produit de ces deux facteurs. Pour un spectre statique, ces deux termes sont des conjuguCs complexes et le produit est donc rCel; on rCcuptre donc la probabilitk de transition standard. Quand le spectre est dynarnique, le produit devient complexe et I'tvolution avec le temps comprend des termes oscillatoires et de dispersion. Ceci signifie qu'un spectre dynamique est encore une somme de transitions individuelles, mais, i cause du processus dynamique, les formes des bandes sont dCformCes par la phase, l'intensitt, la position et la largeur de la bande. Dans ce travail, on a dCveloppt la thtorie gCntrale et on l'a illustree h l'aide d'un calcul du problkme classique de 1'Cchange mutuel dans un systtme de spins AB.

The internal rotation of the aldehyde group with respect to the ring in 2-furanaldehyde (furfural) provides an example of chemical exchange in a two-site system with unequal populations. In a polar solvent, the two isomers are present in unequal amounts. In the present study, rates of exchange for the cis-trans isomerization process of furfural in acetone are measured using a combination of the offset-saturation method for determination of fast rates of exchange, time-domain line shape analysis for measurement of intermediate rates of exchange, and selective-inversion measurements of slow exchange rates. This combination of NMR techniques permits the determination of rates of exchange over 5 orders of magnitude, covering a temperature range of 177-318 K. The utility of the offset-saturation method for fast rate measurement is highlighted in the present system, where the exchange rapidly enters the fast exchange regime. The corresponding values of the activation parameters are the energy of activation E, = 41.9 & 0.9 kJ mol-', the enthalpy of activation AH* = 40.0 i 1 kJ mol-', and the entropy of activation AS* = -26.8 k 5.2 J K-' mol-'.

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