FULL-MATRIX ANALYSIS OF THE ERROR PROPAGATION IN 2-DIMENSIONAL CHEMICAL-EXCHANGE AND CROSS-RELAXATION SPECTROSCOPY

Propagation of errors in a multispin system, from the experimental pea k volumes into magnetization-exchange (cross relaxation or chemical ex change) rates, was calculated analytically. An explicit expression was derived for the error propagator. The error for each magnetization-ex change rate constant has a minimum, with the position dependent on the structure of the exchange network. Error analysis allows optimization of the mixing time for arbitrarily complex exchange systems. In cross -relaxation spectroscopy, the error analysis provides the upper and th e lower boundaries of calculated interproton distances for all spin pa irs. These limits differ throughout the molecule for the same distance . The differences are a consequence of the spin diffusion, which the p resent analysis fully takes into account. (C) 1995 Academic Press, Inc .