Full matrix Analysis of Cross-relaxation Fails in Fractionally Deuterated Molecules.

We have analyzed cross-relaxation in fractionally deuterated molecules and showed that the full matrix analysis fails except when the dilution is extreme. This is because the isotopic dilution alters the matrix exponential relationship between the observed spectrum and the cross-relaxation rate constants sought. Consequently, an average of the spectra of various isotopomers differs from the matrix exponential of an average relaxation matrix. We have derived a series expansion that allows the determination of the cross-relaxation rate constants in arbitrarily deuterated molecules.