By Jerome I. Kaplan
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Extra info for NMR of Chemically Exchanging Systems
5-16) to (5-14) one obtains the result that ~AB = _ Ζ. ( £ Α Β +g A B ^ A B +J _ ( ^ A B ^ ) T _ ~ Α Β )? _ Π) AB or going back to the definitions of £ AB P = -i[X™, p A B AB ] + R p AB and £ AB in (5-11) we have + ( l / r A B) ( p A B (col) - p A B ). (5-18) To abbreviate the exchange contribution in the density matrix equation we fSee precedin g footnote . ( 5 60 V. Chemical Reorganization write £p AB AB = (1 / T ) [p (col) - p AB a b ], (5-18a) where p(col) will be evaluated in the following section.
C. Gordo n an d R. P. McGinnis , / . Chem. Phys. 49, 2455 (1968). Chapter IV RELAXATIO N Most N M R lineshape treatments of exchanging systems simulate relaxa tion effects by use of phenomenological linewidth parameters. These are included in the diagonal elements of the coefficient matrix of the density matrix equations. This is clearly unsatisfactory in all cases in which relaxation has the effect of mixing transitions, for instance, quadrupole relaxation. Then contributions from different relaxation mechanisms have to be specifically included in the density matrix equations by use of the appropriate operators; their derivation is the purpose of this chapter.
T% T a n d the d's appear from where the bj values come from elements of e * elements of spin operators. Intermediate narrowing involves dropping the u0j — ω terms from the denominator on the right-hand side of (4-136) by assuming that 6 > o , " « ) « αω, (4-137) J 4 which is appropriate near resonance since ω θ7 — ω will be at most 10 r a d 1 7 10 1 s e c " , while ω or ω0 is between 10 a n d 7 X 1 0 rad s e c " . D r o p p i n g the (co0y — ω ) τ ς terms (4-136) becomes + 2 2 dca (0)rq/[\ + (ao,0) T q].