By Gheorghe D. Mateescu, Adrian Valeriu
Not like so much really expert books in this topic that emphasize the mathematical foundations of 2nd NMR, this ebook deals an experimentally-based, transparent rationalization of the density-matrix and product operator remedies hence permitting non-experts to determine sequences of various levels of complexity.
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Additional info for 2D Nmr: Density Matrix and Product Operator Treatment
5 Detection Since no other pulse follows after t(3) we will consider only the evolution of the observable (single quantum) elements d12, d34, d13, and d24 in the time domain td. 98) d (3) = ( i 4 )( +c12 − c34 + is13 + is24 ) * 24 Each of the four matrix elements above contains all four frequencies evolving in domain te, namely: Ω12te , Ω34te , Ω13te , and Ω 24te . 99) shows that each td frequency is modulated by all four te frequencies. Thus, we expect sixteen peaks in the 2D plot. , it contains sine/cosine expressions).
They have both precessed a total angle WHte from their starting position along - y. 26)]. The transverse magnetization, calculated from the matrix elements, is 24 Density Matrix Treatment MTH = - ( MoH / 4 )[ 2 i exp( iW H te ) + 2 i exp( iW H te )] = - iMoH exp( iW H te ) After separating the real and imaginary parts in MTH we obtain MTH = - iMoH (cos W H te + i sin W H te ) = MoH (sin W H te - i cos W H te ) MxH = real part of MTH = MoH sin W H te MyH = coefficient of the imaginary part of MTH = - MoH cos W H te This is in full accordance with the vector representation.
Such representation would not have been possible without the complete information provided by the DM treatment. 6a. Vector representation of 2DHETCOR from t(0) to t(2). The magnetization vectors are arbitrarily taken equal for C and H in order to simplify the drawing. Actually the 1H magnetization at equilibrium is 16 times larger than that of 13C. 6b. Vector representation of 2DHETCOR from t(3) to t(5). 6c. Vector representation of 2DHETCOR at time t(6). 95. 6d. Vector representation of 2DHETCOR at t(7) and t(8).
2D Nmr: Density Matrix and Product Operator Treatment by Gheorghe D. Mateescu, Adrian Valeriu