By Gheorghe D. Mateescu, Adrian Valeriu
In contrast to such a lot really good books in this topic that emphasize the mathematical foundations of 2nd NMR, this ebook bargains an experimentally-based, transparent rationalization of the density-matrix and product operator remedies therefore permitting non-experts to see sequences of various levels of complexity.
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Extra resources for 2D Nmr: Density Matrix and Product Operator Treatment
61) In order to compare the results of the density matrix treatment with those of the vectorial representation, we will calculate for every step of the sequence the magnetization components, using the relations (B15) − (B22). We must also consider that here q = p and that MoA = MoX = Mo/2, where Mo refers to magnetization due to adjacent 13C atoms A and X. Thus our magnetization equations become (cf. 2 The First Pulse At time t(0) a nonselective pulse 90xAX is applied. Since all pulses in this sequence are nonselective, the notation AX will be omitted.
The matrix element B is transferred in the slow (24) "slot" and will evolve from now on with the slow frequency W24. The reverse is happening to the matrix element C. 6b t(4) clearly shows that the second evolution te/2 completes the decoupling of proton from carbon. The fast vector 13 catches up with the slow 24 and at t(4) they coincide. 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.
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). The carbon magnetization components at t(7) are My12 = (1 - 4 s ) MoC / 2 My34 = (1 + 4 s ) MoC / 2 s = sin W H ( te + D1 ) The proton magnetization components, both fast and slow, have vanished. INADEQUATE 31 4. THE DENSITY MATRIX DESCRIPTION OF A DOUBLE-QUANTUM COHERENCE EXPERIMENT (INADEQUATE) The main goal of INADEQUATE (Incredible Natural Abundance DoublE QUAntum Transfer Experiment) is to eliminate the strong signal of noncoupled 13C nuclei in order to easily observe the 200 times weaker satellites due to C-C coupling.