By Gheorghe D. Mateescu, Adrian Valeriu
In contrast to such a lot really expert books in this topic that emphasize the mathematical foundations of second NMR, this ebook bargains an experimentally-based, transparent clarification of the density-matrix and product operator remedies therefore permitting non-experts to determine sequences of various levels of complexity.
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Extra info for 2D Nmr: Density Matrix and Product Operator Treatment
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.
Note that dmn(0) is the starting point of the evolution immediately after a given pulse. In our case the elements dmn(0) are those of D(1). 65) where mm and mn are the total magnetic quantum numbers of states m and n (see Appendix B). 65) to our particular case (m1 = 1 ; m2 = m3 = 0 ; m4 = − 1). As expected, the diagonal elements are invariant during evolution since both exponentials are equal to 1. All single quantum coherences above diagonal have mm − mn = 1. 66) where Wmn is the evolution frequency in the rotating frame.
When s varies from +1 to - 1, the quantity 2sMoC varies from +2MoC to - 2MoC , a swing of 4MoC. The remaining of the sequence is designed to make this modulated term observable. For s greater than 1/4, M12 becomes positive while M34 remains negative. In other words, the fast carbons are now predominantly up and the slow ones predominantly down. A correlation has been created between the up-down and the fast-slow quality of the carbon spins. 6d t(7). It is seen that the vector representation can explain how carbon magnetization is affected by the pulse (12 goes in - y and 34 in +y), but it cannot explain the nulling of proton magnetization.