By Gheorghe D. Mateescu, Adrian Valeriu
In contrast to so much really good 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 see sequences of various levels of complexity.
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Additional resources for 2D Nmr: Density Matrix and Product Operator Treatment
Rather than doing the density matrix calculations for an arbitrary phase F, we will take advantage of the fact that we have already treated the x phase in the previous section. 15). 92). 93)]. 15. 2 The Second Pulse The rotation operator for the 90yAX pulse can be obtained by multiplying R90yA by R90yX. These operators are (see Appendix C): R90 yA ⎡1 ⎢ 1 ⎢ −1 = 2⎢0 ⎢ ⎣0 1 1 0 0 0 0 1 −1 0⎤ ⎡1 0 ⎥ ⎢ 0⎥ 1 ⎢0 1 ; R90 yX = 1⎥ 2 ⎢ −1 0 ⎥ ⎢ 1⎦ ⎣ 0 −1 1 0 1 0 0⎤ 1 ⎥⎥ 0⎥ ⎥ 1⎦ The result of the multiplication, R = R90 yAX , is shown below together with its reciprocal, R −1 .
The great advantage of the 2D display consists of the fact that every pair of coupled carbons will exhibit its pair of doublets along its own W14 frequency. This allows us to trace out the carbon skeleton of an organic molecule. 9. The four peaks due to a pair of coupled vertical scale is twice larger than the horizontal scale. 13 C atoms. 10 and to determine its carboncarbon connectivities. The answer is in the footnote on page 59. 81)]. This means that, when incompletely eliminated, the peaks of isolated carbons will be "axial" (dotted circles on the zero frequency line of domain ∆).
However, for the comparison with the vector representation and for an understanding of the polarization transfer, it is necessary to discuss the density matrix D(6). 33). 53). What happens to the proton magnetization can be predicted from the previous vector representation but what happens to the carbon cannot. As far as the proton is concerned, its x components are not affected, while the other components rotate from y to z and from - y to - z, as expected after a 90x pulse. e, it is proton modulated.
2D Nmr: Density Matrix and Product Operator Treatment by Gheorghe D. Mateescu, Adrian Valeriu