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NMR Spectroscopy: Basic Principles, Concepts and Applications in Chemistry

Harald Günther

Chapter 9

Two-Dimensional Nuclear Magnetic Resonance Spectroscopy - all with Video Answers

Educators

Chapter Questions

Problem 1

Draw the detected signal for the homonuclear spin echo experiment without and with X-decoupling, as shown in Figure 9.7a, for angles $\varphi=90^{\circ}, 180^{\circ}$, and $270^{\circ}$.

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Problem 2

Derive in analogy to Figure 9.7 diagrams for spin echo experiments that use a $180^{\circ}$ pulse.

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Problem 3

Redraw the diagrams shown in Figure 9.7 for the "off-resonance" situation with $v(A I)>v(A 2)>v_0$.

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Problem 4

Illustrate the situation discussed above in graphical form (because scalar coupling is absent, Bloch vector pictures can be used).

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Problem 5

Draw vector pictures to explain the origin of axial peaks.

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02:31

Problem 6

Consider why Eq. (9.6) cannot be satisfied by an increase of the $t_1$ increment.

Ryan Hood
Ryan Hood
Numerade Educator
07:32

Problem 7

Figure 9.21 shows the COSY-90 and the COSY-LR ${ }^1 \mathrm{H}$ NMR spectrum of naphthobiphenylene-dianion [(a) and (b), respectively]. Assign the signals 1-6 to the protons $\mathrm{H}_{\mathrm{a}}-\mathrm{H}_{\mathrm{f}}$ ( $\mathrm{S}=$ solvens tetrahydrofuran).

Nima Gharibi
Nima Gharibi
Numerade Educator

Problem 8

Formulate the effect of $90^{\circ}$ pulses in the $+\gamma$ - and $-\gamma$-direction on $\hat{I}_x$ and $\hat{I}_{y^*}$.

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Problem 9

Develop an equation similar to Eq. (9.33) for the $t_2$ evolution of antiphase Amagnetization [term (3) in Eq. (9.31)].

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Problem 10

Analyze the results of COSY experiments with variable pulse angles $\beta=0^{\circ}$, $90^{\circ}$, and $180^{\circ}$ for the mixing pulse with the help of the general results given in
Eq. (8.2.3) on p. 407 of the monograph by Ernst, Bodenhausen, and Wokaun (first ed., see the Literature at the end of this chapter, p. 338).

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Problem 11

Draw the receiver signals for both coherences A and B if the alternative receiver phase cycle ( 0321 ) for the first pulse $P 1$ is used and analyze the result for a situation where only the phase of P2 is changed.

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Problem 12

Discuss the consequences of pulse sequence (2) in Figure 9.29 for the remaining double-quantum coherences as well as for the zero- and single-quantum coherences of the COSY-DQF experiment shown in the Figure given in the Solution to Problems.

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Problem 13

Derive $\sigma_2$ with the help of Eq. (9.23b) (p. 315).

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