7.2: Theory
- Page ID
- 432212
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Learn the difference between 1-D and 2-D NMR spectroscopy
In 1971, Jean Jeener introduced the two dimensional variation of NMR spectroscopy. Since then, scientists have applied the concept to develop the many techniques of two-dimensional (2-D) NMR. Correlation itself is not a new concept in NMR. In 1H NMR spectroscopy, the splitting of resonances indicates that groups were "correlated" to each other due to the spins within each group. Spin-spin splitting gives information about the neighboring nuclei and in the case of 1H NMR, it was how many neighboring hydrogens there were in the molecule. This coupling of hydrogens will be one type of coupling 2-D NMR will consider. The use of 2-D NMR allows for better resolution in signals that normally overlap in 1-D NMR.
All the basic NMR theory for 1-D NMR still applies. In 1-D Fourier transform NMR, a magnetic field is applied to a sample, which is then hit with a series of pulsed radiofrequency (rf), as seen in the pulse sequence below. The Fourier transform of the outgoing signal results in a 1-D spectra as a function chemical shift.
Two-dimensional NMR adds additional experimental variables and thus introducing a second dimension to the resulting spectrum. A simple 2-D experiment pulse sequence consists of a relaxation delay, a pulse, a variable time interval (t1), a second pulse, and acquisition (t2). The pulse sequence is repeated many times while varying the length of time (t1) the system is allowed to evolve during the first pulse. In 2-D experiments, the signal detected during acquisition is a function of acquisition time (t2), which has been modulated as a function of the time interval (t1). This means that magnetization evolves around one frequency during t1 and a different frequency during t2. The output once Fourier transformed is a 2-D spectrum with two axes. One axis (v2) represents the nucleus detected during acquisition (t2), while the other axis (v1) can represent the same nucleus or a different nucleus. With two axes, it leads to cross peaks along a diagonal connecting coupled nuclei. Due to the nature of how the experiment is run, magnetization is redistributed equally in both directions (just like spin-spin coupling), the cross peaks will be symmetrically disposed about the diagonal.
References
Silverstein, R.M, Webster, F.X, and Kiemle D.J. Spectrometric Identification of Organic Compounds. 7th ed. John Wiley & Sons, Inc. 2005.