# The Basics of nmr chapter 1 introduction

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## 2-D TECHNIQUES

### Introduction

In Chapter 6 we saw the mechanics of the spin echo sequence. Recall that a 90 degree pulse rotates magnetization from a single type of spin into the XY plane. The magnetization dephases, and then a 180 degree pulse is applied which refocusses the magnetization.

When a molecule with J coupling (spin-spin coupling) is subjected to a spin-echo sequence, something unique but predictable occurs. Look at what happens to the molecule A2-C-C-B where A and B are spin-1/2 nuclei experiencing resonance. The NMR spectrum from a 90-FID sequence looks like this.

With a spin-echo sequence this same molecule gives a rather peculiar spectrum once the echo is Fourier transformed. Here is a series of spectra recorded at different TE times. The amplitude of the peaks have been standardized to be all positive when TE=0 ms.

To understand what is happening, consider the magnetization vectors from the A nuclei. There are two absorptions lines in the spectrum from the A nuclei, one at +J/2 and one at -J/2. At equilibrium, the magnetization vectors from the +J/2 and -J/2 lines in the spectrum are both along +Z.

A 90 degree pulse rotates both magnetization vectors into the XY plane. Assuming a rotating frame of reference at o = , the vectors precess according to their Larmor frequency and dephase due to T2*. When the 180 degree pulse is applied, it rotates the magnetization vectors by 180 degrees about the X' axis. In addition the +J/2 and -J/2 magnetization vectors change places because the 180 degree pulse also flips the spin state of the B nucleus which is causing the splitting of the A spectral lines.

The two groups of vectors will refocus as they evolve at their own Larmor frequency. In this example the precession in the XY plane has been stopped when the vectors have refocussed. You will notice that the two groups of vecotrs do not refocus on the -Y axis. The phase of the two vectors on refocussing varies as a function of TE. This phase varies as a function of TE at a rate equal to the size of the spin-spin coupling frequency. Therefore, measuring this rate of change of phase will give us the size of the spin-spin coupling constant. This is the basis of one type of two-dimensional (2-D) NMR spectroscopy.

### J-resolved

In a 2-D J-resolved NMR experiment, time domain data is recorded as a function of TE and time. These two time dimensions will referred to as t1 and t2. For the A2-C-C-B molecule, the complete time domain signals look like this.

This data is Fourier transformed first in the t2 direction to give an f2 dimension, and then in the t1 direction to give an f1 dimension.

Displaying the data as shaded contours, we have the following two-dimensional data set. Rotating the data by 45 degrees makes the presentation clearer. The f1 dimension gives us J coupling information while the f2 dimension gives chemical shift information. This type of experiment is called homonuclear J-Resolved 2-D NMR. There is also heteronuclear J-resolved 2-D NMR which uses a spin echo sequence and techniques similar to those described in Chapter 9.

### COSY

The application of two 90 degree pulses to a spin system will give a signal which varies with time t1 where t1 is the time between the two pulses. The Fourier transform of both the t1 and t2 dimensions gives us chemical shift information. The 2-D hydrogen correlated chemical shift spectrum of ethanol will look like this. There is a wealth of information found in a COSY spectrum. A normal (chemical shift) 1-D NMR spectrum can be found along the top and left sides of the 2-D spectrum. Cross peaks exist in the 2-D COSY spectrum where there is spin-spin coupling between hydrogens. There are cross peaks between OH and CH2 hydrogens , and also between CH3 and CH2 hydrogens hydrogens. There are no cross peaks between the CH3 and OH hydrogens because there is no coupling between the CH3 and OH hydrogens.

Heteronuclear correlated 2-D NMR is also possible and useful.

### Examples

The following table presents some of the hundreds of possible 2-D NMR experiments and the data represented by the two dimensions. The interested reader is directed to the NMR literture for more information.
 2-D Experiment (Acronym) Information f1 f2 Homonuclear J resolved J Heteronuclear J resolved JAX X Homoculclear correlated spectroscopy (COSY) A A Heteronuclear correlated spectroscopy (HETCOR) A X Nuclear Overhauser Effect (2D-NOE) H, JHH H, JHH 2D-INADEQUATE A + X X

The following table of molecules contains links to their corresponding two-dimensional NMR spectra. The spectra were recorded on a 300 MHz NMR spectrometer with CDCl3 as the lock solvent.
 Molecule Formula Type Spectrum methyl ethyl ketone CH3(C=O)CH2CH3 COSY ethanol CH3CH2OH COSY 1-propanol CH3CH2CH2OH COSY 2-propanol (CH3)2CHOH COSY 2-butanol CH3CH2CH(OH)CH3 COSY ethyl benzene C6H5CH2CH3 COSY pyridine C5H5N COSY