### by Nikolai V. Shokhirev

Prof. F. Ann Walker Research Group, Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA

## 2D NMR Basics

### 2D NMR Basics

#### Contents

• Introduction
• Basic Pulse Sceme
• 2D time domain spectrum
• 2D frequency domain spectrum
• 2D spectrum of interacting subsystems
• References

### Introduction

The two dimensional (2D) NMR spectroscopy is based on the pulse variant briefly described in the previous section (1D NMR Basics).

### Basic Pulse Scheme

In 2D Basic 3-pulses scheme for 2D spectroscopy

Stages:

• Before the 1st pulse. The system is in equilibrium state: .
• The 1st pulse is non-selective (90°) y -pulse. It turns the z-magnetization along the x-axis: .
• Between the 1st and 2nd pulses the transversal magnetization precesses (rotates) freely in the xy-plane: This stage is called evolution.
• The pulses are separated by the period t1. Before the 2nd pulse the vector of magnetization is: • The 2nd (90°) y -pulse converts the x-magnetization into longitudinal (along the -z-axis) magnetization. The y-component remains unaffected by the pulse and is cancelled by phase-cycling or destroyed by the T2 relaxation.
• Between the 2nd and 3rd pulses the longitudinal magnetization decays due to the T1 relaxation: • If the pulses 3 and 2 are separated by the time tm then the magnetization before the 3rd pulse is: tm is called mixing time.
• the 3rd pulse again convert the z magnetization into the xy-plane and makes it observable: Here t2 = t - tm - t1. This stage is called acquisition.

### 2D time domain spectrum

The x-component of the above magnetization as a function of t1 and t2 has the following shape: ### 2D frequency domain spectrum

Two-dimensional Fourier transformation converts this function into the two-dimensional function in the - domain: The projections of this two-dimensional spectrum on each frequency axis has a well-known shape: ### Two-line 2D spectrum

If a system consists of two non-interacting subsystems then its 2D spectrum has two peaks along the diagonal : Its projection to each frequency axis again is 1D spectrum: ### 2D spectrum of interacting subsystems

The advantage of the 2D spectroscopy becomes apparent for the systems with interaction. In addition to the diagonal peaks it has two cross-peaks: The diagonal peaks are centered at and . The off diagonal peaks are situated at and : The contour map of the 2D spectrum.

The 2D technique is a very useful tool for study of interactions accompanied by magnetization transfer. A chemical exchange is an example of the system with magnetization transfer due to chemical transformation.

### References

1.  R.R.Ernst, G.Bodenhausen, and A.Wokaun. Principles of nuclear magnetic resonance in one and two dimensions. Claredon Press, Oxford, 1987.

©Nikolai V. Shokhirev, F. Ann Walker, 2001-2007

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