2D NMR Basics

by Nikolai Shokhirev

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

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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 1^st and 2^nd 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 2^nd pulse the vector of magnetization is:

  

• The 2^nd (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 2^nd and 3^rd pulses the longitudinal magnetization decays due to the T₁ relaxation:

  

• If the pulses 3 and 2 are separated by the time t_m then the magnetization before the 3^rd pulse is:

  

  t_m is called mixing time.
  
• the 3rd pulse again convert the z magnetization into the xy-plane and makes it observable:

  

  Here t₂ = t - t_m - t₁. This stage is called acquisition.

2D time domain spectrum

 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.

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