by Nikolai V. Shokhirev

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

Chemical Exchange

1D NMR Basics

2D NMR Basics

Chemical Exchange


1D NMR with Chemical Exchange




Chemical reaction 

The fist-order reactions describe such processes as isomerization, conformation change, etc. The kinetics is described by the following equation

 Here Cp is the concentration of reagent p, kpr is the rate for the reaction

The following expression expresses the conservation law

- the total amount of matter (concentration) does not change.


Modified Bloch equation 

Define the bulk magnetization

 Its time derivative is

 Combined kinetic equations are 

In the above equations we neglected the effect of magnetic field influence to chemical reaction: 

Usually this is a very good approximation because magnetic interactions are much less than chemical and other interactions. Note, however, that under specific conditions the magnetic field can affect chemical yield (Magnetic Effect) or chemical reactions produce reagents with non-equilibrium magnetization (CIDNP - Chemically Induced Dynamic Nuclear Polarization). The above equations are called the Modified Bloch Equations. 

The magnetization obtained from the Modified Bloch Equation can be used for calculation of NMR spectra both in CW and Pulse techniques (see 1D NMR Basics). 

Two-site (isomer) reaction

 Let us consider the first-order reversible reaction:

The kinetics is described by the set of two equations

They satisfy the conservation law:

 The solution is


 is the rate of "equilibration". The equilibrium concentrations are

The corresponding equilibrium magnetization can be also easily calculated

2D NMR with chemical exchange

 The stages are essentially the same as in 2D NMR Basics. It was assumed that

All other assumptions are the same as in [1].

After the (90°)y pulse at t = 0 the magnetization at t = t1 is

After the second (90°)y pulse the magnetization is

At the end of the mixing time tm we have the following magnetizations: 


After the third pulse turns to the xy-plane and oscillate with the frequency

Magnetization B behaves in a similar manner. 

Performing a 2D Fourier transform we get the intensities of diagonal peaks and cross-peaks:

In this approach IAB = IBA. T2 determines line width. 

Rate constant extraction 

Excluding the common factor (usually unknown) in intensities  we get the set of two equations:

It can be resolved numerically with respect to and (equilibrium constant).

Usually tm is known and both forward and reverse rate constants can be determined. 

The program TwoSiteExchange utilizes the above equations for fitting the experimental data and the extraction of rate constants. It also can be used for the modeling NMR with chemical exchange.

A brief description of this and other NMR-related programs can be found in the section Programs.

The use of 1D techniques in NMR with chemical exchange will be discussed in the next topic.  


  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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