by Nikolai V. Shokhirev

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

## 1D NMR Basics

## 2D NMR Basics

## Chemical Exchange

## Contents

- Chemical Reaction
- Modified Bloch Equation
- Two-site (isomer) reaction
- 2D NMR with chemical exchange
- Rate constant extraction
- References
## 1D NMR with Chemical Exchange

## Programs

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

Here C_{p} is the concentration of reagent p, k_{pr} is the rate for the reaction
.

The following expression expresses the conservation law

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

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).

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

Here

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

The corresponding equilibrium magnetization can be also easily calculated

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 = t_{1} is

After the second (90°)_{y }pulse the magnetization is

At the end of the mixing time t_{m} we have the following magnetizations:

where

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 *I _{AB} = I_{BA}*. T

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 t_{m} 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.

- 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