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

## 1D NMR with Chemical Exchange

## Contents

- Continuous wave NMR spectrum
- Comparison of the 1D and 2D techniques
- Numerical modeling
- References
## Programs

Continuous wave NMR spectra of reacting molecules can be calculated using the Modified Bloch Equation (see Chemical Exchange) in the same way as the original Bloch Equation is used for an ordinary 1D spectroscopy (see 1D NMR Basics).

For the first-order reactions

a spectrum depends on the RF frequency (or magnetic field strength) and on reaction rates.

Let us consider the case k_{AB} = k_{BA} = k, T_{2A}
= T_{2B} = 1/r, . At k = 0 the specter is a sum of two independent
lines:

k = 0 |

As k increases, the line broaden and move to each other and form a one broad line:

With further increase, the line becomes narrow:

the line width tends to the width of the initial line and the intensity tends to the sum of the initial intensities. It is called a narrowing due to a fast chemical exchange.

The following pictures present this dependence in a continuous form:

Intensity as a function of frequency and rate constant |

The two techniques in many aspects are complementary. Shape transformation of the 1D spectra allow studying chemical reaction in a wide range of reaction rates. In the case of extreme exchange narrowing the both types of spectroscopy can only determine that the rate of reaction is larger than the line splitting. At small reaction rates the change of a 1D spectrum is small relative to the magnitude of peaks. The intensities of peaks are changed even less. The same is true for the diagonal 2D peaks. However the cross peaks are directly related to the reaction rates and canbe detected easier (see Chemical Exchange).

The described transformations can be modeled using the program "TwoLines1D".

Download here.

- 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