Aug 26, 2021

How to Calculate Coupling Constant (J values) in Proton NMR Spectroscopy

Hi Friends, in this article we will see how to calculate coupling constants (J values) in 1H-NMR Spectroscopy.

Key wordsCoupling constant, Multiplicity1H-NMR spectrum, Signal.

Definition of coupling constant

The coupling constant is a distance between sub-peaks expressed in hertz. In 1H-NMR spectrum a peak splits into multiple sub-peaks due to coupling with neighboring protons. The value of coupling constant does not depend upon frequency of machine and solvent used for NMR experiment.

We have discussed various applications of spectroscopy in chemistry, medicine and environmental science in another article. Please check out for more details. [Link]

Introduction

In proton nuclear magnetic resonance (NMR) spectroscopy, the coupling constant is a key parameter that provides valuable information about the molecular structure and bonding in a compound. The coupling constant, denoted as J, represents the splitting of NMR signals observed in a spectrum due to the magnetic interactions between neighboring hydrogen atoms (protons) in a molecule. In this article, we will explore the importance and implications of coupling constants in proton NMR.

Understanding Coupling Constants

The magnitude of the coupling constant is measured in hertz (Hz) and indicates the strength of the magnetic interaction between the coupled protons. It is determined by the nature and distance of the chemical bonds between the protons involved.

The coupling constant provides information about the number of neighboring protons and their relative arrangement with respect to the proton of interest. By analyzing the pattern and splitting of the NMR peaks, chemists can deduce the connectivity and structural features of the molecule under investigation.

Typically, the coupling constant is described by two parameters: the coupling constant value (J) and the coupling multiplicity. The coupling constant value reflects the size of the splitting, while the coupling multiplicity describes the number of peaks observed in the NMR spectrum.

For example, in a simple case of two coupled protons, known as a "doublet," the coupling constant reflects the strength of the interaction between the two protons. The doublet appears as a pair of peaks, usually of equal intensity, with a splitting pattern determined by the coupling constant.

Factors Affecting Coupling Constants

The value of the coupling constant depends on several factors, including 

  1. Bond length between the coupled protons, 
  2. Nature of the bonding (single, double, or triple bond), and 
  3. Hybridization state of the carbon atoms attached to the protons. 

Different types of bonds and molecular environments can give rise to distinct coupling constants.

Applications of Coupling Constants

The coupling constant is useful in structural elucidation and can provide information about the connectivity, stereochemistry, and conformational properties of organic molecules. It serves as a powerful tool for chemists to analyze and interpret proton NMR spectra, allowing them to determine the structure and understand the behavior of organic compounds.

Interpretation of Coupling Constants

Multiplicity of signals and calculation of respective J values is discussed below.

Singlet

A singlet peak is represents single line. Hence there will not be any coupling constant for this peak.

Singlet peak

Doublet

A doublet is consisting of two sub peaks with 1:1 intensity.

Doublet peak

The coupling constant (J value) for doublet peak is calculated by the formula;

J value = (line 1 – line 2) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J value = (6.2600 – 6.2400) x 400

J value = 0.02 x 400

J value = 8.0 Hz

Triplet

A triplet peak is consisting of three sub peaks and they have 1:2:1 intensity.

Triplet peak

The coupling constant (J value) for triplet peak is calculated by the formula;

J value = (line 1 – line 2) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J value = (3.3400 – 3.3300) x 400

J value = 0.01 x 400

J value = 4.0 Hz

Quartet

A quartet peak is consisting of four sub peaks with 1:3:3:1 intensity.

Quartet peak

The coupling constant (J value) for quartet peak is calculated by the formula;

J value = (line 1 – line 2) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J value = (3.3400 – 3.3250) x 400

J value = 0.015 x 400

J value = 6.0 Hz

Quintet

A quintet peak is consisting of five sub peaks. They have 1:4:6:4:1 intensity.

Quintet peak

The coupling constant (J value) for quintet peak is calculated by the formula;

J value = (line 1 – line 2) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J value = (2.5250– 2.5125) x 400

J value = 0.0125 x 400

J value = 5.0 Hz

Sextet

A sextet peak is consisting of six sub peaks. They have 1:5:10:10:5:1 intensity.

Sextet peak

The coupling constant (J value) for sextet peak is calculated by the formula;

J value = (line 1 – line 2) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J value = (3.3600– 3.3530) x 400

J value = 0.007 x 400

J value = 2.8 Hz

In second order spectra the splitting pattern is more complex and it may have more than one coupling constant.

Doublet of doublets

A doublet of doublets peak is consisting of four lines. This is second order splitting pattern and it appears as two doublet peaks.

Doublet of doublets
 There are two coupling constants found in this type of splitting pattern.

The coupling constant (J1 value) for doublet of doublets peak is calculated by the formula;

J1 value = (line 1 – line 3) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J1 value = (4.5505– 4.5305) x 400

J1 value = 0.02 x 400

J1 value = 8.0 Hz

The coupling constant (J2 value) for doublet of doublet peak is calculated by the formula;

J2 value = (line 1 – line 2) x frequency of NMR machine

J2 value = (4.5505– 4.5430) x 400

J2 value = 0.0075 x 400

J2 value = 3.0 Hz

Doublet of triplets

A doublet of triplets peak is consisting of six sub peaks. This is second order splitting pattern and it appears as two triplets.

Doublet of triplets

There are two coupling constants found in this type of splitting pattern. The coupling constant (J1 value) for doublet of triplets peak is calculated by the formula;

J1 value = (line 2 – line 5) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J1 value = (3.3550– 3.3250) x 400

J1 value = 0.03 x 400

J1 value = 12.0 Hz

The coupling constant (J2 value) for doublet of doublet peak is calculated by the formula;

J2 value = (line 1 – line 2) x frequency of NMR machine

J2 value = (3.3662– 3.3550) x 400

J2 value = 0.0112 x 400

J2 value = 4.5 Hz

Doublet of quartet

A doublet of quartets peak is consisting of eight sub peaks. This is second order splitting pattern and it appears as two quartets.

Doublet of quartets

There are two coupling constants found in this type of splitting pattern. The coupling constant (J1 value) for doublet of triplets peak is calculated by the formula;

J1 value = (line 2 – line 6) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J1 value = (2.3874– 2.3577) x 400

J1 value = 0.0297 x 400

J1 value = 11.8 Hz

The coupling constant (J2 value) for doublet of doublet peak is calculated by the formula;

J2 value = (line 1 – line 2) x frequency of NMR machine

J2 value = (2.3944– 2.3874) x 400

J2 value =0.007 x 400

J2 value = 2.8 Hz

Triplet of doublets

A Triplet of doublets peak is consisting of eight sub peaks. It appears as three doublet peaks. This is second order splitting pattern.

Triplet of doublets

There are two coupling constants found in this type of splitting pattern. The coupling constant (J1 value) for triplet of triplets peak is calculated by the formula;

J1 value = (line 1 – line 3) x frequency of NMR machine

Suppose the NMR recorded in 400 MHz machine, therefore

J1 value = (2.5410– 2.5292) x 400

J1 value = 0.0118 x 400

J1 value = 4.7 Hz

The coupling constant (J2 value) for triplet of triplets peak is calculated by the formula;

J2 value = (line 1 – line 2) x frequency of NMR machine

J2 value = (2.5410– 2.5360) x 400

J2 value = 0.005 x 400

J2 value = 2.0 Hz

That's all for this topic. If you have any questions please feel free to ask me in the comment box. 

Also, we have discussed splitting and multiplicity pattern in another article. please see the link below;

Topics in Organic Chemistry: Splitting and Multiplicity in Proton NMR (chemistrywithdrsantosh.com)

Thank you..!

12 comments:

  1. Welcome... Your message means a lot to me.

    ReplyDelete
  2. Thank you friend it is well written

    ReplyDelete
    Replies
    1. Welcome... Please check out other articles as well.

      Delete
  3. its really valuable information ......

    ReplyDelete
  4. Thank you for simplified this topic with excellent information

    ReplyDelete
    Replies
    1. Welcome..! Thank you very much for noticing the work.

      Delete
  5. Simply explain, very informative

    ReplyDelete
  6. Terima kasih, informasi berharga ini, mohon ada penjelasan lebih lanjut penerapan konstanta kopling dan hubungan dengan panjang ikatan, sifat ikatan dan keadaan hibridisasi atom C. Terima kasih

    ReplyDelete