Notation for Spin system( Pople notation )

Pople notation

Notation for spin system in NMR spectroscopy, the term “pople notation” is used which refers to the proton having the same value for a chemical shift or the same set of protons being preserved in one set. They play a significant role in the spin system. Capital letters such as A, B, C, X, or M are used to identify them, among others. For example, nitropropane will have the formula A3M2X2 if there are a number of protons added.

Pople notation generally depends upon three factors ie. spin coupling, chemical shift value, and peak intensity. If the ratio of frequency and coupling constant is greater than 8, then it is weakly coupled and is well separated but when the ratio is less than 8, then they are strongly coupled. AX, AM, and AB are examples of weakly coupled and strongly coupled respectively.

For a system of three sets of protons, each set separated by a large chemical shift can be designated by AaMmXn. If two sets are separated by a small chemical shift and a third widely then the AaBbXx designation is used. If all the shift positions are closed, the system is AaBbCc. The AMX system is first order, ABX systems can be approximated by using first-order rules, but ABC systems cannot be analyzed by inspection. In organic compounds, the AMX, ABX, and ABC patterns, as well as other related spin systems, are quite prevalent. Some of the structural kinds that produce these patterns are listed below.

Three types of the spin system

Now, taking three systems of notation, we are going to explain the AMX system for a clear vision.

Let’s talk about styrene

Notation for spin system

How to sketch the spectrum of styrene?

Having considered three systems, we can now examine the systems AMX, ABX, and ABC, starting with a rigid system. Styrene, whose rigid vinylic group furnishes an AMX first-order spectrum t 600 Mhz, is a good starting point.

The correlation of the structure of a compound with its NMR spectrum requires the following information:

  1. No of the spin system
  2. no of sets in each spin system
  3. no proton in each set
  4. chemical shift value
  5. difference in frequency
  6. value of coupling constant
  7. ratio of
  8. no kind of symmetry
  9. exchange of labile proton
  10. effect of substituents

From above you can easily sketch the spectrum.

For styrene let us correlate the data:

  1. In styrene, there are two spin systems in the molecules.
  2. There are three sets in the vinylic system
  3. There is one proton in each set of the vinylic part.
  4. The difference in frequency for each proton is AM= 300, AX= 888, And MX=588.
  5. Value of J, AM= 1.0, AX= 11, MX=17
  6. The ratio of frequency and coupling constant value are AM= 300, AX= 88, MX=35
  7. The value of chemical shifts is for Ha= 5.25, Hm= 5.76, and Hx= 6.72.
  8. There are two symmetry planes through the molecules
  9. Absence of labile proton
  10. The phenyl group deshielded the Hx and some extend to Hm
AMX system of pople notation
1H NMR spectrum of styrene

The spectrum of the vinylic system of styrene is clearly shown in the above spectra as we concluded that out of three sets each, a doublet of doublets represents a single proton. The x proton has a chemical shift value of 6.72 which is in deshielded region due to the phenyl effect or benzene ring current, the value for m is 5.28 and for a is 5.25. The aromatic ring deshields the X proton the greatest and the A proton the least. With the highest coupling constant, the X proton is coupled trans across the double bond to the M proton; with a little smaller coupling constant, it is connected cis across the double bond to the A proton.

AMX spectrum of the spin system


What is the AMX system?

Three coupled nuclei are represented as an AMX spin system, with their signals separated by large chemical shifts relative to their coupling.

What is the difference between AMX and ABX?

The notation can be used to indicate systems with more than two nuclei. For instance, AMX stands for three nuclei that are moderately spaced apart from one another, and ABX stands for two closely spaced nuclei and a third nucleus that is further apart.

What is a spin system in NMR?

A spin system describes the number, kind, and interrelationship of magnetic nuclei by including nuclei between which spin-spin interaction exists. A capital is assigned to each nucleus (spin  ½).

In which spin system did styrene belong?

Styrene belongs to the AMX system of the spectrum.

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