Spin-spin splitting (n+1) Rule and Pascal's Triangle

Spin-Spin Splitting (n+1) Rule

When spins of two protons combine or couple then it is called spin-spin coupling. A minimum of two sets of protons is required for spin-spin coupling. Due to this coupling phenomenon between two protons that are close to each other splitting of signals observed is called spin-spin splitting. Spin-spin splitting happens due to the neighboring protons in a molecule. The spin state of a hydrogen atom in one solution is not the same as in the other solution. Spin state of atom change with solution types. The spin state or direction (+ 1/2 or – 1/2) of one proton is changed by the adjacent proton spin under the influence of a magnetic field. For example, we have a molecule in which two types of protons are present A and B type. The Spin of A proton influences the spin of B proton thus affecting the chemical shift, this is called coupling and here splitting occurs. As we know shielded and deshielded proton behaves differently in the magnetic field.

Spin-Spin Splitting

Criteria for Splitting

• Splitting occurs in those molecules that have a different chemical environment of their protons. For instance, CH3CH2Br, CH3CH2CH=CH, etc.
• Splitting does not occur in molecules that have symmetrical hydrogen atoms, their environment is identical. Singlet will be observed for example benzene and cyclobutane etc., molecules.
• Splitting also does not observe in a compound that has a set of identical protons but does not have another set of protons attached to nearby carbon. For example, in case of ^aCH3^bCH2CO^cCH3, butanone-2. The singlet peak will appear for proton c (-CH3) because there are no protons attached to carbonyl carbon in the molecule.
• In the case of methanol –OH functional group shows a singlet in the spectrum because no hydrogen atom is attached to carbon, here is a simple OH group present.

n+ 1 Rule

This rule tells that the number of protons present on the adjacent carbon. “n” is the number of protons on adjacent carbon and one is added to that number of protons. See the figure below,

n+1 Rule

Doublet means one proton is present on the adjacent carbon, triplet means two protons are present on the next carbon, and quartet means there are three protons present on the adjacent carbon so, doublet, triplet, quartet, etc. are not shown the number of protons attached to the carbon that gives signal but it shows the number of protons attached to the carbon that is near to that proton (adjacent) carbon.

 The (n+1) Rule, is an empirical rule utilized to find the multiplicity and, with the help of Pascal's triangle, peaks splitting pattern in spectra of proton NMR and 13C NMR.

In NMR spectrum peaks shows the types of protons in molecules. Peak area tells the number of protons and intensities of peaks predicted by Pascal’s triangle. Spin-spin splitting the number of protons adjacent to carbon.

Now we will discuss spin-spin splitting with the help of examples,

Example of Spin-spin splitting

Spin of a proton can arrange differently in the molecules. In the above example, you observe that signal for “a” and “c” type proton shows triplet means on the adjacent carbon there are 2 protons and the spin of these two protons can arrange in three different ways, spins can reinforce the applied magnetic field Bo or arrange parallel to it and also show middle position like one proton spin arrange parallel and other oppose the Bo. All other protons spin also shows this type of arrangement in a magnetic field and splitting of signal occurs that is either doublet or triplet and so on. In this way, spin multiplicity shows in the final NMR spectrum.

NMR and Spin-Spin Splitting 

Pascal's Triangle

You can draw this, first, you draw a single line then draw two lines below the above line far from it. Then join these lines with the first line above it in a dotted line and so on.

Peak intensity ratio is the sum of middle lines and writes 1 both on the left and right side of the number that is above the line.

    

 

Formation of Pascal`s Triangle

By using the n+1 rule we easily find the intensity ratio of the multiplet. In NMR spectrum peak arrangement occurs by following pascal`s triangle. It tells the height intensity of peaks in spectrum. As we observe that in pascal`s triangle 1 show a singlet as a signal and 1:2:1 shows as a triplet signal, this also tells that the height of the first and third peak is low as compared to the middle peak seen in the spectrum of NMR given above The same case is in other signals, in case of a quintet there are five lines in the spectrum and these lines' intensity is different from each other, the middle peak intensity is higher than the other four peaks. In case of a sextet, there is a ratio of 1:5:10: 10:5:1 sex peaks, which means the middle lines have equal and high intensity than the other two lines that have a ratio of 5 and 1 ratio line has a very small peak in the spectrum. See the figure given above.

Pascal`s Triangle