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8.12: Interpreting 1H NMR Signal Splitting: The (n + 1) Rule

JoVE Core
Analytical Chemistry

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Interpreting 1H NMR Signal Splitting: The (n + 1) Rule

8.12: Interpreting 1H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others. Similarly, if A has three neighbors (AX3 spin system), four possible electronic environments result in a quartet of peaks with the relative intensities 1:3:3:1.

Empirically, a proton coupled to n equivalent neighbors yields a multiplet signal split into n + 1 peaks. The relative intensities of the peaks in a multiplet can be predicted using Pascal's triangle, which is an array where each entry is the sum of the entries to its left and right in the row above it.


Keywords: NMR Signal Splitting (n+1) Rule AX Spin System AX2 Spin System AX3 Spin System Multiplet Pascal's Triangle

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