Let us try to understand peak splitting using the following molecule as an example This method of generating numbers is known as binomial expansion. We can explain the rest of Pascal’s triangle in a similar way. Therefore, we end up with the sequence 1 3 3 1 In this case, again 1 is written at the ends and the neighboring numbers are added. In this case, the number 1 is written at the left and right of the triangle and the sum (1+1) is shown in the middle.įor n=3, we get a quartet. Moving on, for n=2 (or 2 neighboring protons), we get a triplet. This is written as 1 on either side of the second row in Pascal’s triangle Similarly, for n=1 (or 1 neighboring proton), we get a doublet (using the n+1 rule). This is depicted as 1 at the apex of Pascal’s triangle With n=0 (or 0 neighboring protons), we get a single peak. If we look at the figure below and consider a quartet, we would observe that the peak of the extreme signals is 1/3 rd of the first and the last peak. The height of the peaks, caused due to spin-spin coupling is in proportion to the values in the row (corresponding to the value n) in Pascal’s triangle. We can use the n+1 rule to determine the number of peaks. This is a number pattern invented by a famous French mathematician, Blaise Pascal. The other relevant information which comes along with knowing the number of peaks is the intensity of the peaks (which is seen as the height of the peaks).Īs a general rule, the height of the peaks or in other words, the relative intensities of the peaks can be determined by using Pascal’s triangle. Since I is always ½, we can rewrite the formula as n+1. There is a formula to calculate the multiplicity of the peaks in the NMR spectrum. The splitting of the NMR signal gives precise information about the number of neighboring protons in a molecule. This phenomenon by which the spins of resonating protons cause the peaks on the NMR spectrum to multiply is known as peak splitting. This multiplicity of the signal is a very important determinant for the structure of the molecule. It is commonly observed that this signal is not always a single peak but has multiple peaks. Peak splitting in NMR spectroscopyĪ closer analysis of an NMR spectrum reveals that each signal on the graph represents one kind of proton present in the molecule. In addition to the chemical shifts, the nature of the peaks in the NMR spectrum is also affected. The effective magnetic field (B eff) experienced by neighboring protons as a result of magnetic spins thereby affect the chemical shift values. The magnetic spins of these resonating nuclei interact with each other and affect each other’s precession frequencies. It is imperative that a minimum of 2 sets of protons are present in adjacent positions. The interaction between the spin magnetic moments of the different sets of H atoms in the molecule under study, is known as spin-spin coupling. Spin-spin coupling between spinning nuclei. The effective magnetic field experienced by the protonĪt the core of the molecule, these spinning nuclei ultimately give rise to the phenomenon of coupling in NMR spectrum. The induced magnetic field is denoted by B i The applied magnetic field is denoted by B 0 The spin states and the energy levels are shown in the diagram below:ĭepending on the orientation of the spins, the effective magnetic field on the proton would either increase or decrease by a small factor. The spins which are aligned with the external magnetic field have a lower energy state than the ones aligned against the magnetic field. In the presence of an external magnetic field, there is a tendency of the nuclei to align either with or against the magnetic field. In the absence of a magnetic field, these spins are quite random. A proton has two possible spin states +1/2 or -1/2. The nuclear magnetic spinĪ nucleus that has an odd number of protons spins along its axis. The spin-spin coupling phenomenon, at its core, involves spinning nuclei. There could also be other complex peak splitting patterns. In fact, the interactions between different types of protons present in the molecule cause a single peak on an NMR spectrum to split into doublet, triplet, or multiplet, a phenomenon known as the spin-spin coupling. In addition to knowing where the peaks are, on the chemical shift scale, and what influences the delta value, one must also consider the fact that the peaks in an NMR spectrum are not always a singlet. The location of the peaks is important in discovering how many protons there are in a molecule, as well as other information about the surrounding electronic environment. One of the factors affecting the location of the peaks in an NMR spectrum is Chemical shift. However, the interpretation of the signals in an NMR spectrum relies on several factors. The structure of a molecule can be predicted using NMR spectroscopy.
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