Introduction to Quantum Mechanics and Multiplet Splitting in 1H NMR Spectrum

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Shortly before the discovery of quantum mechanics, it was discovered that the Zeeman Effect and other “fine structure” spectral lines could be explained if the electrons were spinning about their own axis. This property, known as spin angular momentum, was eventually extended to protons as well. 

Because protons and electrons also have a charge associated with them, this intrinsic spin causes the particle to behave as a very small magnet. These particle-sized “magnets” are randomly oriented in most instances, but can be forced to adopt one of only two orientations by placing the particles inside a strong magnetic field. In this situation, the particles orient themselves along the axis of the applied magnetic field B0 with the particle’s magnetic field Bp oriented either with, or against the applied field. These two states, referred to as “spin up,” and “spin down” have two different energy levels. As all matter prefers to be in the lowest energy level possible, more particles adopt the lower energy spin up orientation with the particle’s magnetic field aligned with the applied magnetic field B0 than adopt the higher energy spin down state. This population difference is what NMR spectroscopy, similar to other optical spectroscopies (UV-VIS, Infra-red, etc.) uses to generate an NMR signal.

The fact that every chemically different proton (for 1H-NMR) is in a slightly different magnetic environment, means that the energy levels available to those nuclei are also slightly different. These small differences in energy from one proton to another allow the NMR signal to become (with sufficient instrumental resolution) an NMR spectrum with a different peak for each chemically unique proton.

The displacement of NMR peaks along the x-axis is known as chemical shift and reveals information about what functional groups are present near the proton responsible for a given signal. In addition, the relative integration of the signals allow NMR spectra to quantify the number of protons that are responsible for generating a given signal, and even to quantify the relative concentration of sample mixtures.

The final piece of information that an NMR spectrum tells us is the multiplicity of the signal and this is what we will focus on in this demonstration. Multiplicity is a splitting of a given NMR spectral signal into a tightly clustered series of peaks based on the number of protons within a given distance from the proton responsible for the signal (typically three bonds between interacting nuclei).

If we once again consider the spinning nuclei, the magnetic field produced by the spin causes small changes in the electron distribution of its bonds. These in turn effect the electron distribution of neighboring bonds, which affect the neighboring nuclei. This process is known as spin-spin coupling and is typically observable out to three bond lengths. Longer range effects are observable, but are beyond the scope of this demonstration. As both neighboring protons can be oriented either spin up or spin down, their effects on the electron cloud, and therefore on each other, will depend on all the possible spin-spin combinations. In the simplest case, when there are only two protons interacting with each other, there exist four total combinations (up-up, up-down, down-up, and down-down), but only two combinations with unique energies (up-up and down-down have identical energies, as do up-down and down-up). This causes the original NMR signal to split in two, and is known as a “doublet.” A proton with two neighboring protons would have four unique combinations but only three unique energies, up-up-up, up-up-down (up-down-up is a unique combination but has the same energy as up-up-down), and up-down-down. Because there are twice as many unique combinations for the up-up-down energy level, the height of that peak will be approximately double that of the outer peaks.

The displacement of NMR signals along the x-axis of an NMR spectrum is dependent upon the magnetic field strength of the instrument, however, the distance between peaks making up a multiplet are not field strength dependent. This is in agreement with the multiplet being a result of the spin orientation of the nucleus on the electron cloud, an interaction that is independent of the field strength.

By measuring the spacing of the multiplet peaks we can directly observe the effect these two quantized nuclear spin states (spin up or spin down) have on their environment.

John Frost, Ph.D., is a chemist at Thermo Fisher Scientific, Rhinelander, WI. He received his Master’s degree in organic chemistry at Michigan Technological University, studying the effects of mono-substituted amides on the intramolecular sulfoxide electrophilic sulfenylation reaction. He received his Ph.D. in analytical and physical chemistry from the University of Wisconsin-Milwaukee, developing a new long-path length spectroscopic technique. John is an alumnus of the Center for Workshops in the Chemical Sciences and an American Chemical Society Science Coach for Overland High School in Aurora, CO.