As described above, J-coupling occurs when the spin of one nucleus affects the spin of another nucleus through the intermediary of bonding electrons. To gain appreciation for how this occurs, let us consider a relatively simple molecule like hydrogen fluoride (HF). The following analysis is not rigorously quantum mechanical nor do we fully discuss energy level transitions, but hopefully it will provide some insight into the phenomenon. We begin with a brief review of spins, orbitals and bonding as background.
First you should recall that the two common isotopes of hydrogen and fluorine (1H and 19F) each have nuclear spins (I) equal to ½. This means that each nucleus has two "observable" spin states, which we will denote as spin-up (↑) and spin-down (↓). Likewise, since all electrons have spin = ½, they can also be described as spin-up (↑) or spin-down (↓).
The reason behind this lies in the fact that protons and electrons are not solid balls, but are better represented as probability distributions described by wavefunctions (Ψ). These wavefunctions overlap in space, meaning there is a small chance of finding an electron even in the middle of the nucleus! In this small overlap region, a so-called hyperfine interaction occurs, that energetically favors to a small degree that the proton and electron spins have an anti-parallel configuration.
A similar hyperfine interaction occurs in the F atom where its electronic and nuclear wavefunctions overlap. An additional feature you need to know about F is that it has 9 electrons, all of which are in paired orbitals except for a lone electron in the 2pz shell. This half-filled shell spatially overlaps with, and has a comparable energy level to, the 1s shell of H where its single electron resides. Electrons from these shells, one from each atom, are primarily responsible for forming the sigma (σ) bond of the HF molecule.
- Types of nuclei. The example above illustrates heteronuclear coupling, where the involved nuclei are different (H and F). In clinical MRS homonuclear coupling between ¹H nuclei is the norm.
- Number of bonds between nuclei. J-coupling effects decrease with increasing distance, and are normally not measurable for nuclei separated by more than 3-4 bonds (unless some of those bonds are double, triple, or aromatic).
- Orientation. The nature of the chemical bonds (σ-, π-, etc.), bond length, and angle between them affects J-coupling in a complex manner. For ¹H nuclei on neighboring carbon atoms, the semi-empirical Karplus equation can be used to relate J-coupling to torsional angle of the molecule.
When reading spectroscopy literature, you may come across the following J-coupling nomenclature and abbreviations, so I have provided a brief translation guide here. The general form of the coupling constant is NJA-X, where the two coupled nuclei are A and X and N = the number of bonds between them. Two-bond coupling constants (2J) are called geminal, while three-bond coupling constants (3J) are called vicinal.
The coupling between H and F on the hydrogen fluoride molecule would therefore be denoted 1JH-F, while the coupling between the two hydrogens on adjacent carbons of chloroethane would be denoted 2JH-H.
It should be noted that couplings are symmetric, meaning that if nucleus X couples in a certain way to nucleus A, nucleus A likewise couples to X. In other words, NJA-X = NJX-A always.
The degree of line splitting equals n+1, where n = the number of J-coupled nuclei. Formation of a quartet is shown with 3 coupled spins in various combinations, producing ratios of 1:3:3:1, which can be predicted by Pascal's triangle.
Coupling constants (J) are therefore expressed in absolute frequencies (Hz) rather than ppm. For ¹H-¹H coupling in organic molecules, J is usually in the range of 0−20 Hz. First-degree heteronuclear coupling constants may be much larger, however, with ¹H-¹³C and ¹H-³¹P in the hundreds of Hz.
The lack of field dependence for J means that at higher magnetic fields the main spectral peaks of metabolites will be more widely separated along the frequency spectrum and potentially easier to identify, but their splitting into doublets, triplets, etc. will appear more tightly spaced because their offsets (J) remain constant along a wider frequency scale.
Karplus M. Vicinal proton coupling in nuclear magnetic resonance. J Am Chem Soc 1963; 85:2870-2871.
Kwan EE. Coupling constants. Lecture notes from Chemistry 117: Practical NMR spectroscopy (my.harvard) available at this link.
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