J-coupling

J-Coupling

Why do some spectra split into smaller peaks while others do not?

J-coupling between two nuclei
mediated by electrons

Splitting of spectral peaks into doublets, triplets or higher order multiplets results from an electron-mediated interaction of two nuclear spins residing on the same molecule. The phenomenon is known as J-coupling, whose mechanism is described more completely in the Advanced Discussion. In brief, the spin of one nucleus polarizes its valence electrons, and this polarization is transferred via bonds to affect the spin of a distant nucleus.

For a spectral line to be split via J-coupling, at least two requirements must be met: 1) the nuclei must lie in relatively close proximity to one another, typically less than 3-4 bonds away, and 2) the nuclei must be chemically distinguishable. The latter criterion means that the four ¹H nuclei of methane (CH4), for example, will produce a single (unsplit) spectral line, as they are chemically and magnetically identical.

If you ever took a college-level organic chemistry course you probably did homework problems using J-coupling to determine the structure of simple compounds such as chloroethane pictured below. (Although like most of my students, you may only vaguely remember having done this!)

High-resolution ¹H NMR spectrum of chloroethane showing splitting of primary resonances at δ = 1.2 and 3.8 into a triplet
and quartet due to J-coupling.

Chloroethane (CH3-CH2-Cl) possesses ¹H-nuclei in two different molecular environments: methyl (−CH3) and methanediyl (−CH2−), with principal resonances at δ ≈ 1.2 and 3.6 ppm respectively. As shown in the high-resolution laboratory NMR spectrum, the two main spectral lines are split (into a triplet and quartet respectively) due to J-coupling.

The spacing between the subpeaks in a multiplet is determined by the coupling constant (J), which for chloroethane has a value of approximately 7 Hz. J is independent of field strength and hence is reported in Hz rather than ppm. For ¹H-¹H coupling in organic molecules, J usually lies in the 0−20 Hz range.

The number of times a given ¹H spectral line will be split can be predicted by the n+1 rule which states that the number of multiplets is one more than the number of hydrogens (n) attached to immediately neighboring carbon atom(s). For cholorethane, the −CH3 hydrogens interact with n = 2 hydrogens on the neighboring carbon (−CH2−), and are hence split into a triplet (2+1=3). Conversely the methanediyl (−CH2−) hydrogens interact with n = 3 methyl (−CH3) hydrogens and are split into a quartet (3+1=4). The relative heights of multiplet subpeaks typically follow the binomial coefficients of Pascal's triangle (1:2:1, 1:3:3:1), while the relative areas under each cluster (3 and 2) reflect the numbers of ¹H-nuclei in each chemical group.

Brain MRS showing J-coupled induced splitting of lactate (Lac) into a doublet while the other major peaks appear as singlets.

In brain MRS the ¹H nuclei giving rise to the three largest peaks — N-acetyl aspartate (NAA), choline (Cho), and creatine (Cr) — do not have nearest neighbor protons, do not experience J-coupling, and manifest as singlets. When present, however, the principal peak of lactate near δ = 1.32 does split into a doublet that is easily visualized. This has given rise to the mistaken notion that lactate is the only peak that splits in the spectrum. This is not true as many metabolites (including NAA) have smaller or secondary peaks that are split by J-coupling (although these may be difficult to see due to their low concentrations or overlap with other resonances).

Advanced Discussion (show/hide)»

A more detailed description of J-coupling

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 (↓).

You are no doubt aware that the ¹H atom consists of one proton and one electron, and four proton-electron spin-state combinations are therefore possible (↑↑, ↑↓ , ↓↑, ↓↓). What may be a little surprising, however, is that all combinations are not equally likely because the energies associated with them are unequal.

Hyperfine interaction of proton and electron spins where their wavefunctions overlap give a very slight energy advantage to anti-parallel configuration, a process known as polarization.

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 2p_z 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.

In forming the HF molecule H and F each supply one electron (e⁻) from their 1s and 2p_z shells to create a σ bond.

Putting these concepts together we can begin to appreciate the role of electrons in the the J-coupling mechanism. The diagram below shows how the spin at F is modulated by electron bonds by the spin at H, and vice-versa.

The strength of J-coupling between two nuclei depends on several factors including types of nuclei, their distance, and orientation.

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.

J-coupling nomenclature

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 ^NJ_A-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 ¹J_H-F, while the coupling between the two hydrogens on adjacent carbons of chloroethane would be denoted ³J_H-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, ^NJ_A-X = ^NJ_X-A always.

Patterns of line splitting

Depending on the number of chemically distinct nuclei involved in a J-coupling interaction, spectral line splitting into doublets, triplets, and higher order multiplets may occur. The exact appearance depends on the size of the coupling constant (J) relative to the frequency difference (Δν) between the nuclei. If J is relatively small compared to Δν, then first-order coupling is seen. First-order coupling is illustrated in the chloroethane spectrum pictured above.

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.

Formation of a quartet with height ratios of 1:3:3:1 caused by 3 J-coupled spins in various combinations

First-order coupling ratios predicted by Pascal's triangle

Many more complicated coupling patterns exist than the ones above, especially if couplings are different or multiple, such as formation of doublets of doublets. When J is relatively large compared to the chemical shift frequency difference (Δν) between the nuclei, second order coupling occurs, manifest in the simplest case by the roofing phenomenon (where coupled multiplets lean toward each other) up to extraordinarily complicated spectra tractable only by experienced chemists.

J-coupling and field strength

Unlike resonant frequencies and chemical shifts, J-coupling interactions are independent of the magnetic field strength (Bo). This occurs because the magnetic moments of nuclei and electrons, the sources of spin-spin coupling, do not depend on the applied field.

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.

It should be noted that although spectral line splitting provides invaluable information about chemical structure, maximum peak height is reduced as the nuclear signals must be spread over several multiplet sub-peaks. Paradoxically, therefore, line splitting can make spectral identification more difficult from the detection point of view.

References
Autschbach J, Le Guennic B. Analyzing and interpreting NMR spin-spin coupling constants using molecular orbital calculations. J Chem Educ 2007; 84:156-171. (Sophisticated but readable review of J-coupling from a MO perspective.)
     Hahn EL, Maxwell DE. Chemical shift and field independent frequency modulation of the spin echo envelope. Phys Rev 1951; 84:1246-7. (Surprising discovery that spin-echo signal decay is modulated by not only chemical shift differences between two protons in a molecule, but also by second frequency (named J) that is independent of field strength.)
Hahn EL, Maxwell DE. Spin echo measurements of nuclear spin coupling in molecules. Phys Rev 1952; 88:1070-1084. (Follow-up paper describing the mechanism of J-coupling more completely).
     Hays TR, Hanson PR, Vyvyan JR. A practical guide to first-order multiplet analysis in ¹H NMR spectroscopy. J Org Chem 1994; 59:4096-4103.
Karplus M. Vicinal proton coupling in nuclear magnetic resonance. J Am Chem Soc 1963; 85:2870-2871.
   Kwan EE. Coupling constants. Lecture notes for Chemistry 117: Practical NMR spectroscopy (from my.harvard) available at this link.

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