In nuclear chemistry and nuclear physics, J-couplings (also called spin-spin coupling or indirect dipole–dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins that arises from hyperfine interactions between the nuclei and local electrons. In NMR spectroscopy, J-coupling contains information about relative bond distances and angles. Most importantly, J-coupling provides information on the connectivity of chemical bonds. It is responsible for the often complex splitting of resonance lines in the NMR spectra of fairly simple molecules. J-coupling is a frequency difference that is not affected by the strength of the magnetic field, so is always stated in Hz.
Vector model and manifestations for chemical structure assignments The origin of J-coupling can be visualized by a vector model for a simple molecule such as hydrogen fluoride (HF). In HF, the two nuclei have spin 1/2. Four states are possible, depending on the relative alignment of the H and F nuclear spins with the external magnetic field. The selection rules of NMR spectroscopy dictate that ΔI = 1, which means that a given photon (in the radio frequency range) can affect ("flip") only one of the two nuclear spins. J-coupling provides three parameters: the multiplicity (the "number of lines"), the magnitude of the coupling (strong, medium, weak), and the sign of the coupling.
Multiplicity The multiplicity provides information on the number of centers coupled to the signal of interest, and their nuclear spin. For simple systems, as in 1H–1H coupling in NMR spectroscopy, the multiplicity is one more than the number of adjacent protons which are magnetically nonequivalent to the protons of interest. For ethanol, each methyl proton is coupled to the two methylene protons, so the methyl signal is a triplet, while each methylene proton is coupled to the three methyl protons, so the methylene signal is a quartet. Nuclei with spins greater than 1/2, which are called quadrupolar, can give rise to greater splitting, although in many cases coupling to quadrupolar nuclei is not observed. Many elements consist of nuclei with nuclear spin and without. In these cases, the observed spectrum is the sum of spectra for each isotopomer. One of the great conveniences of NMR spectroscopy for organic molecules is that several important lighter spin 1/2 nuclei are either monoisotopic, e.g. 31P and 19F, or have very high natural abundance, e.g. 1H. An additional convenience is that 12C and 16O have no nuclear spin so these nuclei, which are common in organic molecules, do not cause splitting patterns in NMR.
Magnitude of J-coupling For 1H–1H coupling, the magnitude of J decreases rapidly with the number of bonds between the coupled nuclei, especially in saturated molecules. Generally speaking two-bond coupling (i.e. 1H–C–1H) is stronger than three-bond coupling (1H–C–C–1H). The magnitude of the coupling also provides information on the dihedral angles relating the coupling partners, as described by the Karplus equation for three-bond coupling constants. For heteronuclear coupling, the magnitude of J is related to the nuclear magnetic moments of the coupling partners. 19F, with a high nuclear magnetic moment, gives rise to large coupling to protons. 103Rh, with a very small nuclear magnetic moment, gives only small couplings to 1H. To correct for the effect of the nuclear magnetic moment (or equivalently the gyromagnetic ratio γ), the "reduced coupling constant" K is often discussed, where
K = 4π2J/hγxγy. For coupling of a 13C nucleus and a directly bonded proton, the dominant term in the coupling constant JC–H is the Fermi contact interaction, which is a measure of the s-character of the bond at the two nuclei. Where the external magnetic field is very low, e.g. as Earth's field NMR, J-coupling signals of the order of hertz usually dominate chemical shifts which are of the order of millihertz and are not normally resolvable.
Sign of J-coupling The value of each coupling constant also has a sign, and coupling constants of comparable magnitude often have opposite signs. If the coupling constant between two given spins is negative, the energy is lower when these two spins are parallel, and conversely if their coupling constant is positive. For a molecule with a single J-coupling constant, the appearance of the NMR spectrum is unchanged if the sign of the coupling constant is reversed, although spectral lines at given positions may represent different transitions. The simple NMR spectrum therefore does not indicate the sign of the coupling constant, which there is no simple way of predicting. However for some molecules with two distinct J-coupling constants, the relative signs of the two constants can be experimentally determined by a double resonance experiment. For example in the diethylthallium ion (C2H5)2Tl+, this method showed that the methyl-thallium (CH3-Tl) and methylene-thallium (CH2-Tl) coupling constants have opposite signs. The first experimental method to determine the absolute sign of a J-coupling constant was proposed in 1962 by Buckingham and Lovering, who suggested the use of a strong electric field to align the molecules of a polar liquid. The field produces a direct dipolar coupling of the two spins, which adds to the observed J-coupling if their signs are parallel and subtracts from the observed J-coupling if their signs are opposed. This method was first applied to 4-nitrotoluene, for which the J-coupling constant between two adjacent (or ortho) ring protons was shown to be positive because the splitting of the two peaks for each proton decreases with the applied electric field. Another way to align molecules for NMR spectroscopy is to dissolve them in a nematic liquid crystal solvent. This method has also been used to determine the absolute sign of J-coupling constants.
J-coupling Hamiltonian The Hamiltonian of a molecular system may be taken as:
H = D1 + D2 + D3, D1 = electron orbital–orbital, spin–orbital, spin–spin and electron-spin–external-field interactions D2 = magnetic interactions between nuclear spin and electron spin D3 = direct interaction of nuclei with each other For a singlet molecular state and frequent molecular collisions, D1 and D3 are almost zero. The full form of the J-coupling interaction between spins 'Ij and Ik on the same molecule is:
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