J-coupling

Scalar or J-couplings (also called indirect dipole dipolecoupling) are mediated through chemical bonds connect-ing two spins. It is an indirect interaction between twonuclear spins which arises from hyperfine interactions be-tween the nuclei and local electrons.[1] J-coupling con-tains information about bond distance and angles. Mostimportantly, J-coupling provides information on the con-nectivity of molecules. In NMR spectroscopy, it is re-sponsible for the appearance of many signals in the NMRspectra of fairly simple molecules.

1 Vector model and manifestationsfor chemical structure assign-ments

The origin of J-coupling can be visualized by a vectormodel for a simple molecule such as hydrogen fluoride(HF). In HF, the two nuclei have spin 1/2. Four statesare possible, depending on the relative alignment of theH 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 fre-quency range) can affect (“flip”) only one of the two nu-clear spins.

Energy diagram showing the effects of J-coupling for themolecule hydrogen fluoride.

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.

1.1 Multiplicity

The multiplicity provides information on the number ofcenters coupled to the signal of interest, and their nu-clear spin. For simple systems, as in 1H-1H couplingin NMR spectroscopy, the multiplicity reflects the num-ber of adjacent, magnetically nonequivalent protons. Nu-clei with spins >1/2, which are called quadrupolar, cangive rise to greater splitting, although in many cases cou-

pling to quadrupolar nuclei is not observed. Many ele-ments consist of nuclei with nuclear spin and without. Inthese cases the observed spectrum is the sum of spec-tra for each isotopomer. One of the great conveniencesof NMR spectroscopy for organic molecules is that themany lighter elements are nearly monoisotopic: 1H, 19F,and 31P each have spin 1/2. 12C and 16O have no nuclearspin.

1.2 Magnitude of J-coupling

For 1H-1H coupling, the magnitude of J provides infor-mation on the proximity of the coupling partners. Gener-ally speaking 2-bond coupling (i.e. 1H-C-1H) is strongerthan three-bond coupling (1H-C-C-1H). The magnitudeof the coupling also provides information on the dihedralangles relating the coupling partners, as described by theKarplus relationship.For heteronuclear coupling, the magnitude of J is relatedto the nuclear magnetic moments of the coupling part-ners. 19F, with a high nuclear magnetic moment, givesrise to large coupling to protons. 103Rh, with a verysmall nuclear magnetic moment, gives only small cou-plings to 1H. To correct for the effect of the nuclear mag-netic moment (or equivalently the gyromagnetic ratio γ),“reduced coupling constant” K is often discussed, whereK = 4π2J/(hγₓγ ). The value of J also has a sign, andcouplings constants of comparable magnitude often haveopposite signs.[2]

2 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 andelectron spin-external field interactionsD2 = magnetic interactions between nuclear spin andelectron spinD3 = direct interaction of nuclei with each otherfor a singlet molecular state and frequent molecular col-lisions, D1 and D3 are almost zero. The full form of J-coupling interaction between spins I and I on the samemolecule is:H = 2π Ij · Jjk · Ik

where J is the j-coupling tensor, a 3x3 real matrix. It

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2 6 REFERENCES

depends on molecular orientation. In isotropic liquid itreduces to a number, so called scalar coupling. In 1DNMR, scalar coupling leads to oscillations in FID as wellas splitting of lines in the spectrum.

3 Decoupling

By selective radio frequency irradiation, NMR spectracan be fully or partially decoupled, eliminating or selec-tively reducing the coupling effect. Carbon-13 NMR areoften run decoupled.

4 History

In October 1951, E. L. Hahn and D. E. Maxwell reporteda spin echo experiment which indicates the existence of aninteraction between two protons in dichloroacetaldehyde.In the echo experiment, two short, intense pulses ofradiofrequency magnetic field are applied to spin ensem-ble at the nuclear resonance condition and are separatedby time interval of τ. The echo appears with a givenmaximum amplitude at time 2τ. For each setting of τ,the maximum of the echo signal is measured and plot-ted as a function of τ. If the spin ensemble consists ofmagnetic moment, a monotonic decay in the echo enve-lope is obtained. In the Hahn-Maxwell experiment, thedecay was modulated by two frequencies: one frequencycorresponded with the difference in chemical shift be-tween the two non equivalent spins and a second fre-quency, J, that was smaller and independent of magneticfield strength. (J/2π = 0.7 cycle per second)Such interaction came as a great surprise. The direct in-teraction between two magnetic dipoles depends on therelative position of two nuclei in such a way that when av-eraged on all various orientation of the molecule it equalsto zero.In November 1951, N. F. Ramsey and E. M. Purcell pro-posed a mechanism that explained the observation andgave rise to an interaction of the form I1.I2. The mech-anism is the magnetic interaction between each nucleusand the electron spin of its own atom together with theexchange coupling of the electron spins with each other.In the 1990s, direct evidence was found for the pres-ence of J-couplings betweenmagnetically active nuclei onboth sides of the hydrogen bond.[3][4] Initially, it was sur-prising to observe such couplings across hydrogen bondssince J-couplings are usually associated with the pres-ence of purely covalent bonds. However, it is now wellestablished that the H-bond J-couplings follow the sameelectron-mediated polarization mechanism as their cova-lent counterparts.[5]

The spin-spin coupling between nonbonded atoms inclose proximity has sometimes been observed be-

tween fluorine, nitrogen, carbon, silicon and phosphorusatoms.[6][7][8]

5 See also• Earth’s field NMR

• Exclusive correlation spectroscopy (ECOSY)

• Magnetic dipole-dipole interaction (dipolar cou-pling)

• Nuclear Magnetic Resonance

• Nuclear magnetic resonance spectroscopy of carbo-hydrates

• Nuclear magnetic resonance spectroscopy of nucleicacids

• Nuclear magnetic resonance spectroscopy of pro-teins

• Proton NMR

• Relaxation (NMR)

• Residual dipolar coupling

6 References[1] E. L. Hahn and D. E. Maxwell (1952). “Spin

Echo Measurements of Nuclear Spin Cou-pling in Molecules”. Phys. Rev. 88 (5):1070–1084. Bibcode:1952PhRv...88.1070H.doi:10.1103/PhysRev.88.1070.

[2] Pregosin, P. S.; Rueegger, H. “Nuclear magnetic reso-nance spectroscopy” McCleverty, Jon A.; Meyer, ThomasJ., Eds., Comprehensive Coordination Chemistry II(2004), 2, 1-35. doi:10.1016/B0-08-043748-6/01061-6

[3] P. Blake, B. Lee, M. Summers, M. Adams, J.-B. Park, Z. Zhou and A. Bax (1992). “Quantita-tive measurement of small through-hydrogen-bond and'through-space' 1H-113Cd and 1H-199Hg J couplingsin metal-substituted rubredoxin from Pyrococcus furio-sus”. Journal of Biomolecular NMR 2 (5): 527–533.doi:10.1007/BF02192814.

[4] P. R. Blake, J. B. Park, M. W. W. Adams and M. F.Summers (1992). “Novel observation of NH--S(Cys)hydrogen-bond-mediated scalar coupling in cadmium-113 substituted rubredoxin from Pyrococcus furiosus”.J. Am. Chem. Soc. 114 (12): 4931–4933.doi:10.1021/ja00038a084.

[5] Andrew J. Dingley, Florence Cordier and Stephan Grze-siek (2001). “An introduction to hydrogen bond scalarcouplings”. Concepts in Magnetic Resonance 13 (2): 103–127. doi:10.1002/1099-0534(2001)13:2<103::AID-CMR1001>3.0.CO;2-M.

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[6] Mallory, F. B. et al. (2000). “Nuclear Spin−SpinCoupling via Nonbonded Interactions. 8. 1 The Dis-tance Dependence of Through-Space Fluorine−FluorineCoupling”. J. Am. Chem. Soc 122: 4108–4116.doi:10.1021/ja993032z.

[7] Zong, J.; Mague, J. T.; Kraml, C. M.; Pascal Jr, R. A.(2013). “A Congested in, in-Diphosphine”. Organic Let-ters 15 (9): 2179–2181. doi:10.1021/ol400728m.

[8] Zong, J.; Mague, J. T.; Welch, E. C.; Eckert, I. M.; PascalJr, R. A. (2013). “Sterically congestedmacrobicycles withheteroatomic bridgehead functionality”. Tetrahedron 69(48): 10316–10321. doi:10.1016/j.tet.2013.10.018.

7 Further reading• H. S. Gutowsky, D. W. McCall, C. P. Slichter(1951). “Coupling among Nuclear MagneticDipoles in Molecules”. Physical Review 84(3): 589–90. Bibcode:1951PhRv...84..589G.doi:10.1103/PhysRev.84.589.2.

• E. L. Hahn and D. E. Maxwell (1951). “ChemicalShift and Field Independent Frequency Modulationof the Spin Echo Envelope”. Physical Review 84(6): 1246–1247. Bibcode:1951PhRv...84.1246H.doi:10.1103/PhysRev.84.1246.

• N. F. Ramsey and E. M. Purcell (1952).“Interactions between Nuclear Spins inMolecules”. Physical Review 85 (1):143–144. Bibcode:1952PhRv...85..143R.doi:10.1103/PhysRev.85.143.

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