# Chemical Sciences: A Manual for CSIR-UGC National Eligibility Test for Lectureship and JRF/J-coupling

J-coupling (also called indirect dipole dipole coupling) is the coupling between two nuclear spins due to the influence of bonding electrons on the magnetic field running between the two nuclei. J-coupling contains information about dihedral angles, which can be estimated using the Karplus equation. It is an important observable effect in 1D nuclear magnetic resonance spectroscopy.

## Discovery

In October 1951, E. L. Hahn and D. E. Maxwell reported a spin echo experiment which indicates the existence of an interaction between two protons in dichloroacetaldehyde. In the echo experiment, two short, intense pulses of radiofrequency magnetic field are applied to spin ensemble at the nuclear resonance condition and are separated by time interval of τ. The echo appears with a given maximum amplitude at time 2τ. For each setting of τ, the maximum of the echo signal is measured and plotted as a function of τ. If the spin ensemble consists of magnetic moment, a monotonic decay in the echo envelope is obtained. In the Hahn-Maxwell experiment, the decay was modulated by two frequencies: one frequency corresponded with the difference in chemical shift between the two non equivalent spins and a second frequency, J, that was smaller and independent of magnetic field strength. (J/2π = 0.7 cycle per second)
Such interaction came as a great surprise. The direct interaction between two magnetic dipole is dependent on the relative position of two nuclei in such a way that when averaged on all various orientation of the molecule it equals to zero.
In November 1951, N. F. Ramsey and E. M. Purcell proposed a mechanism that explained the observation and gave rise to an interaction of the form I$_1$.I$_2$. The mechanism is the magnetic interaction between each nucleus and the electron spin of its own atom together with the exchange coupling of the electron spins with each other.
In 1990s, direct evidence has been found for the presence of J-couplings between magnetically active nuclei on both sides of the hydrogen bond. Initially, it was surprising to observe such couplings across hydrogen bonds since J-couplings are usually associated with the presence of purely covalent bonds. However, it is now well established that the H-bond J-couplings follow the same electron-mediated polarization mechanism as their covalent counterparts.

## J-coupling Hamiltonian

The Hamiltonian of a molecular system may be taken as:
H = D$_1$ +D$_2$ +D$_3$.
D$_1$ = electron orbital-orbital, spin-orbital, spin-spin and electron spin-external field interactions
D$_2$ = magnetic interactions between nuclear spin and electron spin
D$_3$ = direct interaction of nuclei with each other
for a singlet molecular state and frequent molecular collisions, D$_1$ and D$_3$ are almost zero. The full form of J-coupling interaction between spins I$_j$ and I$_k$ on the same molecule is:
H = 2π I$_j$. J$_{jk}$. I$_k$
where J$_{jk}$ is the j-coupling tensor, a 3x3 real matrix. It depends on molecular orientation. In isotropic liquid it reduces to a number, so called scalar coupling. In 1D NMR, scalar coupling leads to oscillations in FID as well as splitting of lines in the spectrum.

## Measurement of J-coupling

The Quantitative J correlation developed by Ad Bax et al. in 1994 is commonly the method of choice for accurate measurements of J couplings.

## References

* ↑ P. Blake, B. Lee, M. Summers, M. Adams, J.-B. Park, Z. Zhou and A. Bax (1992). "Quantitative measurement of small through-hydrogen-bond and 'through-space' $^1$H-$^{113}$Cd and $^1$H-$^{199}$Hg J couplings in metal-substituted rubredoxin from Pyrococcus furiosus". Journal of Biomolecular NMR. 2 (5): 527–533. doi:10.1007/BF02192814.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ 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.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* ↑ Andrew J. Dingley, Florence Cordier and Stephan Grzesiek (2001). "An introduction to hydrogen bond scalar couplings". Concepts in Magnetic Resonance. 13 (2): 103–127. doi:10.1002/1099-0534(2001)13:2<103::AID-CMR1001>3.0.CO;2-M.
* ↑ E. de Alba and N. Tjandra (2006). "Interference between Cross-correlated Relaxation and the Measurement of Scalar and Dipolar Couplings by Quantitative J". Journal of Biomolecular NMR. 35 (1): 1–16. doi:10.1007/s10858-006-0028-4.
* ↑ G. W. Vuister and A. Bax (1993). "Quantitative J correlation: a new approach for measuring homonuclear three-bond J(HNHα) coupling constants in $^{15}$N-enriched proteins". J. Am. Chem. Soc. 115 (17): 7772–7777. doi:10.1021/ja00070a024.

## Further reading

* H. S. Gutowsky, D. W. McCall, C. P. Slichter (1951). "Coupling among Nuclear Magnetic Dipoles in Molecules". Physical Review. 84: 589–90. doi:10.1103/PhysRev.84.589.2.{{cite journal}}: CS1 maint: multiple names: authors list (link)
* E. L. Hahn and D. E. Maxwell (1951). "Chemical Shift and Field Independent Frequency Modulation of the Spin Echo Envelope". Physical Review. 84 (6): 1246. doi:10.1103/PhysRev.84.1246.
* N. F. Ramsey and E. M. Purcell (1952). "Interactions between Nuclear Spins in Molecules". Physical Review. 85 (1): 143. doi:10.1103/PhysRev.85.143.