Spin-Spin Coupling References

The Karplus Equation for 3JHH (H-Csp3-sp3C-H) is:
   3J = 7.8 - 1.0 cos(phi) + 5.6 cos(2*phi)
This basic form of the Karplus equation does not correct for the electronegativity of the substituents.

The Altona equations for vicinal 3JHH (H-Csp3-sp3C-H) are:
   3J = p1 cos2(f) + p2 cos(f) + p3 + S li (p4 + p5 cos2(ei f + p6 |li|))
where the sum is over the four substituents. The order of substitution around each carbon makes a difference. The direction coefficient, ei, is +1 for S1 and S3 and -1 for S2 and S4. The electronegativity of the substituents includes the "beta effect" and is given by:
   li = (Ca -CH) + p7 S ( Cb -CH)
where Ca is the Huggin's electronegativity of the directly attached a atom, CH is the electronegativity of hydrogen, and the sum is over the b atoms that are attached to the a atom. The substituent electronegativity for each attached group is listed under the substituent name. The coefficients have also been modified to use empirical chemical group substituent constants.

Coefficients for the HLA Equation:
HLA electronegativityHLA chemical groups
p113.714.64
p2-0.73-0.78
p30.00.58
p40.560.34
p5-2.47-2.31
p616.916.9
p7-0.14

Please see: C. A. G. Haasnoot, F. A. A. M. DeLeeuw and C. Altona, "The Relationship Between Proton-Proton Coupling Constants and Substituent Electronegativities-I," Tetrahedron, 1981, 36(19), 2783-2792.
The group substituent constants are described in: C. Altona, "Vicinal Coupling Constants and Conformation of Biomolecules,"Encyclopedia of NMR," D. M. Grant, R. Morris, Eds, Wiley, New York, NY, 1996, pp 4909-4923.

The Diez, Altona, Donders equation is:
   3J = c00 + c01 S li + c10 cos(f) + (c20 + c21 S li) cos(2f) + (s211 S ei l2i) sin(2f)
The coefficients for the Diez, Altona, Donders equations with chemical groups are:
   c00 = 7.82 , c01 =-0.79 , c10 = -0.78 , c20 = 6.54 , c21 = -0.64 , s211 = 0.70
Please see: L. A. Donders, F. A. A. M. de Leeuw, C. Altona, "Relationship Between Proton-Proton NMR Coupling Constants and Substituent Electronegativities IV. An Extended Karplus Equation Accounting for Interactions Between Substituents and its Application to Coupling Constant Data Calculated by the Extended Huckel Method," Magn. Reson. Chem., 1989, 27, 556-563.


The 3J vinyl and 4J allylic coupling constants are based on the modified Karplus Equation by Garbisch:
3J = 6.6 cos2(phi) + 2.6 sin2(phi) (0o<= phi <= 90o)
3J = 11.6 cos2(phi) + 2.6 sin2(phi) (90o<= phi <= 180o)
4J = 1.3 cos2(phi) - 2.6 sin2(phi) (0o<= phi <= 90o)
4J = - 2.6 sin2(phi) (90o<= phi <= 180o)
Please see: E. W. Garbisch, Jr., "Conformations. VI. Vinyl-Allylic Proton Spin Couplings," J. Amer. Chem. Soc, 1964, 86, 5561-5564.

For the other coupling types, typical values can be selected from Table 3.26i, 3.27, and 3.29 in D. H. Williams, I. Fleming, "Spectroscopic Methods in Organic Chemistry,4th ed.," McGraw-Hill, London, 1987. pp 143-146. For predicting first-order multiplet patterns, see JMM: First-order multiplet patterns. For more exact calculations, including second-order effects please see JD: Spin-Spin Splitting Simulation


This applet was inspired by the program MestRe-J: A. Navarro-Vazquez, J. C. Cobas, and F. J. Sardina, "A Graphical Tool for the Prediction of Vicinal Proton-Proton 3JHH Coupling Constants," J. Chem. Inf. Comput. Sci., 2004, 44, 1680-1685.

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Colby College Chemistry