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 electronegativity||HLA chemical groups|
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.
|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)|
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
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Colby College Chemistry