Spin-Spin Coupling References

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)	(0^o<= phi <= 90^o)
³J = 11.6 cos²(phi) + 2.6 sin²(phi)	(90^o<= phi <= 180^o)
⁴J = 1.3 cos²(phi) - 2.6 sin²(phi)	(0^o<= phi <= 90^o)
⁴J = - 2.6 sin²(phi)	(90^o<= phi <= 180^o)

Please see: E. W. Garbisch, Jr., "Conformations. VI. Vinyl-Allylic Proton Spin Couplings," J. Amer. Chem. Soc, 1964, 86, 5561-5564.

The Karplus Equation for ³J_HH (H-Csp³-sp³C-H) is:
³J = 7.8 - 1.0 cos(phi) + 5.6 cos(2*phi)

The Altona equations for ³J_HH (H-Csp³-sp³C-H) are developed in: 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.

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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