^{3}J = 6.6 cos^{2}(phi) + 2.6 sin^{2}(phi) | (0^{o}<= phi <= 90^{o}) |
^{3}J = 11.6 cos^{2}(phi) + 2.6 sin^{2}(phi) | (90^{o}<= phi <= 180^{o}) |
^{4}J = 1.3 cos^{2}(phi) - 2.6 sin^{2}(phi) | (0^{o}<= phi <= 90^{o}) |
^{4}J = - 2.6 sin^{2}(phi) | (90^{o}<= phi <= 180^{o}) |
The Karplus Equation for ^{3}J_{HH} (H-Csp^{3}-sp^{3}C-H) is:
^{3}J = 7.8 - 1.0 cos(phi) + 5.6 cos(2*phi)
The Altona equations for ^{3}J_{HH} (H-Csp^{3}-sp^{3}C-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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