An empirical extension of the karplus equation

The Karplus equation is expanded to contain 11 mutually independent structural terms and 22 adjustable parameters. These terms are selected on an empirical basis and combined linearly (Eqn 4). The new equation reproduces 198 NMR vicinal 1H‐1H coupling constants determined in less polar solvents with a standard deviation of 0.33 Hz. The equation can be applied to norbornene derivatives, for which some of the previous modifications did not work well. Among new factors introduced in this modification to the Karplus‐type equation are Mullay's group electro‐negativity used in the evaluation of the α‐ and β‐substituent effects, the CC length and the CCH valence angles of the coupled HCCH system, and the through‐space interactions between a coupled proton and a non‐bonded atom within the molecule. The four most important terms are the two cosine functions, originally used by Karplus, one form of the α‐substituent effect and the CCH valence angles. These four terms alone give an accuracy of 0.42 Hz.