'Objective' determination of coupling constants and conformational equilibria by solvent variation: a re-evaluation

An 'objective' method for determining conformational equilibria in substituted ethanes, proposed by Abraham et al., has been evaluated by computational methods. Abraham's method involves measuring vicinal couplings, such as (3)J(H,H) and (3)J(H,F), between methine and methylene protons with methine, methylene protons and fluorine in a range of solvents, on the assumption that the underlying coupling constants of the individual conformers are constant, but the fractions of each conformer in each solvent are different and unknown. Abraham posited that this would produce an 'over-determined' data set with more equations than unknowns would. Abraham's procedure is re-evaluated, and it is demonstrated that the type of system being considered here, where there are more equations than unknowns, is not necessarily over-determined. A computer equation solver and Monte Carlo-type procedures were employed to demonstrate that multiple numerical solutions exist for a representative 'over-determined' data set provided by Abraham. A statistical method was also developed to determine precisely which parameter sets constitute plausible solutions.