Dependence of Vicinal H–H Coupling Constants in Substituted Ethanes on the Potential Function Characteristics to Internal Rotation. Application to A2B2 PMR Spectrum of Nonsymmetrical 1,2-Disubstituted Ethanes

Abstract

Based on rotational averaging, a theory governing the change of the vicinal coupling parameters $L$ and $N$ in the A₂B₂ PMR spectra of nonsymmetrical 1,2‐disubstituted ethanes, as evidenced in the studies of substituent effect and solvent effect, has been developed in terms of the potential function characteristics to internal rotation about the C–C bond. By taking the average over the entire period of dihedral angle with respect to an appropriate potential function for internal rotation of the compound, a refined Karplus equation for the vicinal H–H coupling constant as a function of dihedral angle, $\mathrm{J\hspace{0.17em}=\hspace{0.17em}A}{\cos }^2\mathrm{\phi \hspace{0.17em}+\hspace{0.17em}B}\cos \mathrm{\phi \hspace{0.17em}+\hspace{0.17em}C}$ , could yield the expression for $\mathrm{L\hspace{0.17em}/\hspace{0.17em}A}$ and/or $\mathrm{N\hspace{0.17em}/\hspace{0.17em}A}$ in terms of hyperbolic Bessel functions which describes an explicit functional dependence of $L$ and/or $N$ on both the ethane barrier and the maximum dipole interaction potential between the two bonds C–X and C–Y. These expressions enable one to determine the physical parameters related to internal rotation upon measurement of $L$ and/or $N$ from NMR spectrum. The determined energy difference between rotamers for several 1,2‐disubstituted ethanes were found in good agreement with the literature values. Solvent effect on the A₂B₂ PMR spectrum was discussed on the light of the theory. The NMR experimental relation $\mathrm{N\mp }\frac{1}{3}\mathrm{|\hspace{0.17em}L\hspace{0.17em}|\hspace{0.17em}=\hspace{0.17em}A}$ was derived from the above expressions. This latter relation enables one to tell whether the trans or the gauche isomer is more stable for the given compound from measurement on $N$ and $L$ with respect to the neat sample or in the medium of various solvent, and it also enables one to evaluate the value of $A$ for each given compound.