The Perlin Effect: bond lengths, bond strengths, and the origins of stereoelectronic effects upon one-bond C–H coupling constants

Abstract

The magnitude of a one-bond C–H coupling constant depends upon the chemical environment of the hydrogen atom and, especially, upon its stereochemical relationship to vicinal lone electron pairs. However, a lone electron pair is not essential for the observation of a stereoelectronic effect, since even cyclohexane exhibits different axial and equatorial C–H coupling constants. We propose the name "Perlin Effect" to describe such observations. An analysis of the extensive experimental data regarding the Perlin Effect reveals that, in cyclohexane and in six-membered rings having one or more heteroatoms of the first row attached to the carbon of interest, 1JC–H is always larger for an equatorial hydrogen than for an axial hydrogen. The magnitude of the Perlin Effect is reduced when the carbon carrying the hydrogen of interest is attached to first row and second row atoms or heteroatoms, and it reverses when the carbon atom carries two heteroatoms from below the first row.The existence of the Perlin Effect in nuclear magnetic resonance spectra is reminiscent of an infrared effect known as the Bohlmann bands, whose origin has previously been explained by quantitative perturbational molecular orbital (PMO) theory in terms of the effects of lone electron pairs upon the lengths and strengths and, therefore, the chemical reactivities of vicinal C—H bonds. Since the magnitude of a one-bond C–H coupling constant is expected to vary inversely with bond length, the origins of the Perlin Effect and of the Bohlmann bands would seem to be the same, i.e., the longer (weaker) C—H bond has the smaller one-bond coupling constant. This expectation has now been confirmed: for 25 molecules, representing a total of 35 different kinds of C—H bonds, the bond lengths, stretching force constants, and charge distributions have been determined from fully optimized 6-31G* molecular orbital calculations. In nine of ten cases for which experimental data exist for pairs of diastereomeric or diastereotopic hydrogens, the shorter C—H bond of the pair has the larger coupling constant; in the tenth case, the experimental difference is only 1–2 Hz. Moreover, a global analysis of the data in terms of the equation J = A + BqCqH + C/r, where J is an experimental coupling constant, q is a total atomic charge, and r is a C—H bond length, correlates 23 different types of C—H bonds linearly with a correlation coefficient of 0.915. The C parameter is the leading term of the correlation. Among the systems studied theoretically are eight molecules of the type CH3CHXY (Y = OH, SH; X = F, Cl, OH, SH), which are representative of systems containing both endocyclic and exocyclic first row and second row anomeric effects. The exocyclic effect is found to be very similar for first row and second row substituents, but the endocyclic effect is larger for the first row substituent. Both findings agree with experimental data in solution. Finally, quantitative PMO analysis has been employed to analyse the origins of the different C—H bond lengths in the various molecules of the study. Keywords: anomeric effect, PMO analysis, NMR, stereochemistry, molecular orbital calculations.