INTERNAL H-C-C ANGLE DEPENDENCE OF VICINAL H-1-H-1 COUPLING-CONSTANTS

Based on simple molecular orbital theory, an explicit expression is derived for vicinal H-H coupling constants 3J(HH')(theta-1,theta-2,phi) in terms of the two internal H-C-C angles theta-1 and theta-2 and the torsion angle phi: 3J(HH')(theta-1,theta-2,phi) = c(a) a(theta-1,theta-2) cos2 phi + SIGMA(i) c(bi) b(i)(theta-1,theta-2) cos-phi + C. Important effects of both internal and torsion angle changes arise from the first term, where a(theta-1,theta-2) = (1 + cos-theta-1)(1 + cos-theta-2), which decreases monotonically with increasing theta-1 and theta-2. The cos-phi term has a more complicated dependence on internal angles. Since this term changes sign for phi = 90-degrees, the theta-dependencies can be exceedingly different for phi < 90-degrees than for phi > 90-degrees. Vicinal H-H coupling constants in ethanic moieties provide examples in which there is relatively little dependence on internal angles for phi < 90-degrees. The coefficients in the expression for 3J(HH')(theta-1,theta-2,phi) depend on the C-C internuclear distances and effective nuclear charges. These are determined empirically from the relatively few examples of vicinal H-H coupling which have been measured in rigid, unsubstituted molecules and from structural data obtained from either ab initio molecular orbital or molecular mechanics calculations. The resulting expressions provide excellent correlations of most features of vicinal H-H coupling in ethanic (CHCH), ethylenic (CH = CH), allylic (C=CHCH), and diene (C = CHCH = C) moieties and provide criteria for assessing the importance of internal angle changes.