The magnitudes of coupling constants
The scalar coupling constant of two nuclei separated by N bonds is denoted NJ, with subscripts for the types of nuclei involved. Thus, 1JCH is the coupling constant for a proton joined directly to a 13C atom, and 2JCH is the coupling constant when the same two nuclei are separated by two bonds (as in 13C-C-H). A typical value of 1JCH is in the range 120 to 250 Hz; 2JCH is between −10 and +20 Hz. Both 3J and 4J can give detect able effects in a spectrum, but couplings over larger numbers of bonds can generally be ignored. One of the longest-range couplings that has been detected is 9JHH = 0.4 Hz between the CH3 and CH2 protons in CH3C≡CC≡CC≡CCH2OH. The sign of JXY indicates whether the energy of two spins is lower when they are parallel (J < 0) or when they are antiparallel (J > 0). It is found that 1JCH is often positive, 2JHH is often negative, 3JHH is often positive, and so on. An additional point is that J varies with the angle between the bonds (Fig. 15.19). Thus, a 3JHH coupling constant is often found to depend on the dihedral angle φ (5) according to the Karplus equation:
J =A+ B cos φ + C cos 2φ
with A, B, and C empirical constants with values close to +7 Hz, −1 Hz, and +5 Hz, respectively, for an HCCH fragment. It follows that the measurement of 3JHH in a series of related compounds can be used to determine their conformations. The coupling constant 1JCH also depends on the hybridization of the C atom, as the following values indicate:
Fig. 15.19 The variation of the spin–spin coupling constant with angle predicted by the Karplus equation for an HCCH group and an HNCH group.
