The A2, AB, and AX Spin Systems

FIGURE 5.29 The case in which first-order coupling (m + 1 Rule) applies (Av large). 

FIGURE 5.30 The splitting patterns of a two-proton system HaHb for various ratios of Av/J. 

FIGURE 5.31 The relationships among the chemical shifts, line positions, and coupling constant in a two-proton spectrum that exhibits second-order splitting eifects. 

FIGURE 5.32 The splitting patterns of a three-proton system — CH—CHj— for various ratios of AvIJ. 

FIGURE 5.33 The splitting patterns of a four-proton system — CH2—CH2— for various ratios of AvU. 

Mathematical analysis by theoreticians has shown that although the chemical shifts of Ha and Hb in the simple first-order AX spectrum correspond to the center point of each doublet, a more complex situation holds in the second-order cases The chemical shifts of Ha and Hb are closer to the inner peaks than to the outer peaks. The actual positions of 8a and 8b must be calculated. The difference in chemical shift must be determined from the line positions (in Hertz) of the individual peak components of the group, using the equation 

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FIGURE 7.41 Splitting patterns of a two-proton system for various values of Av/7. Transition from 

272 Nuclear Magnetic Resonance Spectroscopy Part Three Spin-Spin Coupling 

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