The figure shows the result of a 0° decoupling pulse (a) and of a 90° decoupling pulse (b) obtained on an AM-400 spectrometer with a 5 mm dual probe-head. Note the disappearance of the signals in b. The spectrum c was obtained with a 180° pulse.

7. Comments

We consider a ¹³C, ¹H spin pair. The equilibrium magnetization is converted by the 90° ¹³C pulse into a transverse ¹³C magnetization as described by Equation (1).

I_Cz + I_Hz ⟶ −I_Cy + I_Hz(1)

During the period τ = d2 = 1/2J spin–spin coupling between proton and ¹³C evolves, as in Equation (2).

−I_Cy + I_Hz ⟶ 2I_CxI_Hz sinπJτ − I_Cy cosπJτ + I_Hz(2)

Since τ was set to 1/2J, (2) simplifies to (3).

2I_CxI_Hz sinπJτ − I_Cy cosπJτ + I_Hz = 2I_CxI_Hz + I_Hz(3)

A 90_x° ¹H pulse converts 2I_CxI_Hz into double quantum magnetization as in Equation (4), from which no observable ¹³C signal can be generated. Thus, if the decoupling pulse is exactly 90°, the doublet disappears.

2I_CxI_Hz + I_Hz ⟶ −2I_CxI_Hy − I_Hy(4)

Note that with this method, in contrast to Experiments 2.1 and 2.2, the 90° pulse yields a minimum signal, whereas the 180° pulse inverts the initial phases of the doublet.

8. Own Observations