td2: 1 k data points in F₂
td1: 128 data points in F₁
sw2: 8 ppm
sw1: 8 ppm
o1: middle of ¹H NMR spectrum
p1, p2: 90° ¹H transmitter pulse
d1: 2 s
initial value for t₁ evolution: 3 μs
increment for t₁ evolution: 1/sw1
ds: 2
ns: 4

5. Processing

Apply zero-filling in F₁ to 512 real data points to obtain a symmetrical matrix of 512 × 512 real points. Use unshifted sinusoidal windows in both dimensions. Apply complex Fourier transformation corresponding to the N-type signal selection using the quadrature-off mode in F₁. Phase correction is not necessary, since the data are processed in magnitude mode. Finally the data may be symmetrized.

6. Result

The figure shows the H,H-COSY spectrum obtained on an ARX-200 spectrometer with symmetrization. Note that a cross-peak connecting the hydrogen nucleus at C-2 with those at C-4 appears, although these hydrogens are not in a vicinal relationship. The cross-peak results from an allylic coupling.

7. Comments

For the product operator formalism we consider a spin system of two protons. The key to any COSY protocol is the transformation of antiphase magnetization of proton 1 with respect to proton 2 into antiphase magnetization of proton 2 with respect to proton 1. The first r.f. pulse transforms z-magnetization into transverse magnetization. Then the chemical shift develops during t₁, which is written here only for proton 1, giving Equation (1). In addition, spin-spin coupling develops; thus a term 2I_1yI_2z, with antiphase magnetization of proton 1 with respect to proton 2 appears, as in Equation (2). Other terms are neglected.