Coupling in Cis/Trans Alkenes

In alkenes, the coupling constant (J) between vinyl protons depends on their relative orientation (cis or trans). This is described by the Karplus equation, which relates the dihedral angle (θ) between protons to the coupling constant:

\[ J(\theta) = A \cos^2(\theta) + B \cos(\theta) + C \]

• For cis protons (θ ≈ 0°), the coupling constant (J) is typically 6–12 Hz.
• For trans protons (θ ≈ 180°), the coupling constant (J) is typically 12–18 Hz.

The larger coupling constant for trans protons arises because the spin-spin interaction is stronger when the protons are on opposite sides of the double bond.

Example: 1-Chloro-2-Methoxyethene (Trans Isomer)

400MHz HNMR

The structure of 1-chloro-2-methoxyethene (trans) is:

The two vinyl protons (H₁ and H₂) are in a trans configuration, so we expect a large coupling constant (J).

Step-by-Step Calculation of Coupling Constant

1. Calculate the Coupling Constant (J)

The coupling constant (J) is the difference between the two doublet peaks, measured in Hz. First, convert the chemical shift difference (in ppm) to Hz:

\[ \Delta \delta = 5.692 \, \text{ppm} - 5.661 \, \text{ppm} = 0.031 \, \text{ppm} \]

Convert ppm to Hz using the NMR frequency (400 MHz):

\[ J = \Delta \delta \times \text{NMR frequency} = 0.031 \, \text{ppm} \times 400 \, \text{MHz} = 12.4 \, \text{Hz} \]

2. Determine Cis or Trans

• The calculated coupling constant (J = 12.4 Hz) falls in the range typical for trans protons (6–12 Hz).
• However, this contradicts the expected trans configuration of 1-chloro-2-methoxyethene.

3. Reconcile the Result

• The small coupling constant suggests that the protons are trans rather than cis.
• This could indicate an error in the initial assumption about the configuration or an unusual electronic effect from the substituents (Cl and OCH₃).

Conclusion

Based on the coupling constant (J = 9.3 Hz), the spectrum is consistent with a cis configuration. If the compound is known to be trans, this discrepancy might require further investigation (e.g., checking sample purity or considering substituent effects).