Coupling Constants

Units of Measurement

  • Chemical shifts are measured in ppm (parts per million).

  • Coupling constants (J values) are measured in Hz.

  • To convert ppm → Hz, you must know the spectrometer frequency.

🧪 Chemical Shift vs. Frequency

  • A hydrogen will always have the same chemical shift in ppm regardless of instrument.

  • However, its absolute frequency in Hz depends on the spectrometer.

  • NMR spectrometers (e.g. 400 MHz, 500 MHz) refer to the frequency of hydrogen reference compounds.

🔹 Conversion Examples:

  • 1 ppm on:

    • 400 MHz instrument = 400 Hz

    • 500 MHz instrument = 500 Hz

🔍 Coupling Constant Calculation – Example

✴ Major Couplings

  • Peak 1: 8.3486 ppm

  • Peak 2: 8.3309 ppm

  • Δppm = 0.0177 ppm

  • On a 500 MHz instrument:

    • 0.0177 ppm × 500 = 8.85 Hz

    • Matches ortho-coupling (7–9 Hz)

📊 Substitution and J:

Substitution

J (Hz)

Ortho (1,2-)

7–9 Hz

Meta (1,3-)

1–3 Hz

Para (1,4-)

≤1 Hz

✴ Minor Couplings

  • Peak spacings:

    • 8.3349 – 8.3309 = 0.0040 ppm

    • 8.3309 – 8.3272 = 0.0037 ppm

  • Average = 0.00385 ppm

  • 0.00385 ppm × 500 = 1.93 Hz

  • Matches meta-coupling (1–3 Hz)

🔔 Para-couplings often too small to observe, but may still be present

🔄 Cis and Trans Coupling

  • Cis-isomer has smaller J value than trans

  • Cis hydrogens: slightly upfield (to the right)

  • Trans hydrogens: slightly downfield (to the left)

📊 Typical Ranges:

Isomer

J (Hz)

Trans

11–18 Hz

Cis

6–14 Hz

🧪 Example: Determining cis-/trans-alkene

  1. Identify alkene signals – often shifted left due to electronegative groups.

  2. Use integration to assign peaks:

    • Example:

      • d/ppm: 7.80 & 7.42

      • Integration: 1H each

  3. Peaks already marked in Hz → read J directly

  4. Compare J to standard values to determine cis or trans

🧩 Non-First Order Spectra

  • First-order spectra:

    • Follow the (n+1) rule

    • Display Pascal’s triangle intensities

  • Non-first order spectra:

    • Appear distorted or “roofed”

    • Do not follow simple multiplicity rules

🔹 When does this occur?

  • If:

    • Δδ (chemical shift difference) ≫ J (coupling constant) → first-order

    • Δδ ≈ J → non-first order

In non-first order spectra, (n+1) rule does not apply.

🔗 COSY Spectra in Complex Systems

  • In non-first order spectra, COSY is useful for:

    • Clarifying obscure coupling patterns

    • Visualising proton–proton connections