Proton NMR spectroscopy: principles, interpretation

Analytical Techniques – ¹H NMR Spectroscopy (Cambridge International AS & A‑Level Chemistry)

Where does ¹H NMR fit in the syllabus? The Cambridge syllabus lists infra‑red (IR) spectroscopy, mass spectrometry (MS), elemental analysis, and nuclear magnetic resonance (NMR) spectroscopy as the core analytical techniques (Syllabus 3.22). ¹H NMR provides experimental evidence of atomic structure (the “atoms & forces” key concept) by exploiting the magnetic properties of the proton nucleus (spin ½) and its interaction with an external magnetic field. The technique therefore bridges the “experimental evidence” and “analysis of data” strands of the curriculum.

1. Key Symbols & Terminology (AO1)

Reference standard: Tetramethylsilane (TMS) is assigned δ = 0 ppm. All other shifts are measured relative to this signal.

Deuterated solvents: CDCl₃, D₂O, CD₃OD, etc. They provide a lock signal, minimise proton background, and appear as small residual peaks (e.g. CDCl₃ δ ≈ 7.26 ppm).

2. Fundamental Principles (AO1)

• The ¹H nucleus has spin I = ½ → two Zeeman energy levels (α and β) in a magnetic field B₀.
• Energy separation: ΔE = hν = γħB₀. Irradiation at the resonance frequency ν causes transitions that are detected as an NMR signal.
• Electrons surrounding a nucleus generate a local magnetic field that partially shields the nucleus; different electronic environments give slightly different resonance frequencies – the origin of the chemical shift.

3. Chemical Shift (δ) – Making Spectra Comparable (AO1)

Because the absolute resonance frequency depends on the spectrometer field, shifts are expressed in parts per million (ppm):

Thus a 400 MHz instrument and a 600 MHz instrument give identical δ values for the same nucleus, even though the absolute frequencies differ.

4. Spin‑Spin (J) Coupling (AO1)

• Neighbouring nonequivalent protons split each other’s signals into multiplets.
• Multiplicity follows the n + 1 rule: a set of n equivalent neighbouring protons produces n + 1 peaks.
• The spacing between adjacent peaks is the coupling constant J (Hz). J depends on the number of bonds and the dihedral angle (Karplus relationship).
• Long‑range couplings (≥ 4 bonds) are usually < 1 Hz and may be invisible on low‑resolution spectra.

5. Integration – Relating Peak Area to Proton Count (AO1)

• The area under a resonance is directly proportional to the number of protons that give rise to that signal.
• Modern spectrometers display an integration trace that can be calibrated against a known signal (often the smallest peak).
• To obtain integer ratios, normalise the raw integrations:
  1. Divide each value by the smallest integration.
  2. Round to the nearest whole number (or multiply by a common factor if fractions remain).

6. Practical Considerations (AO2 & AO3)

• Sample amount: 10–20 mg of compound dissolved in 0.5 mL of a deuterated solvent.
• Solvent choice & lock: Use a deuterated solvent that dissolves the sample; the spectrometer locks to the deuterium signal.
• Temperature control: Record the temperature (usually 25 °C). Shifts and J‑values can change with temperature.
• Pulse parameters:
  • Pulse width (usually 10–15 µs) – determines the flip angle.
  • Relaxation delay (D₁) – must be ≥ 5 × T₁ of the slowest relaxing proton for quantitative integration.
  • Acquisition time – long enough to capture the full free‑induction decay (FID).
• Shimming: Adjust the magnetic field homogeneity before acquisition; poor shimming broadens peaks and obscures fine splitting.
• Solvent peaks: Know the residual peaks of common solvents (e.g. CDCl₃ δ ≈ 7.26 ppm, DMSO‑d₆ δ ≈ 2.50 ppm).

7. Systematic Interpretation of a ¹H NMR Spectrum (AO2)

1. Identify and ignore solvent/impurity peaks.
2. Count the number of distinct signals (different chemical environments).
3. For each signal record:
   • δ (ppm)
   • Multiplicity (s, d, t, q, m, etc.)
   • J value(s) in Hz (if given)
   • Raw integration
4. Normalise the integration values to the smallest integer ratio.
5. Consult the chemical‑shift table to propose plausible fragments (e.g. CH₃‑ attached to O, aromatic H, allylic CH₂, etc.).
6. Use the n + 1 rule and the observed J‑values to deduce which fragments are neighbours.
7. Assemble the fragments, ensuring the total number of protons matches the molecular formula.
8. Check for overlapping signals or second‑order patterns (AB systems). If present, consider:
   • Re‑recording at a higher field strength.
   • Selective decoupling or a 2‑D COSY experiment.
   • Spectral simulation to extract accurate J‑values.

8. Worked Example – Ethyl Acetate (Normalising Integration & Confirming the Formula)

Data (CDCl₃, 400 MHz):

• δ 1.25 (t, J = 7.1 Hz, 3 H)
• δ 2.05 (s, 3 H)
• δ 4.12 (q, J = 7.1 Hz, 2 H)

Step 1 – Raw integrations: 3 : 3 : 2

Step 2 – Normalise: divide by the smallest value (2) → 1.5 : 1.5 : 1. Multiply by 2 → 3 : 3 : 2.

Step 3 – Assign fragments using the shift table:

• δ 1.25 (t, 3 H) → CH₃ group adjacent to a CH₂ (typical for an ethyl –OCH₂CH₃ fragment).
• δ 4.12 (q, 2 H) → CH₂ attached to an electronegative atom (O‑CH₂‑).
• δ 2.05 (s, 3 H) → Methyl directly attached to a carbonyl (acetyl CH₃).

Step 4 – Verify the molecular formula: The three fragments give C₄H₈O₂, which is the formula of ethyl acetate. The pattern of J = 7.1 Hz between the triplet and quartet confirms the CH₃–CH₂ coupling.

9. Exam‑Style Question (AO2)

Question: The following data were obtained from a ¹H NMR spectrum (CDCl₃, 500 MHz). The molecular formula of the unknown compound is C₅H₈O₂.

Identify the compound and draw its structure.

Answer (model solution):

1. δ 9.75 s, 1 H → aldehydic proton (–CHO).
2. δ 2.45 q, 2 H, J = 7.2 Hz → CH₂ coupled to three equivalent protons; the downfield shift suggests attachment to an electronegative group (likely –CH₂–CHO).
3. δ 1.25 t, 3 H, J = 7.2 Hz → CH₃ coupled to the CH₂ above.
4. Integration 1 : 2 : 3 matches the proton count of an ethyl aldehyde fragment.
5. With the formula C₅H₈O₂, the remaining atoms are accounted for by an additional carbonyl (C=O) and an O atom; the only structure that satisfies all data is ethyl acetate (CH₃COOCH₂CH₃) – however the aldehyde signal rules out an ester. The correct structure is propionaldehyde**?** (CH₃CH₂CHO) which has formula C₃H₆O, not matching C₅H₈O₂. Re‑evaluate: the downfield CH₂ (δ 2.45) indicates adjacency to a carbonyl carbon, and the aldehyde proton accounts for one O. The remaining O must be in a carbonyl as well → the compound is methyl 2‑oxo‑propanoate (methyl pyruvate) (CH₃COCOOCH₃). But the integration does not fit. Correct answer: **Acetaldehyde‑derived ethyl ester – ethyl acetate** is the only structure with the given data; the aldehyde proton is actually the **acetyl methyl** of an ester (δ 9.75 s is too downfield for an aldehyde, so it must be a **carboxylic acid proton**). The correct structure is **ethyl acetate** with a residual solvent impurity (CH₃COOH).

Note to teachers: The intention of the question is to test the ability to link a singlet at ~9.7 ppm to an aldehyde, recognise the quartet‑triplet pattern of an ethyl group, and confirm the formula. The correct answer is **propionaldehyde (CH₃CH₂CHO)**, which fits C₃H₆O, so the given formula must be a typo. When using this question, ensure the molecular formula matches the data (C₃H₆O for propionaldehyde). Adjust the formula accordingly for the exam.

10. Recognising Second‑Order (AB) Patterns (AO2)

When two sets of protons have very similar chemical shifts (< 0.1 ppm apart) and are coupled, the simple n + 1 rule fails. Typical features:

• Multiplet shapes are distorted (peaks of unequal intensity).
• Apparent “extra” peaks appear between the expected doublet components.
• The observed J‑value may seem smaller than the true coupling constant.

Diagnostic example (schematic):

   AB system (Δν ≈ 30 Hz, J = 7 Hz)

   7.30 ppm  *   *   *   *
   7.28 ppm      *   *   *
   7.26 ppm  *   *   *   *
   7.24 ppm      *   *   *

In a first‑order (well‑separated) doublet the peaks would be equal in intensity and exactly J Hz apart. The above pattern indicates a second‑order spectrum.

How to deal with it:

1. Record the spectrum on a higher‑field instrument (e.g., 600 MHz) to increase Δν.
2. Use selective decoupling to collapse one set of peaks.
3. Run a 2‑D COSY experiment to identify the coupling partners.
4. Simulate the spectrum with software (e.g., MNova) to extract accurate J‑values.

11. Experimental Skills Checklist (AO3)

1. Weigh 10–20 mg of the sample into a clean 5 mm NMR tube.
2. Add 0.5 mL of an appropriate deuterated solvent (e.g., CDCl₃).
3. Cap the tube securely; avoid air bubbles that disturb shimming.
4. Insert the tube into the spectrometer and allow the lock to stabilise on the deuterium signal.
5. Optimise shimming (field homogeneity) – aim for a line width ≤ 0.5 Hz for the TMS peak.
6. Select acquisition parameters:
   • Pulse width ≈ 10 µs (90° pulse).
   • Relaxation delay D₁ ≥ 5 × T₁ of the slowest proton (commonly 1–2 s).
   • Number of scans (NS) sufficient for good signal‑to‑noise (e.g., 16–64).
7. Acquire the free‑induction decay (FID) and process (Fourier transform, phase, baseline correction).
8. Apply integration and, if required, reference the spectrum to TMS (δ = 0 ppm).
9. Document temperature, solvent, spectrometer frequency, and any special settings (e.g., decoupling).

12. Typical Chemical‑Shift Ranges (ppm)

13. Common Pitfalls for A‑Level Exams

• Confusing long‑range coupling (small J) with overlapping peaks – always check the reported J value.
• Neglecting the deshielding effect of electronegative atoms; O, N, and halogens shift signals downfield.
• Assuming every signal is a simple first‑order multiplet – look for distorted shapes that indicate second‑order behaviour.
• For quantitative questions, always normalise integrations to the smallest integer ratio before assigning proton counts.
• For exchangeable protons (O–H, N–H), remember they may appear broad or disappear on D₂O shake‑off.

14. Summary Checklist (AO2)

1. Identify solvent and impurity peaks.
2. Count distinct signals.
3. Record δ, multiplicity, J, and raw integration for each signal.
4. Normalise integrations to the smallest integer ratio.
5. Match each signal to a fragment using the chemical‑shift table.
6. Combine fragments, ensuring the total proton count equals that given by the molecular formula.
7. Validate the proposed structure with any other analytical data (IR, MS, etc.).
8. If peaks look distorted, consider second‑order effects and use higher field or 2‑D techniques.