NMR Spectroscopy

Chemical shift describes where a signal appears on the NMR spectrum, measured in parts per million (ppm) relative to the reference compound tetramethylsilane (TMS, δ = 0 ppm). The position depends on the electronic environment of the nucleus. Electron-withdrawing groups (such as halogens, carbonyl groups, and OH) reduce the electron density around nearby protons, 'deshielding' them and moving their signals downfield (higher ppm). Electron-donating groups shield protons, moving signals upfield (lower ppm). Typical ¹H chemical shifts: TMS reference = 0 ppm; alkyl C–H ≈ 0.9–1.5 ppm; alkene =C–H ≈ 4.5–6.5 ppm; aromatic Ar–H ≈ 6.5–8.5 ppm; aldehyde CHO ≈ 9–10 ppm; carboxylic acid COOH ≈ 10–12 ppm. For ¹³C NMR, carbonyl carbons appear far downfield at 160–220 ppm, while alkyl carbons appear at 10–50 ppm.

In ¹H NMR, the area under each signal (integration) is directly proportional to the number of protons giving rise to that signal. Spectrometers display integration as a stepped line or numerical ratio above each peak. For example, ethyl acetate (CH₃COOCH₂CH₃) shows three signals with an integration ratio of 3:2:3, corresponding to the acetyl CH₃, the OCH₂, and the terminal CH₃ respectively. Note: ¹³C NMR spectra are usually acquired with decoupling methods that distort relative intensities, so integration is not routinely used for carbon counting — each signal simply indicates a distinct carbon environment.

Protons on adjacent carbons interact through bonds, a phenomenon called spin–spin coupling or J-coupling. This causes signal splitting according to the N+1 rule: a proton with N equivalent neighbouring protons on adjacent carbons appears as N+1 lines. A proton with 0 neighbours → singlet (s); 1 neighbour → doublet (d); 2 neighbours → triplet (t); 3 neighbours → quartet (q). The relative intensities of the lines follow Pascal's triangle: doublet 1:1; triplet 1:2:1; quartet 1:3:3:1. Example: in ethanol (CH₃CH₂OH), the CH₂ protons are split into a quartet by the three CH₃ protons (3+1=4 lines), and the CH₃ protons are split into a triplet by the two CH₂ protons (2+1=3 lines). The coupling constant J (in Hz) measures the distance between the lines and is the same for two mutually coupled protons — this is used to confirm which protons are neighbours.

A standard broadband-decoupled ¹³C NMR spectrum shows one singlet peak per unique carbon environment, regardless of how many hydrogens are attached. This greatly simplifies the spectrum. A supplementary experiment called DEPT (Distortionless Enhancement by Polarisation Transfer) distinguishes CH₃, CH₂, CH, and quaternary C environments: CH₃ and CH carbons give positive peaks, CH₂ gives negative peaks, and quaternary carbons (C attached to no H) disappear entirely. This allows complete assignment of carbon types. The number of ¹³C signals immediately tells you the number of chemically distinct carbons — for example, benzene (C₆H₆) shows only ONE ¹³C signal because all six carbons are equivalent by symmetry.

Before interpreting NMR data, chemists calculate the degree of unsaturation (also called the index of hydrogen deficiency, IHD) from the molecular formula. For a molecule CₙHₘOₚNₓ: DoU = (2n + 2 + x − m) / 2. Each ring or double bond contributes 1 DoU; a triple bond contributes 2. A benzene ring contributes 4 (1 ring + 3 double bonds). This tells you how many rings and multiple bonds to account for when proposing a structure. Oxygen does not affect the count. Example: for C₄H₈O, DoU = (2×4 + 2 − 8)/2 = 1, so the molecule contains one ring or double bond — consistent with an aldehyde, ketone, or cyclic ether.

• \delta — Chemical shift (ppm): The position of an NMR signal relative to TMS; higher δ means more deshielded (downfield).
• \nu_{\text{sample}} — Sample resonance frequency (Hz): The radiofrequency at which the sample nucleus absorbs energy in the applied magnetic field.
• \nu_{\text{TMS}} — TMS reference frequency (Hz): The resonance frequency of tetramethylsilane, set as the zero reference (δ = 0 ppm).
• \nu_{\text{spectrometer}} — Spectrometer operating frequency (MHz): The base operating frequency of the NMR instrument (e.g. 300 MHz, 500 MHz); dividing by this makes δ instrument-independent.

Problem. An unknown compound has molecular formula C₃H₆O (DoU = 1). Its ¹H NMR spectrum in CDCl₃ shows: (a) a quartet at δ 2.47 ppm integrating for 2H; (b) a triplet at δ 1.06 ppm integrating for 3H; (c) a singlet at δ 9.78 ppm integrating for 1H. Identify the compound and assign all signals.

Answer. The compound is propanal (CH₃CH₂CHO). Signal assignments: δ 9.78 ppm (1H, s) = aldehyde CHO; δ 2.47 ppm (2H, q) = –CH₂– adjacent to C=O; δ 1.06 ppm (3H, t) = terminal CH₃.

• Infrared (IR) Spectroscopy — IR spectroscopy complements NMR by identifying functional groups (C=O, O–H, N–H, C–H stretches) through characteristic bond vibration frequencies; combining IR and NMR data gives a much more complete structural picture.
• Mass Spectrometry — Mass spectrometry provides the molecular formula (exact mass) and fragmentation pattern of an unknown compound; the molecular formula enables calculation of degrees of unsaturation, which guides NMR interpretation.
• Structural Isomerism — NMR is the definitive tool for distinguishing structural isomers — molecules with the same molecular formula but different connectivity — because different arrangements of atoms produce different numbers of NMR signals at different chemical shifts.
• Functional Groups in Organic Chemistry — Knowledge of functional group characteristic chemical shifts (e.g., aldehyde δ 9–10 ppm, carboxylic acid δ 10–12 ppm) is essential for assigning NMR signals and determining which functional groups are present in an unknown molecule.
• Nuclear Spin and Quantum Numbers — NMR is fundamentally rooted in quantum mechanics — only nuclei with a non-zero nuclear spin quantum number (I ≠ 0), such as ¹H (I = 1/2) and ¹³C (I = 1/2), are NMR-active; understanding spin states explains why only certain nuclei produce NMR signals.