1. Introduction

Nuclear Magnetic Resonance (NMR) spectroscopy is based on the absorption of radiofrequency (RF) radiation by nuclei placed in a strong static magnetic field. It reveals detailed information about structure, dynamics, and local electronic environment in molecules. NMR is applicable to nuclei with non-zero spin quantum number (I ≠ 0), such as ¹H, ¹³C, ¹⁹F, and ³¹P.

2. Principle of NMR Spectroscopy

2.1 Nuclear Spin and Magnetic Moment

Nuclei with odd mass number or odd atomic number possess a nuclear spin (I) and a corresponding magnetic moment. In a static magnetic field B₀, these spins adopt discrete orientations that differ in energy.

2.2 Zeeman Splitting & Population Difference

In the presence of B₀, nuclear energy levels split (Zeeman effect) into lower- and higher-energy states (approximately “parallel” and “antiparallel” to the field). A small Boltzmann population difference between these states enables RF absorption.

2.3 Resonance Condition

When RF of the correct frequency is applied, nuclei undergo transitions between the Zeeman levels. The resonance condition is:

where h is Planck’s constant, ν is the resonance frequency, γ is the gyromagnetic ratio of the nucleus, ℏ is the reduced Planck constant, and B₀ is the magnetic field strength.

2.4 Chemical Shift (δ)

Local electrons shield the nucleus and slightly modify its effective field, shifting the resonance frequency. Chemical shift is reported relative to a reference (typically TMS for ¹H and ¹³C) as:

2.5 Relaxation (T₁ and T₂)

After excitation, nuclei return to equilibrium via relaxation: T₁ (spin–lattice, longitudinal) governs recovery of M_z, and T₂ (spin–spin, transverse) governs decay of coherent transverse magnetization. These time constants affect signal intensity and line width.

2.6 Scalar (J) Coupling & Multiplicity

Through-bond spin–spin coupling (J, in Hz) splits NMR lines into multiplets (e.g., doublets, triplets), encoding connectivity and stereochemical information. Approximate multiplicity often follows the (n + 1) rule for ¹H with n equivalent neighboring protons.

3. Instrumentation (Key Components)

• Superconducting magnet (e.g., 7–23 T) providing a highly homogeneous B₀.
• RF transmitter/receiver for precise pulse generation and detection.
• Probe with tuned coils; samples typically in 5 mm NMR tubes.
• Shim system for field homogeneity; lock for drift correction.
• Digitizer & computer for free-induction decay (FID) acquisition and Fourier transform.

4. Applications of NMR Spectroscopy

4.1 Structural Elucidation

• Assignment of functional groups and molecular frameworks (e.g., ¹H, ¹³C NMR).
• 2D methods (COSY, HSQC, HMBC, NOESY/ROESY) for connectivity and spatial proximity.

4.2 Quantitative NMR (qNMR)

• Accurate concentration measurements from integrated peak areas referenced to an internal standard.

4.3 Dynamics & Conformation

• Exchange processes, conformational equilibria, diffusion (DOSY), relaxation (T₁, T₂), and kinetics.

4.4 Biomolecular NMR

• Structures of proteins, nucleic acids, and complexes in solution; mapping binding sites and dynamics.

4.5 Medical Imaging (MRI)

• Non-invasive imaging based on NMR signal of tissue water; contrast via relaxation, diffusion, and pulse sequences.

5. Advantages

• Non-destructive and highly informative (qualitative and quantitative).
• Rich chemical and spatial information; applicable to solids and solutions (with appropriate techniques).

6. Limitations

• Lower sensitivity for low-abundance/low-γ nuclei (e.g., ¹³C); often requires longer acquisition.
• High instrument cost and need for cryogens; expertise required for advanced experiments.
• Spectral complexity for mixtures; careful sample preparation and parameter optimization needed.