A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
NMR spectroscopy exploits the quantum mechanical property of nuclear spin. For spin-1/2 nuclei (e.g., ¹H, ¹³C), two energy states (α and β) split in an external magnetic field B₀ with energy gap ΔE = γℏB₀ (the Zeeman effect). Resonance occurs when the applied radiofrequency matches the Larmor frequency ν = γB₀/(2π). Chemical shielding by electrons shifts the resonance frequency, giving rise to the chemical shift δ (in ppm). J-coupling between nuclei arises from through-bond electron-mediated interactions and is independent of B₀, enabling structural determination. The Bloch equations describe the macroscopic magnetization dynamics underlying pulsed FT-NMR.
Derive the two-state energy level diagram for a spin-1/2 nucleus in a field, then map it onto real ¹H NMR features: chemical shifts from shielding constants, multiplicities from J-coupling, and peak areas from population differences.
Atomic nuclei with an odd number of protons or neutrons possess intrinsic angular momentum — nuclear spin — and an associated magnetic moment. For a spin-1/2 nucleus like ¹H or ¹³C, this means the nucleus behaves like a tiny bar magnet. When placed in an external magnetic field B₀, quantum mechanics allows only two orientations: aligned with the field (low energy, α state) or opposed to it (high energy, β state). The energy gap between these states is ΔE = γℏB₀, where γ is the nucleus-specific gyromagnetic ratio. This is the Zeeman effect applied to nuclear spins.
Resonance occurs when an oscillating radiofrequency pulse matches the energy gap exactly — that is, when its frequency equals the Larmor frequency ν = γB₀/(2π). The nucleus absorbs the photon and flips from α to β. Different elements resonate at very different frequencies (¹H at ~300 MHz in a 7 T field, ¹³C at ~75 MHz), which is why you must tune the spectrometer to the nucleus you are observing. Within a single nucleus type, however, all protons in the same molecule would resonate at exactly the same frequency in a bare field — NMR would be useless for structure determination.
What makes NMR chemically informative is electron shielding. The electrons surrounding each nucleus partially oppose B₀, creating a local field that is slightly smaller than B₀. This shifts the resonance frequency downward by an amount that depends on the local electron density — more electron-rich protons (e.g., on alkyl groups) are more shielded and resonate at lower frequency than electron-poor protons (e.g., on benzene rings or adjacent to carbonyls). The chemical shift δ = (ν_sample − ν_ref) / ν_spectrometer × 10⁶ measures this offset in ppm relative to a standard like TMS, canceling out the field-strength dependence. The resulting ppm value is a property of the molecular environment, not the instrument.
The multiplicity pattern of NMR peaks — the 1:2:1 triplet, 1:3:3:1 quartet, and so on — arises from J-coupling: the through-bond interaction between nearby nuclear spins. Each neighboring spin-1/2 nucleus can be in either the α or β state, slightly perturbing the local field at the nucleus you are observing. This splitting is transmitted via bonding electrons and is independent of B₀, so J-coupling constants in Hz are the same on any instrument. This field independence is diagnostically useful: as B₀ increases, chemical shift differences in Hz grow (improving resolution of overlapping peaks) while coupling patterns stay fixed, making high-field instruments valuable for complex spectra.
Modern NMR uses pulsed Fourier transform (FT) methods rather than slow continuous frequency sweeps. A brief radiofrequency pulse tips the macroscopic magnetization away from B₀; as it precesses back, it induces a time-domain signal (the free induction decay, FID) in a detector coil. Fourier transforming the FID converts this time-domain signal into the familiar frequency-domain spectrum. The Bloch equations describe how the magnetization components evolve under the pulse and during the relaxation back to equilibrium, providing the theoretical framework for multidimensional NMR experiments that probe connectivity and spatial relationships in large molecules.