2D NMR (COSY, HSQC, HMBC) Reference Cheat Sheet

Key Facts

• COSY shows through-bond proton-proton correlations, most often between hydrogens separated by $^{3}J_{HH}$ coupling.
• HSQC shows direct one-bond carbon-proton correlations, usually $^{1}J_{CH}$, so each cross peak links a proton to the carbon it is attached to.
• HMBC shows longer-range carbon-proton correlations, usually $^{2}J_{CH}$ and $^{3}J_{CH}$, so it helps connect fragments through quaternary carbons, carbonyls, and heteroatom-substituted centers.
• In a typical $^1\mathrm{H}$-$^1\mathrm{H}$ COSY spectrum, both axes are proton chemical shifts, so a cross peak at $(\delta_H = 2.10, \delta_H = 4.25)$ indicates coupling between those two proton signals.
• In HSQC and HMBC spectra, the proton dimension is usually $F_2$ and the carbon dimension is usually $F_1$, so a point is read as $(\delta_H, \delta_C)$.
• A chemical shift difference is reported as $\Delta\delta = \delta_A - \delta_B$, and values are measured in $\mathrm{ppm}$ rather than $\mathrm{Hz}$.
• The frequency separation between two signals is $\Delta\nu = \Delta\delta \times \nu_0$, where $\nu_0$ is the spectrometer frequency in $\mathrm{MHz}$ and $\Delta\nu$ is in $\mathrm{Hz}$.
• A strong structure assignment usually uses COSY for proton spin systems, HSQC for attached $\mathrm{C-H}$ pairs, and HMBC for connecting those fragments into the carbon skeleton.

Vocabulary

COSY

Correlation spectroscopy is a 2D NMR experiment that shows which protons are scalar-coupled to each other through bonds.

HSQC

Heteronuclear single quantum coherence is a 2D NMR experiment that correlates each proton with its directly attached carbon, usually through $^{1}J_{CH}$.

HMBC

Heteronuclear multiple bond correlation is a 2D NMR experiment that correlates protons with carbons two or three bonds away, usually through $^{2}J_{CH}$ or $^{3}J_{CH}$.

Cross peak

A cross peak is an off-diagonal signal in a 2D NMR spectrum that indicates a correlation between two nuclei.

Chemical shift

Chemical shift, written $\delta$, is the position of an NMR signal relative to a reference standard and is measured in $\mathrm{ppm}$.

Scalar coupling

Scalar coupling, written $J$, is through-bond magnetic interaction between nuclei and is measured in $\mathrm{Hz}$.