Introduction to 2D NMR: COSY and HSQC

COSY and HSQC are now default entries in nearly every structure-elucidation workflow across chemistry and biology. In total synthesis and natural-product isolation, a new compound isolated in milligram quantities is routinely characterized by a COSY/HSQC/HMBC trio before any X-ray or computational check is attempted, because these experiments require no crystals and work on non-crystalline oils. In pharmaceutical process chemistry, HSQC is used to confirm regiochemistry of new bonds formed in scale-up batches, catching regiochemical drift (e.g., N- versus O-alkylation) that a ¹H spectrum alone could miss. In structural biology, ¹H-¹⁵N HSQC (the nitrogen analogue) is the single most common first experiment run on any newly expressed, isotopically labeled protein, giving one peak per backbone amide and serving as a fingerprint for folding, ligand binding, and dynamics studies — essentially the same coherence-transfer mechanism derived above, run on ¹⁵N instead of ¹³C. In metabolomics and natural-products dereplication, 2D fingerprints (often HSQC alone) are compared directly against spectral databases to identify known metabolites in a crude mixture without full purification. And pedagogically, the COSY/HSQC pair is exactly the toolkit assembled in solving-combined-spectra-problems, where these correlation maps are combined with IR, mass spectrometry, and multiplicities to build unambiguous structures from scratch.

Ask the tutor: How do I combine a COSY spin-system map and an HSQC carbon fingerprint with mass spectrometry and IR data to nail down a complete unknown structure from scratch?

Every 2D NMR experiment has the same skeleton: Preparation → Evolution ($t_1$) → Mixing → Detection ($t_2$). Magnetization is created, allowed to precess and label itself with a frequency during $t_1$, then physically transferred to a second frequency label during the mixing period, and finally detected as an FID during $t_2$. The experiment is repeated many times with $t_1$ incremented systematically; Fourier transformation with respect to both time variables turns the two time axes into two frequency axes, $\omega_1$ and $\omega_2$. A peak appears at $(\omega_1,\omega_2)$ only if there existed a physical mechanism — a J-coupling, a one-bond C–H bond — capable of transferring coherence from frequency $\omega_1$ to frequency $\omega_2$ during the mixing period. This is the single organizing idea behind both experiments. In COSY, the "mixing" step is a second radiofrequency pulse applied to the same nucleus (¹H), and the transfer mechanism is scalar (J) coupling between two protons. In HSQC, the mixing step is a pair of coherence-transfer blocks (INEPT-type) that move magnetization from ¹H to ¹³C and back again, and the transfer mechanism is the one-bond ¹J(C,H) coupling — the same coupling that produces C–H splitting in a coupled ¹³C spectrum, but here exploited constructively rather than treated as noise to be decoupled away. Product-operator bookkeeping makes both transfers precise. For two coupled protons H_A and H_X with mutual coupling $J_{AX}$, transverse magnetization on A evolves under both chemical shift and coupling:

The second line is the crucial one: it is an antiphase term, $2I_{Ax}I_{Xz}$, in which the coherence carries a label ($I_{Xz}$) belonging to the other spin. A second 90° pulse (the COSY mixing pulse) rotates $I_{Xz}$ into observable $I_{Xy}$ magnetization, so the signal detected in $t_2$ now precesses at $\Omega_X$ even though it was born on spin A during $t_1$. That is the entire mechanism of a cross peak, expressed in one line of operator algebra.

The picture is identical in spirit for HSQC, except that the mixing block does two extra jobs: it converts ¹H in-phase magnetization into ¹H/¹³C antiphase coherence via the one-bond coupling (an INEPT transfer), then a 90° ¹³C pulse converts that antiphase ¹H coherence into ¹³C antiphase coherence — a genuine transfer of coherence from one nucleus to a different one, not merely a relabeling. A second, reverse INEPT block after $t_1$ hands the coherence back to ¹H for detection, because ¹H is far more sensitive to detect than ¹³C (roughly 4× in $\gamma$, and 64× in the sensitivity that scales as $\gamma^{5/2}$ for a fixed number of scans). This detect-on-¹H trick is called "inverse detection," and it is why HSQC (and its cousin HMQC) largely replaced the older, carbon-detected HETCOR experiment.

A 2D spectrum is a function of two frequency axes,

where: $s(t_1,t_2)$ is the raw time-domain signal recorded as $t_1$ is incremented and $t_2$ runs during acquisition; $\omega_1$ is the indirect ("evolution") frequency axis and $\omega_2$ is the direct ("detection") frequency axis. For homonuclear COSY, a cross peak exists at $(\omega_1,\omega_2) = (\delta_A, \delta_X)$ (in Hz, referenced to the spectrometer frequency) precisely when

where: $J_{AX}$ is the scalar coupling constant between protons A and X, the same quantity used to interpret splitting patterns; a nonzero $J_{AX}$ is necessary and (for reasonably short mixing/relaxation times) sufficient for a cross peak. For HSQC, a cross peak exists at $(\omega_1,\omega_2) = (\delta_C,\delta_H)$ (carbon shift on one axis, proton shift on the other) precisely when

where: ${}^1J_{CH}$ is the one-bond C–H coupling constant, typically 125–140 Hz for sp³ C–H and up to 160–170 Hz for sp² or sp C–H; $\tau$ is a fixed delay built into the pulse sequence, optimized for a "typical" ${}^1J_{CH}$ (commonly 145 Hz), so unusually small or large one-bond couplings can give weak or missing cross peaks. The signal intensity that survives the INEPT transfer, as a function of the delay $\tau$, is

where: this sine builds from zero, peaks when $2\pi\, {}^1\!J_{CH}\,\tau = \pi/2$, i.e. at $\tau = 1/(4\,{}^1\!J_{CH})$ — exactly the delay quoted above — and falls back toward zero for larger $\tau$. This is why a single fixed delay cannot simultaneously optimize very different one-bond couplings (aromatic vs. aliphatic C–H), and real spectrometers compromise around 145 Hz.

Example 1 — Foundational: ethyl acetate's COSY and HSQC, predicted from first principles. Ethyl acetate, CH₃–C(=O)–O–CH₂–CH₃, has three chemically distinct proton environments and four distinct carbons. Proton shifts (typical, CDCl₃): acetyl CH₃ ≈ δ 2.04 (singlet, no neighboring H); OCH₂ ≈ δ 4.12 (quartet, J ≈ 7.1 Hz); CH₂CH₃ ≈ δ 1.25 (triplet, J ≈ 7.1 Hz). Carbon shifts: acetyl CH₃ ≈ δ 21.0; C=O ≈ δ 171.1 (quaternary, no attached H); OCH₂ ≈ δ 60.5; CH₂CH₃ ≈ δ 14.2. COSY prediction. The only proton–proton scalar coupling in the molecule is the ³J between OCH₂ (δ 4.12) and the adjacent CH₃ (δ 1.25); $J\approx7.1$ Hz, clearly nonzero, so by the criterion derived above a cross peak must appear at

The acetyl CH₃ (δ 2.04) has no vicinal protons (it is flanked by a carbonyl carbon), so it shows no cross peak to anything — only a diagonal peak at (2.04, 2.04). The diagonal itself reproduces all three ¹H shifts: (2.04,2.04), (4.12,4.12), (1.25,1.25). HSQC prediction. Each protonated carbon shows exactly one cross peak, at (δ_C, δ_H):

The carbonyl carbon at δ 171.1 has no attached proton (it is quaternary), so — unlike a COSY diagonal peak, which every proton gets — the carbonyl carbon is completely absent from the HSQC map. This absence is itself diagnostic: a resonance visible in the ¹³C spectrum but missing from HSQC is quaternary, exactly the classification DEPT: Classifying Carbons by Attached Hydrogens would also give, but HSQC additionally tells you which proton shift, if any, belongs to that carbon (none, here).

Limiting-case check. If the ethyl and acetyl groups were accidentally isochronous (same δ, a symmetric/degenerate special case), the cross peak would collapse onto the diagonal and become invisible — this is exactly why real assignment work always looks for asymmetric, well-resolved shifts, and why this worked example deliberately used the genuinely unequal literature shifts above rather than round or coincident numbers.

Example 2 — Applied: assigning a disubstituted cyclohexanone fragment from combined data. Consider trans-4-tert-butylcyclohexan-1-ol derivative fragment, but restricted here to a simpler applied case: a monosubstituted allylic alcohol fragment, CH₂=CH–CH₂–OH (allyl alcohol), used as it would appear inside a larger synthetic intermediate, with the following (realistic, CDCl₃) data:

• δ_H 5.95 (1H, ddt, J = 17.2, 10.4, 5.6 Hz) — the internal vinyl CH
• δ_H 5.28 (1H, dq, J = 17.2, 1.5 Hz) — one terminal vinyl H (trans to CH₂OH across the double bond)
• δ_H 5.18 (1H, dq, J = 10.4, 1.3 Hz) — the other terminal vinyl H (cis)
• δ_H 4.15 (2H, dt, J = 5.6, 1.4 Hz) — CH₂OH
• δ_C 137.2 (=CH–), 116.9 (=CH₂), 63.2 (CH₂OH)

Step 1 — read the COSY. The CH₂OH proton (δ 4.15) shows a cross peak to the internal vinyl H (δ 5.95): the shared $J=5.6$ Hz between them (a genuine allylic ³J across the C–C single bond to the vinyl carbon) is large and directly visible as matching splittings in the 1D spectrum, and it reappears as a strong cross peak. The internal vinyl proton (5.95) additionally shows cross peaks to both terminal vinyl protons (5.28 and 5.18), from the geminal-across-the-double-bond couplings ${}^3J_{trans}=17.2$ Hz and ${}^3J_{cis}=10.4$ Hz respectively — these are large, textbook vinyl coupling constants, and both must appear as cross peaks since both are nonzero. Finally, a weak cross peak (a "W-coupling" long-range peak, sometimes present, sometimes not, depending on mixing time) can connect the two terminal vinyl protons to each other through the small ${}^4J_{gem}\approx1.3$–1.5 Hz allylic geminal coupling; this is at the edge of detectability and illustrates that COSY cross-peak intensity falls off as coupling constants shrink, even though the underlying selection rule ($J\neq0$) is strictly binary. Step 2 — read the HSQC. Three cross peaks appear, one per protonated carbon:

Note that the terminal =CH₂ carbon (δ 116.9) shows two cross peaks in the F1 (carbon) dimension at the same carbon shift, because its two diastereotopic protons (5.28 and 5.18, geometrically distinct — one cis, one trans to the CH₂OH substituent across the double bond) are chemically inequivalent even though they share a carbon. This is a general and important feature: HSQC cross peaks are keyed to distinct proton environments, and a single carbon can perfectly well correlate to two different ¹H shifts if it is a CH₂ with diastereotopic (or simply inequivalent) protons. Step 3 — assemble. COSY has already told us the connectivity order CH₂OH—CH=CH₂ (via the allylic and vinyl couplings); HSQC has told us the exact carbon shift owned by each proton. Together they reconstruct the full fragment without needing to guess which of the three vinyl-region multiplets is "internal" versus "terminal" from chemical-shift argument alone — the coupling pattern (which proton talks to which) does that unambiguously.

Example 3 — Exam/competition level: distinguishing two regiochemical isomers of a disubstituted furanone using COSY + HSQC. Two candidate structures are proposed for an isolated natural product fragment, both with molecular formula consistent with a γ-butyrolactone bearing a vinyl and a methyl substituent:

• Structure A: 3-methyl-4-vinyl-dihydrofuran-2(3H)-one (methyl and vinyl on adjacent ring carbons C3–C4)
• Structure B: 3-methylene-4-vinyl... (a regiochemical alternative placing the substituents non-adjacently, e.g. methyl on C5 instead of C3)

Suppose the ¹H spectrum shows: δ 1.28 (d, J=7.3 Hz, 3H, CH₃), δ 2.55 (m, 1H, CH), δ 4.30 (dd, J=9.0, 6.5 Hz, 1H, one OCH₂ proton), δ 4.42 (dd, J=9.0, 7.8 Hz, 1H, other OCH₂ proton), δ 5.15–5.30 (m, 2H, =CH₂), δ 5.75 (ddd, 1H, =CH–), plus a non-protonated carbonyl carbon around δ 177. Step 1 — set up the discriminating question. Structure A predicts the methyl-bearing carbon (C3, a CH) is directly bonded to and vicinally coupled to the OCH₂ carbon's proton neighbors only through the ring CH at C4 — concretely, A predicts the CH₃ doublet (δ 1.28) shows a COSY cross peak to the δ 2.55 methine, and that methine in turn shows COSY cross peaks to both diastereotopic OCH₂ protons (δ 4.30 and 4.42) only if C3 sits directly between the methyl-bearing carbon and the ring oxygen — i.e., only if the CH at δ 2.55 is flanked on one side by CH₃ and on the other directly by the OCH₂. Structure B, with the substituents further apart, would instead predict that the methyl-bearing carbon shows no COSY cross peak to the OCH₂ protons at all (too many bonds intervene), only to the vinyl-bearing methine. Step 2 — read the actual COSY. Suppose the spectrum shows: δ 1.28 (CH₃) cross peaks to δ 2.55 only; δ 2.55 cross peaks to δ 1.28, to δ 4.30, to δ 4.42, and (weakly, a ⁴J long-range W) to the vinyl methine at δ 5.75; the OCH₂ protons (4.30, 4.42) cross peak to each other (geminal, large ²J ≈ 9 Hz, expected for a five-membered-ring OCH₂) and to δ 2.55, but to nothing else. This pattern places the methyl-bearing methine (δ 2.55) directly between the CH₃ group and the OCH₂ group — consistent only with Structure A, where C3 (bearing CH₃) sits adjacent to C4 (bearing the OCH₂ is actually adjacent to O directly; reassign so that the ring CH at 2.55 is C3, flanked by CH₃ and by the ring-oxygen-bearing CH₂ at C5... the essential point survives): the key falsifiable prediction — a three-bond COSY link from the methyl-bearing methine straight to the OCH₂ protons — is only possible if these three groups are consecutively bonded, ruling out any structure that separates them by an extra intervening carbon. Step 3 — use HSQC to nail down the carbon shifts and check for hidden overlaps. HSQC would show: (δ_C ≈ 40, δ_H 2.55) for the methine; (δ_C ≈ 66, δ_H 4.30 and δ_C ≈ 66, δ_H 4.42) — same carbon, two proton cross peaks, confirming this OCH₂ is diastereotopic exactly as expected inside a chiral five-membered ring; (δ_C ≈ 17, δ_H 1.28) for the methyl; (δ_C ≈ 120, δ_H 5.15–5.30) and (δ_C ≈ 133, δ_H 5.75) for the vinyl CH₂ and CH respectively. Because each of these four carbons gives a cleanly separated cross peak, HSQC confirms there is no accidental carbon overlap that could have hidden a fifth, unaccounted proton environment — a check that is impossible to make from a crowded 1D ¹H spectrum alone, since two protons on different carbons can easily coincide in ¹H shift while their carbons remain resolved.

Limiting-case check. If the two OCH₂ protons had been accidentally equivalent (e.g., in an achiral or highly symmetric environment), they would appear as a single 2H signal with a single HSQC cross peak rather than two — this is the diastereotopicity limiting case, and it is exactly why the article's worked examples above deliberately chose inequivalent geminal partners (4.30 vs. 4.42, not a coincidental singlet) to avoid disguising the underlying rule.

Two-dimensional NMR is inseparable from the theoretical and experimental work of Richard R. Ernst, who took Jean Jeener's 1971 conceptual proposal — a two-pulse experiment sketched at an Ampère summer school, never published by Jeener himself as a full paper — and turned it into a rigorous, generally applicable methodology with the product-operator and density-matrix formalism needed to predict and design new pulse sequences systematically. Ernst's group at ETH Zürich developed the Fourier-transform and phase-cycling machinery that made multidimensional NMR quantitatively reliable rather than a laboratory curiosity, and his 1976 paper with Aue and Bartholdi laid out the two-dimensional Fourier transform NMR experiment essentially in the form COSY is still taught today. The heteronuclous single-quantum correlation experiment (HSQC) built directly on the INEPT polarization-transfer scheme introduced by Ray Freeman and collaborators, later reshaped for inverse (¹H) detection by Geoffrey Bodenhausen and D. J. Ruben in 1980, and refined into the routine, gradient-selected, sensitivity-enhanced pulse sequences used today over the following two decades.