COSY: Proton–Proton Scalar Coupling

Introduction

In a 1D proton spectrum, a triplet tells you that a CH₂ group has two neighbouring protons, but it does not say which signal those neighbours give. COSY answers that question directly. It is the simplest and most widely used 2D NMR experiment, and its cross-peaks let a chemist walk along a chain of coupled protons, one bond path at a time, building a map of each proton network in the molecule.

Core explanation

The basic COSY sequence is only two 90° pulses separated by the evolution time t₁, followed by detection. The first pulse creates transverse magnetisation on every proton. During t₁ each proton precesses at its chemical shift and, if coupled, its magnetisation develops a component that depends on the coupling constant J to its partner. The second 90° pulse acts as the mixing step. For a pair of coupled protons A and X, it converts part of the coupling-dependent term on A into observable magnetisation on X. That transferred magnetisation carries the frequency of A in F1 and is detected at the frequency of X in F2, giving a cross-peak at (δA, δX). The transfer is symmetric, so a matching cross-peak appears at (δX, δA).

Transfer occurs only through scalar coupling, which is transmitted through bonding electrons. In practice the strongest COSY correlations come from geminal couplings (²J, two bonds, on the same carbon) and vicinal couplings (³J, three bonds, H–C–C–H), which typically lie between about 2 and 15 Hz. Four-bond couplings (⁴J) are usually below 3 Hz but can appear in rigid systems, across aromatic rings or in W-shaped arrangements, and allylic couplings sometimes show as weak cross-peaks.

The intensity of a cross-peak depends on J. The transferred signal grows roughly as sin(πJt₁), so couplings of a few hertz need long evolution and acquisition times to build up, while broad lines can cancel the signal altogether. In the standard magnitude-mode COSY, the fine structure is hidden and peaks look like rounded blobs with star-shaped tails. Phase-sensitive double-quantum-filtered COSY (DQF-COSY) shows cross-peaks with antiphase multiplet structure, in which positive and negative components alternate. Because antiphase components separated by less than the linewidth cancel, a very small coupling can give a weak or missing cross-peak even when the two protons are genuinely coupled. DQF-COSY also suppresses strong singlets such as methyl groups and solvent, cleaning up the diagonal.

Interpreting a COSY is a matter of walking. Start at a well-assigned signal on the diagonal, move horizontally or vertically to a cross-peak, then move back to the diagonal to find the partner. From there, look for the next cross-peak, and so on. Each unbroken chain of cross-peaks defines a spin system : a set of protons linked by resolved couplings. A heteroatom, a quaternary carbon or a carbonyl usually interrupts the chain, because protons on either side are too many bonds apart to couple strongly.

The COSY-45 variant uses a 45° mixing pulse, which simplifies cross-peaks near the diagonal and allows the relative signs of couplings to be deduced from the tilt of the multiplet pattern.

Step-by-step reasoning

1. Identify a distinctive diagonal peak, for example a CH next to oxygen near 4 ppm. 2. Find every cross-peak in its row and column. 3. Drop to the diagonal from each cross-peak to identify the coupled partners. 4. Repeat from each new proton until no new cross-peaks appear. 5. Record the chain as one spin system, noting where it stops.

Visual explanation

Picture the proton spectrum along both axes of a square plot. Draw a staircase: from the CH–O peak on the diagonal go across to a cross-peak, down to the diagonal at the CH₂ signal, across to the next cross-peak, down to the CH₃ signal. The staircase traces the carbon chain.

Real-world analogy

COSY is like a list of who shook hands with whom at a meeting. From the handshakes you can reconstruct who stood next to whom in a queue, but only people within arm's reach show up, and anyone separated by a pillar breaks the chain. The analogy does not capture how coupling strength depends on geometry.

Real-world example

In a sugar ring such as glucose, the anomeric proton H-1 near 4.5–5.2 ppm is easy to recognise. COSY lets a chemist step from H-1 to H-2, then H-3, H-4, H-5 and the two H-6 protons, assigning every ring proton even though several of them overlap between 3.2 and 3.9 ppm in the 1D spectrum.

Why?

Why do protons on either side of a carbonyl group usually show no COSY cross-peak? They are four or more bonds apart, so their scalar coupling is typically near zero. With no coupling, the mixing pulse has no coupling-dependent magnetisation to transfer, so no cross-peak forms.

Common misconception

"No COSY cross-peak means the protons cannot be neighbours." Adjacent protons can have a near-zero ³J when the H–C–C–H dihedral angle is close to 90°, as predicted by the Karplus relationship. Overlap with the diagonal can also hide real correlations.

Worked example

Question: Propan-1-ol shows signals at 3.6 ppm (2H, triplet), 1.6 ppm (2H, sextet), 0.9 ppm (3H, triplet) and a broad OH. Which COSY cross-peaks are expected?

Reasoning: The CH₂O protons couple to the central CH₂, giving cross-peaks at (3.6, 1.6) and (1.6, 3.6). The central CH₂ couples to CH₃, giving (1.6, 0.9) and (0.9, 1.6). The CH₂O and CH₃ are four bonds apart, so no strong cross-peak links them. The OH proton normally exchanges rapidly and shows no coupling in CDCl₃.

Answer: Two symmetric pairs of cross-peaks, forming a chain 3.6 → 1.6 → 0.9 ppm.

Quick check

1. Which type of proton–proton coupling gives the most commonly observed COSY cross-peaks in organic molecules? Answer: Vicinal three-bond coupling, ³J(H–C–C–H), together with geminal two-bond coupling.

Exam focus

State that COSY cross-peaks reflect through-bond scalar coupling, usually over two or three bonds. Show how to walk a spin system using symmetric cross-peaks. Mention that weak couplings, antiphase cancellation and diagonal overlap can hide correlations.

Advanced insight

Because cross-peak intensity follows sin(πJt₁) modulated by relaxation, COSY is effectively a J-filter. Long-range variants add a fixed delay before or after mixing to enhance small couplings, at the cost of sensitivity loss from T₂ relaxation. In crowded spectra, E.COSY and related methods retain selected multiplet components so that individual coupling constants can be measured from cross-peak displacements.

Summary

COSY uses two 90° pulses to transfer magnetisation between scalar-coupled protons, giving symmetric cross-peaks at (δA, δX). Geminal and vicinal couplings dominate. Walking between diagonal peaks and cross-peaks traces spin systems, which break at heteroatoms and quaternary centres. Antiphase cancellation, small couplings and overlap limit what COSY can show.

Practice questions

1. Why are COSY cross-peaks symmetric about the diagonal? Answer: Coupling is mutual, so magnetisation transfers from A to X and from X to A, giving peaks at both (δA, δX) and (δX, δA). 2. In ethyl ethanoate, which signals show a COSY cross-peak? Answer: The OCH₂ quartet near 4.1 ppm and the CH₃ triplet near 1.2 ppm; the acetyl CH₃ singlet near 2.0 ppm has no coupled partner. 3. Why can a genuine 1 Hz coupling fail to give a DQF-COSY cross-peak? Answer: Its antiphase components are separated by less than the linewidth and largely cancel, and the transfer grows too slowly to build up before relaxation. 4. What does a break in a chain of COSY cross-peaks usually indicate? Answer: An atom without protons, such as a quaternary carbon, carbonyl or heteroatom, separating two proton networks.