{ "id": "epwtrwqcre", "slug": "correlation-spectroscopy", "title": "Correlation spectroscopy", "updated": "2026-10-15", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.chemistry", "label": "Chemistry", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.chemistry" }, { "id": "physical.chemistry.methods", "label": "Chemical principles and methods", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.chemistry.methods" }, { "id": "physical.chemistry.methods.analytical-chemistry", "label": "Analytical chemistry", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.chemistry.methods.analytical-chemistry" }, { "id": "physical.chemistry.methods.analytical-chemistry.nuclear-magnetic-resonance-spectroscopy", "label": "Nuclear magnetic resonance spectroscopy", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.chemistry.methods.analytical-chemistry.nuclear-magnetic-resonance-spectroscopy" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.chemistry.methods.analytical-chemistry", "label": "Non-geographic · 1946 to 2000: Analytical chemistry", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.chemistry.methods.analytical-chemistry", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.chemistry", "label": "Chemistry", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.chemistry" }, { "id": "geo.nongeo.t1946.physical.chemistry.methods", "label": "Chemical principles and methods", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.chemistry.methods" }, { "id": "geo.nongeo.t1946.physical.chemistry.methods.analytical-chemistry", "label": "Analytical chemistry", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.chemistry.methods.analytical-chemistry" } ] } ], "excerpt": "Correlation spectroscopy (COSY) is a two-dimensional NMR experiment, introduced in 1976 by Aue, Bartholdi, and Ernst, whose cross-peaks identify coupled protons for molecular structure assignment.", "snippet": "Correlation spectroscopy (COSY) is a two-dimensional NMR experiment, introduced in 1976 by Aue, Bartholdi, and Ernst, whose cross-peaks identify coupled protons for molecular structure assignment.", "node": "physical.chemistry.methods.analytical-chemistry.nuclear-magnetic-resonance-spectroscopy", "markdown": "# Correlation spectroscopy\n\nCorrelation spectroscopy (COSY) is a two-dimensional nuclear magnetic resonance (NMR) experiment in which a cross-peak appears wherever two nuclear spins are connected by scalar (J) coupling, letting a chemist read molecular connectivity directly off a contour plot. The diagonal reproduces the one-dimensional spectrum; the off-diagonal cross-peaks identify which protons are coupled, typically across two or three bonds, and so anchor the assignment workflow of small-molecule structure elucidation.[1](https://doi.org/10.1063/1.432450) • [2](https://www.science.org/doi/10.1126/science.3518060)\n\n| Key fact | Value |\n|---|---|\n| Basic pulse sequence | 90° – \\( t_{1} \\) – 90° – acquire, with \\( t_{1} \\) incremented stepwise[1](https://doi.org/10.1063/1.432450) |\n| Cross-peak transfer function | \\( \\sin(\\pi \\cdot J \\cdot t_{1}) \\); maximal at \\( t_{1} = 1/(2 \\cdot J) \\), zero at \\( t_{1} = 1/J \\)[3](https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf) |\n| Founding publication | Aue, Bartholdi, and Ernst, J. Chem. Phys. 64, 2229 (1976)[1](https://doi.org/10.1063/1.432450) |\n| Typical conventional acquisition | ~1.4 h for a magnitude COSY[4](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf) |\n| Gradient-selected COSY | 1 scan per \\( t_{1} \\) increment; ~5 min at 1 mg/ml[5](https://nmr.chem.columbia.edu/sites/nmr.chem.columbia.edu/files/content/COSY,%20J-Resolved%20Spectra%20and%20Homonuclear%20Decoupling.pdf) |\n| Single-scan (ultrafast) 2D | Phase-sensitive COSY/TOCSY in ≈0.22 s[6](https://pubmed.ncbi.nlm.nih.gov/12461169/) |\n| NOESY cross-peak meaning | Through-space dipolar proximity of 2–5 Å[7](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance/2D_NMR/Homonuclear_Correlations) |\n\n## How it works\n\nThe COSY sequence is two nonselective 90° pulses separated by the evolution period \\( t_{1} \\), followed by acquisition during \\( t_{2} \\).[1](https://doi.org/10.1063/1.432450) The first pulse creates transverse magnetization that precesses at its chemical shift and evolves under homonuclear J-coupling during \\( t_{1} \\). Scalar coupling splits this magnetization into an in-phase component modulated by cosine and an antiphase component modulated by sine.[8](https://www.nmr.sinica.edu.tw/~thh/lectures/NMR/Product_operator.pdf) The second mixing pulse then transfers magnetization among all transitions of the coupled spin system, so magnetization that started on spin A can be detected on spin B.[4](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf) • [9](https://imserc.northwestern.edu/guide/eNMR/eNMR2D/cosy.html)\n\nIn the product-operator picture, the in-phase term \\( I_{1x} \\) stays on the same spin in \\( t_{1} \\) and \\( t_{2} \\) and gives the diagonal peak, while the antiphase term \\( 2 I_{1z} \\cdot I_{2y} \\) is transferred by the second pulse and gives the cross-peak.[10](https://chem.rutgers.edu/images/murali/course-materials/Chem_542_Spring2010_Lecture_6.pdf) Cross-peak intensity follows the transfer function \\( \\sin(\\pi \\cdot J \\cdot t_{1}) \\): it maximizes at \\( t_{1} = 1/(2 \\cdot J) \\) and vanishes at \\( t_{1} = 1/J \\), which is why 128–512 \\( t_{1} \\) increments cover normal proton–proton couplings of 3–15 Hz.[3](https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf) Because the diagonal (cos·cos) and cross-peak (sin·sin) terms are always 90° out of phase in both dimensions, simple COSY cannot be phased absorptive; cross peaks are antiphase absorptive while diagonal peaks are dispersive.[8](https://www.nmr.sinica.edu.tw/~thh/lectures/NMR/Product_operator.pdf) • [3](https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf)\n\n## How it is done\n\nThe operator sets a relaxation delay, then acquires a series of 1D spectra with \\( t_{1} \\) incremented by \\( 1/SW_{1} \\) per step (\\( TD_{1} \\)/ni increments), typically 128–512 increments.[3](https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf) • [11](https://pmc.ncbi.nlm.nih.gov/articles/PMC8611666/) After two-dimensional Fourier transformation, \\( t_{1} \\) and \\( t_{2} \\) become the \\( F_{1} \\) and \\( F_{2} \\) frequency axes. Pure-absorption, frequency-discriminated spectra require hypercomplex (States) acquisition or States-TPPI; otherwise phase-twisted lineshapes result, and magnitude mode with sinebell windowing is the simpler alternative.[10](https://chem.rutgers.edu/images/murali/course-materials/Chem_542_Spring2010_Lecture_6.pdf) Processing may include diagonal suppression (convolution, shifted convolution, or wavelet approaches), and forward linear prediction can extend F1, though over-prediction creates artifacts.[12](https://nmr.oxinst.com/assets/uploads/MagRes/App%20Notes/X-Pulse/App_Note_10_COSY_Oct_2019.pdf) • [13](https://nmr.natsci.msu.edu/experiments/2d-nmr/gcosy.aspx)\n\n## Origin\n\nNeither the lecture nor those experiments were published.[14](https://www.chem.uci.edu/~unicorn/249/pdfs/Ernst2DNMR.pdf) The 1976 paper analyzed the Jeener experiment with density-matrix theory and remains the prototype of 2D [Fourier transform](https://www.edgepedia.org/fourier-transform) spectroscopy.[15](https://ismar.org/wp-content/uploads/2021/09/BMR_01_005-026_1979.pdf) Related early records include two-dimensional Fourier transformation imaging, two-dimensional carbon-13 NMR, SECSY for biological macromolecules, and the 2D NOE (NOESY) experiment.[16](https://doi.org/10.1016/0022-2364%2875%2990224-3) • [17](https://doi.org/10.1063/1.431284) • [18](https://doi.org/10.1016/0006-291x%2879%2991625-5) • [19](https://doi.org/10.1016/0006-291x%2880%2990695-6)\n\n## Variants\n\n**Through-bond homonuclear experiments** report J-coupled connectivities. COSY-90 uses two 90° pulses; DQF-COSY adds a third pulse that converts double-quantum coherence into observable magnetization, giving pure-absorption cross peaks, partial diagonal cancellation, and removal of singlets such as tert-butyl groups and HOD, at the cost of roughly halved sensitivity.[4](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf) • [7](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance/2D_NMR/Homonuclear_Correlations) Long-range COSY inserts a fixed delay \\( D_{4} \\), typically 50–200 ms (up to 500 ms for small molecules), to boost cross peaks from small couplings such as 0.8 Hz.[3](https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf) TOCSY, introduced by L. Braunschweiler and R.R. Ernst in 1983, uses isotropic mixing during an MLEV-17 spin lock (typically 20–100 ms, allowing about \\( 1/(10 \\cdot J_{\\mathrm{HH}}) \\) per transfer step) to relay magnetization across an entire unbroken chain of coupled spins.[20](https://doi.org/10.1016/0022-2364%2883%2990226-3) • [4](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf)\n\n**Through-space experiments** report dipolar proximity instead of bonding. NOESY cross peaks indicate spins within about 2–5 Å and serve stereochemistry and 3D-structure work; ROESY uses spin-lock mixing (typically 50–300 ms) to detect through-space proximity.[7](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance/2D_NMR/Homonuclear_Correlations) • [4](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf)\n\n**Heteronuclear experiments** detect protons through a bonded heteronucleus. HSQC reports one-bond \\( ^{1}\\mathrm{H} \\)–\\( ^{13}\\mathrm{C} \\) (or \\( ^{15}\\mathrm{N} \\)) correlations, usually with multiplicity editing (CH/CH₃ positive, CH₂ negative); HMBC reports multiple-bond correlations, tuned to long-range couplings of 3–10 Hz (7–8 Hz is a common choice) and used mainly to confirm or reject proposed assignments. By the late 1980s these \\( ^{1}\\mathrm{H} \\)-detected sequences had largely replaced \\( ^{13}\\mathrm{C} \\)-detected HETCOR because of proton sensitivity, and recent HSQC modifications give a more than twofold signal-to-noise gain.[21](https://nmr.sdsu.edu/index.php/nmr-seminar/7-common-2d-cosy-hsqc-hmbc/) • [22](https://www.sciencedirect.com/science/article/abs/pii/B9780123970190000017)\n\n## Applications\n\nCOSY is the most widely used 2D experiment and, in magnitude form, is sufficient for the large majority of small-molecule problems.[9](https://imserc.northwestern.edu/guide/eNMR/eNMR2D/cosy.html) • [5](https://nmr.chem.columbia.edu/sites/nmr.chem.columbia.edu/files/content/COSY,%20J-Resolved%20Spectra%20and%20Homonuclear%20Decoupling.pdf) A documented magnitude COSY takes about 1.4 h; on a 60 MHz benchtop instrument, a COSY-90 of pyrimethamine was acquired in about 17 min with four scans and 128 increments.[4](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf) • [12](https://nmr.oxinst.com/assets/uploads/MagRes/App%20Notes/X-Pulse/App_Note_10_COSY_Oct_2019.pdf) Pulsed field gradients replace phase cycling and allow coherence selection with a single scan per \\( t_{1} \\) increment, so a full COSY at 1 mg/ml or less takes about 5 min.[4](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf) • [5](https://nmr.chem.columbia.edu/sites/nmr.chem.columbia.edu/files/content/COSY,%20J-Resolved%20Spectra%20and%20Homonuclear%20Decoupling.pdf) [Covariance](https://www.edgepedia.org/covariance) processing, introduced by [Rafael Brüschweiler](https://www.edgepedia.org/rafael-bruschweiler) and Fengli Zhang in 2004, extends COSY-type data to multistep correlations.[23](https://doi.org/10.1063/1.1647054) Ultrafast 2D NMR, introduced by [Lucio Frydman](https://www.edgepedia.org/lucio-frydman), Tali Scherf, and Adonis Lupulescu in 2002, spatially encodes the indirect dimension with gradients and frequency-selective pulses and reads out with an echo-planar (EPI-type) acquisition, delivering homo- or heteronuclear 2D spectra in a single scan; a phase-sensitive single-scan COSY/TOCSY of n-butylchloride was recorded in about 0.22 s.[24](https://doi.org/10.1073/pnas.252644399) • [6](https://pubmed.ncbi.nlm.nih.gov/12461169/) NOAH supersequences, introduced by Ēriks Kupče and Tim D. W. Claridge in 2017, chain modules into one sequence sharing a single recovery delay; parallel NOAH (p-NOAH), introduced by Ēriks Kupče, Jonathan R. J. Yong, Göran Widmalm, and Tim D. W. Claridge in 2021, records as many as ten 2D spectra (HMBC, HSQC, COSY, TOCSY, CLIP-COSY, NOESY, ROESY modules) in one measurement, in as little as 9 min 34 s with one scan per increment.[25](https://doi.org/10.1002/anie.201705506) • [11](https://pmc.ncbi.nlm.nih.gov/articles/PMC8611666/) • [26](https://doi.org/10.1021/jacsau.1c00423) Deep neural networks now process correlation spectra directly: FID-Net-type networks combined with Fourier transformation deliver high-quality \\( ^{13}\\mathrm{C} - ^{1}\\mathrm{H} \\) correlation spectra of large non-deuterated proteins,[27](https://www.nature.com/articles/s41467-024-49378-8) TransPeakNet predicts HSQC cross-peaks from SMILES and solvent, outperforming ChemDraw and Mestrenova,[28](https://www.nature.com/articles/s42004-025-01455-9) and deep-learning pipelines such as ARTINA deliver signal positions, assignments, and structures without human intervention.[29](https://pubs.rsc.org/en/content/articlehtml/2024/sc/d4sc04742g)\n\n## Limitations and alternatives\n\nThe intrinsic 90° phase difference between diagonal and cross peaks makes simple COSY unphaseable and produces dispersive diagonal ridges; DQF-COSY equalizes the antiphase structure so the whole spectrum can be phased absorptive, at halved sensitivity.[3](https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf) • [7](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance/2D_NMR/Homonuclear_Correlations) Cross peaks are antiphase, so if the linewidth exceeds the J coupling the antiphase components cancel and the peak vanishes, while in-phase diagonal peaks survive overlap.[10](https://chem.rutgers.edu/images/murali/course-materials/Chem_542_Spring2010_Lecture_6.pdf) Low proton chemical shift dispersion causes peak overlap in crowded spectra.[30](https://link.springer.com/content/pdf/10.1007/s10858-011-9494-4.pdf) Weak long-range couplings give small signals because intensity scales as \\( \\sin^{2}(\\pi \\cdot J \\cdot D) \\) away from the optimum delay \\( D = 1/(2 \\cdot J) \\).[31](https://case.edu/artsci/chem/faculty/mateescu/2dnmr/2dnmr-full.pdf) Covariance-derived multistep correlations are artifacts in the strict sense and become misleading when coupled protons overlap; linear prediction in F1 improves apparent resolution but can create artifacts, and samples must not be spun during gradient-selected acquisition.[32](https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/10.1002/mrc.2260) • [13](https://nmr.natsci.msu.edu/experiments/2d-nmr/gcosy.aspx) Against one-dimensional NMR, 2D correlation trades time for the removal of overlap and direct connectivity readout; against heteronuclear 2D methods, COSY is faster and more sensitive but less resolved, so the two are complementary in assignment workflows.[2](https://www.science.org/doi/10.1126/science.3518060) • [30](https://link.springer.com/content/pdf/10.1007/s10858-011-9494-4.pdf)\n\n## References\n\n1. [W. P. Aue, E. Bartholdi, R. R. Ernst (1976). Two-dimensional spectroscopy. Application to nuclear magnetic resonance. The Journal of Chemical Physics.](https://doi.org/10.1063/1.432450)\n2. [Two-Dimensional Nuclear Magnetic Resonance Spectroscopy (Science, 1986)](https://www.science.org/doi/10.1126/science.3518060)\n3. [Intro to 2D NMR: COSY, lr-COSY, DQ-COSY (UW–Madison C636 course guide)](https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf)\n4. [Bruker 2D homonuclear NMR manual (COSY, DQF-COSY, TOCSY, ROESY, NOESY chapters)](https://web.ncbr.muni.cz/~fiala/Graphics/2D_homonuclear.pdf)\n5. [Magnitude COSY, J-resolved, and Homonuclear Decoupling, Columbia University NMR handout (John Decatur, v6.1, 2016)](https://nmr.chem.columbia.edu/sites/nmr.chem.columbia.edu/files/content/COSY,%20J-Resolved%20Spectra%20and%20Homonuclear%20Decoupling.pdf)\n6. [The acquisition of multidimensional NMR spectra within a single scan (PNAS 2002, Frydman et al.)](https://pubmed.ncbi.nlm.nih.gov/12461169/)\n7. [Homonuclear Correlations (chem.libretexts.org)](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Spectroscopy/Magnetic_Resonance_Spectroscopies/Nuclear_Magnetic_Resonance/2D_NMR/Homonuclear_Correlations)\n8. [Non-Classical Vector Model chapter, Biophysical Society Online NMR Textbook](https://www.nmr.sinica.edu.tw/~thh/lectures/NMR/Product_operator.pdf)\n9. [2D COSY Experiment, Northwestern University eNMR guide (Bruker AVANCE)](https://imserc.northwestern.edu/guide/eNMR/eNMR2D/cosy.html)\n10. [Rutgers Chem 542 Lecture 6: 2D NMR, COSY, DQF-COSY, TOCSY, States/TPPI processing](https://chem.rutgers.edu/images/murali/course-materials/Chem_542_Spring2010_Lecture_6.pdf)\n11. [Parallel NMR Supersequences: Ten Spectra in a Single Measurement (p-NOAH)](https://pmc.ncbi.nlm.nih.gov/articles/PMC8611666/)\n12. [Oxford Instruments Application Note 10: 2D NMR experiments at 60 MHz, COSY-90 and COSY-45](https://nmr.oxinst.com/assets/uploads/MagRes/App%20Notes/X-Pulse/App_Note_10_COSY_Oct_2019.pdf)\n13. [gCOSY, Max T. Rogers NMR Facility, Michigan State University](https://nmr.natsci.msu.edu/experiments/2d-nmr/gcosy.aspx)\n14. [Two-dimensional spectroscopy. Application to nuclear magnetic resonance (Aue, Bartholdi, Ernst, J. Chem. Phys. 1976)](https://www.chem.uci.edu/~unicorn/249/pdfs/Ernst2DNMR.pdf)\n15. [Two-Dimensional Fourier Transformation in NMR (Bulletin of Magnetic Resonance 1979)](https://ismar.org/wp-content/uploads/2021/09/BMR_01_005-026_1979.pdf)\n16. [NMR Fourier zeugmatography (Journal of Magnetic Resonance (1969), 1975)](https://doi.org/10.1016/0022-2364%2875%2990224-3)\n17. [Luciano Müller, Anil Kumar, R. R. Ernst (1975). Two-dimensional carbon-13 NMR spectroscopy. The Journal of Chemical Physics.](https://doi.org/10.1063/1.431284)\n18. [Two-dimensional spin echo correlated spectroscopy (SECSY) for 1H NMR studies of biological macromolecules (Biochemical and Biophysical Research Communications, 1979)](https://doi.org/10.1016/0006-291x%2879%2991625-5)\n19. [A two-dimensional nuclear Overhauser enhancement (2D NOE) experiment for the elucidation of complete proton-proton cross-relaxation networks in biological macromolecules (Biochemical and Biophysical Research Communications, 1980)](https://doi.org/10.1016/0006-291x%2880%2990695-6)\n20. [Coherence transfer by isotropic mixing: Application to proton correlation spectroscopy (Journal of Magnetic Resonance (1969), 1983)](https://doi.org/10.1016/0022-2364%2883%2990226-3)\n21. [Common 2D (COSY, HSQC, HMBC), SDSU NMR Facility](https://nmr.sdsu.edu/index.php/nmr-seminar/7-common-2d-cosy-hsqc-hmbc/)\n22. [Getting the Most Out of HSQC and HMBC Spectra (book chapter)](https://www.sciencedirect.com/science/article/abs/pii/B9780123970190000017)\n23. [Rafael Brüschweiler, Fengli Zhang (2004). Covariance nuclear magnetic resonance spectroscopy. The Journal of Chemical Physics.](https://doi.org/10.1063/1.1647054)\n24. [Lucio Frydman, Tali Scherf, Adonis Lupulescu (2002). The acquisition of multidimensional NMR spectra within a single scan. Proceedings of the National Academy of Sciences.](https://doi.org/10.1073/pnas.252644399)\n25. [Ēriks Kupče, Tim D. W. Claridge (2017). NOAH: NMR Supersequences for Small Molecule Analysis and Structure Elucidation. Angewandte Chemie International Edition.](https://doi.org/10.1002/anie.201705506)\n26. [Ēriks Kupče and colleagues (2021). Parallel NMR Supersequences: Ten Spectra in a Single Measurement. JACS Au.](https://doi.org/10.1021/jacsau.1c00423)\n27. [Solution-state methyl NMR spectroscopy of large non-deuterated proteins enabled by deep neural networks | Nature Communications](https://www.nature.com/articles/s41467-024-49378-8)\n28. [TransPeakNet for solvent-aware 2D NMR prediction via multi-task pre-training and unsupervised learning (Communications Chemistry, 2025)](https://www.nature.com/articles/s42004-025-01455-9)\n29. [Deep learning enabled ultra-high quality NMR chemical shift resolved spectra (Chemical Science, 2024)](https://pubs.rsc.org/en/content/articlehtml/2024/sc/d4sc04742g)\n30. [Two-dimensional concurrent HMQC-COSY for small molecule chemical shift assignment (J. Biomol. NMR)](https://link.springer.com/content/pdf/10.1007/s10858-011-9494-4.pdf)\n31. [2D NMR: A guide to density matrix and product operator calculations (Mateescu & Lambert, Case Western Reserve)](https://case.edu/artsci/chem/faculty/mateescu/2dnmr/2dnmr-full.pdf)\n32. [Multistep correlations via covariance processing of COSY/GCOSY spectra: opportunities and artifacts (Magn. Reson. Chem. 2008)](https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/10.1002/mrc.2260)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Chemistry › Chemical principles and methods › Analytical chemistry › Nuclear magnetic resonance spectroscopy*\n\n*Initially written Sep 29, 2026 · Reviewed: Sep 30, 2026 · Edited: Oct 15, 2026 · Last review: Sep 30, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [ "https://www2.chem.wisc.edu/~cic/nmr/Guides/Other/C636f14/fall2014c636/HW/HW8_cosy.pdf", "https://www.chem.uci.edu/~unicorn/249/pdfs/Ernst2DNMR.pdf", "https://case.edu/artsci/chem/faculty/mateescu/2dnmr/2dnmr-full.pdf" ], "url": "https://www.edgepedia.org/correlation-spectroscopy", "markdown_url": "https://www.edgepedia.org/correlation-spectroscopy.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Correlation spectroscopy\", Edgepedia (EdgeChat), https://www.edgepedia.org/correlation-spectroscopy. Edgepedia Community License 1.0.", "credit_md": "\"[Correlation spectroscopy](https://www.edgepedia.org/correlation-spectroscopy)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/correlation-spectroscopy](https://www.edgepedia.org/correlation-spectroscopy). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Correlation spectroscopy\", Edgepedia (EdgeChat), https://www.edgepedia.org/correlation-spectroscopy. Edgepedia Community License 1.0.", "speakable": "Correlation spectroscopy is a two-dimensional NMR experiment, introduced in 1976 by Aue, Bartholdi, and Ernst, whose cross-peaks identify coupled protons for molecular structure assignment." }