Long-lived coherences for line-narrowing in high-field NMR Riddhiman Sarkar a,b , Puneet Ahuja b,⇑ , Paul R. Vasos b,c , Aurélien Bornet b , Olivier Wagnières b , Geoffrey Bodenhausen b,d,e,f a School of Chemistry, University of Southampton, Southampton SO17 1BJ, England b Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, EPFL, Batochime, 1015 Lausanne, Switzerland c Université Paris Descartes, UMR 8601 CNRS, 45, rue des Saints Pères 75006, Paris, France d Université Pierre-et-Marie Curie, Paris, France e Département de Chimie, Ecole Normale Supérieure, 24 Rue Lhomond, 75231, Paris Cedex 05, France f CNRS, UMR 7203, France article info Article history: Received 8 June 2010 Accepted 14 October 2010 Available online 21 October 2010 Keywords: Long-lived states Long-lived coherences Line narrowing Coherent superpositions Transverse relaxation Ó 2010 Elsevier B.V. All rights reserved. Contents 1. Introduction .......................................................................................................... 83 2. The tailored Hamiltonian ................................................................................................ 84 3. Definition of long-lived coherences ....................................................................................... 85 4. Relaxation of long-lived coherences ....................................................................................... 85 5. Designing suitable experiments .......................................................................................... 86 6. Long-lived coherences in a small molecule ................................................................................. 86 7. Long-lived coherences in a protein ........................................................................................ 87 8. Simultaneous excitation of several long-lived coherences ..................................................................... 87 9. Conclusions ........................................................................................................... 88 Acknowledgements .................................................................................................... 89 Appendix A ............................................................................................................ 89 References ........................................................................................................... 90 1. Introduction In conventional nuclear magnetic resonance spectroscopy (NMR), there is a well-known cascade of causes that lead to line- broadening effects: the larger the size of the molecules under investigation, the slower the rotational diffusion, the stronger the low-frequency components of the spectral density functions, the faster the transverse relaxation, hence the broader the spectral lines. This not only holds for ‘conventional’ spectroscopy of allowed transitions, i.e., for the observation of single-quantum transitions, but also for zero- and multiple-quantum spectra. The line broaden- ing associated with slow tumbling makes NMR of large molecules and supramolecular assemblies difficult. If we consider a pair of coupled spin-½ nuclei I and S that are reasonably isolated from unpaired electrons and other nuclei with significant magnetic moments, the longitudinal (‘spin-lattice’) relaxation rate R 1 = 1/T 1 and the transverse (‘spin–spin’) relaxation 0079-6565/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.pnmrs.2010.10.002 ⇑ Corresponding author. E-mail address: puneet.ahuja@epfl.ch (P. Ahuja). Progress in Nuclear Magnetic Resonance Spectroscopy 59 (2011) 83–90 Contents lists available at ScienceDirect Progress in Nuclear Magnetic Resonance Spectroscopy journal homepage: www.elsevier.com/locate/pnmrs