Determination of transverse relaxation rates of individual spins while quenching echo modulations due to homonuclear scalar couplings Nicolas Aeby a , Geoffrey Bodenhausen a,b, * a Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, Batochime, 1015 Lausanne, Switzerland b Département de Chimie, Associé au CNRS, Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France article info Article history: Received 8 April 2008 In final form 10 August 2008 Available online 24 August 2008 abstract The envelopes of spin-echo amplitudes obtained with trains of multiple refocusing pulses are normally modulated by homonuclear scalar couplings. Echo modulations make it difficult to determine transverse relaxation rate constants R 2 . Provided that the pulses are of moderate amplitude so that spins at different offsets experience different tilted effective fields, and provided one avoids recoupling conditions, it is pos- sible to quench the modulations of spin echoes. When the modulations are quenched, apparent trans- verse relaxation rate constants R 2 (I) can be determined for individual spins I. The principle is demonstrated for solutions of glycine with single or double carbon-13 enrichment. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction The formation of spin echoes [1–3] allows one to determine homogeneous transverse relaxation rates when they are masked by inhomogeneous broadening [4], to determine coefficients of translational diffusion [5–7], and to separate line-width contribu- tions from chemical exchange and homogeneous transverse relax- ation [8–13]. When refocusing methods are applied to systems with homonuclear scalar couplings, as frequently encountered for protons and for carbon-13 or nitrogen-15 in isotopically enriched molecules, echo modulations [4,14–16] make it difficult to deter- mine transverse relaxation rate constants R 2 (I) = 1/T 2 (I) of individ- ual spins I. For the most part, refocusing experiments have therefore remained confined to the study of isolated carbon-13 or nitrogen-15 spins. Under ideal circumstances, the amplitudes hI(t)i of the spin ech- oes of a spin I observed with a multiple refocusing sequence (p/ 2) y –[s  (p) x  s] n are modulated due to homonuclear scalar cou- plings, i.e., hI(t)i = hI(0)icos(pJ IS t) at the top of the nth echo, where t = n(s + s p + s). As shown by Gutowsky et al. [15] and by Allerhand [16], these modulations can be quenched when the pulse repeti- tion rate m rep = 1/(s + s p + s) is much larger than the offset of the coupling partner, i.e., when m rep  X S /(2p). This type of quenching (henceforth referred to as ‘mechanism A’, see Table 1) can occur even when the radio-frequency (RF) pulses are ideal, i.e., when they are perfectly homogeneous, properly calibrated to induce rotations through an angle p, and have an RF amplitude m 1 = x 1 /(2p)= cB 1 /(2p) that is much stronger than the largest offset with respect to the carrier frequency, i.e., when m 1  X S /(2p). In a perhaps more trivial manner, echo modulations can also be quenched by applying very weak RF pulses, i.e., when m 1  X S / (2p). In this case, if the RF carrier frequency x RF is set in the vicinity of the chemical shift of the nucleus I under investigation (x RF  X I ), the magnetization of the coupling partner S is barely affected (‘mechanism B’). Recently, it has been discovered [17–21] that echo modulations can also be quenched through a new effect (‘mecha- nism C’), when using moderately strong RF pulses that are on-reso- nance for spin I and affect the coupling partners S to some degree but fail to bring about an ideal rotation of their magnetization, be- cause the effective fields associated with the RF pulses are tilted in the rotating frame. This quenching phenomenon, also known at SIT- COM effect (for ‘Stabilization by interconversion within a triad of coherences under multiple refocusing’ [19]) typically occurs when the pulse repetition rates are much slower than the offset of the coupling partner, i.e. when m rep  X S /(2p), in contrast to mecha- nism A. However, the echo modulations re-appear (the scalar inter- action is ‘recoupled’) when the offset approaches a multiple of the pulse repetition rate, i.e., for X S  2kpm rep with integer k. These con- ditions correspond to the so-called DANTE sidebands. Provided that these narrow recoupling conditions are avoided, the echoes of spin I are not modulated by the coupling J IS and the envelopes of the spin- echo decays are to a good approximation mono-exponential, so that it is possible to determine the apparent transverse relaxation rate constant R 2 (I) = 1/T 2 (I) of an individual spin I. This Letter presents experimental evidence of mono-exponen- tial transverse relaxation in systems with two coupled 13 C spins in doubly-enriched glycine when the echo modulations are quenched through mechanism C of Table 1. The apparent decay rates are compared with those determined under similar condi- tions in glycine that is singly enriched in either C 0 or C a positions, 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.08.078 * Corresponding author. Address: Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne, Batochime, 1015 Lausanne, Switzerland. E-mail address: Geoffrey.Bodenhausen@ens.fr (G. Bodenhausen). Chemical Physics Letters 463 (2008) 418–421 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett