10 July 1998 Ž . Chemical Physics Letters 291 1998 121–129 Effects of intermolecular dipolar couplings in solution NMR in separated time intervals: the competition for coherence transfer pathways Sangdoo Ahn, Warren S. Warren ) Department of Chemistry, Princeton UniÕersity, Princeton, NJ 08544-1009, USA Received 3 February 1998; in final form 6 April 1998 Abstract We investigate the competition between intermolecular dipolar effects in multiple time intervals and develop a theoretical framework to understand coherence transfer when this competition is important. The quantum picture permits explicit evaluation of coherence transfer pathways, which have been verified by experimental data obtained from pulse sequences with multiple-quantum selective phase cycling. Implications for sequences in common use in biological applications are discussed. q 1998. Published by Elsevier Science B.V. All rights reserved. Ž . Numerous two-dimensional 2D solution NMR experiments give anomalous cross-peaks and additional w x resonances in the indirectly detected dimension because of dipolar couplings between distant nuclei 1–11 . This Ž . work started with the CRAZED sequence pr2-t -gradient, length T – pr2-gradient, length nT-t , shown in Fig. 1 2 1a, which generates resonances in the indirectly detected dimension with all of the experimental properties of Ž . intermolecular multiple-quantum coherences iMQC . Analytical solutions for the time evolution with multiple resonance frequencies and with scalar couplings have been found in recent years, even for much more complex w x sequences 12,13 . In all of these cases, however, the effects of the dipolar field are only explicitly included during a single time interval — generally after the final pulse, or for two intervals sandwiching a p-pulse Ž . which reduces to the same case, since the dipolar interaction is unaffected by the pulse . This is well justified Ž for the sequences studied to date, but in more complex sequences such as the ones in common use in protein . NMR dipolar evolution in multiple time intervals are important, as we discuss further below. Here we Ž . investigate theoretically and experimentally the competition between dipolar effects in multiple time intervals and develop a theoretical framework to understand coherence transfer when this competition is important. Previous experimental results have been explained by two superficially quite different theoretical models, which give the same predictions but turn out to have quite different strengths. In a full quantum treatment using Ž density matrix theory which retains the individual dipolar couplings and discards the high temperature . approximation , the peaks come from iMQCs which are created from multiple-spin terms in the equilibrium w x density matrix r and are detected by dipolar couplings during the final time interval t 4,11 . Thus, for eq 2 ) Corresponding author. E-mail: wwarren@princeton.edu 0009-2614r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 98 00532-6