Longitudinal relaxation in dipole-coupled homonuclear three-spin systems: Distinct correlations and odd spectral densities
- Department of Chemistry, Division of Biophysical Chemistry, Lund University, P.O. Box 124, SE-22100 Lund (Sweden)
A system of three dipole-coupled spins exhibits a surprisingly intricate relaxation behavior. Following Hubbard’s pioneering 1958 study, many authors have investigated different aspects of this problem. Nevertheless, on revisiting this classic relaxation problem, we obtain several new results, some of which are at variance with conventional wisdom. Most notably from a fundamental point of view, we find that the odd-valued spectral density function influences longitudinal relaxation. We also show that the effective longitudinal relaxation rate for a non-isochronous three-spin system can exhibit an unusual inverted dispersion step. To clarify these and other issues, we present a comprehensive theoretical treatment of longitudinal relaxation in a three-spin system of arbitrary geometry and with arbitrary rotational dynamics. By using the Liouville-space formulation of Bloch-Wangsness-Redfield theory and a basis of irreducible spherical tensor operators, we show that the number of relaxation components in the different cases can be deduced from symmetry arguments. For the isochronous case, we present the relaxation matrix in analytical form, whereas, for the non-isochronous case, we employ a computationally efficient approach based on the stochastic Liouville equation.
- OSTI ID:
- 22493344
- Journal Information:
- Journal of Chemical Physics, Vol. 143, Issue 23; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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