General method for finding explicit relationships between jump models of intramolecular dynamics and spectral densities

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Abstract

In this paper, general equations are derived providing explicit relationships between any jump model of intramolecular dynamics and the spectral density functions of dipole relaxation. One gets these equations by reformulating the implicit relationships derived by Tropp (Tropp, J. J. Chem. Phys. 1980, 72, 6035-6043). The matrix form of the spectral density of two interacting spins, eq 15, shows that three factors determine the spectral density: (i) the probability distribution of the molecular conformations, given by the P diagonal matrix, (ii) the relative position of the spins in each conformation, represented by the S(n) vector, and (iii) the dynamics of the conformational changes, encoded by the D(n) matrix. The general relationships found simplify the analysis of the NMR dipole relaxation data by eliminating the need for numerical solutions of the kinetic equations of the jump model. It is pointed out that the relationships are especially simple at the limit of high angular frequencies. Cross-relaxation rates have been calculated at high angular frequencies and at different motional limits. As an example, the spectral density function is determined for the complex dynamics of a lysine side chain. Finally, the role of the multidimensional NMR experiments in the determination of the rate constants of the jump models is discussed.

Original languageEnglish
Pages (from-to)10719-10724
Number of pages6
JournalJournal of Physical Chemistry
Volume96
Issue number26
DOIs
StatePublished - 1992

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