TY - JOUR

T1 - General method for finding explicit relationships between jump models of intramolecular dynamics and spectral densities

AU - Sugar, Istvan P.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4244069994&partnerID=8YFLogxK

U2 - 10.1021/j100205a027

DO - 10.1021/j100205a027

M3 - Article

AN - SCOPUS:4244069994

SN - 0022-3654

VL - 96

SP - 10719

EP - 10724

JO - Journal of Physical Chemistry

JF - Journal of Physical Chemistry

IS - 26

ER -