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#

The Relaxation Matrix

The basis for the refinement is the calculation of the volume of a
cross peak
between spins and , , from the atomic coordinates
by means
of the relaxation matrix **R**(Ernst, Bodenhausen, Wokaun, 1987; Macura and Ernst, 1980) (Keepers and James 1984):

(39.1) |

**R**is a function of the transition rates

(39.2) |

(39.3) |

is the gyromagnetic ratio of the proton and the distance between spins and . At present, only protons can be used in the refinement. describes the non-NOE magnetization losses from the lattice.

In the simplest model, it is assumed that a single
isotropic correlation time is
sufficient to describe the spectral densities
(Solomon, 1955):

A step beyond this simple model is the “model-free" approach of
Lipari and Szabo (1982), where the internal motion is described by two
parameters,
an effective correlation time and an order parameter :

Groups of protons whose resonances are degenerate due to motion (in general, mostly methyl groups) are treated roughly as in CORMA, version 1.5 (Keepers and James 1984). (Note that cross peaks which are ambiguous due to overlap should be dealt with in a different way; see the example input file in Section 39.7.) Each such group is represented by one spin, whose intensity is scaled by the number of protons in the group, and the distance to the group is calculated as the or average over the protons in the group (Eq. 39.4). In addition, a diagonal leakage rate is added for each group of protons.

Protons can be removed from the spin system (exchangeable protons in DO spectra, deuterium-labeled molecules), or their appropriate occupancy can be specified (exchangeable protons in HO spectra).

*Xplor-NIH 2024-09-13*