The NS 3-site R

This is the numerical model for 3-site exchange using 3D magnetisation vectors.
It is selected by setting the model to `NS R1rho 3-site'.
The constraints
*p*_{A} > *p*_{B} and
*p*_{A} > *p*_{C} is used to decrease the size of the optimisation space, as both sides of the limit are mirror image spaces.

For this model, as for the 2-site model above, the equations from Korzhnev et al. (2005b) have been used.
These have been however rearranged to match the notation in Palmer and Massi (2006).
The
R_{1ρ} value for state A magnetisation is defined as

R_{1ρ} = - ⋅lnM_{0}^{T}⋅e^{R⋅Trelax}⋅M_{0}, |
(11.85) |

where

M_{0} |
= , | (11.86) |

θ |
= arctan. | (11.87) |

This assumes that the starting magnetisation has an X and Z component only for the A state. The relaxation evolution matrix is defined as

R |
= | |

+ | ||

+ | ||

+ | ||

+ | ||

+ , | (11.88) |

where
*δ*_{A, B, C} are defined as in Equations 11.78a and 11.78b.
For the model, the assumptions
R_{1ρA}' =
R_{1ρB}' =
R_{1ρC}' =
R_{1ρ}' and
R_{1A} =
R_{1B} =
R_{1C} =
R_{1} have been made.

More information about the NS R1rho 3-site model is available from:

- the relax wiki at http://wiki.nmr-relax.com/NS_R1rho_3-site,
- the API documentation at http://www.nmr-relax.com/api/3.2/lib.dispersion.ns_r1rho_3site-module.html,
- the relaxation dispersion page of the relax website at http://www.nmr-relax.com/analyses/relaxation_dispersion.html#NS_R1rho_3-site.

The relax user manual (PDF), created 2019-03-08.