The NS 3-site linear R1ρ model

This is the numerical model for 3-site linear exchange using 3D magnetisation vectors. The assumption that kAC = kCA = 0 has been made to linearise this model. It is selected by setting the model to `NS R1rho 3-site linear'. The constraints pA > pB and pA > pC is used to decrease the size of the optimisation space, as both sides of the limit are mirror image spaces. To simplify the optimisation space for the model as in the `NS R1ρ 3-site' model, the assumptions R2A0 = R2B0 = R2C0 = R20 and R1A = R1B = R1C = R1 have been made.

The equations are the same as for the `NS R1rho 3-site' model except for the relaxation evolution matrix which simplifies to

R = $\displaystyle \begin{pmatrix}-\mathrm{R}_{1\rho A}'-\textrm{k}_{\textrm{AB}}& -...
...{k}_{\textrm{AB}}& \cdots \\ \vdots & \vdots & \vdots & \ddots \\ \end{pmatrix}$    
  + $\displaystyle \begin{pmatrix}\ddots & \vdots & \vdots & \vdots & \iddots \\ \cd...
...rm{BC}}& \cdots \\ \iddots & \vdots & \vdots & \vdots & \ddots \\ \end{pmatrix}$    
  + $\displaystyle \begin{pmatrix}\ddots & \vdots & \vdots & \vdots \\ \cdots & -\ma...
...& \omega_1 & -\mathrm{R}_{\textrm{1C}}-\textrm{k}_{\textrm{CB}}\\ \end{pmatrix}$    
  + $\displaystyle \begin{pmatrix}& & & \textrm{k}_{\textrm{BA}}& 0 & 0 & \cdots \\ ...
...{AB}}& & & & \\ \vdots & \vdots & \vdots & & \vdots & & \ddots \\ \end{pmatrix}$    
  + $\displaystyle \begin{pmatrix}\ddots & & \vdots & & \vdots & \vdots & \vdots \\ ...
...& & \ddots & \\ \cdots & 0 & 0 & \textrm{k}_{\textrm{BC}}& & & \\ \end{pmatrix}$, (11.89)

where δA, B, C are defined as in Equations 11.78a and 11.78b. For the model, the assumptions R1ρA' = R1ρB' = R1ρC' = R1ρ' and R1A = R1B = R1C = R1 have been made.

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

The relax user manual (PDF), created 2016-10-28.