The NS 3-site linear R_1ρ model

This is the numerical model for 3-site linear exchange using 3D magnetisation vectors. The assumption that k_AC = k_CA = 0 has been made to linearise this model. It is selected by setting the model to `NS R1rho 3-site linear'. The constraints p<sub>A</sub> > p<sub>B</sub> and p<sub>A</sub> > p<sub>C</sub> 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 R_1ρ 3-site' model, the assumptions R_2A⁰ = R_2B⁰ = R_2C⁰ = R₂⁰ and R_1A = R_1B = R_1C = 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

$$\begin{pmatrix} -\mathrm{R}_{1\rho A}'-\textrm{k}_{\textrm{AB}}& ... ...}_{\textrm{AB}}& \cdots \\ \vdots & \vdots & \vdots & \ddots \\ \end{pmatrix}$$ R

$$\begin{pmatrix} \ddots & \vdots & \vdots & \vdots & \iddots \\ \... ...{BC}}& \cdots \\ \iddots & \vdots & \vdots & \vdots & \ddots \\ \end{pmatrix}$$

$$\begin{pmatrix} \ddots & \vdots & \vdots & \vdots \\ \cdots & -\... ... \omega_1 & -\mathrm{R}_{\textrm{1C}}-\textrm{k}_{\textrm{CB}}\\ \end{pmatrix}$$

$$\begin{pmatrix} & & & \textrm{k}_{\textrm{BA}}& 0 & 0 & \cdots \\... ...B}}& & & & \\ \vdots & \vdots & \vdots & & \vdots & & \ddots \\ \end{pmatrix}$$

$$\begin{pmatrix} \ddots & & \vdots & & \vdots & \vdots & \vdots \\... ...& \ddots & \\ \cdots & 0 & 0 & \textrm{k}_{\textrm{BC}}& & & \\ \end{pmatrix}$$ (11.89)

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 = R₁ have been made.

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

• the relax wiki at http://wiki.nmr-relax.com/NS_R1rho_3-site_linear,
• 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_linear.