The NS MMQ 3-site model

This is the numerical model for 3-site exchange for proton-heteronuclear SQ, ZQ, DQ and MQ CPMG data, as derived in (Korzhnev et al., 2004b,2005a,2004a). However it has been extended to allow the A↔C transition. To simplify the optimisation space for the model as in the `NS MMQ 3-site linear' model, the assumption R_2A⁰ = R_2B⁰ = R_2C⁰ = R₂⁰ has been made.

The SQ, ZD and DQ equations

The basic evolution matrices for single, zero and double quantum CPMG-type data for this model are

A_± = e^{a_±⋅τ_CPMG}, (11.70)

where

$$\begin{pmatrix} -\textrm{k}_{\textrm{AB}}-\textrm{k}_{\textrm{AC}... ...{CB}}-\textrm{k}_{\textrm{CA}}\pm\imath\Delta\omega_{\textrm{AC}} \end{pmatrix}$$ a_±

$$\begin{pmatrix} \mathrm{R}_{\mathrm{2A}}^0& 0 & 0 \\ 0 & \mathrm{R}_{\mathrm{2B}}^0& 0 \\ 0 & 0 & \mathrm{R}_{\mathrm{2C}}^0 \end{pmatrix}$$ (11.71)

The MQ equations

The m_j matrices for this model are

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

• the relax wiki at http://wiki.nmr-relax.com/NS_MMQ_3-site,
• the API documentation at http://www.nmr-relax.com/api/3.2/lib.dispersion.ns_mmq_3site-module.html,
• the relaxation dispersion page of the relax website at http://www.nmr-relax.com/analyses/relaxation_dispersion.html#NS_MMQ_3-site.