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The relaxation dispersion model for the numeric solution (NS) to the Bloch-McConnell equations for 2-site exchange for [[R1rho-type data]]. This model is labelled as '''NS R1rho 2-site''' in [[Relaxation dispersion citation for relax|relax]]. == Equation == This is the numerical model for 2-site exchange using 3D magnetisation vectors.It is selected by setting the model to '''NS R1rho 2-site'''.The simple constraint {{:pA}} > {{:pB}} is used to halve the optimisation space, as both sides of the limit are mirror image spaces. For this model, the equations from Korzhnev05 have been used.The {{:R1rho}} value for state A magnetisation is defined as <math>\begin{equation} \mathrm{R}_{1\rho} = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot e^{R \cdot T_\textrm{relax}} \cdot M_0 \right),\end{equation}</math> where <math>\begin{align} M_0 &= \begin{pmatrix} \sin{\theta} \\ 0 \\ \cos{\theta} \\ 0 \\ 0 \\ 0 \end{pmatrix}, \\ \theta &= \arctan \left( \frac{\omega_1}{\Omega_\textrm{A}} \right).\end{align}</math> The relaxation evolution matrix is defined as <math>\begin{equation} R = \begin{pmatrix} -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{AB} & -\delta_A & 0 & \textrm{k}_\textrm{BA} & 0 & 0 \\ \delta_A & -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{AB} & -\omega_1 & 0 & \textrm{k}_\textrm{BA} & 0 \\ 0 & \omega_1 & -\mathrm{R}_1-\textrm{k}_\textrm{AB} & 0 & 0 & \textrm{k}_\textrm{BA} \\ \textrm{k}_\textrm{AB} & 0 & 0 & -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{BA} & -\delta_B & 0 \\ 0 & \textrm{k}_\textrm{AB} & 0 & \delta_B & -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{BA} & -\omega_1 \\ 0 & 0 & \textrm{k}_\textrm{AB} & 0 & \omega_1 & -\mathrm{R}_1-\textrm{k}_\textrm{BA} \\ \end{pmatrix},\end{equation}</math> === Essentials ===It is essential to read in {{:R1}} values before starting a calculation:<source lang="python">relax_data.read(ri_id='R1', ri_type='R1', frq=cdp.spectrometer_frq_list[0], file='R1_values.txt', mol_name_col=1, res_num_col=2, res_name_col=3, spin_num_col=4, spin_name_col=5, data_col=6, error_col=7)</source> Where the data could be stored like<source lang="text"># mol_name res_num res_name spin_num spin_name value error None 13 L None N 1.323940 0.146870None 15 R None N 1.344280 0.140560None 16 T None N 1.715140 0.136510</source> == Parameters == The NS R1rho 2-site model has the parameters {{{:R1rhoprime}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}. == Reference == The reference for the NS R1rho 2-site model is: * {{#lst:Citations|Korzhnev05b}} == Links == The [[Relaxation dispersion citation for relax|implementation of the NS R1rho 2-site model in relax]] can be seen in the:* [http://www.nmr-relax.com/manual/The_NS_2_site_R1_rho_model.html relax manual], * [http://www.nmr-relax.com/api/3.1/lib.dispersion.ns_r1rho_2site-module.html API documentation],* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#NS_R1rho_2-site relaxation dispersion page of the relax website].

[[Category:Relaxation_dispersionModels]][[Category:Dispersion models]][[Category:Relaxation dispersion analysis]]