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The Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales whereby the simplification {{:R2Azero}} = {{:R2Bzero}} is assumed. This model is labelled as '''CR72''' in [[Relaxation dispersion citation for relax|relax]]. == Equation ==[http://www.nmr-relax.com/manual/Dispersion_model_summary.html Please see the summary of the model parameters here.] <math>R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-)) \\\phantom{R_{2,\textrm{eff}}} = R_2 + \frac{k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-)) </math> Which have the following definitions <math>\zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}}) \\\phantom{\zeta} = - 2 \Delta \omega \, ( p_A k_{\textrm{EX}} - p_B k_{\textrm{EX}}) \\\phantom{\zeta} = - 2 \Delta \omega \, ( k_{\textrm{BA}} - k_{\textrm{AB}}) \\\phantom{\zeta} = - 2 \Delta \omega \, k_{\textrm{EX}} ( 2p_A - 1) \\\Psi = (p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}})^2 + 4 p_A p_B k_{\textrm{ex}}^2 - \Delta \omega^2 \\\phantom{\Psi} = ( p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}} )^2 - \Delta \omega^2 \\\phantom{\Psi} = k_{\textrm{ex}}^2 - \Delta \omega^2 \\\eta_+ = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\\eta_- = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right) \\D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+\zeta^2}} \right)</math> {{:kex}} is the chemical exchange rate constant, {{:pA}} and {{:pB}} are the populations of states A and B, and {{:Deltaomega}} is the chemical shift difference between the two states in ppm. == Parameters == The CR72 model has the parameters {{{:R2zero}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}. == Code == The library code: {{relax url|path=lib/dispersion/cr72.py}} == Reference == The reference for the CR72 model is: * {{#lst:Citations|CarverRichards72}} == Related models == The CR72 model is a parametric restriction of the [[CR72 full]] model. == Links == The [[Relaxation dispersion citation for relax|implementation of the CR72 model in relax]] can be seen in the:* [http://www.nmr-relax.com/manual/The_reduced_CR72_2_site_CPMG_model.html relax manual],* [http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html API documentation],* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72 relaxation dispersion page of the relax website].

[[Category:Models]][[Category:Dispersion models]][[Category:Relaxation_dispersionanalysis]]