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The full Carver and Richards 1972 2-site relaxation dispersion model for [[SQ CPMG-type data]] for most time scales. It This model is labelled as '''CR72 full''' 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.] * relax manual http://www.nmr-relax.com/manual/full_CR72_2_site_CPMG_model.html* relaxation dispersion page of the relax website http://www.nmr-relax.com/analyses/relaxation_dispersion.html#CR72_full <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_-))</math> Which have the following definitions <math>\alpha_- = R_2^A - R_2^B + k_{\textrm{AB}} - k_{\textrm{BA}} \\\zeta = 2 \Delta \omega \, (R_2^A - R_2^B +k_{\textrm{AB}} - k_{\textrm{BA}} ) \\\phantom{\zeta} = 2 \Delta \omega \, (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} ) \\\phantom{\zeta} = 2 \Delta \omega \alpha_- \\\Psi = (R_2^A - R_2^B + p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}} )^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^2 \\\phantom{\Psi} = \alpha_-^2 - \Delta \omega^2 + 4 p_A p_B k_{\textrm{ex}}^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> <math>k_{\textrm{EX}}</math> is the chemical exchange rate constant, <math>p_A</math> and <math>p_B</math> are the populations of states A and B, and <math>\Delta \omega</math> is the chemical shift difference between the two states in ppm. == Parameters == The CR72 full model has the parameters {R20A{{:R2Azero}}, R20B{{:R2Bzero}}, ..., {{:pA}}, ∆ω{{:Deltaomega}}, {{:kex}}}. == Reference == The reference for the CR72 full model is: * {{#lst:Citations|CarverRichards72}} == Related models == The [[CR72]] model is a parametric restriction of this model.  == Links == The [[Relaxation dispersion citation for relax|implementation of the CR72 full model in relax]] can be seen in the:* [http://www.nmr-relax.com/manual/full_CR72_2_site_CPMG_modelThe_full_CR72_2_site_CPMG_model.html CR72 model in relaxmanual] can be seen in the , * [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_full relaxation dispersion page of the relax website].

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