Changes

The Baldwin 2014 2-site exact solution relaxation dispersion model for [[SQ CPMG-type data]]for all time scales whereby the simplification {{:R2Azero}} = {{:R2Bzero}} is assumed. This model is labelled as '''B14''' in [[Relaxation dispersion citation for relax|relax]].

The advantage of this code will be that you'll always get the right answer provided you've got 2-site exchange, in-phase magnetisation and on-resonance pulses.  == Comments from the Author ==During the implementation of model B14, Andrew Baldwin wished to raise the attention to: '''1) Danger of errors of approximations'''.<br>'''2) That optimal accuracy analysis should include off resonance effects'''. Please read:* {{#lst:Citations|MyintIshima09}}* {{#lst:Citations|Bain11}} '''This model is not implemented yetDifferential relaxation effects''':<br> Please read:* {{#lst:Citations|Vallurupalli07}}* {{#lst:Citations|Vallurupalli08}}

The paper main equation 50<br><math>R_{2, needs following definitions\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2}-\frac{N_{\textrm{CYC}}}{T_{\textrm{rel}}}\cosh{}^{-1}(v_{1c}) - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D )\right)} \\= R_{2,\textrm{eff}}^{\textrm{CR72}} - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D )\right)}</math>

R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2}-\frac{N_{\textrm{CYC}}}{T_{\textrm{rel}}}\cosh{}^{-1}(v_{1c}) - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(\approx v_2 + 2k_{\textrm{AB}}p_D \right)} \\= R_</math><br>This occurs when <math>k_{2,\textrm{effAB}}^{\textrm{CR72}} - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(p_D</math> tends to zero, and so <math>v_2 + 2k_=v_3</math>.<br>Setting <math>k_{\textrm{AB}}p_D </math> to zero, amounts to neglecting magnetisation that starts on the ground state ensemble and end on the excited state ensemble and vice versa. <br>This will be a good approximation when <math>p_A \right)}gg p_B</math>.<br>In practise, significant deviations from the Carver Richards equation can be incurred if <math>p_B > 1\%</math>.<br>Incorporation of the correction term into equation (50), results in an improved description of the CPMG experiment over the Carver Richards equation.

\alpha_- = \Delta R_2 + k_{\textrm{AB}} - k_{\textrm{BA}} \\

\xi = \frac{2\tau_{\textrm{CP}}}{\sqrt{2}}\sqrt{\Psi + \sqrt{\Psi^2 + z\zeta^2}} = 2h_3 \tau_{\textrm{CP}} = \tau_{\textrm{CP}}E_0\\\eta = \frac{2\tau_{\textrm{CP}}}{\sqrt{2}}\sqrt{-\Psi + \sqrt{\Psi^2 + z\zeta^2}} = 2h_4 \tau_{\textrm{CP}} = \tau_{\textrm{CP}}E_2\\D_+=\frac{1}{2}\left(1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+z\zeta^2}} \right) = F_0 \\D_-=\frac{1}{2}\left(-1+\frac{\Psi+2\Delta \omega^2}{\sqrt{\Psi^2+z\zeta^2}} \right) = F_2

The B14 model has the parameters{{{:R2zero}}, ..., {{:pA}}, {{:Deltaomega}}, {{:kex}}}. == Code ==[http://search.gmane.org/?query=https%3A%2F%2Fgna.org%2Fsupport%2F%3F3154&author=&group=gmane.science.nmr.relax.scm&sort=revdate&DEFAULTOP=and&TOPDOC=10&xP=https%09gna%09org%09support%093154&xFILTERS=Gscience.nmr.relax.scm---A Commits that created the code, approx 20-30 commits, with corrections. ] [https://gna.org/support/?3154 Here is gna.org tracker that followed this code. It includes valuable comments.] The library code: {{relax url|path=lib/dispersion/b14.py}} The target function func_B14(): {{relax url|path=target_functions/relax_disp.py}} === Example graph of test data ===[[File:CPMG Model B14 Example data disp 1 H.png|thumb|center|upright=2|Graph from systemtest "relax -s Relax_disp.test_baldwin_synthetic"]]

* A.J. Baldwin (2014). An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange. ''J. Magn. Reson.'', 2014. ([http{{#lst://dx.doi.org/10.1016/j.jmr.2014.02.023 10.1016/j.jmr.2014.02.023]).Citations|Baldwin14}}

The [[Relaxation dispersion citation for relax|implementation of the CR72 B14 model in relax]] can be seen in the:* [http://www.nmr-relax.com/manual/The_reduced_B14_2_site_CPMG_model.html relax manual],* [http://www.nmr-relax.com/api/3.1/lib.dispersion.b14-module.html API documentation],* [http://www.nmr-relax.com/analyses/relaxation_dispersion.html#B14 relaxation dispersion page of the relax website].

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