This is the simplest of all models in that the dispersion component of the base data  the peak intensity values  is not modelled. It is used to determine either the R_{2eff} or R_{1ρ} values and errors as required for the base data for all other models. It can be selected by setting the model to `R2eff'. Depending on the experiment type, this model will be handled differently. The R_{2eff}/ R_{1ρ} values determined can be later copied to the data pipes of the other dispersion models using the appropriate user functions.
For the fixed relaxation time period CPMGtype experiments, the R_{2eff}/ R_{1ρ} values are determined by direct calculation using the formula
The values and errors are determined with a single call of the minimise.calculate user function. The R_{1ρ} version of the equation is essentially the same:
R_{1ρ}(ω_{1}) =  ⋅ln.  (11.3) 
Errors are calculated using the formula
The derivation of this is simple enough. Rearranging 11.2,
R_{2}⋅T_{relax} =  ln.  (11.5) 
Using the rule
ln = ln(X)  ln(Y),  (11.6) 
where X and Y are normally distributed variables, then
R_{2}⋅T_{relax} = ln(I_{0})  ln(I_{1}),  (11.7) 
and
R_{2} =  ⋅ln(I_{0})  ln(I_{1}),  (11.8) 
Using the estimate from https://en.wikipedia.org/wiki/Propagation_of_uncertainty that for
f = a ln(A),  (11.9) 
the variance of f is
σ_{f}^{2} = a*,  (11.10) 
then the R_{2} variance is
σ_{R2}^{2} = ⋅ + ⋅.  (11.11) 
Rearranging gives 11.4.
In a number of publications, the error formula from Ishima and Torchia (2005) has been used. This is the collapse of Equation 11.4 by setting σ_{I0} to zero:
This is not implemented in relax as it can be shown by simple simulation that the formula is incorrect (see Figure 11.1). This formula significantly underestimates the real errors. The use of the same I_{0} value for all dispersion points does not cause a decrease in the R_{2eff} error but rather a correlation in the errors.

For the variable relaxation time period type experiments, the R_{2eff}/ R_{1ρ} values are determined by fitting to the simple two parameter exponential as in a R_{1} or R_{2} analysis. Both R_{2eff}/ R_{1ρ} and the initial peak intensity I_{0} are optimised using the minimise user function for each exponential curve separately. Monte Carlo simulations are used to obtain the parameter errors.
More information about the R2eff model is available from:
The relax user manual (PDF), created 20240608.