Hi Edward.
An interesting paper I just found in the alerts.
http://dx.doi.org/10.1016/j.jmr.2014.02.023An exact solution for R2,eff in CPMG experiments in the case of two site chemical exchange
By Andrew J. Baldwin
Specifically these lines in the introduction took my attention:
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http://wiki.nmr-relax.com/CR72" When the population of the minor state exceeds approximately 1%, calculation errors that are
larger than the experimental uncertainty can accumulate when the Carver-Richards equation is used (Figure 1), which can lead to errors in the extracted parameters."
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http://wiki.nmr-relax.com/NS_CPMG_2-site_expanded
"As described in Supplementary Section 8, while exact, this algorithm can lead to significant errors when evaluated at double floating point precision, as used by software such as MATLAB".
"an exact solution for the effective transverse relaxation rate in a CPMG experiment, R2,eff, in the commonly encountered scenario of two-site exchange of in-phase magnetisation (Equation (50)) is derived. The result is expressed as a linear correction to the Carver Richards equation (summarised in Appendix 1), and algorithms based on this have significant advantages in both precision and speed over existing formulaic approaches."
Paper describing exact solution of CMPG, 130 faster than numerical solution