The LM63 3-site fast exchange CPMG model

This is the original Luz and Meiboom (1963) model for 3-site fast exchange for CPMG-type experiments. It is selected by setting the model to `LM63 3-site'. Taking the original Equation 11.16, the equation for 3-site exchange is simply:

R_{ex} = ⋅1 - ⋅tanh, |
(11.18) |

The reference for this equation is:

This model is only provided as a demonstration and should not be used for a normal analysis.
Without data at multiple temperatures, a feature not currently supported within relax, that there are infinite lines of solutions and that the
*Φ*_{ex, B},
*Φ*_{ex, C},
k_{B} and
k_{C} parameters are all convoluted together.

This equation was made more practically relevant in the paper of O'Connell et al. (2009).
This relies on the assumption that site 1 (or A) has a much larger equilibrium population than the other sites (
*p*_{A} *p*_{B} and
*p*_{A} *p*_{C}).
As stated, “if the different values of ji are well-separated (by a factor of 3-10), then Eq. 3 reduces approximately to the sum of n - 1 independent two-state processes for exchange between site 1 and the n - 1 other sites”.
In this situation, the following relationships hold

and

with

The parameter deconvolutions for this model can be performed after a relax analysis, if desired.

More information about the LM63 3-site model is available from:

- the relax wiki at http://wiki.nmr-relax.com/LM63_3-site,
- the API documentation at http://www.nmr-relax.com/api/3.2/lib.dispersion.lm63_3site-module.html,
- the relaxation dispersion page of the relax website at http://www.nmr-relax.com/analyses/relaxation_dispersion.html#LM63_3-site.

The relax user manual (PDF), created 2020-08-26.