mailRe: The "eta_scale" in CR72.


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Posted by Edward d'Auvergne on May 03, 2014 - 13:46:
Hi,

The origin of this was exactly what Andy Baldwin said at
http://thread.gmane.org/gmane.science.nmr.relax.devel/5410/focus=5448
- that there are many different tau_CPMG definitions and there is an
error in one of the equations in the original paper.  The code in
relax is however correct.  The eta_scale value should be
0.35355339059327373.  Feel free to fix the equations in the
documentation of the wiki, manual and lib.dispersion.cr72 docstring.
I wrote these before the code was fully tested and hence there is now
a mismatch.  As for using 2.0**(-3.0/2.0) in the code, this is for the
fastest operation, avoiding the square root.  But now that I look at
it, one mathematical operation can be dropped for speed and the factor
changed to 2.0**(-1.5).

Cheers,

Edward


On 3 May 2014 12:28, Troels Emtekær Linnet <tlinnet@xxxxxxxxxxxxx> wrote:
Dear Edward.

I was inspecting the code of model CR72.

http://svn.gna.org/viewcvs/*checkout*/relax/trunk/lib/dispersion/cr72.py?revision=HEAD

This is calculated as:

eta_scale = 2.0**(-3.0/2.0) = 0.35
which is: 1 / sqrt(2**3).

This differs from the definition in:
http://wiki.nmr-relax.com/CR72_full#Equation
http://www.nmr-relax.com/manual/full_CR72_2_site_CPMG_model.html
http://www.nmr-relax.com/api/3.1/lib.dispersion.cr72-module.html

where:
eta_scale = 2.0**(2/3) = 1.58
which is {3}sqrt(2**2).

If I compare to:
http://wiki.nmr-relax.com/B14#Equation_compared_to_Carver_Richards_72
(DOI: 10.1016/j.jmr.2014.02.023 , eq 70,)

And to, (DOI: 10.1016/S0076-6879(01)39315-1 , eq 25, with the twist
that "tcp_Pa is the delay between 180 pulses in the CPMG pulse train",
 "delay/180/delay/delay/180/delay " so that tcp_Pa = 2xdelay

Then really the manual should use:
eta_scale = 2.0**(-3/2)
or
1 / 2 sqrt(2)

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