The observed ratio of RGfree to RGwork. The expected RG ratio
is the value that should be achievable at the end of a structure
refinement when only random uncorrelated errors exist in the data
and the model provided that the observations are properly
weighted. When compared with the observed RG ratio it may
indicate that a structure has not reached convergence or a
model has been over-refined with no corresponding improvement
in the model.
In an unrestrained refinement, the ratio of RGfree to RGwork with
only random uncorrelated errors at convergence depends only
on the number of reflections and the number of parameters
according to
sqrt[(f + m) / (f - m) ]
where f = the number of included structure amplitudes and
target distances, and
m = the number of parameters being refined.
In the restrained case, RGfree is calculated from a random
selection of residuals including both structure amplitudes
and restraints. When restraints are included in the refinement,
the RG ratio requires a term for the contribution to the
minimized residual at convergence, Drestr, due to those
restraints:
Drestr = r - sum [w_i . (a_i)t . (H)-1 a_i]
where
r is the number of geometrical, displacement-parameter and
other restraints
H is the (m,m) normal matrix given by At.W.A
W is the (n,n) symmetric weight matrix of the included
observations
A is the least-squares design matrix of derivatives of
order (n,m)
a_i is the ith row of A
Then the expected RGratio becomes
sqrt [ (f + (m - r + Drestr))/ (f - (m - r + Drestr)) ]
There is no data name for the expected value of RGfree/RGwork yet.
Ref: Tickle, I. J., Laskowski, R. A. & Moss, D. S. (1998).
Acta Cryst. D54, 547-557.
