and 
can be determined empirically from the discrepancy between 
and 
. The most convenient time for their calculation is when the calculated
and observed data are scaled to each other. In TNT the scaling parameters
are found by minimizing
This is a four-parameter scaling function. The parameter k converts
the units of the calculated structure factors to the arbitrary units of
the observed structure factors. B is the correction for the error
in the mean temperature factor of the model.
and
have been discussed.
Minimizing Equation 10 can be described
as fitting a curve with the sum of two Gaussians. This type of problem
is difficult because the exponential coefficients B and
are highly correlated. The method chosen to fit these parameters is the
Levenberg-Marquardt method [Press
et al., 1986]. This method combines the best of the full-matrix
and steepest descent methods and will usually converge to a reasonable
set of parameters within 10 cycles.
Figure ii shows the individual shell scale
factors from Figure i with the solvent-corrected
scale factor function superimposed. The curve fits the individual points
in all major respects.
