Considering organic
compounds, in previous work the simulated annealing algorithm has been
applied ignoring the overlap of the peaks, with a cost function based in
the fit of the complete diffraction pattern (R_{wp}) [1],
evaluating correlated individual Bragg intensities from Pawley fits [2]
and from a reconstructed pattern [3].
The first one has the advantage that it considers implicitly the overlap
of the Bragg reflections in the powder pattern, however it requires more
computational time.

In our work, the
goodness of the trial solutions (cost function) was first determined through
the R agreement factor, defined as:

**R = ( S _{i}
| I_{trial model, i} - I_{Le Bail, i }| ) / ( S_{i
}I_{Le
Bail, i }) x 100**

where i ran over the first 40 Bragg reflections of the pattern. In some cases, no overlap correction is necessary for the integrated intensities obtained in the Le Bail fits. The packing in the structures I to VII was found using the first 40 reflection peaks and the validity of the solutions was later confirmed when the models were used in Rietveld refinements of the complete diffraction pattern.

For other materials
(like b-haematin,
triclinic, Z=2, a=12.196(2) , b=14.684(2), c=8.040(1), a=90.22(1)°,
b=96.80(1)°,
g=97.92(1)°),
the overlap of the reflection peaks makes not possible to solve the structure
without any correction. We note that a reasonable profile factor can be
approximate from the integrated intensities alone [4]. Thus, we redefined
the cost function as follows:

**S = ( I _{Le
Bail, total} - I_{trial model, total })^{2
}/ ( I_{Le
Bail, total} )^{2}**

based in the difference
squared of the total Le Bail and trial model integrated intensity of the
diffraction pattern. Since we have a set of overlapping individual integrated
intensities for the hkl reflections extracted in the Le Bail fit (A_{i})
and the same set is calculated for each trial structure (B_{i}),
we write:

**S = ò2q
{ (S _{i
}A_{i
}f_{i}(2q)
- S_{i
}B_{i
}f_{i}(2q)
}^{2} /_{ } { ò2q
S_{i
}A_{i }f_{i}(2q)
}^{2}**

where f_{i
}are
the profile functions for each diffraction peak in the powder pattern (area
normalized to 1 after integration). In the integration of the previous
equation, the overlap coefficients F_{i, i' }are defined as follows:

**F _{i, i'}
= òd2q
f _{i}(2q)
f_{ i' }(2q)**

The integrals can
be evaluated analytically. Since F_{i, i' }= F_{i', i }the
expresion of S can be reordered as:

**S = { S _{i,i'
}(A_{i}
- B_{i}) F_{i, i'} (A_{i'
}- B_{i'})} /
{ S_{i}A_{i
}}^{2}**

In practice, the
overlap coefficients are calculated for the i=5 adjacent reflections in
the powder pattern.

**References:**

[1]-Y. G. Andreev
and P. G. Bruce, J. Chem. Soc., Dalton Trans., (1998) 4071-4080.

[2]-W. I. F. David,
K. Shankland and N. Shankland, Chem. Comm. (1998) 931-932.

[3]-A. Le Bail,
to be published in the proceedings of EPDIC-7.

[4]-S. Pagola, P.
W. Stephens, D. S. Bohle, A. D. Kosar and S. K. Madsen, Nature 404 (2000)
307-310.