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It is assumed that the positions of the heavy atoms are known and that there is a sufficient number of reflections whose signs are determined by the heavy atoms. These reflections do not obey the probability relation (2.6).

(2.6) |

On subtracting the heavy atom contribution from the observed structure factors of these reflections, one obtains the sign of the light atom contributions for these reflections. Thereafter one can solve the remaining light atom structure by applying equation (2.6) to obtain the signs of the reflections that do not have contributions from the heavy atoms.

The procedure was used to solve the structure of the complex
Au[S_{2}C_{2}(CN)_{2}]_{2}Au[S_{2}CN(C_{4}H_{9})_{2}]_{2}. The space group was
found to be *P*2_{1}/*c*, with two formula units per unit cell. The reflections
*hkl* (*h* = 2*n*, *k* + *l* = 2*n*) were all very strong and the gold atoms were
placed at the (special) position 000, 00,
, and 0. 1337
observed `strong' reflections (with equal positive contributions from the gold
atoms) and 538 observed `weak' reflections (without any contributions from the
gold atoms) were used.

The first step was a calculation of the Wilson plot. The following expression was used:

(2.7) |

where is the observed intensity on a relative
scale, *K* = *K*_{L} = *K*_{H} is the scale factor, denotes a summation over
all light atoms in the unit cell, *F*_{H} is the heavy atom contribution to the
structure factor and *B*_{L} and *B*_{H} are the overall temperature factor
parameters of the light and heavy atoms respectively. The average is taken over
reflections *h* within a given sin interval.

For the `weak' reflections (*F*_{H} = 0) the second term in equation (2.7)
vanishes and a Wilson plot for these reflections gave the scale factor *K*_{L}
(1.29) and the value of *B*_{L} (3.24 Å^{2}). On substituting these results
in equation (2.7) a Wilson plot for the `strong' reflections gave the scale
factor *K*_{H} (1.26) and the value of *B*_{H} (2.91 Å^{2}). A small difference
in *K*_{L} and *K*_{H} will not affect the following steps.

The second step is the calculation of the normalized structure factors *E*. The
formulae normally used for the calculation of *E* values do not make sense for a
structure containing heavy atoms. For the corresponding light atom structure
the *E* values, *E*_{L}, are defined by:

(2.8) |

where *F*_{L} is the light atom contribution to the structure factor and, for
space group = 2 for *h*01 and 0*k*0 reflections and
= 1 for all other reflections.^{6}

The `strong' reflections have positive structure factors and we have ; the magnitude and the sign of the *E*_{L} value is obtained by
equation (2.8). This resulted in 365 signed *E*_{L} values, with |*E*_{L}| > 1.3.
For the `weak' reflections we have |*F*_{L}| = and only the magnitude
of the *E*_{L} value is obtained. This resulted in 270 reflections with |*E*_{L}|
> 1.3.

The third step is the application of equation (2.6) to obtain the signs of the
`weak' reflections. When several interactions of the type () =
(*h*) + () occur for |*E*_{L}| > 1.3, where both *S*_{h} and
are known, several predictions of the sign are obtained by application of (2.6). These predictions should be reasonably
consistent before is considered to be determined and singly
occurring interactions should never be trusted. We have followed a procedure
similar to the sign correlation procedure. The origin is partly fixed by the
choice of the gold atom positions and further determined by assigning arbitrary
signs to two `weak' reflections: 221 (|*E*_{L}| = 4.0) and 34(|*E*_{L}| = 2.9). We define the following sets of reflections, all |*E*_{L}| >
2.0:

*h*are `strong' reflections,_{1}*hkl*(*h*= 2*n*,*k*+ 1 = 2*n*).*h*are the two origin determining choices._{2}*h*are the reflections_{3}*h*+_{1}*h*and ._{2}*h*are the reflections_{4}*h*+_{1}*h*,_{3}*h*+_{2}*h*and ._{3}

Continued application of equation (2.6) on 365 `strong' reflections, 2
reflections *h _{2}* and 24 reflections

The above described procedure may be generalized for heavy atoms on general
positions. In this case there also exist reflections with intermediate heavy
atom contributions. For these reflections |*F*_{L}| = | | and the lowest *F*_{L} value is taken to avoid incorrect sign indications. In our
opinion this procedure is well suited to an automatic solution of structures
containing heavy atoms.

**Copyright © 1981, 1998 International Union of
Crystallography**