= Heavy-atom derivative
A \b[heavy-atom derivative] is a modified <crystal> containing ordered heavy-atom sites that can provide a reference scattering contribution for <X-ray crystallography>. The crystal before modification is called native. For <single isomorphous replacement> or <multiple isomorphous replacement>, the desired <crystal isomorphism> means that the parent <crystal structure> is sufficiently preserved for its contribution to be shared between data sets. Merely detecting the added <chemical element> does not establish that model.
The early <myoglobin> work provides an experimental example. Several crystals with <mercury (element)> or <gold> at single sites on the protein were compared with unsubstituted crystals to infer phases. These are chemically modified reference specimens, not computational substitute structures.<Structure of Myoglobin: A Three-Dimensional Fourier Synthesis at 2 Å. Resolution by J. C. Kendrew and others>[p422, opening paragraph on the earlier6Å analysis]{ref}
<Crystallographic site occupancy> describes the fraction present at a modeled site. The IUCr heavy-atom dictionary defines an occupancy separately for each site and derivative.<Heavy-atom site occupancy in the PDBx mmCIF Dictionary>[item `_phasing_MIR_der_site.occupancy`]{ref} In a simplified single-site model with fixed position and displacement behavior, let $A_H$ be the full-occupancy complex amplitude and let $q$ be occupancy. Then
$$
F_H=qA_H,\qquad F_{PH}=F_P+qA_H.
$$
For an original illustrative reflection, choose $F_P=4+3i$ and $A_H=6$. With $q=1/2$, the derivative amplitude is $7+3i$ and its squared magnitude is58. At full occupancy it is $10+3i$ and its squared magnitude is109. The native squared magnitude is25. Thus doubling occupancy doubles this modeled heavy-atom amplitude, but does not generally double the measured intensity change: interference with the parent contribution matters.
Useful derivative assessment therefore concerns ordered scattering and comparability as well as chemical uptake. If modification changes the parent structure substantially, the assumed decomposition into unchanged parent plus added reference is inadequate. <Heavy-atom labeling> describes the motivation for introducing the reference; a heavy-atom derivative is the resulting experimental specimen.
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