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A 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 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.^[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.^[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. ThenFor 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.

John Cowdery Kendrew helped establish how X-ray crystallography can reveal the three-dimensional arrangement of a protein. Nobel's primary nomination archive names John Cowdery Kendrew, also identifying J. C. Kendrew in its award-sharing comment.^[ref]

His team's1960 myoglobin paper presented a Fourier analysis at2-angstrom resolution. Its opening recalls how earlier phase determination compared native crystals with heavy-atom derivatives containing localized mercury or gold sites. Such comparisons supply information missing from a simple measurement of diffraction intensity.^[ref]

An original one-dimensional example explains that phase problem. Write a periodic electron density using Fourier series coefficients $F_k$. The two positive densitieshave $F_0=3$, $F_{\pm 1}=1/2$ and $F_{\pm 2}=\pm 1/4$, with the final sign distinguishing them. Their squared coefficient magnitudes are identical:9 for mode zero,1/4 for modes $\pm 1$ and1/16 for modes $\pm 2$. The relative phase of the second harmonic has changed while the first harmonic is fixed. Thus equal intensities need not identify one density.

The myoglobin experiment was more demanding than this toy calculation, but the distinction motivates its chemical strategy: modifying crystals at known heavy-atom sites changes their scattering in a way that constrains phase information. Reconstructing an electron density map therefore requires both measured diffraction and a justified phase-determination method, rather than treating the recorded spots as a direct photograph of the molecule.

Multiple isomorphous replacement combines a native X-ray diffraction data set with data from two or more heavy-atom derivatives to estimate the native structure factor phases. In the ideal crystal isomorphism model, each derivative adds a constraint $|F_P+F_{H,j}|=|F_{PH,j}|$. Consistently referenced heavy-atom models can distinguish the two alternatives left by single isomorphous replacement.^[ref]

Continue the original example in single isomorphous replacement, where $F_P=4\pm 3i$ both fit the native amplitude5 and first derivative with $F_{H,1}=3$. Choose a second reference $F_{H,2}=2i$. Its predicted squared amplitudes differ:A measured second-derivative amplitude $\sqrt{41}$ therefore selects $4+3i$ in this exact model. If the second reference had instead been real, both candidates would still have equal magnitudes after adding it. An additional derivative must contribute useful geometry, rather than merely repeat a constraint.

The heavy-atom models must share a consistent coordinate origin and handedness. Resolving a circle-crossing ambiguity does not by itself determine absolute handedness: conjugating all the amplitudes preserves their magnitudes. CCP4's diagrams explicitly retain this distinction.^[ref]

The method has a concrete experimental history. The opening of the1960 myoglobin structure report describes several mercury- or gold-containing derivatives whose X-ray diffraction patterns were compared with the unsubstituted protein. These measurements had supplied phases for the earlier map at spacings greater than6Å; the new report advanced the analysis to2Å.^[ref] Different labeled crystals supplied information unavailable from native intensities alone.