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Crystallographic disorder is variation in atomic positions, orientations or chemical occupation that is represented by an average crystal structure rather than one perfectly repeated local arrangement. A split-site disorder model can describe alternative positions with fractional crystallographic site occupancies. The IUCr disorder-group convention distinguishes atoms present together in one configuration from mutually alternative configurations.^[ref]

For an original single-atom model, suppose an atom occupies position0 along an axis with probability0.6 and position $d$ with probability0.4. ThenAt $d=1\mathring{\mathrm{A}}$, the mean is $0.4\mathring{\mathrm{A}}$ and the variance is $0.24{\mathring{\mathrm{A}}}^2$. There need be no atom at the mean position in any individual configuration. Fitting only an average position with a large atomic displacement parameter can conceal this distinction.

The same average occupation could arise from different unit cells adopting different configurations, from motion among configurations during measurement, or from a mixture of these effects. A static average alone does not determine an interchange rate.

Experimental interpretation therefore combines the electron density map, the allowed chemical geometry, occupation constraints and other evidence. Weak or broadened density should not automatically be assigned one specific dynamic mechanism.

Crystallographic site multiplicity is the number of distinct equivalent positions generated from one representative site by the space group within the conventional unit cell. It is a property of the Wyckoff position. If the site-symmetry group leaves a representative position fixed, fewer distinct positions are generated than at a general site.^[ref]

The relation can be writtenwhere $m_{\mathrm{general}}$ is the general-position multiplicity and $|G_{\mathrm{site}}|$ is the order of the site-symmetry group. For an original compatible example, general multiplicity8 and site-symmetry order2 give $m=4$.

Multiplicity is distinct from crystallographic site occupancy $q$. For one atom type represented at equivalent positions, its average contribution to the atom count per unit cell isA multiplicity8 site occupied to0.25 contributes2 atoms per cell on average. A fully occupied multiplicity4 site contributes4. If these are separate inequivalent sites for the same element, their total contribution is6.

Full occupancy at a symmetry-special site is still $q=1$, rather than automatically a fractional value. The symmetry reduction is already counted by $m$. Dividing occupancy again by the site-symmetry order would count that reduction twice. These distinctions connect a list of representative coordinates to the chemical contents of the unit cell.

A difference electron density map is an electron density map calculated to reveal disagreement between measured diffraction amplitudes and those predicted by a crystal structure model. The common $F_o-F_c$ map combines observed-minus-calculated amplitude information with phases, usually derived from the model. In practice map coefficients include weighting rather than simply subtracting raw measured intensities.^[ref]

For one simplified convention, let $F_c(\mathbf{h})=|F_c(\mathbf{h})|e^{i{\varphi }_c(\mathbf{h})}$. A schematic unweighted difference map isThe crystallographic phases remain necessary even though the coefficients represent differences. Positive features can indicate density missing from the model; negative features can indicate excessive modeled density. Errors in positions, crystallographic site occupancies or atomic displacement parameters can all contribute.

An original one-dimensional idealization takes ${\rho }_o(x)=3+2\cos (2\pi x)$ and ${\rho }_c(x)=3+\cos (2\pi x)$, with matching phases. Their difference isIt is positive near0 and negative near $1/2$, although its integral over one period is zero. Positive and negative residuals therefore need not mean that the total electron count is wrong.

Experimentally the difference electron density map guides corrections to a fitted macromolecular structural model. Finite diffraction data, uncertain phases and model-derived coefficients affect its interpretation; a peak alone does not uniquely identify an atom or chemical species.

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.

A macromolecular structural model is a representation of the three-dimensional organization of a biological macromolecule or complex. It can include atom identities, coordinates, crystallographic site occupancy, atomic displacement parameters and alternative conformations. A deposited coordinate set is an interpreted model supported by measurements, rather than the measurements themselves.^[ref]

For X-ray crystallography, an electron density map constrains where atoms can be placed, while chemical geometry and experimental uncertainty constrain interpretation. Poorly resolved regions can remain absent from the model or be represented less precisely. A numerical coordinate printed to several decimal places does not establish equally fine positional accuracy.

An original coordinate comparison illustrates the distinction. Suppose two models place the same atom at $(0,0,0)$ and $(0.2,0,0)$ in angstrom units. Their separation is $0.2\mathring{\mathrm{A}}$, but that number alone cannot say which model is better. One must examine agreement with the data and the relevant uncertainty, not merely the number of digits or the difference between the coordinates.

A concrete example is calmodulin structure1CLL in the Protein Data Bank. The record contains a refined model with four calcium ions, while its primary citation describes poorly defined terminal residues. Both the observed binding environment and the unresolved regions are part of interpreting the structure.^[ref]

Structural claims should therefore specify which components and conformations are modeled, what experiment supports them and what remains unresolved. A model useful for one question does not automatically establish the complete dynamics or every biochemical activity of the molecule.

A split-site disorder model represents alternative atomic positions explicitly within an average crystal structure. Each alternative has its own coordinate and crystallographic site occupancy. For one atom distributed between exactly two alternatives, with no vacancy, the occupancies sum to1. Correlated alternative arrangements can be collected into disorder groups: atoms within one group occur together, while different groups in the same assembly represent alternatives.^[ref]

For an original scattering example, put the alternatives at fractional coordinates $(0,0,0)$ and $(1/2,0,0)$ with occupancies0.7 and0.3. Give both the same real atomic scattering amplitude $f$, and omit all other atoms and displacement attenuation. The coherent average contribution to a reflection $(h00)$ isFor an even integer $h$, this equals $f$; for an odd integer $h$, it equals $0.4f$. The corresponding squared amplitudes are $f^2$ and $0.16f^2$. Treating both alternatives as fully occupied would predict a different structure factor. This calculation concerns the periodic average contribution, not a complete description of diffuse scattering from local fluctuations.

A split-site disorder model is useful when an electron density map supports distinct alternative locations instead of one broad peak. An anisotropic atomic displacement parameter can describe directional broadening, but does not by itself encode two mutually exclusive chemical arrangements.

Occupancy constraints depend on the physical model: alternatives for a fully present atom sum to1, whereas a model admitting vacancies need not. An average crystal structure alone also cannot establish whether the alternatives exchange during the measurement, occur in different cells, or have particular local correlations.