Optimization of site occupancies in minerals using quadratic programming

Atomic sites with multiple substituents are common in minerals, and correct site assignment of substituents in structure refinement is of fundamental importance. Substituents must be assigned to particular sites to fit the ob served site scattering and chemical analysis, but the assignments are rarel y made with mathematical rigor. We propose a quadratic programming approach to calculating optimal site assignments, thereby providing crystallographe rs with a mathematically robust starting point for the determination of sit e occupancies. Our program, OCCQP, implements this approach within the wide ly used MATLAB programming environment. User-defined weights may be assigne d to the structural formula, site scattering, and bond-valence sums. The pr ogram is useful for evaluation of site occupancies in newly refined structu res and re-evaluation of previously published structures with ad hoc site a ssignments.