Molecular-dynamics-derived numerical probability density functions (PDFs) have been used to illustrate the effect of different models for thermal motion on the parameters refined in a crystal structure determination. Specifically, anharmonic curved or asymmetric PDFs have been modelled using the traditional harmonic approximation and the anharmonic Gram-Charlier series treatment. The results show that in cases of extreme anharmonicity the mean and covariance matrix of the harmonic treatment can deviate significantly from physically meaningful values. The use of a Gram-Charlier anharmonic PDF gives means and covariance matrices closer to the true (numerically determined) anharmonic values. The physical significance of the maxima of the anharmonic distributions (the most probable or mode positions) is also discussed. As the data sets used for the modelling process are theoretical in origin, these most probable positions can be compared to equilibrium positions that represent the system at the bottom of its potential-energy surface. The two types of position differ significantly in some cases but the most probable position is still worthy of report in crystal structure determinations.
|Journal||Acta Crystallographica Section A: Foundations of Crystallography|
|Issue number||pt. 4|
|Publication status||Published - Jul 2011|
- anisotropic displacement parameters
- equilibrium structures
- molecular dynamics