Using molecular-dynamics simulations to understand and improve the treatment of anharmonic vibrations. I. Study of positional parameters

Abstract

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.

X-ray refinement significantly underestimates the level of microscopic heterogeneity in biomolecular crystals

“…First, it would be interesting to see whether the effects of averaging would differ significantly in structure solution methods other than MR. Second, an extension in the direction of exploring the effects of disordered and ordered solvent molecules on the refinement process by using MD simulations would also be a logical next step. Third and most important, our results suggest that further improvements may be required when it comes to models used to describe the richness of atomic displacements in crystallographic refinement (as also suggested by other studies)5152. However, the dangers in the application of complex models with a high number of parameters in refinement lie in possible over-fitting of the data53.…”

TLSfrom fundamentals to practice

“…Often the purpose is no more than the correction of bond lengths… ”. Such examples can be found in (41, 42, 51–55). …”

“…This term is responsible for two effects (helpful illustrations of both can be found in (41, 42)). The first one is the curvature of electron density for individual atoms that appears as “ banana-shaped contours ” (27); some authors use the term “ boomerang shape ”.…”

Proton Transfer Influence on Geometry and Electron Density in Benzoic Acid–Pyridine Complexes

“…Differences between the theoretical curves and the experimental data show that the influence of the proton transfer on the geometry of the COOH group is hidden by effects of packing of the complex in the crystal lattice. Additional effects that influence the spreading are thermal motions and anharmonicity of vibrations of the COOH group as well as isotropic refinements of the structures determined by diffraction ( i.e ., time averaged over the motions) so the shorter CO distances are observed at higher temperatures. Excellent agreement is observed for the experimental and theoretical NH and O(1)···N bond lengths but not for C=O(2) and C–C(1) bonds.…”