Analysis of Thermal Motion Effects on the Electron Density via Computational Simulations

Abstract

The Electron Density (ED) of a molecular structure can only be observed for large ensembles of molecules packed tightly in crystal structures in the solid state. Even then it cannot truly be observed, instead experimental measurements are taken via X-Ray Diffraction (XRD) and the resulting data is fitted to a theoretical ED model describing the probability of finding an electron inside an infinitesimal volume element.

The atoms (made up of negatively charged electrons orbiting a positively charged nucleus), which are bound together by electrostatic forces to form the molecule, are constantly in vibrational motion. Even at very low temperatures, quantum effects cause the nuclei to maintain vibration in approximately harmonic oscillations. This nuclear motion takes place on a much faster time scale than the XRD experiment which yields a thermally averaged view of the molecule in the XRD data.

A topological analysis of the static ED (the ED with non-vibrating nuclei centered at mean positions from the observations) are invaluable to chemistry as it yields many chemical properties of the molecule under observation. It is thus important to partition the observed (thermally averaged, dynamic) ED into contributions from the static ED and contributions from nuclear thermal smearing. This partitioning involves an approximation in which the atomic ED is believed to rigidly follow the motion of the nuclei and the resulting dynamic ED is expressed as the convolution between the static ED and the probability of nuclear displacements. The process of fitting parameters to the observed XRD data involves continually refining static and dynamic parameters (the parameters defining the static ED and the nuclear motion, respectively).

In this computational study, the refinement process is simulated and various aspects of the process are evaluated. Among others, important aspects under evaluation include the accuracy of the convolution approximation, the representation and expression of dynamic parameters, the uncertainty of the refinement parameters, and the expression of the static ED.