Topological Properties of Chemical Bonds from Static and Dynamic Electron Densities

Dynamic and static electron densities (EDs) based on the independent spherical atom model (IAM) and multipole (MP) models of crambin were successfully computed, holding no series-termination effects. The densities are compared to EDs of small biological molecules at diverse temperatures. It is outlined that proteins exhibit an intrinsic flexibility, present as frozen disorder at 100 K, in contrast to small molecules. The flexibility of the proteins is reflected by atomic displacement parameters (B-factors), which are considerably larger than for small molecules at 298 K. Thus, an optimal deconvolution of deformation density and thermal motion is not guaranteed, which prevents a free refinement of MP parameters but allows an application of transferable, fixed MP parameters. The analysis of the topological properties, such as the density at bond critical points (BCPs) and the Laplacian, reveals systematic differences between static and dynamic EDs. Zero-point-vibrations, yet present in dynamic EDs at low temperature, affect but marginally the EDs of small molecules. The zero-point-vibrations cause a smearing of the ED, which becomes more pronounced with increasing temperature. Topological properties, primarily the Laplacian, of covalent bonds appear to be more sensitive to effects by temperature and the polarity of the bonds. However, dynamic EDs at ca. 20 K based on MP models provide a good characterization of chemical bonding. Both the density at BCPs and the Laplacian of hydrogen bonds constitute similar values from static and dynamic EDs for all studied temperatures. Deformation densities demonstrate the necessity of the employment of MP parameters in order to comprise the nature of covalent bonds. The character of hydrogen bonds can be roughly pictured by IAM, whereas MP parameters are recommended for a classification of hydrogen bonds beyond a solely interpretation of topological properties.