Experimental dynamic electron densities of multipole models at different temperatures.

Abstract

It is shown that the dynamic electron density corresponding to a structure model can be computed by inverse Fourier transform of accurately calculated structure factors, employing the method of fast Fourier transform. Maps free of series-termination effects are obtained for resolutions better than 0.04 Å in direct space, corresponding to resolutions larger than 6 Å(-1) in reciprocal space. Multipole (MP) models of α-glycine and D,L-serine at different temperatures have been determined by refinement against X-ray diffraction data obtained from the scientific literature. The successful construction of dynamic electron densities is demonstrated by their topological properties, which indicate local maxima and bond-critical points (BCPs) at positions expected on the basis of the corresponding static electron densities, while non-atomic maxima have not been found. Density values near atomic maxima are much smaller in dynamic than in static electron densities. Static and low-temperature (∼20 K) dynamic electron-density maps are found to be surprisingly similar in the low-density regions. Especially at BCPs, values of the ∼20 K dynamic density maps are only slightly smaller than values of the corresponding static density maps. The major effect of these zero-point vibrations is a modification of the second derivatives of the density, which is most pronounced for values at the BCPs of polar C-O bonds. Nevertheless, dynamic MP electron densities provide an estimate of reasonable accuracy for the topological properties at BCPs of the corresponding static electron densities. The difference between static and dynamic electron densities increases with increasing temperature. These differences might provide information on temperature-dependent molecular or solid-state properties like chemical stability and reactivity. In regions of still lower densities, like in hydrogen bonds, static and dynamic electron densities have similar appearances within the complete range of temperatures that have been considered (20-298 K), providing similar values of both the density and its Laplacian at BCPs in static and dynamic electron densities at all temperatures.