Manifestation of space-time electron delocalization in an x-ray study

We report a manifestation of the space-time electron delocalization in an x-ray diffraction structural analysis upon the condition that the relaxation time of the structure is less than the lifetime of the delocalized electron at any site, between which electron transfer occurs. In this case, the x-ray diffraction data may provide informative parameters characterizing the fraction of the time for the presence of an extra electron at each site. Such parameters are bond lengths in the coordination unit and mean square displacements of the atoms. The differences in the lengths of the bridging oxygen-iron bonds are explained for mixed-valence trinuclear iron carboxylates with the general formula Fe₃O(COOR₁)₆3R₂]R₃. An expression was obtained, which gives the ratio of the lifetime of an electron at each of the sites using the bond lengths l = Fe–Ol₁:l₂:l₃ = ₁:₂:₃. The direction and magnitude of the displacement of the atoms upon rearrangement related to electron transfer (r) may be determined using this expression for the mean square atomic displacements u²=u₀ ²+(1–)·r² in the case of an experiment at two temperatures.Institute of Chemical Physics, Academy of Sciences of the USSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 30, No. 5, pp. 90–95, September–October, 1989.