On the Interplay Between Real and Reciprocal Space Properties

Abstract

The relationship between charge density distributions and physical properties in solids is highly complex and usually not obvious. It is therefore the aim of this Chapter to outline concepts how to explore and to analyze the interplay of real space properties (e.g. the charge density distribution or its Laplacian) and reciprocal space properties in solids (e.g. electronic conductivity, superconductivity) by means of charge density analyses. In our case study, we will focus on quasi-one dimensional organometallic carbides, which are textbook examples of extended systems displaying pronounced orbital interactions and anisotropic physical properties in real and reciprocal space. We therefore investigated the electronic structures of the complex carbides Sc3 TC4 (T=Fe (1), Co (2), Ni (3)) by combined theoretical and experimental charge density studies. The structures of these organometallic carbides are closely related and display one-dimensional infinite TC4 ribbons embedded in a scandium matrix. Our study highlights that despite the structural similarities of 1–3 even tiny differences in the electronic band structure are faithfully recovered in the properties of the Laplacian of the electron density. In our case, the shift of the Fermi level to higher energies for the Co(d 9) and Ni(d 10) carbides 2 and 3 relative to the Fe(d 8) analogue 1 is reflected in the charge density picture by a significant change in the polarization pattern displayed by the valence shell charge concentrations (VSCC) of the individual transition metal centers in the TC4 units. Hence, precise high-resolution X-ray diffraction data provide a reliable tool to discriminate and analyze the local electronic structures of isotypic solids even in the presence of a severe coloring problem (Z(Fe)/Z(Co)/Z(Ni)=26/27/28). We further demonstrate that the presence of an axial VSCC at the iron atom is due to localized d z 2 states near the Fermi energy and reflected by a high electronic heat capacity at low temperatures (Sommerfeld coefficient γ=17mJ/K2mol in 1). On contrast, the lack of a narrow conduction band (and axial VSCCs at the transition metal) could be correlated in 2 and 3 with their smaller Sommerfeld coefficients (γ=5.7 and 7.7mJ/K2mol, respectively). Finally, we demonstrate that also the cobalt carbide 2 can be discriminated from its isotypic nickel congener 3 on the basis of its electronic properties. Indeed, only 2 is superconducting below 4.5K and displays a structural phase transition around 70K. Hence, this Chapter should help filling the gap between the various chemical and physical viewpoints on the interplay of chemical bonding and physical properties in solids.