The cyclic cluster model at hartree–fock level

Abstract

We present the implementation of the cyclic cluster model (CCM) formalism at the Hartree-Fock (HF) level. In contrast to other periodic models, the CCM is a Γ-point approach. Integration is carried out in real space within a finite interaction area determined by the size and the shape of the cluster that corresponds to a supercell of the solid, surface, or polymer. Particular care has to be taken for the proper treatment of three- and four-center integrals that involve basis functions located at the boundaries of the Wigner-Seitz supercell, which defines the interaction region. The similarity between the CCM formalism and molecular approaches allows in principle the application of sophisticated post HF methods to solid-state problems with only moderate modification of the molecular code. We show for selected model systems, that with our approach, the electronic structure and energetics obtained by the conventional supercell model is fully reproduced.

Single-step synthesis of nanostructured γ-alumina with solvent reusability to maximise yield and morphological purity

“…Based on these results a temperature of 500 C is used for the calcination of boehmite, in agreement to the conditions used in the literature (between 300 and 500 C). 5,6 The enthalpy change corresponding to the endothermic, isomorphous transformation is +8.98 kJ mol À1 and +6.61 kJ mol À1 for the nanorods and nanoplates respectively. Fig.…”

“…[1][2][3] Amongst all alumina polymorphs, g-Al 2 O 3 has the highest specic surface area and is thus the favoured transition form for catalyst supports. 4 Out of the numerable aluminium minerals such as the hydroxides and oxy hydroxides, boehmite (g-AlOOH, aluminium oxy hydroxide), is oen the most viable precursor to obtain g-Al 2 O 3 , achieved by calcination at temperatures between 300 and 500 C. 5,6 g-AlOOH presents an orthorhombic crystal structure which consists of octahedral AlO 6 units coupled by hydrogen bonding in the {010} direction forming a layered or lamellar structure. 7 By contrast, the g-Al 2 O 3 crystal structure is analogous to that of spinel (MgAl 2 O 4 ) with additional tetragonal distortion due to the absence of divalent cations.…”