期刊:Acta crystallographica [International Union of Crystallography] 日期:1994-10-01卷期号:50 (5): 481-510被引量:141
标识
DOI:10.1107/s0108768193014466
摘要
The goals of theoretical crystallography may be summarized as follows: (1) predict the stoichiometry of the stable compounds; (2) predict the bond topology (i.e. the approximate atomic arrangement) of the stable compounds; (3) given the bond topology, calculate accurate bond lengths and angles (i.e. accurate atomic coordinates and cell dimensions); (4) given accurate atomic coordinates, calculate accurate static and dynamic properties of a crystal. For oxides and oxysalts, we are now quite successful at (3) and (4), but fail miserably at (1) and (2). The current situation in the first two areas is briefly reviewed, prior to discussing in some detail an approach to topological aspects of structure in oxide and oxysalt crystals. The structure of a molecule or crystal may be represented by a graph, in which the vertices represent orbitals, atoms or groups of atoms, and the edges represent orbital interactions or chemical bonds. The topological characteristics of the bond network are contained in the (weighted) adjacency matrix of the graph and the corresponding eigenvalues constitute the spectrum of the graph. Simple graph theory arguments show that molecular (fundamental) building blocks are actually orbital (or energetic) building blocks, showing that there is an energetic basis for the use of fundamental building blocks in the representation